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L. 26, NO. 6 FEBRUARY 1951
Public Roads
A JOURNAL © F HIGHWAY RESEARCH
Mnfrs Nes Ne,
UBLISHED BY
‘HE BUREAU OF 'UBLIC ROADS,
J. S. DEPARTMENT »F COMMERCE, NASHINGTON
Charts for the graphic solution of intersection capacity problems
are presented in this issue
IN THIS ISSUE
Design Capacity Charts
for Signalized Street and Highway Intersections
Introduction Introduction: 252 sea oe ee ee ee ee ee 105 Datamneeded forscapacitymanalysis = seens sak eee eee eee ee 105 Development woltmcapactty: icliartc = = esse =e eeeeen epee eee eee 105 General terms used... ON 2 Sei ea es We, OO ah LN Je 105 Part 1—Two-Way Streets
Design capacity: taclors 22. eee ee ob 2 ee ee ee 106 Relation of design capacity to possible capacity.______»____ 106 Intersections with) averac ec. COnUILO Ns sae = eens eee eee eee eens 107 Intersectionse with sparking sono mb tec me emeeen ae meena 108 Imtetcectionsawitie parkin om penmiitt cc meee nee ees ee 109 Intersections with separate turning lanes and no separate signal indication 110
Wathweight-turn dane Ses R as. Ae ieee oe ek ee ee eee ee 110
Wath léft-turn® lane 2s a ee ee eee 1,
With botherieht- and) lett-furnis lanes mse, ee eee | 11 Intersections with separate turning lanes and separate signal indication —__ 112 Special conditions... eo eee) |S
Part II1.—One-Way Streets
Desens capacity: tactors.c. = weet eee ee ee Ahi Relation of design capacity to possible capacity ...___-_ «dG Procegute seat ee = ee eee Ol Ls Sn Ek, Rane Se Ah Se Ey, 117 Part II1Il_—Expressways Features of expressways......_..___-- LS See ae ee We Eixpressways with separate turning lanes _...___..__. C9 Expressways widened through intersections —......______. __________.._. 120 Part IV.—Over-All Intersection Capacity Useming preliminary) GeSioisese ule eae eee ee eee ee, UPA! Solutions with hourlyntratic eyOlumes ames oes eben oe eee eee ee eee 121 Solution with average daily traffic volumes 2. «di Limitations | in tise piecharte¥i4d and, 15.22%) ta We ee ee ee 123
The Annual Report of the Bureau of Public Roads for the fiscal year 1950 is now available from the Su- perintendent of Documents, U. S$. Government Print- ing Office, Washington 25, D. C., at 25 cents a copy.
Contents of this publication may be reprinted. Mention of source is requested.
A JOURNAL OF HIGHWAY RESEARCH
4‘ a ¥
Vol. 26, No. 6 February 1951 Published Bimonthly F
BUREAU OF PUBLIC ROAD® Washington 25, D. C,
REGIONAL HEADQUARTERS 180 New Montgomery St. San Francisco 5, Calif,
DIVISION OFFICES
No. 1. 718 Standard Bldg., Albany 7, N. Y. Connecticut, Maine, Massachusetts, New Hamp- shire, New Jersey, New York, Rhode Island, and Vermont. No. 2. 2034 Alcott Hall, Washington 25, D. C. Delaware, District of Columbia, Maryland, Ohio, Pennsylvania, Virginia, and West Vir-_ gima. No. 3. 504 Atlanta National Bldg., Atlanta 3, Ga. Alabama, Florida, Georgia, Mississippi, North Carolina, South Carolina, and Tennessee. No. 4. South Chicago Post Office, Chicago 17, II. Illinois, Indiana, Kentucky, and Michigan. No. 5. (NorTH). Main Post Office, St. Paul 1,| Minn. Minnesota, North Dakota, South Dakota, and Wisconsin. No. 5. (Sour). Fidelity Bldg., Kansas City 6, Mo. Iowa, Kansas, Missouri, and Nebraska. No. 6. 502 U. S. Courthouse, Fort Worth 2, Tex.! Arkansas, Louisiana, Oklahoma, and Texas. No. 7. 180 New Montgomery St., San Francisco 5) Calif. Arizona, California, Nevada, and Hawaii. : No. 8. 753 Morgan Bldg., Portland 8, Oreg. Idaho, Montana, Oregon, and Washington. No. 9. 254 New Customhouse, Denver 2, Colo. Colorado, New Mexico, Utah, and Wyoming.
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PuBLic ROADS is sold by the Superintendent of Documents, Government Printing Office, Washington 25, D. C., at $1 per year (foreign subscription $1.25) or 20 cents per single copy. Free distribution is limited to public officials actually engaged in planning or constructing highways, and to instructors of highway engineering. There are no vacancies in the free list at present. ‘
The printing of this publication has been approved by th Director of the Bureau of the Budget January 7, %1949,
2 BUREAU OF PUBLIC ROADS
U. S$. DEPARTMENT OF COMMERCE E. A, STROMBERG, Edito
HE recently published Highway Capac- ity Manual* has furnished highway Jad traffic engineers with much-needed data
id highways. This up-to-date informa- m, which is largely based on field ob- lirvations rather than on theory, should : applied to all design problems to assure
ghway facilities. The capacity of most -reets or urban highways, except those | the freeway class, is determined largely _| y the volumes of traffic that can be handled | the intersections. Part V of the Manual resents a method of analysis for the cal- alation of capacity at signalized intersec- ( ons under various conditions. Although
A graphic analysis method, based on art V of the Manual, is presented here 9 facilitate the determination of capacities f signalized intersections. The value of harts is recognized in all fields of engineer- ng, and their application is well demon- trated as a short cut for the use of
ations. Such charts are of considerable ‘alue in visual demonstration of the effect ‘f each variable included. The design ca- _ )acity charts developed here for the analysis _/f various types of signal-controlled inter- _ections on two-way streets, one-way streets, and. expressways are presented with prob- em examples to demonstrate their use.
A highway intersection, like any other “structure, must be designed for the loads tis required to carry. In the case of a signalized intersection the loads are estab- lished by the volume, density, composition, and distribution of traffic using the inter- ¥ secting facilities. The geometric features »¢ Of design are determined by these traffic loads and their relation to physical char- acteristics and economic considerations of the site or locality, and to the type of
acilities involved. a
j| Acknowledgment is made to D. W. Loutzenheiser, V. P. Walker, J. S. Biscoe, and J. A. Desch for assist- Ap) ance in the preparation and review of the manuscript. pe Capacity Manual, by the Committee on way Capacity, Department of Traffic and Opera- ms, Highway Research Board; published by the u of Public Roads, 1950. Hereafter referred to n the text as the Marual.
Introduction
The rational determination of highway capacity is now recognized as an important part of highway planning and design. The recently published Highway Capacity Manual provided, for the first time, a complete, practical method for the calculation of inter- section capacities. The miethod developed was an arithmetic process, and for those who prefer a graphic procedure the charts presented in this article were devised. In addition the charts are of value in visual demonstration vf the
effects of the many variables involved.
to their convenience,
Data Needed for Capacity Analysis
Knowing the design traffic loads and the physical and economic limitations, an inter- section design can be made in one of two manners: (1) a geometric layout can be prepared and by capacity analysis checked for its suitability to carry the anticipated traffic; or (2) the design traffic loads can be used in capacity analyses to determine the necessary control dimensions and op- erating conditions. In either event a capac- ity analysis is required, for which proper data are essential. Often only the average daily traffic on each intersecting street is available. This can serve as a general guide but may be of little direct value in the intersection design. For proper ca- pacity analyses the following information is needed:
Traffic volume and distribution.—Direc- tional design volumes of traffic on each ap- proach to the intersection, with breakdown as to through, left-turning, and right-turn- ing movements, together with factors for anticipated future traffic increases. In urban and suburban areas, data are needed for simultaneous movements during both the morning and evening peaks to deter- mine the critical conditions.
Trucks and busses.—Classification of these traffic volumes to show percentage of trucks and busses.
Bus stops.—Near-side or far-side location of bus stops and approximate number of busses using them during the peak hours.
Type of area.—Classification of intersec- tion site conditions as downtown, interme- diate, or outlying area.
Traffic signals—Type and over-all con- trol conditions of traffic signals used.
By J. E. LEISCH,’ Highway Engineer, Urban Highway Branch, Bureau of Public Roads
Miscellaneous.—Requirements for park- ing and for pedestrians, space limitations of pavement and right-of-way areas, and other physical controls.
Development of Capacity Charts
The design capacity charts are based on the information contained in part V, Sig- nalized Intersections, of the Manual, par- ticularly the data given in figures 24 and 26 (pp. 79, 84), and the section on ad- justments for specific conditions (pp. 87- 91). Any one intersection may have as many as eight conditions for which ad- justments must be made in order to deter- mine its capacity.
The charts presented here incorporate all of these ‘adjustments, so that for any known condition the intersection capacity can be obtained directly without reference to the various Manual adjustment values. In constructing the charts all of the ad- justments are precisely accounted for and no short-cuts or approximations are made. The results obtained by the use of these charts are the same as those from the long-hand method in the Manual. There is one added adjustment to the Manual data, as explained later, in the form of a factor to obtain “design” capacity.
The material on capacity of signalized intersections could have been combined on a few charts to cover all conditions for the various types of facilities, but such charts would be unduly complex. Accordingly, it was decided to prepare a larger number of charts, each containing the data for a selected condition. These charts are indi- vidually explained in the following discus- sion, and examples of their proper use are given in each case.
General Terras Used
In order to simplify the terms on the charts and in the examples, a system of symbols was adopted for the variable con- ditions that affect capacity, as follows:
W/2 Pavement width, in feet, of one approach to the intersection. For the two- way facilities it is normally, but not neces- sarily, one-half of the curb-to-curb width. For one-way facilities it is the normal curb-to-curb width, exclusive of separate turning lanes.
105
T Trucks and busses on the one ap- proach, expressed as a percentage of the total volume on that approach (exclusive of light delivery trucks).
Fk Right-turning vehicles (of all types) on the one approach, expressed as a per- centage of the total volume on that ap- proach.
L Left-turning vehicles (of all types) on the one approach, expressed as a per- centage of the total volume on that ap-
DESIGN CAPACITY FACTORS
The basic data for intersection capacities of two-way streets, expressed in terms of average maximum volumes observed at street intersections, are shown in figure 1.° These data, to a large degree, represent a condition with a continual backlog of vehicles on the intersection approach so that some drivers waited through two or more cycle changes. In view of this, the Manual recommends the use of 90 percent of the values in figure 1 for what is termed prac- tical capacity. At practical capacity, ac- cording to the Manual, traffic will pass through the intersection with few drivers having to wait longer than "for the first green period. In examining these data, the Committee on Planning and Design Policies of the American Association of State Highway Officials considered that the constant factor of 90 percent for design was not representative for all cases. With recognition of the variable conditions of Street width, type of area, and parking regulation, the Committee recommends that design capacity be determined by applica- tion of a factor in the range of 70 to 90 percent of the values obtained from the
®* This is figure 24 (p. 79) in the Manual.
proach.
B Location (or nonexistence) of a bus stop at the intersection, described as near- side stop, far-side stop, or no bus stop.
D Distance in feet that parking is pro- hibited in advance of the intersection, on the approach under consideration.
G/C Proportion of total time during the peak hour that the signal is green for the movement of traffic from the one ap- proach, where G is the green interval in
Part L—Two-Way Streets
Manual data and shown here in figure 1. The percentages for conversion of the average values of figure 1 to design ca- pacities, as used herein to construct the charts, are shown in table 1.
It may be noted that an 80- or 90-percent factor is used for the majority of cases. The 70-percent factor is used only for the narrower streets on which parking is per- mitted on both sides and only one lane is available for moving traffic in each direc- tion,
To demonstrate the application of table 1, consider a two-way, 60-foot street, with parking on both sides, situated in an in- termediate area. On this street four lanes (two in each direction) are available for movement of traffic. In figure 1, using a 60-foot street and curve for intermediate area with parking permitted, an average maximum volume of 1,440 vehicles per hour of green is given for one approach. In table 1, for intermediate area, four traffic lanes, and with two parking lanes, the adjustment factor is 80 percent. De- sign capacity of one approach on this street is 1,440X0.80=1,150 vehicles per hour of green.
In addition to this adjustment for design capacity, which is incorporated in the de-
Table 1.—Conversion of average maximum volumes to design capacity volumes
Percentages to convert average maximum volumes! to design
Parking conditions
capacities, when the number of traffic lanes ? is—
Two lanes Four lanes Six lanes Eight lanes Downtown areas: Withoutparking lanes.:.00). 4. Gei.c bars Cone 80 80 80 With two) parking lanes’)... boo 50.62. Se be es 70 80 90 ie SSeS oe per, Intermediate areas: Without parking lanes.......... ara Nayen en ate SPs 80 80 90 Withitworxparking lanes'. vas san Searls cuneate eres 70 80 20 Si eh teeter. fare
‘From figure 1. ? Exclusive of parking lanes; percentages apply to lane widths for moving traffic in range of 10-12 feet
Table 2.—Factor f for conversion of design capacity to possible capacity
Type of area 22 or less No parking: PROVING Ws Sectenscl-tyetery. 3 eats etude oo eae oo 1.4 PECOCIMCRUBLE ener She os tard Shas ot aot aha 1.4 With parking: EIGER, Secreto: vio) uke arco lela ints Giclees 1.6 LES ETS CCU Re I ee 1.6 106
Factor f, when W/2 (in feet) is—
24-26 28-30 32-34 36-38 40-42 44-48 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.25 1.2 1.2 1.2 1.2 1.d 1.4 1.3 1.25 1.2 1.2 1.5 1.4 1.3 1.3 1.25 1.2
seconds and C is the total cycle (incl the green, amber, and red intervals i seconds. 4 K Design capacity of one approach, pressed in vehicles per hour. P Possible capacity of one approa expressed in vehicles per hour.
These terms apply to all charts. <A¢ tional terms relative to special conditi are described as they occur in the text
sign capacity charts, it may be necessi| to make a further adjustment to reflj the character and habits of drivers ir} particular city or locality. Since the di in figure 1 are the average of all int} sections measured, and are representat| 1 of many cities throughout the country, | "
sections were either above or below average curves shown in figure 1. | relation between actual intersection cape) ties in a given locality and those obtaiii by either the Manual method or the des capacity charts can be expressed asal factor, which may be more or less thiy unity. This relation, referred to as | “city factor,’ may be determined as
TO POSSIBLE CAPACITY
Design capacity is by no means the me! mum volume that can be handled at i intersection, but is a value that prefera} should be used in design to provide fav? able operating conditions. Whereas des: capacity represents a volume of tra that will pass through the intersect’ with few drivers having to wait lon; than for the first green period, possi capacity represents the maximum volu of traffic that can pass through the int section with a continual backlog of wait vehicles. The latter condition would considered by most drivers as too congest since some drivers would be obliged wait through two or more signal cy¢ before proceeding through the intersecti Because of site conditions and right-of-yv costs at some intersections, it may not feasible to provide facilities based on sign capacity. In such cases facilities a quate for possible capacity may be best that can be provided.
Possible capacity, according to the ME ual, is 110 percent of the average maxim® volumes reported in figure 1. Design pacity, on the other hand, as used her) is expressed as 70, 80, or 90 percent the values in figure 1. The relation tween design capacity and possible capac¥
February 1951 © PUBLIC RO/
CONDITIONS:
VEHICLES PER HOUR OF GREEN
TOTAL VOLUME FOR ONE APPROAGH
| as ny sat ed fh I
cin)
TWO-DIRECTIONAL UNDIVIDED STREETS FIXED-TIME SIGNAL
10°. COMMERCIAL VEHICLES
20°. TURNING MOVEMENTS
30 40
TOTAL WIDTH OF TWO-WAY STREET IN FEET
he mie} d at efetil | e fam) 5 del t tf _the ratio of these percentage values. »w@lis ratio provides a factor for determin- - Jongh possible capacity directly from the chart (ilues for design capacity. Table 2 shows
, i Various conditions and ranges of ap- y@/0ach width. wild’ | Dae knowledge of possible capacity is nged teded in many instances. Although an ige tersection may be designed for design ca- ieity, possible capacity will indicate the wh lures that can be handled (with some .tq{Sestion ) on certain peak days during le year. Or, knowing possible capacity, ja estimate can be made of the future point | time when no further increase in traffic n be handled. Moreover, where separate turning lanes re provided, it may not be feasible, accord- ig to the distribution of traffic, to accom- lodate each movement at design capacity. /ne of the turning movements may have ) be designed to operate at or near possible Apacity. Design capacity of a separate ning lane is considered to be the same
parking regulation.
capacity on an average is 80 percent of possible capacity, the possible capacity of a separate turning lane is 1.2 times its prac- tical capacity.
Experience has indicated that in some instances, particularly in highly developed areas, practical and economic considerations preclude widening or otherwise improving an intersection to accommodate the traffic demand without some congestion. Since the traffic for which an intersection is designed is a future volume (design volume), the in- tersection generally will operate satisfac- torily initially even when designed for pos- sible capacity. However, in the future when traffic builds up and equals the possible ca- pacity, a new facility to accommodate fur- ther expansion of traffic becomes essential. Furthermore, when the traffic demand ex- ceeds the possible capacity, operating con- ditions will not only be unsatisfactory but the total number of vehicles desiring to use the street cannot be served. Thus, the use of possible capacity in design, where the use of design capacity is not feasible, definitely limits the life of the facility to
* INCLUDES STREET SPACE OCCUPIED BY PARKED VEHICLES, CAR TRACKS AND LOADING PLATFORMS IF ANY
Figure 1.—Average maximum volumes at intersections on two-way streets, for different widths and by type of area and
the date when the assumed volume is reached.
Possible capacity determined by use of the design capacity charts and table 2 is the same as that obtained by the Manual method. However, the design capacity as found by these charts, except for the nar- row streets with parking on which only one lane is available for movement of traffic in each direction, is 0-10 percent lower than the practical capacity given in the Manual. The value of practical capacity, if desired, can also be obtained from the design ca- pacity charts, as follows: (1) obtain de- sign capacity from charts 2-6, (2) mul- tiply by appropriate f in table 2, and (38) multiply the result by 0.80.
INTERSECTIONS WITH AVERAGE CONDITIONS
The first step in the development of the capacity charts was the conversion of aver- age maximum volumes to design capacity volumes for average conditions. This was accomplished by application of the percent-
107
ages in table 1 to the curves of figure 1, resulting in curves I-IV in the upper part of chart 1.4 These curves serve as bases for the construction of other charts for two-way streets. They give design capacity in vehicles per hour of green (horizontal scale not shown). To convert such values into form for direct design use, the G/C ratio curves are plotted in the lower part of the chart. Using these, values can be read on the right vertical scale as design. ca- pacity in vehicles per hour.
Chart 1 is applicable only to average con- ditions, but is convenient for use in ad- vance planning and in early stages of pre- liminary design. It can also be used to obtain an approximate value of design ca- pacity at any intersection where all of the conditions are not precisely known but where the proportions of commercial vehicles, turn- ing movements, etc., may be termed aver- age. The subsequent charts include the adjustment factors applied to these aver- age basic values, to obtain capacities for specifie conditions,
Problems 1, 2, and 3 demonstrate the use of chart 1. The sequence through the chart may be as follows: enter at left with given width of approach; proceed right to appro- priate curve designating the type of area and parking regulation; at this point turn at right angles and project downward to proper G/C curve; again turn at right angles and proceed right; read result, de- sign capacity of one approach in vehicles per hour, on the right vertical scale. The chart may also be used in the reverse order, by entering at the right with a given ap- proach volume and reading the result, width of approach required, on the upper left scale.
Problem 1
What is the design capacity of a two- way street, 66 feet wide curb-to-curb, with parking prohibited, in an intermediate area? Major intersections are signalized. Specific data regarding commercial vehicles, turning movements, etc., are not known, but conditions are assumed to be average. Half of the time during the hour can be allotted to green on this street.
Solution: Using W/2==66/2=33 and G/C=0.50, and following the arrows indi- cated in chart 1, it is found that design ca- pacity K=880 v.p.h. in one direction. If parking were permitted, K would be 650 v.p-h.
Problem 2
A major street consisting of a narrow median and two 24-foot pavements, with no parking, in a downtown area, carries a volume of 950 v.p.h. in one direction dur- ing the peak hour. A signal is to be in- stalled at a cross street. If conditions are assumed to be average, what should be the :inimum green interval on the major street in order to accommodate 950 v.p.h., if a cycle
—[—_[{2 eee
4The illustrative figures, incorporated in the text, and the graphic analysis charts, grouped for con- venience on pp. 125-139, are independently numbered as separate series.
108
of 70 seconds is used?
Solution: Enter chart 1 at left with W/2=24, proceed right to curve I, then down to lower graph until a horizontal pro- jection of 950 v.p.h. is intersected; G/C is interpolated as 0.67. The minimum green interval with a 70-second cycle is, therefore, 70X0.67=47 seconds.
Problem 3
In a downtown area a two-way 58-foot street, with parking, intersects a two-way 44-foot street with no parking. The former is to accommodate a peak-hour volume of 530 v.p.h. in one direction. If conditions are assumed to be average, and a 60-second cycle is used (of which 6 seconds are al- lotted to amber) what should be the green interval on the 58-foot street for operation at design capacity? What would be the resultant green interval and design capacity of one approach on the 44-foot street? What would be the possible capacity of this approach?
Solution: Enter chart 1 at left with W/2=58/2=29, proceed to right to curve III, then down to lower graph until a hori- zontal projection of 530 v.p.h. is intersected ; G/C=0.57. G on 58-foot street=60 X0.57= 384 seconds. G on 44-foot street=60—34— 6=20 seconds; and G/C=20/60=0.338.
For the design capacity of the 44-foot street, using W/2=—44/2—22, curve I, and G/C=0.338, in chart 1, K=420 v.p.h. in one direction.
For the possible capacity of the 44-foot street, using f=1.4 from table 2 for a 22- foot approach in a downtown area with no parking, P=420X1.4= 590 v.p.h. in one direction.
INTERSECTIONS WITH PARKING PROHIBITED
Charts 2 and 3 include the adjustments for specific intersection conditions on two- way streets where parking is prohibited. The basic design capacity data are taken from curves I (downtown area) and II (in- termediate area) in chart 1. The adjust- ments included are those enumerated in item I on page 88 of the Manual, covering proportions of trucks and busses, right turns, left turns, and type of bus stop. These and the following charts give the adjusted design capacity applicable for di- rect or final design use, whereas chart 1 is suitable primarily for preliminary in- vestigation.
Chart 2, applicable to downtown areas with no parking allowed, permits graphical solution for a series of capacity adjustment factors. The basic scales at the left side and at the bottom are the same as in chart 1, The intermediate groups of curves cover the likely range in values for the capacity adjustments as enumerated in the Manual. In use, the sequence through the chart re- quires a right-angle change at the applicable value for each adjustment.
The T, Rk, and L adjustments are propor- tional corrections in terms of the vehicles involved, expressed as a percentage of the
total. The B adjustment is a corre applied for the far-side, near-side, o bus-stop condition. This adjustment cow the cases where there is a normal numbe} busses stopping to pick up or discharge }§ sengers, resulting in some signal cycles ¢ } ing which no busses utilize the bus-# area. The Bz line applies to special cif with high bus volumes, explained lateip in the section on Special Conditions. — Chart 2 will often be used by proceeit from the left-side to bottom scales, as sh Q by arrows. The chart can also be use } the reverse order to obtain the widtlf approach required to handle a given ume. Or, with a given approach volf and a given width, the necessary ratif? green time to cycle time can be determf readily. In the event that the appri width and the G/C ratio cannot be alte® but capacity must be increased, the ami of increase by either elimination of turns or by changing the bus-stop cc tion, or both, can be found on the chart. Chart 3 is similar in form and us chart 2, but is for intermediate areas no parking allowed. In figure 1 it ma noted that the curves for intermediate a without parking and those for outlying a nearly coincide. Since the deviationlT tween the two is generally within about | 3 percent, chart 3 may be used for bot} termediate and outlying areas. Charts 2 and 3 apply to intersectior proaches having the conditions describe the charts. The direct use of the ch as indicated by example arrows, howy@ is applicable specifically to the condi where the volume of left-turning vel} on the approach can be handled withou quiring a separate signal indication check for the capacity of left-turn r ment should always be made when 1 charts 2 and 3, as explained later on i section on Special Conditions, item 5. simplicity in demonstration and bette: derstanding of chart use, examples 4—|2} purposely selected so that the volu left-turning vehicles does not exceec/th capacity of the left-turn movement. maximum volume of left-turning ve, that can be accommodated without a&q arate signal indication on major stre§ generally in the range of 80 to 120 fp} Further examples illustrate the use o/h, important control.
Problem 4
What is the design capacity, in a | town area, of one approach on a 60 street on which there is no parking, ‘ha the cycle is 60 seconds and green in is 27 seconds? Other pertinent dat shown in the upper part of chart 2.
Solution: Enter chart 2 at left® W/2-=32 and follow the arrows accc to each condition; K=780 v.p.h. i direction,
Problem 5
Determine the design capacity an¢ sible capacity of one approach on a 40
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February 1951 @ PUBLIC
st on which there is no -parking, in a atown area, with other conditions at intersection as follows: T=5%, R= , L=10%, B=near-side stop, G=86 sec- , and C=60 seconds.
jution: With W/2==23 and G/C=36/60 30, from chart 2, K=700 v.p.h. In @: 2, f=1.4; therefore P=700X1.4=—980 pp. lem 6
new two-way street on which there be no parking, in a downtown area, is med to cross an existing street. Ac- ling to the volume on the existing street, fercent of the cycle time must be allotted yreen on that street. Determine the led width of pavement on the new street he design peak-hour volume in one di- fion is 1,200 v.p.h., and other conditions fas follows: T=10%, R=12%, L=5%, no bus stop, and C=preferably not over Da seconds, with 6 seconds amber per cycle. ar olution: Sixty-seven percent of the cycle | 2 is available for amber and for green the new street. Therefore, (G+am- i+C=0.67, or (G+6)+70=0.67; G=41 mds, and G/C=0.59.
inter chart 2 at bottom with a peak-hour Jigghtme of 1,200 v.p-h. in one direction, and jy}eeed through the chart, turning at G/C= ), B=no bus stop, L=5%, R=12%, and 110%; W/2=81.5. If 11-foot lanes are ibe used, the new street should be the »{rest multiple, doubled for both direc- hs; 883X2—66 feet wide.
| intermediate area, where other condi- as are as shown in the example at the ‘of chart 3.
Jolution: Enter chart at left with W/2= and follow the arrows according to each dition; K=650 v.p.h. in one direction.
tht and 45 turn left. On the critical ap- pach of the new highway the design vol- le is 1,030 v.p.h., of which 7% are trucks, d turning movements are 10% and 4% to 2 right and left, respectively. There will no parking and no bus stops at the in- Jsection on either facility. If 12-foot les are to be used, how many lanes are re- jired on one approach of the new facility? Solution: It is first necessary to deter- jet ne the proportion of green time required ate the existing parkway. From chart 3, qng W/2=20, T=0%, R=80+520=15%, =45+520—9%, and no bus stops, and in- rsecting from a volume of 520 v.p.h., it is und that G/C=0.43.
af Assume C=60 seconds and total amber 2tiod is 6 seconds. Then, G for parkway
art d,
OMBLIC ROADS Vol. 26, No. 6
traffic is 0.483X60=26 seconds, and G for traffic on the new highway is 60—26—6=28 seconds,
To determine the required width of the new facility, enter chart 3 at the bottom with a design volume of 1,030 v.p.h. and proceed up and to the left using G/C=28 /60 =0.47, B=no bus stop, L=4%, R=10%, and T=7%; W/2=87 feet. At least three 12-foot lanes, therefore, are required on the new highway in each direction of travel.
INTERSECTIONS WITH PARKING PERMITTED
Charts 4 (for downtown areas) and 6 (for intermediate areas) include the ad- justments for specific intersection condi- tions on two-way streets with parking permitted.” Basic data are from curves III and IV of chart 1. The adjustments in- cluded are those enumerated in item I on pages 88 and 89 of the Manual. Charts 4 and 6 are similar to charts 2 and 8 in form and use, except that a new factor Z, for correctica for bus stops, is introduced.
Chart 5 1s a supplement to charts 4 and 6 to derive the adjustment factor for the combined correction for bus-stop condition and parking restriction. This correetion is determined separately for near-side, far- side, and no-bus-stop condition. In chart 5A, for the near-side bus-stop condition, Z is determined directly from the R+L values. In chart 5B, for the far-side bus- stop condition, Z is determined from D, G, and R-+L values, used jointly. In chart 5C, for the condition with no bus stops, the same three values are used jointly in a different relation. On determination of the Z value from chart 5 for the proper condition, use is then made of charts 4 and 6 in the manner previously described for charts 2 and 3.
As in the case of charts 2 and 3, the direct use of charts 4 and 6 applies to the condition where the volume of left-turning vehicles on the approach can be accommo- dated without requiring a separate signal in- dication. For simplicity in presentation, ex- amples 9-18 were selected so that this con- dition is satisfied, although in actual prac- tice a check for the capacity of left-turn movement should always be made when using charts 4 and 6, as later explained in the section on Special Conditions, item 5.
Problem 9
Determine the design capacity of one approach on a two-way, 84-foot street, with parking, in a downtown area, on which other conditions at the intersection are as listed at the top of chart 4.
Solution: Since the bus stop is on the far side, chart 5B is used: for D=155 feet, G=34 seconds, and R+L=22%, Z=17.5. Using this and the other conditions listed, the arrows in chart 4 indicate a design capacity K of 950 v.p.h. on the one approach.
5In this article, as in the Manual, parking parallel to the curb is the only type considered. Diagonal park- ing would obviously have a much different effect on traffic flow.
Problem 10
If all of the conditions in problem 9 remain the same except that the bus stop is placed on the near side, and there is no parking restriction on the far side, what will be the design capacity?
Solution: In this case chart 5A is used first to obtain (with R+L—=22%) a value of Z=5.5. Then, using chart 4, K=860 v.p.h. Shifting the bus stop from the far to the near side would decrease the capacity by 90 v.p.h.
Problem 11
If, in problem 10, the 155-foot parking restriction in advance of the intersection is retained, and all of the conditions remain the same except that the bus stop is com- pletely removed, what will be the design capacity?
Solution: Chart 5C must be used, from which a value of Z=12 is obtained. Then, using chart 4, K=910 v.p.h. This is 50 v.p-h. more than with the bus stop on the near side (problem 10), but 40 v.p.h. less than with the bus stop on the far side (problem 9). The reason for the latter difference is that the bus-stop area on the far side (in problem 9) is used to some extent when no bus is standing, by vehicles proceeding through the intersection.
Problem 12
If the one approach of a two-way street with parking, in an intermediate area, is 32 feet wide, what is the design capacity when other controlling conditions are as listed at the top of chart 6?
Solution: Using chart 5A, with R+L= 29%, Z—6. Then, with the other conditions as listed, the arrows on chart 6 indicate a design capacity K of 770 v.p.h. on the one approach.
Problem 13
As shown in figure 2, an east-west, two- way street in an intermediate area is 52 feet wide and has parking permitted on the north side only. Two lares are avail- abie for moving traffic or both the west and east approaches. The critical condition on the west approach occurs during the evening peak hour and on the east approach during the morning peak hour. What are the design and possible capacities of the two approaches under the conditions in- dicated? To what extent can capacity be increased on the east approach by elimi- nating parking for a half-block length (D= 170 feet or more) in advance of the inter- section?
Solution: For the west approach, since there is no parking, chart 3 is applicable and, with the conditions given in figure 2, K=640 v.p.h.
In table 2, for an approach width of 21 feet, no parking, in an intermediate area, f=1.4; then P=640X1.4=895 v.p.h.
For the east approach, since there is parking, charts 5 and 6 are applicable. A value of Z=—6 is obtained first from chart 5C with D=20 feet or less and with R+L=
109
INTERMEDIATE AREA FIXED-TIME SIGNAL
WEST APPROACH-EVENING PEAK
T=6% R=15%
L=5%
B= NO BUS STOP Ss
EAST APPROACH- MORNING PEAK T=8% L=I18% R=10% B=NO BUS STOP
G (E-W STREET)=30 SEC. AMBER: 6 SEC. G6 /C = 30/60= 0.50
Figure 2.—Illustrative problem 13.
28%. (Since D is 20 feet or less, enter chart 5C with D~20 and proceed right along the upper scale to R+L.) Then, in chart 6, using W/2=31 and the other conditions shown in figure 2, K=525 v.p.h.
In table 2, for an approach width of 31 feet, with parking, in an intermediate area, f=1.35; P=525X1.85=710 v.p.h.
If parking is eliminated on the east ap- proach for a distance of 170 feet in advance of the cross walk, chart 5C is used with D =170 feet, G=80 seconds, and R+L=28%; Z=—22. Using this in chart 6, with the other conditions as before, K=680 v.p.h. and P=680X1.85=920 v.p.h.
INTERSECTIONS WITH SEPARATE TURNING LANES AND NO SEPARATE SIGNAL INDICATION
Charts 7-9 cover intersections with sep- arate turning lanes but with no separate signal indication. Chart 7 is used where there is a right-turn lane, chart 8 where there is a left-turn lane, and chart 9 where there are both right- and left-turn lanes.
These three charts incorporate the ad- justments enumerated in item II on page 89 of the Manual. They provide graphic solutions for the design capacity of the separate turning lane and procedures for determination of the design capacity of one approach. Since the lengths of turn- ing lanes are essential dimensions in the determination of capacity, the charts in- clude means for determining such required lengths.
With Right-Turn Lane
Chart 7 gives the design capacity and required length of the separate right-turn lane, as well as instructions for obtaining the (total) capacity of the approach, when traffic in all lanes on the approach is per- mitted to move simultaneously on a com- mon green indication. The following addi- tional terms are introduced in chart 7.
D, Effective length of right-turn lane, in feet, for the storage of turning vehicles, exclusive of cross walk and taper.
V. Volume of traffic turning right on one approach, in vehicles per hour.
T. Trucks and busses turning right, ex-
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pressed as a percentage of the total right- turn volume V2 on one approach.
M. Design capacity of combined through and left-turn movement, exclusive of the movement on a separate right-turn lane; for use in chart 7 to obtain the (total) capacity of the approach.
K. Design capacity of the added lane for right-turn movement, in vehicles per hour.
The capacity of a right-turn lane is largely dependent on the proportion of truck traffic T, and the G/C ratio available for movement of traffic in the lane. Charts 7A and 7B show design capacity in terms of these factors. Right-turn lane capacity is also dependent on the radius of the turn, the amount of pedestrian interference, and the length of lane provided. From avail- able data, distinction has been made for two general conditions in regard to radius and pedestrians. Chart 7A represents av- erage curb return (corner radius at edge of pavement) and pedestrian interference, based on an average flow of 600 vehicles per hour of green. For better conditions with an adequate curb return and little or no pedestrian interference, chart 7B is constructed on the basis of an average of 800 vehicles per hour of green. Design capacity as expressed in the charts is 90 percent of these average values. In each case the intersection diagrams above the charts are indicative of the conditions rep- resented.
Another control in capacity of an added turning lane is the length of that lane. If not long enough to store the vehicles that can make the turn on the proper green interval, the capacity otherwise possible cannot be attained. The Manual adjust- ments, in item II-3 on page 89, include a volume check in terms of D:, the length of added turning lane. Chart 7C gives the solution for this length of added lane required to accommodate given volumes for different signal timings. In this form the length can be determined both for capacity volumes and for known smaller turning volumes for a specific condition. Since con- trol values are in terms of passenger ve- hicles only, the adjustment for percentage of trucks and busses is included.
The required length of added right- lane is determined as the distance n to store the average number of turning hicles that will accumulate per cycle duriy*’ the red and amber signals, recognizing t}”’ maximum that actually can move on t}” green signal. A length of 25 feet is us for each passenger vehicle, and 40 feet 4 each truck or bus.
The sloping lines in the lower part chart 7C are curved to terminate at the hi” in logical minimum design values, acco? fs ing to the proportion of trucks and busi 4 in the total traffic:
m
j U
1 it
pr
feet None? i. a es oie eee ees 50 10=20.percenti77. 2. ce tees 65 30 percent or more ........... 80.
The minimum length of turning lane ;) : plies to the full width of turning lay This full length is not available for re unless preceded by a taper of suitael length. While a taper length of 70 to () feet may be considered desirable for nort| 3 street conditions, a taper of at least { feet (about 5 feet of length per foot | turning lane width) should be providiy This taper is in addition to the minim» length of turning lane shown in chart |
Included on chart 7 are instructions ‘5 determining the design capacity of ¢ approach as the sum of separate vabs) for the capacity of the through and te ' turn lanes and that of the right-turn las :
a
Since the through-lane capacity is depeiiiil upon the turning movements involved, capacity for the whole is determined , a particular condition of turning ni ments. This value differs from a capacy. sum of left plus through plus right | that it includes adjustment for any | of the three parts being at capacity wl the other two are below capacity. ’ Since FR and L are defined as percenta’s _ of the total approach volume, a simple [> . portion calculation is needed in step! of the instructions to find a right-t) oe volume V, on the arithmetic basis of thro : plus left. When V;, is less than the rigl q turn lane capacity K:, the design capa 7 is the sum of the values found in step. i, and 3. If V2 exceeds Ke, it is necessary@ determine an adjusted volume for the er. bined through and left movement M’, baid - on the controlling value of the right-t2 . lane capacity as indicated in step 5. ‘ i formula shown is derived from the forma _ in step 3, with K: substituted for V2. ‘le design capacity of the approach, thenJs the sum of the adjusted through-plus- 4 volume and the right-turn lane capaci The steps enumerated in chart 7 design capacity of one approach are the condition where each of the movem involved—left, through, and right—does exceed the design capacity. Actually perfect balance between these three m¢ ments will seldom, if ever, exist. It likly that one or both of the turning me ments may exceed the design capacity velt
February 1951 © PUBLIC ROS
may have to operate at or near possible @pacity. In such cases, the value of K: ujm tep 5 may be used as greater than design acity, up to a maximum of the possible acity. (This also applies to charts 8,
With Left-Turn Lane
‘hart 8 gives the design capacity and fh length of the separate left-turn lane, 'well as instructions for obtaining the ital) capacity of the approach, and is ilar in form to chart 7. Additional ms introduced are as follows:
), Effective length of left-turn lane, infeet, for the storage of turning vehicles, lusive of cross walk and taper.
7, Volume of traffic turning left on one yroach, in vehicles per hour.
", Trucks and busses turning left, ex- ‘pissed as a percentage of the total left- n volume V;, on one approach.
7%, Volume of through traffic on the op- _Bsite approach, in vehicles per hour, that in direct conflict, during the same period time, with the left-turning movement on #: approach in question.
[ Trucks and busses, expressed as a eeentage of the total through volume Jon the opposite approach.
VU, Design capacity of a combined ‘trough and right-turn movement, exclusive the movement on a separate left-turn ie; for use in chart 8 in obtaining the , btal) capacity of the approach.
| AK Design capacity of the added lane ir left-turn movement, in vehicles per hour. ‘The capacity of a left-turn lane is de- iiined primarily by the volume of traffic (posing the left turn during the green mal indication. Normally, on major “freets in downtown areas and on wide
imal). Using design capacity of turning "Ines as 80 percent of possible capacity, e design capacity of a left-turn lane is, ‘en, 1.6 vehicles per cycle. Chart 8B gives iis relation in terms of vehicles per hour |/ dependent upon the length of cycle.
(| On some streets, where the opposing ‘) ough volume is relatively light, the ca- htt icity of a left-turn lane may be much ‘eater than indicated above. For such | condition the average capacity of a left- jun lane per hour of green is estimated as {ie difference between 1,200 (item II-3-b, * 89 of the Manual) and Vo, both figures
lesign capacity is 90 percent of this differ- we ace. Chart 8A provides a solution for @ lis condition, being the relation between ¢ 4 G/C, and design capacity K: To ex- ‘ress the capacity in terms of vehicles of
s ovement T, and that in the left-turn yf Movement T; are applied. To determine
| ¥y 'UBLIC ROADS © Vol. 26, No. 6
the capacity of a left-turn lane, K; should be found on both charts 8A and 8B, and the larger of the two values used. In most cases on major streets, the values from chart 8B will govern.
Because of the interference of opposing through traffic, left-turning vehicles gen- erally are delayed for longer periods of time than right-turning vehicles. The re- quired green time per vehicle to make the turn is greater and the left-turn lane ca- pacity is less than that for a right-turn lane. Moreover, when drivers not in the added left-turn lane await an opportunity to turn, those going right generally offer little interference to through traffic but those going left often block a through lane. Thus, within capacity conditions, a longer added lane for left turns is needed for a given volume than for an added lane for right turns of the same volume. Figure 8C shows required lengths of left-turn lanes based on storage space for 1.5 times the average number of turning vehicles that will accumulate per cycle. This is an assumed factor (50 percent increase over right-turn requirements).
With Both Right- and Lefit-Turn Lanes
Where lanes are added for both right and left turns, the determination of design capacity of an approach is made by steps as shown in chart 9. Design capacities of the added lanes, K2 and K;, are determined from charts 7 and 8 and, depending upon actual turning volumes involved, adjust- ments are made to find the proper through capacity M:. M,; is the design capacity of the lanes for through movement, exclusive of the movements on separate right- and left-turn lanes, for use in chart 9 to obtain the (total) capacity of the approach. Step 2 determines the through capacity from charts 2 or 8. In step 4 the through ca- pacity, thus determined, is added to the turning volumes calculated in step 3. Step 5 adjusts for the through volume when one of the turning volumes exceeds design capacity, the basis being the same as described for chart 7. If both turning movements exceed design capacity, a sep- arate step 5 solution should be made for each and the smaller of the two values obtained will govern the design capacity of the approach. Step 6 derives D. and D,; from charts 7 and 8.
These six steps are for the determination of design capacity of one approach for the condition when no movement exceeds design capacity. Sometimes the traffic load may be such that the through movement can be accommodated at design capacity M: as determined in step 2, but the proportional volumes V. and V;, as found in step 3, exceed the design capacities K. and Ks. In such a case it would be necessary to per- mit the turning movements to operate at above design capacity but not to exceed the possible capacity of each. Thus, the capacity of the approach may be equal to M:+V:
N DOWNTOWN AREA TWO- PHASE SIGNAL CONTROL C=62 SEC.
=
SOUTH APPROACH
G= 36 SEC.
T= 12%
R= 25%
L= 5%
B= NO BUS STOP
AVERAGE CURB RETURN AND PEDESTRIAN INTERFERENCE
Figure 3.—Illustrative problem 14.
(not to exceed 1.2 K:)+V; (not to exceed E23)
Problems 14-17, which follow, are illus- trative of the uses of charts 7, 8, and 9.
Problem 14
What is the design capacity of the south approach for the conditions indicated in figure 3? What should be the length of the right-turn lane?
Solution: The percentage that the right- turning trucks are of the right-turn volume is not given, so J, is assumed to be the same as 7, or 12%. Using G/C=36/62= 0.58 and 7.=12%, from chart 7A K.= 305 v.p.h.
From chart 2, using W/2=22, T=12%, R=0%, L=5%, B=no bus stop, and G/C =0.58, the design capacity of combined through and left-turn movement M., (K on chart 2) =830 v.p.h. (see step 2 in chart 7).
On this basis, (from step 3, chart 7) the right-turn volume V2=(830X25)+(100— 25)'=275 v.p-h.
Since this is less than K:, the design capacity of the south approach K=830+275 =1,105 v.p.h. (step 4 in chart 7).
The length of right-turn lane required, D. from chart 7C, using V2=275 v.p.h., C =62 seconds, and T,=10 to 20%, is 160 feet.
Problem 15
Determine the length of green interval required to handle the traffic at design capacity on the east approach of the inter- section shown in figure 4.
Solution: Signal timing based on a com- bined volume of through and right-turn movement is obtained from chart 3 using W/2=20, T=(15+40)+(175+505) =8%, R =175+930:=19%, L=0% (since left turn is on separate lane), B=no bus stop, and approach volume = 175+505 = 680 v.p.h.; G/C=0.57.
Then check, in charts 8A and 8B, the capacity of the left-turn lane with this signal timing. Entering chart 8A with
111
INTERMEDIATE AREA TWO-PHASE SIGNAL CONTROL C= 70 SEC.
NO PARKING ON E-W ST.
THRU (EVENING PEAK
P= 265 T= 15
280
EAST APPROACH- EVENING PEAK NO BUS STOPS
TOTAL APPROACH VOLUME = 175+505 + 250 = 930 VPH
P=PASSENGER VEHICLES PER HOUR
50 T=TRUCKS PER HOUR 250
Figure 4.—Illustrative problems 15 and 16.
V.—280 v.p.h. and proceeding to right and bottom with T,—15+280=5%, G/C=0.57, and 7;=—50+250=20% (see arrows), the design capacity of the left-turn lane is K;==280 v.p.h. Chart 8A governs since in this case the value of 82 from chart 8B is much less. Thus, the indicated left-turning volume of 250 v.p.h. can be accommodated.
Therefore, for the east approach an ade- quate green interval G=0.57X70=40 sec- onds.
The required length of the left-turn lane to handle a volume of 250 v.p.h. is obtained from chart 8C. Using C=T70 seconds and T;:=20%, D:=205 feet.
Problem 16
If in problem 15 the G/C ratio of 0.57 is retained and other conditions (fig. 4) remain the same except that parking is permitted and a bus stop is placed on the near side, what will be the design capacity and possible capacity of the east approach?
Solution: The capacity of the combined through and right-turn movement is ob- tained from charts 5 and 6. Using chart 5A first, with R--L=19+0=19% (L used as 0% since it is on separate lane), Z=5 is obtained. Chart 6 is then used according to instructions in step 2 of chart 8. With W/2=20, T=8%, R=19%, L—0%, Z=—5, and G/C=0.57, design capacity (exclusive of left turn) M; is found to be 380 v.p.h.
Left-turn movement L, according to the traffic distribution shown in figure 4, is 250=930=27%. The left-turn volume V; on the basis of M; is (380X27)+(100—27) = 140 v.p.h. (see step 3 in chart 8).
Design capacity of east approach=380+ 140=520 v.p.h. With no parking and no bus stop (problem 15), design capacity is the sum of volumes indicated in figure 4, or 175+505+250=930 v.p.h.
In table 2, for W/2=20, with parking, in an intermediate area, f=—1.6. Possible capacity of combined through and right- turn movement = M;X1.6 = 380X1.6 = 610 v.p.h. Corresponding left-turn volume (from the formula in step 8, chart 8) = (610X27)+ (100—27) =225 v.p.h., which can be handled since K;=280 v.p.h. (as determined in problem 15).
112
Possible capacity of east approach=610- 225=835 v.p.h.
Problem 17
What is the design capacity of the east approach shown in figure 5? A large lum- ber mill to the north on the cross road ac- counts for the sizable proportion of vehicles and the high percentage of trucks turning right.
Solution: From chart 7B, K.=280 v.p.h. Since chart 8B generally governs the ca- pacity of the left turn on major multilane streets, it is used initially, obtaining K;,=95 v.p.h.
According to step 2 in chart 9, chart 3 is used, with W/2=22, T=6%, R=0%, L= 0%, B=far-side bus stop, and G/C=30/60= 0.50; M; is 610 v.p.h.
On this basis, V.= (610 X32)+(100—32— 8) =825 v.p.h. and V:=(610X8)+(100— 32—8) =80 v.p.h. (see step 3 in chart 9). Thus V; is larger than K2 and, in order that no movement shall exceed the design ca- pacity, it is necessary to recalculate M; as shown in step 5 of chart 9: M’:=280 (100— 32—8)+32=525 v.p.h.; then left-turn vol- ume V’;= (525 X8)+(100—32—8) =70 v.p.h., which can be handled since it is less than Ks.
Design capacity of the east approach (when no individual movement exceeds its design capacity) =525+280+70=875 v.p.h.
Required lengths of turning lanes are:
Figure 5.—Illustrative problem 17.
from chart 7C, D.—165 feet; from ch : 8C, D:=70 feet. ¥
In the event that a through volume about 610 v.p.h. (as determined initial}. had to be accommodated and other cong tions could not be altered, the 325 righ turning vehicles could still be handled ]f at near possible capacity, since possible pacity of the right-turn lane would be Kz, or 1.2 X 280=335 v.p.h. (see note in ch§ , 9): :
The capacity of the east approach, wi, the through movement operating at des capacity and the right-turn movement near possible capacity, =M.4+-V2+V:=618 325+80=1,015 v.p.h. :
INTERSECTIONS WITH SEPARATE TURNING LANES AND SEPARATE § SIGNAL INDICATION :
Chart 10, which is similar to charts} 8, and 9, gives the design capacity a the required length of right- or left-tim; lane, when traffic on this lane moves 01g) green indication separate from that | other traffic on the approach; i. e., a rig or left-arrow indication for the turng) movement. |
Additional terms introduced in chart are as follows:
G’ Green interval, in seconds, of sj arate signal indication for the movem} of traffic on a separate turning lane.
a Width of turning lane, in feet, | the movement of traffic on a separate § nal indication.
With a separate signal indication, right- or left-turn movement is assumed} be free from interference of other tra streams and pedestrian movements. "I | average capacity of the turning lane is 0) vehicles per hour of separate green indi tion (item III, p. 89 of the Manual) fo lane 10 feet wide, and varies directly wh) the lane width. Design capacity is 90 pe cent of this value. Chart 10A gives a ste. tion for this capacity in terms of G/C i the width of lane a. Since the control Wh. ues are in terms of passenger vehicles, i}. adjustment for the percentage of trucks :i@ busses turning (JT. or T:.) is included. "i design capacity of the turning lane is > same whether the movement is to the rit”
EAST APPROACH-MORNING PEA -— T (THRU MOVEMENT) = 6% R= 32 %.> To = 40 %
L= 8% T3= 10%
G = 30 SEC. B = FAR-SIDE STI
— ee *
OUTLYING AREA
TWO-PHASE SIGNAL CONTROL C= 60 SEC.
February 1951 ® PUBLIC RO’
to the left and whether the lane is hin the normal pavement width or is added lane.
hart 10B provides the solution for the guired length of turning lane, identical mh chart 8C. In the case of separate ,jgaal indication there is no opposing traf- i as in chart 8C, but otherwise the con- jflions are comparable. Usually the sep- ite signal phase is green while other ough movements are stopped, and the rage lane must be long enough to pre- it blocking of a through lane. This calls -a space greater than that needed to re the average number of vehicles ar- ing per cycle, since the number arriving |some cycle intervals will be in excess ® the average. Accordingly, a length to re 1.5 times the average number of ve- yles per cycle is used. This is an as- med factor (50 percent increase over ‘}-mal requirements).
The procedure for determining design ca- rity of one approach is the same as that P2viously explained for charts 7 and 8. ty clarity in the terms and charts, the Sips are shown separately for right-turn
ate green indication of 20 seconds is used ct of a 90-second cycle, and on which acks and busses comprise 15 percent of m,4e total right-turning traffic? What should | its length if a volume equivalent to de- : on capacity is to be accommodated?
_ Solution: From chart 10A, using G’/C= /90--0.22, a=11, and T:=15% (see ar- inf WS) 5 K:=165 v.p.h. From chart 10B, ) ling V.=165 v.p.h., C=90, and T.=10 to ys D.=175 feet. iNeblem 19
i§ What should be the green interval for (“ch phase on the east approach of the witersection shown in figure 6 for opera- lon at design capacity, if a total approach dsthlume of 650 v.p.h. is to be accommodated? i "hat will be the green interval for the ,0vement of traffic on the cross street? ot) Solution: Volume of left-turning traffic 20 percent of 650=130 v.p.h. The volume , a) through and right-turn movements to 7. 2 accommodated on a width of 22 feet is )0—130=520 v.p.h. The proportion of reen time required for this movement, om chart 2, with W/2=22, T=11%, R= [%, L=0%, B=far-side stop, and K=520, — G/C=0.40. G=80X0.40=32 seconds. — The proportion of green time required for i) le separate phase of left-turn lane is ob- L tined from chart 10A. Using a volume of 4 v.p.h., T:=15%, and a=12 feet, obtain _}/C=0.17. Hence G’=80X0.17=14 sec- ads, Green time available for movement of taffic on the cross street is 80—32—14—9 for amber) =25 seconds.
£ sf
pvatic ROADS e Vol. 26, No. 6
NO PARKING —- DOWNTOWN AREA THREE-PHASE SIGNAL (SEPARATE INDICATION FOR LEFT TURNS ON E-W ST.)
C = 80 SEC.
EAST APPROACH T (THROUGH AND RIGHT) = 11% R=12% 13 = 15% L=20% B= FAR-SIDE STOP
AMBER = 3 x 3=9 SEC.
Figure 6.—HIllustrative problem 19.
SPECIAL CONDITIONS
Charts 1-10 cover the general conditions found at four-way intersections under traf- fic-signal control. In addition there are numerous other conditions, the majority of which are discussed in the Manual as fur- ther adjustments. For each of these spe- cial conditions the chart procedure involves a series of steps or a special instruction to be followed.
1. High Volume of Stopping Busses, With No Parking on Approach
Where either a near- or far-side bus stop is provided, and where there is a high vol- ume of stopping busses, i. e., at least one bus loading or unloading at all times (one or two stopping to load and unload per cycle in one direction of travel), use chart 2 or 3 in the normal manner, except:
(a) Enter chart with W/2 equal to actual approach width minus 12 feet.
(b) Use T as a percentage of trucks only, exclusive of stopping busses.
(c) Use line Bz for bus-stop condition.
(d) To the design capacity obtained from the chart, add the number of stopping busses per hour in one direction to determine total design capacity.
Problem 20
If, in problem 4 (p. 108), all of the con- ditions remain the same except that 90 busses stop during the peak hour on the one approach and the percentage of trucks alone is 5 percent, what will be the design capacity?
Solution: Using chart 2, with W/2=32— 12—20, T=5%, bus-stop condition line Bz, R=7%, L=15%, and G/C=0.45, a value of 510 v.p.h. is obtained. Total K=510+ 90—600 v.p.h. in one direction.
2. High Volume of Stopping Busses, With Parking on Approach
Where either a near-side or far-side bus stop is provided and where there is a high volume of stopping busses as described in item 1 above, use charts 4 or 6 in the normal manner, except:
(a) Enter chart with W/2 equal to actual approach width minus 6 feet.
(b) Use T as percentage of trucks ex- clusive of stopping busses.
(c) Use line By for bus-stop condition. Do not use chart 5.
(d) Obtain result, but add to this the number of stopping busses per hour in one direction to determine total design capacity.
Problem 21
If, in problem 9 (p. 109), all of the condi- tions remain the same except that 80 busses stop during the peak hour on the one ap- proach, and the percentage of trucks alone is 4 percent, what will be the design ca- pacity? What will be the possible capacity of this approach?
Solution: Using chart 4, with W/2=42— 6=36, T=4%, bus-stop condition line By, R=15%, L=7%, and G/C=0.52, a value of 700 v.p.h. is obtained. Total K=700+80= 780 v.p.h. in one direction.
From table 2, f=1.2. P=(700X1.2) + 80=920 v.p.h. in one direction.
3. Wéidened Intersections, with No Parking
Where the pavement approach is widened in advance of the intersection for a distance in feet equal to or greater than five times the green interval in seconds (5G), and the same pavement widening is continued be- yond the intersection for a distance in feet equal to 5G or more: Enter chart 2 or 3 with W/2 equal to total width of one ap- proach including the widening on that ap- proach; then use the chart in normal man- ner.
Problem 22
What is the design capacity of the south approach, widened through the intersection, as shown in figure 7?
Solution: Since the length of widening in advance of and beyond the intersection is greater than 5G (5X28=140 feet), the full width of approach, 21+11=—32 feet, is used to determine the capacity.
Using chart 3, for the conditions given, design capacity of south approach=625 v.p-h.
113
NO PARKING INTERMEDIATE AREA FIXED-TIME SIGNAL C=60 SEC.
SOUTH APPROACH T= 18% L=7% R=20% G=28SEC. B= FAR-SIDE STOP
Figure 7.—Illustrative problem 22.
4. Elimination of Parking at Intersections
Where parking on a street is eliminated in advance of the intersection for a distance in feet equal to or greater than 5G and parking is also eliminated beyond the inter- section for a distance equal to or greater than 5G: Use chart 2 or 3, instead of chart 4, 5, or 6, as if there were no parking on the street.
Problem 23
To improve operation at a major inter- section in a downtown area on a 42-foot street on which parking is permitted, it was decided to remove the bus stops and to prohibit parking for an effective distance in advance of and beyond this intersection. Other conditions on one approach are T= 15%, R=20%, L=10%, G=80 seconds, and C=60 seconds. Determine design capacity and possible capacity of one approach.
Solution: To be fully effective, parking must be eliminated on each side of the in- tersection for a distance of at least 5G or 150 feet.
From chart 2, using W/2=21 and other conditions as listed, K=570 v.p.h. P=570X 1.4 (from table 2) =800 v.p.h.
5. Check for Capacity of Left Turn
Any intersection approach on a two-way street that does not involve a separate left- turn lane should be checked for capacity of the left-turn movement. This may be done in the same manner as for a separate left-turn lane, since the number of left- turning vehicles that can be accommodated with two-phase control, whether on a sep- arate lane or not, is governed either by the
114
volume of traffic opposing the left turn or by the length of cycle. Charts 8A and 8B should be used for such a check, which should be made for every intersection in- volving two-way streets. If the volume of left-turning vehicles exceeds the possible ca- pacity as determined in charts 8A and 8B, serious congestion may result and the over- all capacity of the approach may be ma- terially reduced. In such cases, the left- turn movement should be prohibited or, if feasible, accommodated on a separate sig- nal indication.
Problem 24
Check whether the left-turn volume in problem 6 (page 109) can be handled satis- factorily.
Solution: Left-turn volume is 5% of 1,200, or 60 v.p.h. For the conditions given, it is found in chart 8B that 82 v.p.h. can be accommodated at design capacity; there- fore, the solution in example 6 is satisfac- tory.
6. Special Treatment of Turning Movements
On the intersection approach of a two-way facility where the right-turn path is rea- sonably direct, and pedestrian interference is minor, the right-turn movement may be considered as part of the through move- ment; in which case, R=0% would be used in the chart solution.
On the intersection approach of a one- way facility where the turning conditions are as described above, either the right- or left-turn movement, or both, may be con- sidered as part of the through movement. Such conditions are likely to occur at high- type, channelized intersections.
7. Capacity Controlled by Intersection Exit
Generally the capacity of the approaches controls the capacity of the intersection. At some locations, however, where all pave- ments of the intersection legs are not of the same width or where traffic backs up from an adjacent intersection, the capacity of the intersection may be dependent upon the exit lanes. The capacity of the exit pavement may be estimated as follows:
No parking on exit——Enter chart 2 or 3 with W/2 equal to the width of exit pave- ment; proceed through chart in normal manner, but use T=percentage of trucks in through movement only, R=0%, L=0%, B=no bus stop (except where bus stop is on the far side, use B=far-side stop), and G/C equivalent to that used on the approach.
With parking on exit——Enter chart 4 or 6 with W/2 equal to the width of exit pave- ment (including the parking width); pro-~ ceed through chart in normal manner, but use T’=percentage of trucks in through movement only, R=0%, L=0%, Z=0, and G/C equivalent to that used on the approach.
8. T or Y Intersections
The capacity of the approach on an tercepted street at T or Y intersect (east approach in figure 8) may be obtairj from charts 2-6, as follows: Use the cha; in normal manner except that the left-tt movement is considered to be the throu movement, since it is equivalent to } through movement on a crossing (the o difference being the curved path), wh} makes L=0%. If parking is permitted | the intercepted approach, use supplemen) charts 5A and 5C, but R+L is always eq) to R only, because L=0. |
ee ae
+
Problem 25
What is the design capacity of the | tercepted street (east approach), fry which traffic can turn only right and | into the north-south street, for the con) tions indicated in figure 8?
Solution: In chart 2, using W/2=20, 3 10%, R=40%, L=0%, B=no bus stop, @ G/C=0.40, K=460 v.p.h. is obtained. T5 is the combined volume turning right ef left into the north-south street.
9. Multiple-Type Intersections
The capacity of any form of signalisi intersection, regardless of the number } approach roads and extent of channeli\ tion, can be obtained from the charts jy examining each approach road separat/ The design of complex intersections, p| ticularly those requiring multiphase e¢b trol, may necessitate some study and til solutions before determining the final pli Multiple intersections often present sevell possibilities in the pattern of operation ed in the number and arrangement of sigil) phases. Such alternate arrangements apt to result in different geometric layout thus affecting the size, shape, and locat! of islands, widths of pavements, size storage areas, and over-all space requil ments for the intersection. The geometi layout should be determined jointly wh capacity analyses. Care should be tall
NO PARKING DOWNTOWN AREA TWO-PHASE SIGNAL CONTRO
EAST APPROACH T= 10% L=60% R=40% 6/6 =0.40 B=NO BUS STOP
Figure 8.—Illustrative problem 25. February 1951 ® PUBLIC RO:
i
ech
eft pene oS thre : to Bem the --—> ie
ita PHASE 1 1 ena F
VS
them
ind |
2 0 |
2), }
Op, ‘oo
l { ‘
wht
|
i
nal
abet)
nes | DOWNTOWN AREA
aril FIXED- TIME SIGNAL
| check the length and width of those traf- sel Bitanncls where vehicles will store dur- ion ‘e certain signal phases to preclude the ‘gmdition of traffic backing up from one is: (tersection point to another. The alter- aed? solutions will show differences in ; _ pacity, and in operational and economic iy WWantages, from which the most feasible
cat an may be determined.
oe *oblem 26
In figure 9 is shown a plan of a multiple || Sane selected from a study in which eral layouts were examined. The prob- ‘mis to check the arrangement for opera- | OM at or near design capacity and to de- wi imine the signal timing, using a 60-sec- ‘ad cycle, for the two-phase control indi- ited at the upper right of figure 9. There té no bus stops, and T is assumed to be _) percent on all movements.
| | In order that the exit lanes (due to stored thicles ) do not limit the capacity of ap- a ‘roaches, a lagging green indication in sev- . ral instances is considered necessary, as on onstrated below.
lovement H to E—phase 1
Ap proach H: From chart 10A, required i /e— =0.32, and G=60X0.32=19 seconds. a chart 10B, required length of left- arn lane is 180 feet.
1 4) bee
UBLIC ROADS © Vol. 26, No. 6
. (VOLUMES SHOWN ARE FOR EVENING PEAK HOUR)
Figure 9.—Illustrative problem 26.
Approach J: To prevent an excessive number of vehicles from storing at J and thereby limiting the capacity of this move- ment at H, a green indication at intersec- tion 3 to lag behind that at intersection 1 is introduced. For a distance of 140 feet from H to J and an assumed speed of 15 m.p.h. (20 feet per second), the green lag= 140/20=7 seconds. This will preclude the storage of but a few vehicles at J. Thus, for approach J, G=19-++7=25 seconds, and G/C=0.42.
Approach K—phase 1
Although there is parking about 70 feet in back of the stop line, it is not likely to have any effect on the capacity of the 24- foot pavement at intersection 1 due to the variable width involved. Moreover, since all traffic turns right on a rather direct path, the movement is considered to be a through movement without turns (see Special Condition, item 6). In chart 2, for W/2=24, no turns, etc., and G/C=0.382, (same as at H), design capacity=520 v.p.h., which is more than adequate for the load.
Approach G—phase 2
Using a 3-second amber period with each phase, the available green time per cycle is 60—19—6=85 seconds, or G/C=0.58. From chart 2, design capacity =1,370 v.p-h., which is adequate since the load is 1,280 v.p.h.
—~ =~®
6 - “pans (Sey fe
PHASE 2 Li He
Approach B—phase 2
During phase 1, approach G should be left clear, or nearly so, of vehicles from B to make room for the storage of movement C to G. During phase 2, this is accomplished by a lagging green at intersection 1 be- yond that at intersection 2. For an as- sumed speed of about 20 m.p.h. (30 feet per second) and a distance of 200 feet, the lag is 7 seconds. Thus the green interval for approach B is 85—7=28 seconds, or G/C= 0.47.
Through and right-turn movement: From chart 2, design capacity=1,100 v.p.h. This is satisfactory since the load, 1,100+50= 1,150 v.p.h., is only slightly above design capacity.
Left-turn movement: From chart 8B, de- sign capacity of left-turn lane is about 95 v.p-h.; left-turn volume is 30 v.p.h. Re- quired length of left-turn lane for this vol- ume, from chart 8C, is 65 feet.
Approach A—phase 2
From chart 2, for a width of 36 feet and G/C=0.47, (same as at B), design capac- ity=1,070 v.p.h.; traffic load=900 v.p.h.
Approach C—phase I
Available green time per cycle is 60—28— 6=26 seconds, or G/C=0.43. It is first necessary to check the capacity of left turn in accordance with Special Conditions, item
115
5. From chart 8A, using V.=120 v.p.h., T.=15%, G/C=0.48, and T;=15%, capacity of left turn is found to be 280 v.p.h., com- pared to a volume of 180 v.p.h. The capac- ity of the approach, as a whole, is obtained from chart 2. Since L+(R/2) is greater than 35, R=10% and L=30% are used in the solution (see single-asterisk note in chart 2); and for the 20-foot approach, de- sign capacity=370 v.p.h.; traffic load=330 v.p-h.
Storage space occupied by movement C to G on approach G during phase 1 may be ob- tained from chart 10B. For a volume of 180 v.p.h., the length required for storage, if in a single lane, is 1385 feet.® In three Janes the length occupied would be about 45 feet. Available length on approach G is approximately 100 feet.
Approach F—phase 1
As above, G/C=0.43. The left-turn vol- ume obviously can be handled. From chart 2, for an approach width of 22 feet, de- sign capacity = 480 v.p.h. Since this is much in excess of the traffic load, the green interval on this approach could be decreased to give, in effect, a short advance green to movement C to G.
Length of storage on the two lanes of approach F for a volume of 160 v.p.h., from chart 10B, is 115+2, or about 60 feet.° Available length is approximately 120 feet. This leaves sufficient space ahead of the stop line at D to consider the exit from ap- proach D unimpeded in regard to capacity.
Separate design capacity charts for one- way streets could have been developed but because of the definite relation between the capacity of two-way and one-way streets, this was considered unnecessary. Instead, a procedure is given for evaluation of in- tersection capacities of one-way streets by use of the charts for two-way streets.
DESIGN CAPACITY FACTORS
The basic data for intersection capacities of one-way streets, expressed in terms of average maximum volumes, are shown in figure 10.7. This chart gives the same type of information for one-way streets as figure 1 for two-way streets. Since the same average conditions are represented in both, a definite relation can be established for the four upper curves of figure 10 and the com- parable curves of figure 1. Thus, a series of factors to convert the maximum volumes accommodated by one approach on two-way
* Storage space from chart 10B is based on 1.5 times the average number of vehicles storing per cycle. Actually the maximum that may be stored can be as high as two times the average number per cycle. Thus, where feasible, the length of such storage area should be predicated on chart 12E. In this problem, however, the space is adequate on either basis.
7 Figure 26, p. 84 of the Manual.
116
Approach D—phase 2
Movement D to K flows freely at all times. The green interval for left-turn movement D to F is 60—25—6=29 seconds (25 seconds is the green interval on ap- proach J, previously determined), and G’'/C=0.48. From chart 10A, design capac- ity of movement D to F is about 350 v.p.h. Since this is much in excess of the volume, the lagging green on approach J, phase 1, could be increased. Required length of left-turn lane, from chart 10B, is 120 feet.
Exit E—phase 1
Since exit E receives traffic from J and C simultaneously, the capacity of this com- bined movement should be checked as con- trolled by the exit (see Special Conditions, item 7). Total volume during phase 1 is 260+110=370 v.p.h. From chart 2, using
/2=22, no turns, etc., and G/C=0.42, de- sign capacity of exit=620 v.p.h.
According to the above analysis, the in- tersection design is found to be satisfactory for operation during the evening peak hour. A similar capacity check should be made for the morning peak hour, which may show a different signal timing or a need for some modification in the geometric layout. Length of turning lanes and other storage areas would be based on the larger of the two values determined for the morning and evening peaks.
10. Interpolation in Charts
Where the intersection is in an area hav- ing characteristics between those of a down-
Part [1—One-Way Streets
streets to the maximum volumes on one-way streets can be obtained by making a ratio, for comparable conditions, of the volumes in figure 10 to the volumes in figure 1. For example, in figure 10, for an approach (one- way street) width of 34 feet, in an inter- mediate area, with no parking, a volume of 2,500 vehicles per hour of green is given; in figure 1 for the same approach width (68-foot two-way street) under the same conditions, a volume of 2,000 vehicles per hour of green is given. The conversion fac- tor thus is 2,500/2,000=1.25.
Table 3 shows these conversion factors, i, for the range of approach widths up to 50 feet. It is to be emphasized that the parking on a one-way street represents parking on one side only. This condition is comparable to one approach of a two- way street, and so permits use of the two- way capacity charts. To find the design capacity of an approach on the one-way street, use charts 1-6, with W/2 equal to the whole width of the one-way street; then multiply the given K by appropriate i in table 3. Design capacities and required lengths of separate turning lanes on one- way streets are the same as those on two- way streets, for which charts 7-10 are used.
town and an intermediate area, interpc tion is made between the capacity values charts 2 and 3, or charts 4 and 6. Where the characteristics of the int secting facility are between those of a str and an expressway, capacity values can interpolated between those of charts streets and those for expressways.
11. Use of City or Local Facto
In localities where driver characterist or other conditions, are believed to be ¢ ferent from those represented by the be data in the Manual, a further adjustm to the Manual or chart values may be plicable. This adjustment can be expres as a “city factor,” established by relat actual hourly volumes measured at exist intersections loaded to their possible cap ity (continual backlog of waiting vehic on the approach during one hour), to possible capacity, for comparable cor tions, obtained from the Manual (1.10 tir the value given in figure 24 therein and justed as necessary for specific conditior Such field measurements should includ sufficient number and type of intersecti to be representative for the city or lor ity as a whole. The ratio of measured } sible capacities to those calculated by Manual methods gives the “city fact The numerical value of this factor may a constant for all intersection appro conditions, or it may vary with the type area and parking regulation.
When parking exists on both sides 0 one-way street the operating conditions not similar and the two-way values and justments cannot be used. In such cé reference should be made to item IV page 90 of the Manual for adjustments the values in figure 10. It will be ne that the values in figure 10, for a gi width of street, show one-way street cay ity with parking on both sides to be ak 70-75 percent of that with parking on side in downtown areas, and about 80 percent in intermediate areas.
RELATION OF DESIGN CAPACITY TO POSSIBLE CAPACITY
The relation between design and poss capacities developed for two-way st also is applicable to one-way streets. factors f from table 2 apply directly w used with W/2 as the whole width of a ¢ way street. Factors for the condition “y parking” are applicable to parking on side only of one-way streets. The } cedure to obtain possible capacity of a ¢ way street is: (1) determine design ca ity for an equivalent approach from ch: 1-6; (2) multiply by factor i in table 3;
February 1951 @ PUBLIC R
4400 4000 3600 3200 2800 2400 2000
1600
CONDITIONS:
FIXED-TIME SIGNAL 10°. COMMERCIAL VEHICLES 20°/. TURNING MOVEMENTS
1200
800
400
TOTAL VOLUME —VEHICLES PER HOUR OF GREEN
0 0 10
20 30 40
TOTAL WIDTH OF STREET IN FEET (CURB To CURB)
Figure 10.—Average maximum volumes at intersections on one-way streets, for different widths and by type of
') multiply by factor f in table 2. Possi- és 4), capacities of separate turning lanes on US\e@-way streets are the same as those on
Kc ey streets; i. e., 1.2K. or 1.2Ks.
IV) a) The following procedures, employing ‘arts 1-10 and tables 2 and 3, are used to ‘termine the capacity of one-way streets. a3 ready reference, each major condition
¢ treated separately.
PROCEDURE
|
| A.—Average Conditions | Proceed through chart 1 in the normal ‘anner, with W/2 equal to the width of
. 38ign capacity of one-way street. If the jHiart is entered on the right with a given ‘ilolume, in order to obtain either a value ‘1? G/C or W’/2, divide this volume by fac-
| 4 ROADS @ Vol. 26, No. 6
area and parking regulation.
assumed to be operating under average con- ditions. What is the design capacity if the signal is so timed that G/C=0.60? What will be the possible capacity?
Solution: In chart 1, using W/2=30, curve III, and G/C=0.60, read = 600 v.p.h. From tables 3 and 2, i=1.25 and f=1.40.
K=-600 X1.25=750 v.p.h.
P=750 X1.40=1,050 v.p.h.
Problem 28
If, in problem 27, the approach volume to be accommodated is only 625 v.p.h., to what may the ratio of G/C be reduced?
Solution: Enter chart 1 with W/2=80, proceed to curve III, and project a line downward. Then enter the chart with a volume of 625+1.25—500 v.p.h., proceed to the left and intersect the vertical line previously projected; read G/C=0.50.
Table 3.—Factor i to convert capacity value (charts 1-6) on one approach on a two-way street to that on a one-way street’
No parking Parking on one side W /2 =Approach_width ? ; Downtown Intermediate Downtown Intermediate ary | Feet | DO EER te Pee on cei S) nth cs Frade cal Mss gr cs) of oped atl me 0.88 0.94 Beek aes DOE. PURER, Ree na rere ENA. cnt ets aN .94 1.00 me - DO ie ns ny Beye STR OIC ABA CHT G. SNe ° acta .98 1.04 a : PAN SADLER RATS Waa HE ES get MT Pee POR 1.02 1.09 | ie, 1.09 ee ee ae. Sr ow On Me MEy sO | 1.05 1.13 1.22 1.13 SO FV TA eae Ee. Se ic ee oer -Re Sp. 1.08 1.18 1.25 sp beg Pe SA Oe 8 Oe es 2 See er ae step Bi! 1.22 1.29 1°21 Met Cnet app eeela SCRE RR Ae, APE RAI PRS Race 1.13 1.25 1.31 | 1.24 CRT peak eg prs anes RENE cE ON wea RC ene ey 1.15 1.29 1.34 | 1.26 SS Aer aac, teenie ecames gam amass it ot lye 1.32 1.37 1.28 OT eed ae ee, Rae Oo eo Pg eer ere 1.19 1.35 1.40 1.30 OO st be ws SENN CECI ROS CH ICIDICRET ict Sar yates ear 127 1.38 1.42 1.82 AAnY, Se Peiees. 2 ter here NAS d+ toh 1.23 1.41 1.44 1.88 7 a ae a Rn eer cee neo age eS oe trae 1.25 1.44 1.46 1.35 ASTI at, ee a ai ahn, APE ake am gag 3 1.26 1.47 1.47 1.36 STA EE SPC ie ATF 1.27 1.48 1.48 1.38 J nnn ELE EEEESment
1 For the same width of approach, type of area, and parking regulation. , 2 For one-way streets, the total curb-to-curb width, exclusive of separate turning lanes; for two-way streets, one-half
(normally) of the curb-to-curb width.
117
B.—No Parking, in Downtown or Intermediate Area
Enter chart 2 or 3 with W/2 equal to the width of the one-way street. Proceed through the chart in normal manner, but instead of actual L use (L/2)+5. Multiply the result by factor i from table 3 to obtain design capacity of the one-way street. The single-asterisk note in charts 2 and 3 does not apply to one-way streets.
Problem 29
A 40-foot street in a downtown area is converted to one-way operation with no parking. Other conditions are T=18%, R=12%, L=20%, B=no bus stop, and 85% of the cycle time must be devoted to the cross street. What is the design capac- ity of the one-way street if two-phase sig- nal control is used with C=60 seconds and each amber=3 seconds? What will be the possible capacity?
Solution: Green time that must be al- lotted to the cross street is 35% of 60=21 seconds. Green time available for the one- way street is 60—21— (2X3) =833 seconds, and G/C=83/60=0.55.
Using chart 2, with W/2=40, T=18%, R=12%, L=(20/2)+5=15%, B=no bus stop, and G/C=0.55, obtain a capacity value of 1,100 v.p.h. From tables 3 and 2, i=1.19 and: f=1740.
K=1,100 X1.19=1,300 v.p.h.
P=1,300 X 1.40=1,820 v.p.h.
C.—With Parking on One Side, in
Downtown or Intermediate Area
Enter chart 4 or 6 with W/2 equal to the width of the one-way street. Proceed through the chart in normal manner, ex- cept instead of actual L use (L/2)+5. Use supplemental chart 5 in normal manner, as for two-way streets. Multiply the result from chart 4 or 6 by factor i from table 3 to obtain capacity of the one-way street. The single-asterisk note on charts 4 and 6 does not apply.
Problem 30
If, in problem 29, all of the conditions re- main the same except that parking is per- mitted on one side and D=20 feet, what will be the design capacity?
Solution: First use chart 5C, with R+L=— 12+20-=32%, and D=20, obtaining Z=—6. Then, from chart 4, a capacity value of 640 v.p-h. is found. In table 3, i=1.40 for a
FEATURES OF EXPRESSWAYS
An expressway is defined as a divided arterial highway for through traffic with full or partial control of access and gen- erally with grade separations at intersec- tions.” The salient geometric features of
118
40-foot approach with parking on one side. K=640 X1.40=900 v.p.h.
D.—With Separate Turning Lanes, No Separate Signal Indication
With right-turn lane: Follow the instruc- tions given on chart 7, except in obtaining the capacity of the combined through and left-turn movement M, use (L/2) +5 instead of actual L in chart 2 or 3; multiply this by factor 71 from table 3.
With left-turn lane: Use chart 7, since chart 8 is not applicable to one-way streets. In obtaining the capacity of the combined through and right-turn movement, use L=5% (instead of 0%) in chart 2, 3, 4, or 6; multiply this by factor i from table 3.
With both right- and left-turn lanes: Follow the instructions on chart 9, except in obtaining the capacity of the through movement M, use L=5% (instead of 0%) in the solution on charts 2 and 3; multiply this by factor i from table 3.
Problem 31
If, in problem 29, all of the conditions remain the same, except that the approach is widened by addition of a left-turn lane with an adequate curb return (and there is little if any pedestrian interference), what will be the design capacity?
Solution: The design capacity of the left- turn lane, from chart 7B, using G/C=0.55 and T;=—18% (assuming the percentage of trucks is the same for all movements), is 360 v.p.h.
A capacity value for the combined through and right-turn movement, from chart 2, using W/2=40, T=18%, R=12%, L=5%, B=no bus stop, and G/C=0.55, is 1,220 v.p.h. From table 3, i=1.19. The design capacity of the through plus right- turn lanes=1,220 X1.19=1,450 v.p.h.
From step 3, chart 7, left-turn volume= (1,450 X 20) +(100—20) =860 v.p.h., which is the same as the design capacity found above. Design capacity of approach = 1,450+360=1,810 v.p.h. The length of left- turn lane required, from chart 7C, is ap- proximately 200 feet.
E.—With Separate Turning Lanes and Separate Signal Indication
With right-turn lane: Follow the instruc- tions on chart 10, except for step 2 in the series on the right side of the figure sub- stitute the following: Obtain design capac- ity of the combined through and left-turn
Part [ii—Expressways
an expressway are: a divided highway de- signed to high standards, insulated for the most part from the adjacent development; shoulder space for emergency use (no park- ing adjacent to the traveled way); bus
§ Definition adopted by the American Association of State Highway Officials, Jume 25, 1949.
movement M: in the usual manner charts 2-6. Use W/2 as the normal of approach, exclusive of turning 1] (L/2)+5 instead of actual L; and R= Multiply the result obtained by fac from table 3. 7H! With left-turn lane: Follow the instru/} tions on chart 10, except for step 2 in series on the left side of the figure su tute the following: Obtain design capaci of the combined through and right-tu movement M; in the usual manner fre|} charts 2-6. Use W/2 as the normal wid of approach, exclusive of turning lane, ai L=5%. Multiply the result by factor from table 3. :
F.—Special Conditions Z The items listed under the heading St i cial Conditions for two-way streets (palp 113) also apply to one-way streets, exce that the charts are to be used as describ above in sections B—E.
Problem 32
What is the design capacity, in probli} 29, if all of the conditions remain the sani except that a bus stop is provided at ti. intersection on the one-way street with awh proximately 90 busses stopping per hoi}; and 7, exclusive of stopping busses, is 59) What is the possible capacity?
Solution: According to item 1, page L, : W/2=—40—12=28 feet. Using thts in chet): 2, with T=5%, R=12%, L=(20/2) +5: 15%, bus-stop condition line Bz, and G/Cr 0.55, a capacity value of 890 is obtain}, From tables 3 and 2, i=1.19 and f=1.40. |@
Design capacity= (8901. 19) +90 buss =1,150 v.p.h.
Possible capacity= (1,060 <1.40) +39, busses:=1,570 v.p.h. (
Problem 33
What is the design capacity in prot 25, page 114, if all of the conditions remé the same, except that the 40-foot inti cepted street is converted to a one-wy} street for travel in the westerly directio? }
Solution: According to item 8, page 1,7} the left-turn movement is considered be equivalent to the through movement, | that in the solutions L=(0/2)+5=5% (i section B above). Using chart 2 w W/2 = 40, T = 10%, R = 30% or more, I 5%, B=no bus stop, and G/C=0.40,} capacity value of 880 is obtained. Fr table 8, i=1.19. Design capacity of { one-way east approach=880X1.19= “4 v.p-h.
eye, Ste are ay
stops (if any) on separate turnouts; properly designed and controlled inte tions. Where partial control of acces used, the expressway will intersect so streets or highways at grade. These tersections will require added turning la’
of adequate design, pedestrian cross-wi
February 1951 e PUBLIC RO.
q . be
®
A
' @itrols, and in some instances traffic signal itrols for all traffic. Jn expressways, where the above condi- h ns are satisfied, intersection capacities pressed in terms of vehicles per hour -@green per unit of width will be higher lian on ordinary streets or highways, and i » capacity data represented on charts “10 are not applicable. Charts 11, 12, ‘wd 13 are design capacity adjustments li- specific conditions on high-type facili- \$s, based on the data in item V on page \§ of the Manual. These charts are ap- l@@cable to both rural and urban conditions, gd to divided two-way highways or to ‘e-way facilities. Two general conditions rvern and are treated separately: charts | and 12 are applicable where separate ¢Wrning lanes exist; and chart 13 where f ydened approaches are used. an | NW.
= =
|
EXPRESSWAYS WITH SEPARATE TURNING LANES
Charts 11 and 12 give all of the neces- Wry information for evaluating the ex- ‘Wtessway design capacity at signalized ‘itersections having separate turning lanes lithe type of layout shown in the upper ‘li ght-hand corner of chart 12). Added sirning lanes are arranged for the exclusive se of turning vehicles, and other traffic “Eimnot use them to proceed through the i \tersection. Added lanes designed to per- \\it their use by through traffic are dis- lissed in the next section, concerning ull idened intersections.
Ail! Chart 11 gives the solution for the design lif apacity of the through movement K; on | ie expressway at a signalized intersection. ; is based on the Manual value of 1,000 lassenger vehicles per hour of green per D feet of lane width. With adjustment the percentage of trucks and busses d for the G/C value, the design capacity / an be read directly for the width of through _imes (W/2 on the sketch in chart 12). ‘his capacity value must be used jointly _ ith separately determined capacities for ight- and left-turn movements obtained a com chart 12. The procedure is the same _ 8 that described for charts 9 and 10.
' Chart 12 gives solutions for design capaci- les of separate turning lanes, in which { harts A, B, and C are for controls without 4 | separate signal indication and chart D vith a separate signal indication. Since "he conditions are identical with those in . thart 8, the design capacity of a left-turn ane is obtained from chart 12A or 12B, he larger value governing. Chart 12C is ‘4 the same form as that of chart 7B, but s based on a control value of 1,000 vehicles oer hour of green per 10 feet of width ‘ instead of 800. A third adjustment is in- ; luded i in chart 12C in terms of three degrees , )£ pedestrian interference. Chart 12D is the same as chart 10A except that the con- | 2 value of 1,000 is used instead of 800. he length of right- or left-turn lane, vith or without separate signa] indication,
10
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PUBLIC ROADS @ Vol. 26, No. 6
Table 4.—Minimum lengths of speed-change lanes and taper to or from a stop position
For deceleration lanes
Highway design speed
Length Length of exclusive taper of taper
Miles per hour
For acceleration lanes !
Total Length Length of Total length exclusive taper length of taper
! Applies only to conditions with widened approaches or to intersections without signal control.
is given in chart 12E and predicated on the maximum number of vehicles that can be stored per cycle, which is assumed to be twice the average number. Since express- ways are intended for rapid vehicular movement with a minimum of operational delay, the length of turning lanes should be predicated on the likely approach speeds of traffic during the green signal periods. For this purpose the turning lanes should be sufficiently long to permit turning ve- hicles to decelerate to the safe speed of the turn, with allowance for drivers to bring their vehicles to a stop if necessary. Minimum lengths of deceleration lanes to allow for such operation are given in table 4. Comparative values are obtained from chart 12E and from the second column of table 4 and the larger of the two should be used in design. The length of taper should never be less than that shown in the third column of table 4.
On expressways, bus stops in the vicinity of cross streets should be located off the through lanes and on the far side of the intersection. When thus positioned at an intersection with corner islands, as in the sketch on chart 12, bus stops have little if any effect on intersection capacity. Thus, charts 11 and 12 apply to inter- sections with bus stops on the far side as well as to those with no bus stops. In the event that a near-side bus stop is pro- vided, the capacity should be reduced ac- cording to the adjustment in item V-3B on page 91 of the Manual.
Another condition adjustment is shown in item V-2A(2) in the Manual, for right- turn movements as affected by frontage- road traffic. When a frontage road is sufficiently close to affect a right-turn move-
S
ment, the capacity condition is the same as that of a left turn from an added lane without a separate signal indication, and values from charts 12A and 12B are ap- plicable.
Intersections on expressways should be designed so that anticipated volumes will not exceed the design capacity. For cer- tain combinations of traffic volumes and distributions, however, it may not be prac- ticable to accommodate each approach move- ment at design capacity. One of the turning movements may have to operate above design capacity, but the excess should not be large. The relative amount can be determined by calculating possible capacity.
On expressways, possible capacity for any movement may be obtained by multiply- ing the design capacity by 1.2.
Problems 34-37 illustrate the use of charts 11 and 12.
Problem 34
On the expressway shown in figure 11, traffic from east to west during the peak hour is approximately 60% of the total two-way traffic on the expressway. On the east approach, what is the design ca- pacity of the through lanes, the right-turn lane, and the left-turn lane, when trucks comprise 10% of each movement, C=65 seconds, and G=39 seconds?
Solution: Design capacity of the through pavement, K;, using chart 11 with W/2=25, T=10%, and G/C=89/65=0.60, is 1,350 v.p.h.
Design capacity of the right-turn lane Ks, using chart 12C with G/C=0.60, a= 11, T.=10%, and light to moderate pedes- trian interference, is 530 v.p.h.
INTERMEDIATE AREA TWO-PHASE SIGNAL CONTROL
Figure 11.—Illustrative problems 34-37.
119
Design capacity of the left-turn lane Ks is determined by the larger of the two values from charts 12A and 12B. The volume opposing the left turn Vo, as used in chart 12A, is 40% of the total peak-hour volume on the expressway, or 1,350 40/60 — 900 v.p.h. Using this in chart 12A gives a zero capacity. Minimum capacity in chart 12B, with C=65 seconds, is 88. _ Thus, the value in chart 12B governs and K.=90 v.p.h. (using a rounded figure).
Problem 35
Determine the minimum signal timing and lengths of turning lanes of the east approach of the intersection shown in fig- ure 11 if the design speed is 50 m.p.h. and the design volumes during the evening peak hour are as follows: through movement, 1,120 v.p.h. of which 5% are trucks; right- turn movement, 280 v.p.h. of which 30% are trucks; and left-turn movement, 90 v.p.h. of which 2% are trucks.
Solution: The proportion of green time, G/C, needed for the through movement is obtained from chart 11: Using W/2=25, T=5%, and an approach through volume of 1,120 v.p.h., the required G/C=0.47.
For the right-turn movement chart 12C is used. Entering the chart at the bottom with a volume of 280 v.p.h., and using light to moderate pedestrian interference, T.= 30%, and a=11, the required G/C=0.88.
It is apparent from the approach volumes indicated and from the distribution of traffic by direction, as shown in problem 34, that the capacity of the left-turn lane is not governed by the condition in chart 12A. Thus, using chart 12B, it is found that for a left-turn volume of 90 v.p.h. a cycle length C of 64 seconds is required.
The through movement, for which the required G/C=0.47, governs the design ca- pacity of the east approach. Assuming that a 64-second cycle is satisfactory, G= 64X0.47=30 seconds and, if each amber period is 3 seconds, the signal timing will be 380 seconds green and 6 seconds amber, leaving 28 seconds red (green on the cross street).
In the event that a longer eycle had to be used, say 75 seconds, the design capacity of the left-turn lane (chart 12B) would be 77 v.p.h. The 90 v.p-h. could still be hanvdied, although not as satisfactorily, since possible capacity would be 77 X1.2—92 v.p.h.
The lengths of turning lanes, from chart 12K, required to handle the volumes indi- cated are:
Right-turn lane: Using V.=280 v.p.h., C=64 seconds, and 7.=30%; D:=800 feet.
Left-turn lane: Using V;=90 v.p.h., C= 64 seconds, and T;=2%; D:=80 feet.
The length of each turning lane required for speed change, from table 4, is 90 feet plus a taper of 150 feet. Thus, the right- turn lane should be 300 feet long plus a 150-foot taper, and the left-turn lane 90 feet long plus a 150-foot taper.
Problem 36 If, in problem 85, all of the condi- tions remain the same, except that a one-
120
way frontage road is provided (dash lines in figure 11), what will be the design capacity of the right-turn lane on the east approach when a volume of 250 v.p.h. on the frontage road, of which 12% are trucks, receives a green signal at the same time as the expressway traffic?
Solution: In this case it is necessary to check the capacity of the right-turn lane as affected by the crossing of frontage-road traffic, which can be determined from charts 12 A and 12 B (see page 119, cols. 2-3).
Using Vo=250 v.p.h. in chart 12A as the volume conflicting with the right-turning movement, 7»—12%, G/C=0.47, and Ts (which in this case is the percentage of trucks in the right-turn movement) =30%, the design capacity, as controlled by the frontage road traffic, is found to be 190 v.p.h.
This indicates that, with a frontage road, a right-turn volume of 280 v.p.h. cannot be accommodated, and three-phase control is needed at the intersection of the frontage road and the cross street.
Problem 37
If, in problem 35, all of the conditions remain the same, except that the left-turn volume on the east approach is 140 v.p.h., what will be the signal timing if the left turn is to be accommodated on a separate signal indication? The 28-second green in- terval on the cross street is to be retained to give pedestrians sufficient time to cross the street. Left-turn movement on the west approach also will move on this phase.
Solution: In problem 35 it is shown that a value of G/C=0.47 is required for the through movement, during which the right turn will also be accommodated. The sepa- rate phase for the left turn will require an additional G’/C=0.18, as determined from chart 12D with a volume of 140 v.p.h., Ts= 2%, and a=11 feet.
To retain the 28-second green period on the cross street, the length of cycle must be: C=0.47C+0.13C--28+ (3X38) amber= 93 seconds.
The green signal times are thus: For through and right-turn movement on the expressway, 93 0.47=44 seconds; for left turns on the expressway, 93X0.13=12 sec- onds; for the cross street, 28 seconds. Each of the three phases is followed by a 3-second amber period.
It may be noted that, while the 28-second green interval has been retained for the cross street, the proportion of green time (G/C) for movement of traffic on this street, because of lengthened cycle, has been decreased; thus, the capacity of the cross street is less than that in problem 35.
EXPRESSWAYS WIDENED THROUGH INTERSECTIONS
On expressways where the cross roads at grade are widely spaced it may be necessary to widen the expressway pave- ments at the intersections to prevent their capacity from being diminished at these
points. Such treatment is illustrated }), a sketch in the upper right-hand corn of chart 18, and from this chart the de; capacity can be determined or the numb
can be established. In this condition the added lanes, sha y as e. and ez in the sketch, are carried throug)) the intersection, unobstructed by triangule| islands. When the expressway is operatin . at relatively low volumes, through traff will proceed through the intersection 9) the normal width of pavement, W/2, e elusive of widening. During such tim the added lanes e2 and e; will function ¢ speed-change lanes for turning vehicle) At or near design capacity, however, throug s traffic will be stored on the added lanes an): proceed through the intersection when # signal changes. Turning vehicles will aly use these lanes at the same time. For th) reason an adjustment in capacity must } P made. This is accounted for in chart 1 An adjustment for bus stops is not : cluded in chart 13. Since this type % : intersection generally is used to maintajl” the high capacity available on other portion z of the expressway without intersections r grade, bus stops should be excluded fro all lanes intended for regular traffic us If bus stops are necessary at such location they should be provided on frontage roa or on separate turnouts. ‘Chart 13 is constructed on the same bas as chart 11 (see pp. 87 and 103 of t Manual), with a design capacity of 1,0( vehicles per hour of green per 10 feet / width. The upper left and lower rigl portions of chart 13 are identical wil chart 11. The added adjustments for tur ing movements are the same as in previo # charts, the percentage reduction being 0.5) for right turns and 1.0L for left turns.| For this capacity condition the widened a} proach pavement must be of sufficient leng) } to encourage its use by through | as well as be adequate for deceleration at storage of turning vehicles. Controls fi the required lengths are given in the not below the sketch in the upper right corn) of chart 138. The widened length in fe in advance of the intersection, shown | Da, should be at least five times the gret interval in seconds (see Manual, p. 8! and also should be adequate for decelerati purposes, as indicated in the second colun of table 4. In addition it should have proper taper, as shown in table 4. For the maneuvering of traffic, the wi ened pavement D» beyond the intersecti should be of length somewhat longer than 4 the approach side, for which a factor of 1 is assumed. Further, the length should checked for suitability for acceleration, 2 cording to the fifth column of table 4. T? sixth column of table 4 gives the need length of taper.
Problem 38
An expressway with two one-way pa¥ ments, separated by a median about 1 feet wide, intersects a cross road at gra¢
February 1951 ® PUBLIC ROA
7 d a signal must be installed. If the r ‘mal width of each expressway pavement
83 feet, and at the intersection each vement is widened by 12 feet on the left d on the right for an adequate distance advance of and beyond the intersection, jat is the design capacity of one approach, T—10%, R=15%, L=12%, and G/C= 34? Solution: The total width of approach W/2-+-e:+e:,=33+12+12=57 feet. Using is in chart 13 with the conditions given yove, K=2,260 v.p.h. The wide median, effect, separates the expressway into yo one-way facilities; therefore, it is not sxcessary to check for the capacity of the ft turn.
roblem 39
An urban expressway in rolling terrain, Sesigned for a speed of 50 m.p.h., has two 2-foot lanes in each direction, and all cross Jireets are separated in grade except at ine isolated intersection. The volume of laffic on the cross street can be accom- iodated by a two-phase traffic signal with J% of the elapsed time allowed for the
USE IN PRELIMINARY DESIGN
. ‘In planning or in preliminary design -ihere often is need for a quick, approximate )\etermination of intersection capacities. he problem usually resolves itself into ne of two conditions: (1) where the in- L ersecting volumes are known and street |) widths are established, to determine whether ‘Tiapacity is adequate; or (2) where the ) ntersecting volumes and the width of one ) street are given, to determine the width q of the intersecting street.
| These problems can be solved with charts eal by first determining the proportion of xreen time required for one approach, as- suming a cycle length and appropriate ) amber periods; then calculating the result- ) ant G/C for the cross-street approach; and finally determining, according to the cross- ‘street volume, either its adequacy for ca- Reeity or its necessary width.
SOLUTION WITH HOURLY TRAFFIC VOLUMES
of systems or for early stages of design, Jas well as for review of preliminary plans, where a quick method is needed for de- termining intersection capacities or re- ‘quired street widths at a four-way inter- ‘section under signal control. Chart 14 combines the necessary information for _ both of the intersecting streets on one chart and gives results in terms of over-all ca- pacity. It takes into account jointly, for "average conditions, the intersection of any Na
. ROADS e Vol. 26, Nc.6
| | Chart 14 was devised for use in planning
(ERRATA SHEET)
cross street, and a 20-second green interval for pedestrians.
If the intersection treatment is to be of the type shown in the upper right-hand corner of chart 13, determine the minimum number of lanes on the expressway, at the intersection, that will enable the intersection approaches to accommodate a volume of traffic equal to the capacity of the two 12-foot lanes where flow is uninterrupted. On the critical approach, during the peak hour, T=15%, R=18%, and L=4%.
Solution: On the basis that 30% of the cycle is required for the cross movement with a green interval of 20. seconds, the shortest cycle that can be used is 20+-0.30= 67 seconds. Allowing 7 seconds for the amber periods, the green interval available for expressway traffic is 67—7—20=40 seconds, and G/C=40/67=0.60.
The capacity of the expressway on the portions where the flow is uninterrupted, with 15% trucks in rolling terrain, is found
91,500 xX 0.70 = 1,050 v.p.h. Practical or design capacity of urban expressways is given as_ 1,500 vehicles per hour per lane on p. 47 of the Manual; 0.70 is a factor interpolated in table 9, p. 56 of the Manual, for the effect of commercial vehicies on practical capacity.
two facilities, regardless of the type of each (one-way or two-way street or ex- pressway), type of area, and parking regu- lation. The left half of the chart is used for the approach on one street and the right half for the approach on the other (intersecting) street. A line projected be- tween the inner sides of the two charts determines, at the point where it inter- sects the center axis, y-y, the adequacy of intersection capacity.
The two parts of chart 14 are identical except for the reverse plotting. The ar- rangement of each part is similar to that of chart 1, but the G/C ratio is made the outer scale and the volume is shown as the lower series of curves. In addition to the four area—parking conditions shown on chart 1, conditions for one-way streets and expressways are represented in the upper parts of chart 14 by other sloping lines. These are control values previously pre- sented, including adjustments to obtain de- sign capacity. Notes at the lower left show the proper W/2 value to be used for each case. The G/C ratio on the inner side scales is the proportion of time required on the one approach for operation at design capacity. With an assumption of 10 per- cent of the cycle time being used in the amber periods, design capacity is obtained when the total of two green intervals is 90 percent of the cycle (the sum of the two G/C values=0.90). The zero point on the y-y axis is located so that a straight line between any two G/C values passes through it when their sum is 0.90. The scale values
to be 1,050 v.p.h. per lane,® or a one-way flow on the facility of 2,100 v.p.h. The total number of lanes on the one approach to handle this volume can be obtained from chart 13. Entering the chart at the bot- tom with a volume of 2,100 v.p.h. and using G/C=0.60, L=4%, R=18%, and T—15%, the total approach width, W/2+e2+e:, is found to be 47 feet.
Four lanes will therefore be required on the one approach at the intersection, or an extra lane on each side of the normal pavement, to accommodate a volume equal to the uninterrupted capacity flow of the expressway.
Since the expressway is a two-way facili- ty it is necessary to check separately in chart 12 for capacity of the left-turn lane. Obviously chart 12B governs, from which it is found for C=67 seconds that 86 left- turning vehicles can be handled. This is satisfactory since 4% of 2,100 is 84 v.p.h.
The minimum lengths of widened pave- ment, from the notes under the sketch on chart 18, should be: For Da, 200 feet plus 150-foot taper; for Ds, 300 feet plus 200-foot taper.
Part 1V—Over-All Intersection Capacity
above and below the zero point on the y-y axis show the proportion by which the sum of the G/C values is deficient or in excess of the design capacity condition. As in- dicated on the chart, a design capacity deficiency of 20 percent is about the possible capacity condition.
With chart 14, graphic solutions can be made for various combinations of control conditions to determine one missing factor. It must be remembered that this solution is for average conditions only, with as- sumptions that trucks and busses constitute 10 percent and turning movements on streets 20 percent (15 percent on expressways) of the total approach volume. Where spe- cific conditions are otherwise, the solutions should be obtained from charts 2-13.
Problem 40
In a downtown area a two-way street (approach A) 62 feet wide with parking intersects a two-way street (approach B) 44 feet wide without parking. A _ fixed- time signal is used and conditions are as- sumed to be average. When the peak-hour volume on approach A is 400 v.p.h. in one direction and on approach B is 600 v.p.h. in one direction, is the capacity of the in- tersection adequate?
Solution: For approach A, enter chart 14 at the left with W/2=—62/2=31, proceed to the right to the curve for downtown two- way street with parking, then down to an approach volume of 400 v.p.h., and to the right to G/C=0.38. For approach B, enter the chart at the extreme right with W/2=
121
qd a signal must be installed. If the jrmal width of each expressway pavement } 88 feet, and at the intersection each jyvement is widened by 12 feet on the left ud on the right for an adequate distance ; advance of and beyond the intersection, jaat is the design capacity of one approach, i T7—10%, R=15%, L=12%, and G/C—
The total width of approach | W/2-+ e2.+¢e;=33+12+12=—57 feet. Using
ove, K=2,260 v.p.h. The wide median, | effect, separates the expressway into yo one-way facilities; therefore, it is not scessary to check for the capacity of the
| An urban expressway in rolling terrain, esigned for a speed of 50 m.p.h., has two 2-foot lanes in each direction, and all cross treets are separated in grade except at ine isolated intersection. The volume of raffic on the cross street can be accom- aodated by a two-phase traffic signal with 0% of the elapsed time allowed for the
i wbove and below the zero point on the y-y ixis show the proportion by which the sum if the G/C values is deficient or in excess % the design capacity condition. As in- dicated on the chart, a design capacity leficiency of 20 percent is about the possible capacity condition,
With chart 14, graphic solutions can be made for various combinations of control conditions to determine one missing factor. { must be remembered that this solution is for average conditions only, with as- sumptions that trucks and busses constitute
10 percent and turning movements on streets - 20 percent (15 percent on expressways) of the total approach volume. Where spe- cific conditions are otherwise, the solutions should be obtained from ae 2-13.
! Bite. 40
In a downtown area a two-way street (approach A) 62 feet wide with parking intersects a two-way street (approach B) 44 feet wide without parking. A fixed- time signal is used and conditions are as- sumed to be average. When the peak-hour volume on approach A is 400 v.p.h. in one direction and on approach B is 600 v.p.h. in one direction, is the capacity of the in- tersection adequate?
Solution: For approach A, enter chart 14 at the left with W/2—62/2=31, proceed to the right to the curve for downtown two- Way street with parking, then down to an approach volume of 400 v.p.h., and to the j right to G/C=0.38. For approach B, enter the chart at the extreme right with W/2=
cross street, and a 20-second green interval for pedestrians.
If the intersection treatment is to be of the type shown in the upper right-hand corner of chart 13, determine the minimum number of lanes on the expressway, at the intersection, that will enable the intersection approaches to accommodate a volume of traffic equal to the capacity of the two 12-foot lanes where flow is uninterrupted. On the critical approach, during the peak hour, T=15%, R=18%, and L=4%.
Solution: On the basis that 30% of the cycle is required for the cross movement with a green interval of 20 seconds, the shortest cycle that can be used is 20+0.30= 67 seconds. Allowing 7 seconds for the amber periods, the green interval available for expressway traffic is 67—7—20=—40 seconds, and G/C=40/67=0.60.
The capacity of the expressway on the portions where the flow is uninterrupted, with 15% trucks in rolling terrain, is found
91,500 X 0.70 = 1,050 v.p.h. Practical or design capacity of urban expressways is given as 1,500 vehicles per hour per lane on p. 47 of the Manual; 0.70 is a factor interpolated in table 9, p. 56 of the Manual, for the effect of commercial vehicles on practical capacity.
two facilities, regardless of the type of each (one-way or two-way street or ex- pressway), type of area, and parking regu- lation. The left half of the chart is used for the approach on one street and the right half for the approach on the other (intersecting) street. A line projected be- tween the inner sides of the two charts determines, at the point where it inter- sects the center axis, y-y, the adequacy of intersection capacity.
The two parts of chart 14 are identical except for the reverse plotting. The ar- rangement of each part is similar to that of chart 1, but the G/C ratio is made the outer scale and the volume is shown as the lower series of curves. In addition to the four area—parking conditions shown on chart 1, conditions for one-way streets and expressways are represented in the upper parts of chart 14 by other sloping lines. These are control values previously pre- sented, including adjustments to obtain de- sign capacity. Notes at the lower left show the proper W/2 value to be used for each case. The G/C ratio on the inner side scales is the proportion of time required on the one approach for operation at design capacity. With an assumption of 10 per- cent of the cycle time being used in the amber periods, design capacity is obtained when the total of two green intervals is 90 percent of the cycle (the sum of the two G/C values=0.90). The zero point on the y-y axis is located so that a straight line between any two G/C values passes through it when their sum is 0.90. The scale values
to be 1,050 v.p.h. per lane,® or a one-way flow on the facility of 2,100 v.p.h. The total number of lanes on the one approach to handle this volume can be obtained from chart 13. Entering the chart at the bot- tom with a volume of 2,100 v.p.h. and using G/C=0.60, L=4%, R=18%, and T—15%, the total approach width, W/2+ e+e, is found to be 47 feet.
Four lanes will therefore be required on the one approach at the intersection, or an extra lane on each side of the normal pavement, to accommodate a volume equal to the uninterrupted capacity flow of the expressway.
Since the expressway is a two-way facili- ty it is necessary to check separately in chart 12 for capacity of the left-turn lane. Obviously chart 12B governs, from which it is found for C=67 seconds that 86 left- turning vehicles can be handled. This is satisfactory since 4% of 2,100 is 84 v.p.h.
The minimum lengths of widened pave- ment, from the notes under the sketch on chart 138, should be: For Da, 200 feet plus 150-foot taper; for D», 300 feet plus 200-foot taper.
Part [VW—Over-All Intersection Capacity
USE IN PRELIMINARY DESIGN
In planning or in preliminary design there often is need for a quick, approximate determination of intersection capacities. The problem usually resolves itself into one of two conditions: (1) where the in- tersecting volumes are known and street widths are established, to determine whether capacity is adequate; or (2) where the intersecting volumes and the width of one street are given, to determine the width of the intersecting street.
These problems can be solved with charts 1-138 by first determining the proportion of green time required for one approach, as- suming a cycle length and appropriate amber periods; then calculating the result- ant G/C for the cross-street approach; and finally determining, according to the cross- street volume, either its adequacy for ca- pacity or its necessary width.
SOLUTION WITH HOURLY TRAFFIC VOLUMES
Chart 14 was devised for use in planning of systems or for early stages of design, as well as for review of preliminary plans, where a quick method is needed for de- termining intersection capacities or re- quired street widths at a four-way inter- section under signai control. Chart 14 combines the necessary information for both of the intersecting streets on one chart and gives results in terms of over-all ca- pacity. It takes into account jointly, for average conditions, the intersection of any
121
44/2=-22, proceed to the left to the curve for downtown two-way street without park- ing, then down to an approach volume of 600 v.p.h., and to the left to G/C=0.47. A straight line between the two values of G/C falls below the zero point on the y-y axis so capacity is adequate; in fact, there is about 6% excess capacity.
Adjusted signal timing, if desired, can be obtained by dividing each G/C by the portion of capacity required in respect to design capacity. In this case, with 6% excess capacity, the factor is (100—6)~+ 100=0.94, and the signal timing would be: For approach A, 0.38+-0.94=0.40; for approach B, 0.47+0.94=0.50; for amber (the remainder), 0.10.
Problem 41
If, in problem 40, all of the conditions remain the same except that approach B has to accommodate a peak-hour volume of 930 v.p.h. in one direction, to what extent must this approach be widened to make the intersection operate at design capacity?
Solution: For approach A, use the left portion of the chart as in the previous ex- ample, obtaining a value of G/C=0.38. From this point project a straight line through the zero point (design capacity) of line y-y to intersect the G/C scale on the right portion of the chart. From this point (G/C=0.52), proceed to the right to an approach volume of 930 v.p.h., then up to the curve for downtown two-way street without parking, and to the right to W/2= 30. Approach B would have to be widened to 60 feet if the intersection is to operate at design capacity.
Problem 42
A two-way expressway (approach A) with two 24-foot pavements and added turn- ing lanes intersects a 52-foot one-way street without parking (approach B). The inter- section is situated in an intermediate area and is to be controlled by a fixed-time signal. The plan is in a preliminary design stage with only general traffic information of 1,400 v.p.h in one direction on approach A and 1,200 v.p.h. on approach B. Can these volumes be handled satisfactorily?
Solution: Enter chart 14 at left with width of approach A=24 feet, proceed to the right to the curve for expressway with turning lanes, then down to an approach volume of 1,400 v.p.h., and to the right to G/C=0.56. Enter the chart at right with a width of approach B=52 feet, proceed to the left to one-way street without parking in intermediate area, then down to an ap- proach volume of 1,200 v.p.h., and to the left to G/C=0.37. A straight line between the two values of G/C shows that the in- tersection will operate at slightly above design capacity, or about 3% deficient; this is sufficiently close to consider the design satisfactory.
122
pe \ fee :
——— ONE = WAN
(e)
(2)
TRAFFIC VOLUMES SHOWN ARE OL AVERAGE DAILY TRAFFIC = ot
Figure 12.—Illustrative problems 43 and 44.
SOLUTION WITH AVERAGE DAILY TRAFFIC VOLUMES
In the first stages of preliminary design, when the pattern of highways and their intersections are being developed, street widths often must be tentatively established as a starting point. Only general traffic values are then available, customarily ex- pressed in terms of average daily traffic volumes. Such information is of little value in final design of intersections, but in the absence of peak-hour volumes the average daily traffic volumies may be considered ap- propriate for preliminary design.
Where the design volumes are given in terms of average daily traffic it is necessary to convert them to peak-hour volumes in one direction of travel. Chart 15 gives this relation for average conditions. The peak-hour volume for design is assumed as 12 percent of the two-way average daily traffic, and as 55, 60, and 65 percent of the total peak-hour traffic as the predominant movement in one direction of travel for downtown, intermediate, and outlying areas, respectively. Chart 15 may be entered at the top with the total two-directional aver- age daily traffic volume, or at the bottom with a one-way average daily traffic volume. Thus, the chart is applicable to both one- and two-way facilities. The vertical scale gives the design peak-hour volume in one direction of travel.
It will be noted that the assumption of the peak hour traffic as 12 percent of the two-way average daily traffic, and the use of three d values, results in different peak- hour percentages of the one-way average daily traffic, when the latter is one-half of the two-way daily volume. Thus, for one- way facilities, in chart 15, the resulting percentages that the peak-hour volume is of the one-way average daily traffic (ob- tained by dividing V by % ADT), are: downtown, 13.2; intermediate, 14.4; and outlying, 15.6.
=<=-16;(.00
INTERMEDIATE AREA FIXED-TIME SIGNALS
~— 12,500 — — Se
ee AMY = |
—— — — —— —= 12, 500 —> s- ‘
Problem 43
Shown in figure 12 is a portion of preliminary plan on which an east-we four-lane expressway is planned to cro at grade a north-south major street. T) only traffic information available is in tern of average daily traffic, as indicated ¢ the figure. The north-south street cann be widened, but right-of-way permits wi) ening of the approaches on the expresswa Determine the number of lanes requir at the intersection in each direction on tl expressway if the intersection is to opera at design capacity. 7
Solution: It is first necessary to conve the average daily traffic volume to pea: hour volume in one direction of travel. C the north-south street the two-direction daily volume of 11,200 vehicles in an inte mediate area, from chart 15, is equivale) to a peak-hour volume in one direction ' 800 vehicles; and on the expressway tl daily volume of 12,500 vehicles in 01} direction corresponds to a peak-hour volun! of 1,800 vehicles.
Using the north approach on the maj: street as approach A in chart 14, wi W/2=64/2=32, two-way street with }) parking in intermediate area, and an a proach volume of 800 v.p.h., a value | G/C=0.46 is obtained. From this point . : straight line is projected to the rig: through the zero point of line y-y, inte: secting a value of G/C=0.44 for approai. B. From this point proceed to the rig to an approach volume of 1,800 v.p.h., thy up to expressway with widened approach«, and read at the right a required approa: width of about 50 feet.
The two-lane pavement in each directi’ on the expressway should therefore widened in advance of and beyond the inte- section to 50/12—4.2, or four lanes. T) length of widened pavements should — of sufficient length, as noted under t sketch in chart 13.
.
y
blem 44
n figure 12, the north-south major street rsects a one-way street at a point sev- | hundred feet north of the expressway. ording to the average daily traffic ames indicated and street widths pro- ad, determine whether adequate capacity wailable at this intersection.
0 ution: The left portion of chart 14 ised for one approach on the north-south xet, as in problem 43. The right portion the chart is used for the east approach the one-way street with W/2—44, one- 7 street with parking in intermediate ja, and an approach volume of 960 v.p.h. Wirived from chart 15 as the equivalent fan average daily traffic in one direction 13,700). A straight line between the two lalting values of G/C indicates, at the nrsection of the y-y line, that more than (quate capacity is provided.
1
LIMITATIONS IN USE OF ' CHARTS 14 AND 15
) though charts 14 and 15 are convenient Wis for preliminary design, the limitations
ROADS e Vol. 26, No. 6
“a
in their use should be recognized:
1. Results are approximate, since average conditions are assumed.
2. On two-way facilities it is assumed that the volume of left-turning vehicles can be accommodated without requiring three-phase signal control. Generally on major facilities not more than 80 to 120 left-turning vehicles per hour can be handled without a separate signal indication. Even in preliminary design, if it is known that the left turns on one approach will exceed about 100 vehicles per hour, the more de- tailed charts should be used.
3. Where average daily traffic volumes are used as the traffic basis, and corre- sponding one-way peak-hour volumes are taken from chart 15, it should be remem- bered that the peak-hour volumes on each approach may not occur simultaneously. At intersections involving two-way streets on which the signal timing remains the same throughout the day, the peak-hour volumes thus obtained and used may be ap- propriate. However, if the signal timing
is different during the morning peak from that during the evening peak, because of load distribution, or if one or both of the intersecting streets are one-way, the peak- hour volumes based on average daily traffic may not be representative. If the designer has some knowledge of the peak distribu- tions, he can make adjustments in the hourly approach volumes to arrive at the informa- tion needed for both the morning and eve- ning peak hours, one or both of which may govern the design; if not, the direct use of chart 15 for each approach will give results in design on the safe side.
4, Chart 14 may not always apply to those intersections where a given minimum green interval must be maintained, as for a pedestrian crossing. However, the values of G/C obtained in the solution for any intersection can be tested with logical cycle lengths to determine whether the required green interval may be obtained.
5. For approximate results, chart 14 may also be used for T or Y intersections.
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A complete list of the publications of the Bureau of Public Roads, classified according to subject and including the more important articles in PUBLIC ROADS, may be obtained upon request addressed to Bureau of Public Roads, Washington 25, D. C. a
PUBLICATIONS
of the Bureau of Public Roads
The following publications are sold by the Superintendent of Documents, Government Printing Office, Washington 25, D. C. Orders should be sent direct to the Superintendent of Documents. Prepayment is required.
ANNUAL REPORTS
(See also adjacent column)
Reports of the Chief of the Bureau of Public Roads: 1937, 10 cents. 1938, 10 cents. 1939, 10 cents.
Work of the Public Roads Administration:
1940, 10 cents. 1942, 10 cents. 1941, 15 cents. 1946, 20 cents. 1947, 20 cents.
Annual Report, Bureau of Public Roads, 1950, 25 cents.
1948, 20 cents. 1949, 25 cents.
HOUSE DOCUMENT NO. 462
Part 1... Nonuniformity of State Motor-Vehicle Traffic Laws. 15 cents.
Part 2... Skilled Investigation at the Scene of the Acci- dent Needed to Develop Causes. 10 cents.
Part 3... Inadequacy of State Motor-Vehicle Accident Reporting. 10 cents.
Part 4... Official Inspection of Vehicles. 10 cents.
Part 5... Case Histories of Fatal Highway Accidents. 10 cents.
Part 6... The Accident-Prone Driver. 10 cents.
UNIFORM VEHICLE CODE
Act I—Uniform Motor-Vehicle Administration, Registra- tion, Certificate of Title, and Antitheft Act. 10
cents.
Act I1—Uniform Motor-Vehicle Operators’ and Chauffeurs’ License Act. 10 cents.
Act II].—Uniform Motor-Vehicle Civil Liability Act. 10 cents.
Act IV.—Uniform Motor-Vehicle Safety Responsibility Act. 10 cents.
Act V.—Uniform Act Regulating Traffic on Highways. 20 cents.
“Model Traffic Ordinance. 15 cents.
kb
MISCELLANEOUS PUBLICATIONS
Bibliography of Highway Planning Reports. 30 cents. Construction of Private Driveways (No. 272MP). 10 cents.
Economic and Statistical Analysis of Highway Construction
Expenditures. 15 cents.
Electrical Equipment on Movable Bridges (No. 265T). 40 cents.
Federal Legislation and Regulations Relating to Highway Con- struction. 40 cents.
Financing of Highways by Counties and Local Rural Govern-
ments, 1931-41. 45 cents.
Guides to Traffic Safety. 10 cents.
Highway Accidents. 10 cents.
Highway Bond Calculations. 10 cents.
Highway Bridge Location (No. 1486D). 15 cents. Highway Capacity Manual. 65 cents.
Highway Needs of the National Defense (House Document No. 249). 50 cents.
Highway Practice in the United States of America. 50 cents. Highway Statistics, 1945. 35 cents.
Highway Statistics, 1946. 50 cents.
Highway Statistics, 1947. 45 cents.
Highway Statistics, 1948. 65 cents.
Highway Statistics, Summary to 1945. 40 cents.
Highways of History. 25 cents.
Identification of Rock Types. 10 cents.
Interregional Highways (House Document No. 379). 75 cents. Legal Aspects of Controlling Highway Access. 15 cents.
Manual on Uniform Traffic Control Devices for Streets and Highways. 50 cents.
Principles of Highway Construction as Applied to Airports, Flight Strips, and Other Landing Areas for Aircraft. $1.75.
Public Control of Highway Access and Roadside Development. 35 cents.
Public Land Acquisition for Highway Purposes. 10 cents.
Roadside Improvement (No. 191MP). 10 cents.
Specifications for Construction of Roads and Bridges in Na-
tional Forests and National Parks (I*P—41). $1.50. Taxation of Motor Vehicles in 1932. 35 cents. The Local Rural Road Problem. 20 cents.
Tire ee and Tire Failures on Various Road Surfaces. 10 cents.
Transition Curves for Highways. $1.25.
Single copies of the following publications are available to highway engineers and administrators for official use, and may be obtained by those so qualified upon request addressed io the Bureau of Public Roads. They are not sold by the Superintendent of Documents.
ANNUAL REPORTS
(See also adjacent column)
Public Roads Administration Annual Reports: 1943. 1944, 1945.
MISCELLANEOUS PUBLICATIONS
Bibliography on Automobile Parking in the United States. Bibliography on Highway Lighting.
Bibliography on Highway Safety.
Bibliography on Land Acquisition for Public Roads, Bibliography on Roadside Control.
Express Highways in the United States: a Bibliography. Indexes to PUBLIC ROADS, volumes 17-19, 22, and 238.
Road Work on Farm Outlets Needs Skill and Right Equipment.
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