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RP545
WIND PRESSURE ON A MODEL OF THE EMPIRE STATE
BUILDING
By Hugh L. Dry den and George C. Hill
ABSTRACT
Measurements have been made of the distribution of wind pressure over a
model of the Empire State Building for the purpose of comparing the results of
model tests with measurements on the actual building now in progress under
the direction of the Research Committee of the American Institute of Steel Con-
struction. This paper describes the results of measurements on the model.
The pressure was measured at 102 stations on the model, 30 of which represent
stations in the actual building, at 11 wind directions. In addition, the over-
turning moments were measured for the same wind directions. The results show
that the pressure varies from point to point, and that reduced pressure is found
over the larger part of the model. The greatest loads on the building occur when
the wind blows directly against one face. A suitable value of the pressure for
use in the design of tall buildings is 0.0038 V2 (in lbs./ft.2) where V is the wind
speed in miles per hour against which provision is to be made.
It was found that the speed of the air rushing by close to the building is greater
than that of the approaching wind. Hence, an instrument mounted 15 feet above
the top of the building reads too high by a factor 1.23.
An outline is given of a method of procedure for the comparison of the results
on the model with those on the actual building.
CONTENTS
Page
I. Introduction 493
II. Measurements of pressure distribution 495
1. Apparatus 495
2. General procedure 497
3. Reduction of observations 498
4. Results 501
5. Discussion 516
III. Measurements of overturning moment 517
1. Apparatus and method 517
2. Results 518
3. Discussion 520
IV. Remarks on the method of comparing model results with full-scale
measurements 521
V. Conclusion 523
I. INTRODUCTION
In the design of tall buildings or other structures, the pressure
exerted by high winds plays an important role. If the structure is
designed for a very large wind pressure, the cost is unnecessarily
increased, a matter of concern to the owners of the structure. If the
design is made for too small a wind pressure, the structure is unsafe, a
matter of concern to those living or working in the building and to the
general public.
The forecasting of the wind pressure to which a building may be
subjected is difficult. It is practically certain that the speed of the
wind will exceed 5 miles per hour at some time during nearly every day
of the year. In Washington, D. C, the speed exceeds 40 miles per
hour about four times a year, and has not reached 100 miles per hour
in the 60 years for which records are available. It is a practical
493
494 Bureau of Standards Journal of Research [Vol. w
impossibility to design all buildings to withstand the maximum speeds
which have ever been experienced anywhere. The line must be drawn
at some speed which is not likely to be exceeded in the life of the
building.
To obtain information on wind pressure from observations on a
building in a natural wind would require years of measurement and a
statistical study of the results. The data obtained from such an
investigation would not be applicable to buildings of a different shape
or to buildings with a different exposure; for example, located in
another part of the country. Some better procedure must be
adopted.
The only long-continued observations on the wind are those made
by the Vfeather Bureau. These observations give the speed and
direction of the wind for different parts of the country. From these
observations, the probability that a given speed will be exceeded say
once in a hundred years may be computed.1 To obtain the pressure
on the building, the relation between the pressure and the speed
must be known. Two methods are available for determining this
relation: (1) By experiments on models in wind tunnels, and (2) by
observations in natural winds.
Experiments on models have been found invaluable in hydraulics
and aeronautics and are well known to engineers working in those
fields. Studies of wind pressure have been made by this method in
this country and abroad,2 but full confidence has not been placed in
the results, because of some feeling of uncertainty as to the application
to buildings in a natural wind. It seemed to us that the next impor-
tant step in the study of wind pressure was a coordinated program of
model and full-scale experiments as applied to some existing structure.
Both methods of experiment have advantages and disadvantages.
In wind-tunnel experiments, the speed and direction of the wind are
under continuous control. Standard reference speeds and pressures
are easily obtainable and the total force on the model may be measured
1 The Weather Bureau observations give usually only the mean speed, which is exceeded in gusts. For a
discussion of this aspect of the subject see S. P. Wing, Proc. Am. Soc. Civ. Eng. 58 p. 1103, 1932. See also
R. H. Sherlock and M. B. Stout, Bull. Nat. Elec. Light Assoc, January, 1931, and January, 1932.
2 The following papers illustrate the variety of publications in this field:
A. Betz (Winddruck) Messungen von Bruckentragern. Ergebnisse der Aerodynamischen Versuehsan-
stalt zu Gottingen, vol. 3, p. 146, 1927.
British Elect, and Allied Industries Research Assoc. Investigations of Wind Pressure on Poles and
Cables for Overhead Transmission Lines, 1925. Interim Report upon Research on Wind Pressure on
Latticed Towers, 1928.
H. L. Dryden and G. C. Hill, Wind Pressures on Structures, B. S. Sci. Paper S. 523, Bull. 20, p. 697.
H. L. Dryden and G. C. Hill, Wind Pressure on Circular Cylinders and Chimneys, B. S. Jour. Research,
vol. 5(RP221), 1930.
H. L. Dryden and G. C. Hill, Wind Pressure on a Model of a Mill Building, B. S. Jour. Research, vol. 6
(RP301), 1931.
O. Flachsbart. Winddruck auf geschiossene und ofiene Gebaude. p. 128. Winddruck auf Gasbehalter
p. 134. Ergebnisse der Aerodynamischen Versuchsanstalt zu Gottingen, vol. 4. (R. Oldenbourg, Berlin)
1932.
O. Flachsbart. Winddruck auf Bauwerke. Die Naturwissenschaften, vol. 18, p. 475; 1930.
O. Flachsbart. Der gegenwiirtige Stand der Winddruckforschung, Jahrbuch, 1930, d. Deutschen Gesell.
f. Bauingenieurwesen, vol. 6, p. 108, 1931.
O. Flachsbart. Grundsatzliches zur Frage des Winddrucks auf Gebaude. Bauwelt., pp. 660 and 692,
1932.
J. O. Irminger and C. N0kkentvcd. Wind Pressure on Buildings. Ingeni0rvidenskobelige Skrifter, A
Nr. 23, K0benhavn, 1930.
F. Nagel (Winddruck) Messungen von Profiltragern. Ergebnisse der Aerodynamischen Versuchsanstalt
zu Gottingen, vol. 3, p. 151, 1927.
C. N0kkentved. Wind Pressure on Buildings. Int. Assoc, for Bridge and Structural Engineering, Zurich,
1932.
R. L. A. Schoemaker and I. Wouters. Windbelasting op Bouwwerken, Het. Bouwbedrijf, Oct. 21,
1932.
R. Seiferth. Winddruckmessungen an einem Gasbehalter. Ergebnisse der Aerodynamischen Versuch-
sanstalt zur Gottingen, vol. 3, p. 144. 1927.
H. M. Sylvester. An Investigation of Pressures and Vacua Produced on Structures by Wind. Rensse-
laer Poly. Inst. Eng. and Sci. Series No. 31, 1931.
fmcn] Wind Pressure on Model oj Empire State Building 495
as well as the detailed distribution of the "pressure. The chief dis-
advantages are (1) that the line detail of the actual building can not
be reproduced on the model and (2) that the pressure on the full-
scale building may be somewhat different than that at the correspond-
ing location on the model because of the existence of a scale effect. It
is our belief that the errors due to failure to reproduce the fine detail
and due to scale effect are not very large, but until this belief is actually
confirmed by full-scale experiments, results from model tests will not
command the full confidence of engineers engaged in the design of
buildings.
In experiments in natural winds, the conditions are reversed. It
is no longer easy to obtain conditions favorable for measurement, in
that the speed and direction of the wind change continuously. In
addition, it is very difficult to obtain a steady reference pressure, or
otherwise expressed, to measure the " normal" atmospheric pressure.
On the other hand, there is no question of scale effect or of lack of
detail of a model.
When it was announced by the American Institute of Steel Construc-
tion that a program of wind-pressure measurements would be con-
ducted on the Empire State Building, the Bureau of Standards saw
an opportunity to test the utility and validity of model measurements.
Through the cooperation of the engineer, H. G. Balcom, drawings of
the building were generously supplied. A model was designed and
constructed by the Bureau of Standards, and measurements of wind
pressure were made in the 10-foot wind tunnel. The results of meas-
urements on the model are described in this paper. Measurements
on the actual building are in progress under the direction of F. H.
Frankland, chairman of the Research Committee of the American
Institute of Steel Construction. When the results become available,
comparisons can be made.
II. MEASUREMENTS OF PRESSURE DISTRIBUTION
1. APPARATUS
The Empire State Building is 1,250 feet high; the model, shown in
Figure 1, is 5 feet high. The model is made of rolled aluminum plates
one-quarter inch thick, except the tower, which is constructed of
wood. It represents the building in external shape except for the
minor irregularities of the surface on a scale of 1 to 250. It does not
I represent the actual building in material, method of construction, or
,' strength. It is not tested to failure, but is used only for measure-
ments of the wind pressure at different wind speeds.
The wind pressure on the actual building is to be measured on the
i thirty-sixth, fifty-fifth, and seventy-fifth floors by means of pipes
j running from the outside face of the walls to manometers mounted at
suitable observing stations. At the levels on the model correspond-
ing to these floors as shown in Figure 4, 17 pressure stations were pre-
pared as follows: A hole approximately one-quarter inch in diameter
' was drilled and tapped at each station. A hollow cylindrical threaded
plug about five-eighths inch long and closed at one end was screwed
into the hole and the closed end carefully worked down so as to make
i it flush with the outer surface of the model. After polishing, a small
hole approximately 0.040 inch in diameter was drilled along the axis
; of the plug from the outside face inward. By means of rubber tubing,
496
Bureau of Standards Journal of Research
[Vol. 10
connection could then be made through the interior of the model from
each station to the pressure gauge.
Fourteen of the seventeen stations at each level were located on
two adjacent faces of the model as shown by the short solid lines in
Figures 2 and 3, stations designated as 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13,
15, 16, and 17. Three were located on the other faces. Because of
the symmetry of the model, the complete distribution at each wind
direction could be obtained by two runs, one with the wind striking the
faces containing the large number of stations, the second with the
mode] rotated through 180°. The levels are denoted by the letters
A, B, and C, and the stations by numbers from 1 to 34. The short
solid lines show stations actually present in the model; the dotted
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FlGUBJ 2. — Location of pressure stations at section A. (See fig. 4)
^limMhl'iri"! m ;" io'!S YTTn! in tho mo,le1' the dotted lines> those for whi(,h ™^ss are obtained
■ -h »■ . , ! <t , ' TRhf 8° ! th,e num >ers inclosed Iu oircles- those Present in the actual huilding.
i nc OMgnttira of wind direction is shown by the arrows.
lines represent stations for which values are obtained by rotating the
model through 180°, while the numbers inclosed in circles correspond
to stations present in the actual building.
correspond
The model rests od and is attached to a circular plate as shown in
figure l, which also shows the mounting in the wind tunnel. The
cuxular plate can be rotated with respect to a second square plate
>Hnu , the Bquare plate being fastened to a wooden platform. Since
tll(; tunnel is cylindrical, the platform rests on two wooden segments
put to the (Mux m(. .re of the tunnel wall. Both plates have an opening
1 ™ (/-M1,,M' {ll l)m.ml n,° Passage of the 51 connecting tubes from
'<> Btatoons. I he circumferentia] edge of the circular plate is grad-
;' ;;' J intervals ol «• and the square stationary plate has an index
mark at the renter ol its upstream face.
B. S. Journal of Research, RP545
Figure 1. — Model of the Empire State Building in the wind tunnel, looking
downstream
The brass screws holding the model together and the brass plugs in which the pressure holes are
drilled appear as dark spots.
Dryden]
Hill
Wind Pressure on Model of Empire State Building
497
The 10-foot wind tunnel winch was used for these measurements
has been described in Scientific Paper No. 523. That paper also
gives an account of the method of measuring wind speed, and a de-
scription of the manometer used for measuring pressures. In the
present tests, speeds up to about 55 miles per hour were used.
2. GENERAL PROCEDURE
The general procedure in making the measurements of pressure
distribution was as follows: The model was first set with the narrow
face containing the five pressure stations normal to the wind direction,
an azimuth designated as 90°. Twelve stations were connected to
the 12 tubes of a multiple-tube manometer, the reservior of the
manometer being connected to a static plate upstream from the
model. The pressure at the opening of the static plate served as the
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SECTIONS B4-C
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16
6
2.4
Figure 3. — Location of pressure stations at sections B and C. {See fig. 4)
See note for Figure 2.
base pressure from which all other pressures were measured. At
wind speeds of approximately 40, 60, and 80 feet per second (27, 41,
and 55 miles per hour), an observer read successively the 12 tubes of
the manometer, which gave readings proportional to the differences in
pressure between the holes at the surface of the model and the pressure
at the static plate. Twelve other stations were then connected,
readings taken, and the process repeated until observations were
completed for the 51 stations. The model was then turned through
an angle of 180° and the series repeated. A complete set of observa-
tions at the 102 stations was made for wind directions from 90° to
180° at intervals of 10° and at 135°.
498
Bureau of Standards Journal oj Research
[Vol.10
3. REDUCTION OF OBSERVATIONS
When an air stream blows against an object, the pressure, p, at any
point on its surface may be regarded as consisting of two parts — the
static pressure,3 ps, which in a
natural wind is the baromet-
ric pressure; and the excess,
p—ps, caused by the presence
of the object. This excess,
p—ps, arises solely from the
motion of the air with refer-
ence to the model. It will be
called simply the wind pres-
sure, and will be denoted by
pw. If there is no wind or no
object present, then p=ps
everywhere, and the wind
pressure is everywhere zero.
The wind pressure may be
either positive or negative or
zero; that is, p, which by
definition of pw is equal to
ps + pw, may be either greater
or less than ps or equal to it.
It may be remarked that pw
generally does not exceed 1
or 2 per cent of ps for
speeds not exceeding 100
miles per hour.
In the comparison of wind
pressures carrying the nega-
tive sign, the lower numerical
value corresponds to the
higher absolute pressure.
Thus, —0.2 is a higher pres-
sure than —0.4 (just as 10°
below zero is a higher tem-
perature than 20° below zero).
pw is the quantity usually
measured, corresponding to
the common practice of
using " gauge" pressure in
dealing with pressures in
steam boilers, compressed air
tanks, etc., rather than abso-
lute pressure. Dimensional
will be given by an expression of the form
f-
l
PLfcNE OF
PRESSURE HOLES
PLftME OF
PRESSURE HOLES
PLkftE OF
PRESSURE HOLES
C
Figure 4. — Location of sections A, B, and C
and the axes of reference on the model
The Xaxis runs into the plane of the paper at right angles
to the Fand Zaxes which are snown
reasoning teaches that pt
where q is the velocity pressure (KpF2), p the air density, V the wind
speed, n the viscosity of the air, and L a linear dimension fixing the
3 The term static pressure is u ed to indicate the pressure which would be measured by a pressure gauge
moving with the air, and, therefore, "static" with respect to the air. In actual practice the measurement
is made by means of holes in the side of a closed tube, the axis of which is parallel to the wind direction.
The form of the tube is such that the air flows smoothly past the holes.
Sen] Wind Pressure on Model of Empire State Building 499
scale. The expression applies only to geometrically similar bodies.
The wind pressure, pw could be measured in any convenient units,
but there are advantages in using the velocity pressure, g=KpV2, as
the unit. For bodies without curved surfaces and with sharp corners,
pjq is practically independent of the wind speed and the size of the
model (that is, / ( J is a constant for any station) , so that from
a single value of it for any given shape of body the pressure at the
corresponding point on a similar bod}- of any size at any wind speed
can be readily computed with the aid of a table of velocity pressures.
The ratio is a pure number independent of the units used so long as
the pressures are all measured in the same units.
The engineer is in most cases more directly concerned with the
resulting forces than with the pressures themselves and their distri-
bution. These resulting forces always involve the pressure acting on
the opposite sides of the surface or object. In the case of a hollow
object, such as a building, which is open to the outside at various
places, air currents are set up within the building, and there is a
distribution of wind pressure over the interior as well as the exterior
surfaces of the walls. At any point of the wall the force per unit
area tending to move the wall normal to itself equals the difference
between the wind pressure on the two sides and is in the direction
from the higher toward the lower pressure. Little is known at the
present time as to the distribution of wind pressure over the interior
walls of actual buildings in high winds and in the presentation of
data for the distribution over the exterior it is commonly assumed
that the interior is at a constant pressure equal to the static pressure,
ps; that is, pw is zero for the interior. If the pressure on the interior
is constant, it has no effect on the resultant force tending to overturn
the building, no matter what its value.
By definition, ps is the same at every point of the surface and, hence,
it contributes nothing to the resulting forces and may be ignored in
the computations. The force on any element, dA, is equal to pdA
and acts in the direction of the normal to the surface.4 In the case of
a building with plane surfaces, with all angles between the planes
right angles, the component of force along each axis of the building
is readily computed. The faces parallel to an axis contribute nothing
to the component of the force along that axis. Each of the faces
perpendicular to the axis contributes the summation of the forces on
the elements, that is, f fpdA\ but account must be taken of the fact
that forces on opposite faces oppose each other. Since the net
effect of ps vanishes, we need only compute f \fpwdA. Dividing by
q, we have the force F given by
Fk = ffpwdA
It is found convenient to divide this expression by the area of projec-
tion, Ap, of the body on a plane normal to the axis under considera-
tion. The quotient F/Apq is called the force coefficient.6 It is the
average force per unit projected area divided by the velocity pressure;
that is, the ratio of the effective resultant pressure on the total
projected area to the velocity pressure. The force in any particular
case is obtained by multiplying the force coefficient by the projected
area and by the velocity pressure.
4 Excluding frictional effects, which are of importance only in special cases.
5 The terras "resistance coefficient," "drag coefficient," "shape coefficient" are also used.
500
Bureau of Standards Journal of Research
[Vol. 10
In the case of the present model we shall be interested in the average
loading at a given elevation. In this case the force per unit length
is equal to the summation of pwds; that is, fpwds where ds is an ele-
ment of the width of the face. Again it is convenient to divide
fpwds by the width and by the velocity pressure q so as to obtain a
coefficient applicable to the particular section, giving the average
force per unit area per unit velocity pressure.
It will be noted that in all cases, an average value of — is deter-
mined, which if uniformly distributed over the area in question would
give the correct value of F/q.
For the convenience of the reader, the relation between the indi-
cated speeds, as measured by 3 and 4 cup U. S. Weather Bureau
anemometers, and the true speed is given in Table 1, and the velocity
pressures at various true speeds for air of standard density is given
in Table 2.
Table 1. — Indicated wind speeds by Robinson cup anemometers l
True speed (miles per hour)
Indicated
speed,
old 4-cup
standard
Indicated
speed,
new 3-cup
standard
True speed (miles per hour)
Indicated
speed,
old 4-cup
standard
Indicated
speed,
new 3-cup
standard
5
5
11
17
23
30
37
44
50
57
64
71
5
10
15
20
25
31
3d
41
47
52
57
60 .
78
85
91
98
105
112
118
125
132
138
145
63
10...
65
68
15
70
73
20
75
79
25
80
84
30
85
89
35
90
95
40
95
100
45
100
105
50
105
111
55
110
116
' Before Jan. 1, 1928, the U. S. Weather Bureau used the 4-cup instrument; from then until Dec. 31, 1931,
3-^P lnstrument. After that date all wind speeds have been corrected before publication, thus giving
Table 2. — Velocity pressures at several wind speeds
wind speed
(miles per hour)
Velocity
pressure
True wind speed
(miles per hour)
Velocity
pressure
True wind speed
(miles per hour)
Velocity
pressure
B
Lbs. 1 ft. t
0.064
.256
1.023
1.600
2. 302
3.133
4.092
45
Lbs./fU
5.179
6.394
7.737
9.208
10.81
12.53
14.39
16.37
85
Lbs. /ft*
18.48
20.72
23.08
:
50
15
20
55
95
60
65 .
70 „
100
105
110....
25.58
28.20
30.95
M
75
80..
115
120....
33.83
36.83
NoTE.-YrWitv pressure in lbs./ft.»- 0.001189 (Vx *m> where V is the true speed in miles per hour,
and the density is that at 15° C, 760 mm Hg.
I'J an actual structure the wind pressure is modified by the presence
of the -round, so that some method must be used in the artificial
win. I to produce the effect of the -round. In the present experiments
the model rested on the floor of the tunnel except for the interposition
oi asmalJ platform to provide for the curvature of the tunnel wall.
case the wind is not uniform over the region occupied by the
[figure 5 shows the measured speed above the tunnel floor
mode].
DrydeWl
Hill J
Wind Pressure on Model of Empire State Building
501
in the absence of the model along the line subsequently occupied by
the vertical axis of the model. The speeds are expressed as ratios
to the reference speeds given by a Pitot tube located upstream and
to one side. The speeds at points within the area occupied by the
model are approximately the same at a given elevation. From the
curve it is seen that the wind speed above an elevation of 18 inches
is approximately uniform. Since the elevation of the lowest pressure
holes is 20.76 inches, all pressure stations on the model are within
the region of uniform speed. When a speed of 80 feet per second is
desired at the model, the reference
speed must be set a little lower as
indicated by the curve.
The results finally desired are pw,
the changes in pressure produced by
the presence of the model. It was
necessary, therefore, to measure the
difference in pressure between the ref-
erence (static plate) pressure and the
static pressure in the tunnel (with
the model removed) at the place
previously occupied by the model
and to add this value with proper
sign to the observed pressure.
The procedure in reducing the
observations was as follows: The
readings of the manometer were
reduced to absolute pressure differ-
ences in pounds per square foot from
a knowledge of the slope of the ma-
nometer and the density of the liquid
used (kerosene).
The pressure differences were then
corrected for the difference between
the reference pressure and the static
pressure and expressed as fractions
of the velocity pressure. The values
for any one station at the three
speeds were, in general, very nearly
the same, the variation from the
mean in most cases not exceeding 0.03.
16
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4. RESULTS
90 100 HO
Speed in Per Cent of Reference
Speed
Figure 5. — Variation of wind speed
above the platform in the absence
of the model
The mean values of pw/q are given
in Tables 3 to 6, inclusive, and plotted
in Figures 6 to 16, inclusive. In these
figures, two horizontal sections of
the model are shown, the upper for
elevation A, the lower for elevations B and C. Just outside the section
drawings are four fine base lines from which the values of pw/q are plotted
to the scale shown. In the lower plot, the solid curves are for elevation
B and the dash curves for elevation C. At each elevation there are four
holes in the recesses, and the values of pw/q for these holes are indicated
by the small circles and crosses. In the lower plot, the circles are for
elevation B. the crosses for elevation C. The wind direction is
502
Bureau of Standards Journal oj Research
[Vol. w
indicated by the arrow, and the number gives the angle which the
wind makes with the face containing pressure stations 1 to 6. When p
is larger than ps, pw/q is positive; when p is smaller than ps, pw/q is
1
90\
M
~ $ ~— -»- <
Figure 6. — Distribution of pressure at sections A, B, and C
at 90° to the wind
Above, section A; below, solid lines, section B; dotted lines, section C
The pressures are measured from the static pressure as base and expressed as ratios to the velocity pressure.
The ratios are plotted outward from the thin base lines to the scale shown. Minus signs denote that the
pressure is lower than the static pressure. The circles and crosses give the values at stations 10, 14, 27,
and 31 on the side walls of the embrasures.
negative. Both positive and negative values are plotted outward
from the datum line for convenience and are distinguished by the use
of plus and minus signs.
Wind Pressure on Model of Empire State Building 503
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Figure 7. — Distribution of pressure at sections A, B, and C
at 100° to the wind
See legend of Figure 6
504
Bureau oj Standards Journal of Research
[Vol.10
I 0
0
Figure 8. — Distribution of pressure at sections A, B, and C
at 110° to the wind
See legend of Figure 6
Dryden I
HiU J
II Tind Pressure on Model of Empire State Building
505
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Figure 9. — Distribution of pressure at sections A, B, and C
at 120° to the wind
See legend of Figure 6
161541—33 €
506
Bureau of Standards Journal of Research
[Vol. 10
+ />
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l
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Figure 10. — Distribution of pressure at sections A, B, and C
at 130° to the wind
See legend of Figure 6
Drydenl
Hilt
Wind Pressure on Model of Empire State Building 507
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Figuue 11. — Distribution of pressure at sections A, B, and
C at 135° to the wind
See legend of Figure 6
508
Bureau of Standards Journal of Research [Vol. to
I 0
+
+
\
o o
* — *
-N
7
1
+
Figure 12. — Distribution of pressure at sections A, B, and
C at 140° to the wind
See legend of Figure
Drydenl
Hill J
Wind Pressure on Model oj Empire State Building 509
I 0
o o
\
o o
% *
/
7
I 1
+
Figure 13. — Distribution of pressure at sections A, B, and
C at 150° to the wind
See legend of Figure 6
510
Bureau qf Standards Journal of Research
[Vol.10
(
Figure 14. — Distribution of pressure at sections A, B, and C
at 160° to the wind
See legend of Figure 6
Drydenl
Hill J
Wind Pressure on Model of Empire State Building
511
S
+
Figure 15. — Distribution of pressure at sections A, B, and
Cat 170° to the wind
See legend of Figure 6
512
Bureau oj Standards Journal of Research
[Vol. 10
+
I 0
\
o o
ft ft
-I-
Figure 16. — Distribution of pressure at sectio?is A, B, and
C at ISO0 to the wind
See legend of Figure 6
Wind Pressure on Model oj Empire State Building
513
Table 3. — Pressure distribution over model, at various angles to the wind
(See flgs. 2, 3, and 4 for position of holes and sections)
Pw/q
Hole No.
11
12
13
14
15
M
17
a
19
K
2!
22
28
24
28
M
27
2*
20
30
u
32
H
34
80°
Sec-
tion
,4
0.52
.82
.98
.98
.82
.56
-.89
-.94
-.85
-.75
-.79
-.79
-.80
-.78
-.81
-.82
-.83
-.76
-.75
-.75
-.75
-.76
-.76
-.79
-.78
-.78
-.79
-.78
-.79
-.75
-.78
-.83
-.91
-.85
Sec-
tion
B
0.66
1.05
1.05
Sec-
tion
C
0.61
.83
.99
.99
.83
.63
-.67
-.68
-.70
-.68
-.69
-.71
-.64
-.63
-.06
-.71
-.73
-.58
-.56
-.53
-.54
-.56
-.60
-.80
-.76
-.72
-.70
-.71
-.71
-.60
100°
Sec-
tion
A
0.62
.89
.42
-.87
-.91
-.83
-.73
-.76
-.77
-.76
-.73
-.77
-.78
-.79
-.74
-.74
-. 75
-.75
-.76
-.78
-.70
-.75
-.88
-1.08
-1.03
-1.08
-1.05
-1.05
-1.23
-1.18
-1.15
Sec-
tion
B
0.72
.93
1.03
.96
.77
.44
-.62
-.60
-.62
-.64
-.64
-.61
-.62
-. 65
-.67
-.58
77
Sec-
tion
C
0.71
.95
1.03
1. 00
.81
.57
-.51
-.52
-.52
-.50
-.53
-.54
-.55
-.53
-.56
-.58
-.61
-.46
-. 45
-.45
-.46
-.46
-1.05
-.98
-.87
-.97
-. 88
-1.08
-1.05
-1.03
110°
Sec-
tion
A
0.84
LOO
.97
.83
.52
.24
-. 93
-.92
-.76
-.71
-.70
-.72
-.73
-.70
-.75
-.75
-.75
-.77
-.75
-.75
-.75
-.80
-.80
-.50
-.41
-.40
-.20
-.16
-.45
-.46
-.68
Sec-
tion
/;
0.91
1.02
1.01
.89
.64
.38
-.Of J
-.62
-.63
-.63
-.62
-.63
-.63
-.62
-.63
-. 63
-.64
-.62
-.60
-.60
-.62
-.60
-.61
-.46
-.39
-.41
-.54
-.58
-.62
-.88
-.68
-.05
-.67
-.65
Sec-
tion
C
0.91
1. 05
1.03
.89
.64
.42
-. 50
-. 51
-. 52
-. 52
-. 53
-.55
-.52
-.51
-.53
-. 55
-.58
-.55
-.55
-.55
-.55
-.54
-.48
-.32
-.15
-.32
-.38
-.62
-. 55
514
Bureau of Standards Journal oj Research
Table 4. — Pressure distribution over
model,
at various angles to the wind
(See figs. 2, 3, and 4 for position of holes and sections)
pWa
120°
130°
135°
Hole No.
Section
Section
Section
Section
Section
Section
Section
Section
Section
A
B
C
A
B
C
A
B
C
!
1.02
1.00
0.99
0.95
1.02
0.98
0.80
0.83
0.82
2...
1.03
.87
1.00
.90
1.00
.89
.86
.64
.91
.73
.91
.69
.69
.49
.74
.57
.74
3
.54
4
.66
.70
.69
.43
.52
.50
.28
.37
.34
5
.33
.40
.43
.13
.22
.22
0
.09
.09
6
.04
-.96
-.90
-.78
-.74
-.74
.17
-.68
-.66
-.66
-.69
-.67
.22
-.50
-.50
-.52
-.51
-. 53
-.12
-.80
-.80
-.73
-.69
-.71
-.07
-.68
-.67
-.68
-.68
-.69
.02
-.53
-.53
-.54
-.51
-.54
-.22
-.83
-.82
-.77
-.73
-.75
-.14
-.73
-.71
-.71
-.71
-.72
-.24
7
-.58
8
-.58
-.60
-.72
-.58
9..
10
11
12...
-.75
-.69
-.55
-.73
-.70
-.56
-.76
-.72
-.60
13
-.74
-.68
-.56
-.71
-.70
-.58
-.76
-.73
-.64
14
-.73
-.70
-.51
-.69
-.71
-.57
-.74
-.74
-.62
15. ._
-.76
-.68
-.56
-.73
-.70
-.57
-.77
-.73
-.63
16..
-.77
-.70
-.58
-.75
-.71
-.57
-.78
-.74
-.63
17...
-.79
-.72
-.60
-.75
-.72
-.57
-.79
-.74
-.64
18...
-.76
-.69
-.50
-.74
-.69
-.53
-.78
-.76
-.59
19...
-.75
-.69
-.50
-.73
-.68
-.52
-.77
-.75
-.59
20..
-.76
—.77
-.87
-.91
-.48
-.30
-.33
-.70
-.70
-.69
-.70
-.44
-.22
-.13
-.50
-.49
-.48
-.49
-.30
-.11
-.04
-:73
-.74
-.87
-.91
-.33
-.08
-.40
-.68
-.67
-.66
-.70
-.30
-.02
.10
-.52
-.52
-.52
-.52
-.21
.05
.16
-.77
-.79
-.94
-.98
-.29
-.03
-.28
-.74
-.74
-.73
-.73
-.29
.06
.22
-.58
-.58
-.57
-. 56
-.31
.12
.25
21
22..
23
24
25
26.. ..
27
.72
.56
.26
.11
.29
.19
.15
.18
.31
.22
.17
.21
.99
.83
.54
.40
.52
.44
.43
.47
.55
.45
.41
.46
.97
.89
.77
.42
.67
.58
.56
.59
.67
.59
.98
.56
28..
29
30.-.
31...
.13
.25
.16
-.11
.22
.28
. 13
-. 10
.26
.31
.05
-. 12
.38
. 55
.67
.79
.50
.68
.83
.51
.58
.69
.82
.51
.65
.78
.91
.65
.70
.84
.98
.62
.69
.81
.93
32...
33...
34
Wind Pressure on Model of Empire State Building
515
Table 5. — Pressure distribution over model, at various angles to the wind
(Sec figs. 2, 3, and 4 for position of holes and sections)
140°
150°
160°
Hole No.
Sec-
tion
A
Sec-
tion
B
Sec-
tion
C
Sec-
tion
.4
Sec-
tion
B
Sec-
tion
C
Sec-
tion
A
Sec-
tion
h
Sec-
tion
C
1
0.39
.55
.36
.17
-.10
-.30
-.80
-.79
-.74
-.71
-.71
-.73
-.71
-.70
-.72
-.73
-.73
-.73
-.73
-.72
-.75
-.93
-.97
-.21
.07
.01
.83
. 77
.75
. 57
.62
.82
.94
1.04
0.57
.58
.42
.22
-.01
-.20
-.67
-.67
-.67
-.68
-.67
-.68
-.68
-.71
-.68
-.69
-.70
-.72
-.71
-.69
-.69
-.69
-16
.18
.36
.81
.71
.70
.72
.76
.84
.95
1.05
0.55
.59
.40
.22
.01
-.15
-.54
-.54
-.56
-.54
-.53
-.54
-.58
-.56
-.57
-.57
-.58
-.57-
-.57
-.57
-.56
-.53
-.53
-.08
.22
.39
.80
.72
.70
.72
.78
.85
.95
1.05
-0.48
-.51
-.13
-.04
-.26
-.45
-.84
-.79
-.72
-.72
-.71
-.73
-.73
-.74
-.73
-.74
-.73
-.74
-.73
-.73
-.76
-1.00
-1.02
-.02
.31
.45
.84
.82
.86
.84
.86
.96
1.01
.96
-0.46
-.49
-.13
.02
-.19
-.35
-.68
-.66
-.66
-.68
-.67
-.67
-.68
-.69
-.67
-.67
-.68
-.71
-.70
-.68
-.68
-.68
-.69
.01
.40
.59
.94
.92
.89
.90
.92
.98
1.02
.94
-0.56
-.51
.03
-.02
-.19
-.29
-.54
-.55
-.56
-.53
-.54
-.54
-.56
-.57
-.56
-.56
-.56
-.58
-.57
-.55
-.55
-.53
-.53
.09
.47
.58
1.00
.93
.90
.94
.94
1.02
1.07
.99
-1.15
-1.22
-1.23
-.82
-.55
-.60
-.93
-.75
-.70
-.76
-.69
-.71
-.76
-.76
-.76
-.76
-.77
-.76
-.74
-.75
-.77
-1.01
-.96
.15
.50
.57
1.02
.93
.93
.94
.98
.97
.94
.74
-1.16
-1.16
-1.18
-1.11
-.90
-.73
-.66
-.68
-.68
-.68
-.70
-.68
-.69
-.71
-.69
-.69
-.69
-.71
-.71
-.69
-.69
-.68
-.66
.18
.58
.72
1.01
.99
.99
.96
.99
1.03
.98
.72
-1.37
2.
-1.35
3
-1.22
4
-.88
5.
—.47
6.
-.42
-.55
8.
-.56
9
-.55
10
-.55
11.
-.53
I2_
-.52
13
-.55
14
15.
-.56
—.57
16
-.57
17
-.57
18.
-.63
19-..
-.61
20
-.58
21.
-.57
22-. .
-.54
23
-.51
24
.25
25
.64
26
.70
27
1.00
2S
1.04
29.
1.04
30...
.99
31
1.03
32
1.02
33.
.99
34. .
.69
516
Bureau of Standards Journal of Research
[Vol. 10
Table 6. — Pressure distribution over model, at various angles
(See figs. 2, 3, and 4, for position of holes and sections)
Pv/q
to the wind
170°
180°
Hole No.
Section
A
Section
B
Section
C
Section
A
Section
B
Section
C
1...
-0.83
-.85
-.84
-.81
-.79
-.81
-.75
-.75
-.75
-.79
-.77
-.78
-.78
-.80
-.78
-.78
-.78
-.79
-.79
-.78
-.81
-1.20
-1.18
.26
.62
.77
.95
.96
.97
.97
.96
.96
.88
.63
-0.76
-.77
-.79
-.80
-.84
-.92
-.74
-.75
-.74
-.72
-.72
-.72
-.74
-.73
-.73
-.74
-.75
-.76
-.75
-.75
-.73
-.71
-.71
.29
.71
.87
1.04
1.00
1.01
1.01
1.03
1.02
.93
.63
-0.73
-.74
-.78
-.81
-.80
-.83
-.62
-.58
-.56
-.54
-.54
-.54
-.55
-.56
-.55
-.54
-.56
-.56
-.55
-.62
-.59
-.56
-.56
.37
.76
.87
1.03
1.03
1.03
1.02
1.03
1.01
.94
.64
-1.10
-1.21
-.84
-.79
-.79
-.78
-.79
-.79
-.79
-.79
-.80
-.81
-.78
-.77
-.79
-.79
-.78
-.79
-.78
-.78
-.82
-1.18
-1.14
.42
.75
.86
.98
.94
.94
.93
.96
.86
.73
.44
-0.74
-.74
-.75
-.77
-.80
-.80
-.74
-.72
-.72
-.71
-.72
-.72
-.72
-.72
-.73
-.72
-.73
-.78
-.78
-.75
-.73
-.71
-.74
.44
.83
.97
1.04
1.02
1.02
1.01
1.03
.97
.84
.51
-0.58
-.59
-.62
-.66
-.72
-.75
-.60
-.58
-.57
-.55
-.57
-.57
-.56
-.56
-.57
-.57
-.60
-.73
-.72
-.68
-.64
-.61
-.59
.49
.85
.95
1.02
1.03
1.03
1.00
1.02
.95
.84
.51
2
3
4
5
6. .
7..
8
9
10
11
12
13
14
15
16
17
18
19.
20 ..
21
22
23
24.
25. .
26
27
28
29
30
31
32
33
34
5
. DISCI
JSSION
Some of the more striking features of the pressure distribution will
be described for purposes of emphasis. The greater part of the model
is under reduced pressure. The lee faces are subjected to a nearly
constant reduced pressure, although the absolute pressure is usually
higher at the lower elevation. A fine thread showed that the air pass-
ing over the top of the model was deflected downward and that a large
eddy is formed behind the model extending downstream some 3 feet.
Near the building on the lee side the current is upward as indicated by
the pressure distribution.
The behaviour of the embrasures is of interest. In most cases the
embrasures carry the pressure of the adjacent wall. When however
the embrasure is on the windward side, the pressure is increased
relative to that on the neighboring wall. This behaviour is perceptible
in Figure 8 for 110° and is very marked in Figure 11 for 135°, especially
for elevation A.
When a face is struck directly by the wind (figs. 6 and 16), the
pressure is greatest in the center, falling off toward the edges. The
placing of wind bracing in the end panels alone does not seem to be
the most suitable to withstand this type of loading.
Dryderi
Hill
Wind Pressure on Model oj Empire State Building 517
III. MEASUREMENTS OF OVERTURNING MOMENT
I. APPARATUS AND METHOD
In addition to measurements of the pressure distribution, the
overturning moments were directly measured. For this purpose, the
'""""8 »i
'
,.. r~
a.
LHi
/
r—
H
3
n
3 /
\
u
•<s>
I-
so O
e -~
03 CO
model and attached circular plate were placed on a horizontal bar 1
inch wide and one-half inch thick. The ends of the bar carried the
inner races of ball bearings; the outer races of the bearings were
supported in housings secured to the platform on the floor of the
tunnel. The model and the circular plate could be rotated with
518
Bureau of Standards Journal of Research
[Vol. w
respect to the bar about a vertical axis and held at any desired azimuth
as in the pressure distribution tests. (Fig. 17.) For measuring the
resultant overturning moment, it was necessary to measure the com-
ponents about two horizontal axes, one parallel to the wind direction,
the other at right angles to the wind direction, since, in general, the
resultant force on the model has a component transverse to the direc-
tion of the wind. The two components of the overturning moment
were measured separately. In the first set-up, the axis of rotation
was horizontal and at right angles to the wind direction. A fine
steel wire attached to the model at the base of the tower ran hori-
zontally fore and aft. The upstream end was joined to two other
wires at a point about 4 feet upstream from the model. One of
these wires ran vertically upward to a balance in the room over the
wind tunnel ; the
i.50| 1 r 1 — — — — r~ — — ~i other ran forward
and downward at an
angle of 45° to the
floor of the tunnel
where it was fas-
tened. The down-
stream end of the
horizontal wire was
similarly joined to
two other wires, one
of which ran verti-
cally downward
through a hole in
the tunnel floor and
carried a counter-
weight ; the other ran
to the rear and up-
ward at 45° to the
ceiling of the tunnel
where it was fas-
tened. The balance attachment was made through a turnbuckle by
means of which compensation could be made for motion of the balance
pan. In the second set-up, the axis of rotation was horizontal and
parallel to the wind direction. The balance arrangement was essen-
tially as in the first set-up except that all the wires were in a plane
perpendicular to the wind direction, the balance being on the right
looking downstream.
The overturning moment about either axis is equal to the net
balance reading times the perpendicular distance h' between the
axis of rotation and the horizontal wire. Readings wrere taken at
the same angles and speeds for which the pressure distribution
measurements wrere made. In reducing the observations, the over-
turning moment at each of the three speeds was divided by the
velocity pressure q and the three values averaged. In general, the
individual readings were within 2 per cent of the mean value.
2. RESULTS
The moments were measured about axes parallel and perpendicular
to the wind direction, to make the balance arrangements as simple as
possible. It is more convenient in practice to refer moments to the
-0.50
90
S80
110' 150-
Anqle of Face to Wind
Figure 18. — The x-force coefficient derived from meas-
urements of the overturning moment
Dryden
Hill
Wind Pressure on Model of Empire State Building 519
principal axes of the building, designated as in Figure 4. (The X
axis is directed into the plane of the paper at right angles to the Y
and Z axes and is parallel to the wind direction when the model
setting is 90°.) At any given angle 0 of the model, call FD and Fcw
the net balance readings for measurements about the axes perpendicu-
lar and parallel to the wind, Fx and Fv' the values which would have
been observed if the wire and balance system had been placed in the
YZ and XZ planes, respectively. It is easily seen that
Fxf=Fj>co$ (0-90°)- Fcw sin (0-90°)
F9'=FDmn (d~90°) + Fcw cos (0-90°)
For comparison with the pressure measurements, it is desirable to
divide the overturn-
ing moments about iso
the X and Y axes
b\^ the areas of the
YZ and XZ faces
(designated Avz and ,0°
Axz) and by the dis-
tance from the line
of action of the re-
sultant force from
the axis of rotation.
This latter distance
is however not
known. A suitable
conventional dis-
tance would be the
distance h from the
axis to the center of
gravity of the area
of projection of the
model on a plane
normal to the wind direction. This distance, however, varies with the
angular setting from 25.07 inches at 90° to 22.90 at 180°. The mean
value is 23.98 inches or 1.998 feet. The results were finally expressed
in terms of coefficients derived from fictitious forces Fx and Fv which if
applied at the mean height h of the center of area would give the
observed overturning moments. The final coefficients given in the
sLxth column of Tables 7 and 8 and plotted in Figures 18 and 19 are
defined by
Fx FX'W
H
Lx-K
-0.50
90
ieo
12.0 150
Angle of Face to Wind
Figure 19. — The y-force coefficient derived from meas-
urements of the overturning moment
and
qAvz qhAx
Fv'h:
qAxz qhA.
where for the model h' = 4.413 feet, A = 1.998 feet, Avz = 2.486 ft.2,
Axz = 3.915 ft.2. The overturning moments at a given velocity
pressure may be obtained by multiplying the coefficients by the
product of velocity pressure, projected area on the vertical plane
containing the axis of rotation, and mean distance h from the axis
to the center of area.
520
Bureau of Standards Journal of Research
Table 7. — The x components of the force coefficients
[Voi 10
Angle of
wind
(degrees)
From pressure distribution data
From
over-
Differ-
Elevation
A
Elevation
B
Elevation
C
Mean
turning
moments
ence
90
1.57
1.48
1.40
1.48
1.38
0.10
100
1.54
1.42
1.31
1.42
1.37
.05
110
1.56
1.44
1.39
1.46
1.34
.12
120
1.56
1.42
1.22
1.40
1.30
.10
130
1.35
1.25
1.08
1.23
1.15
.08
135
1.24
1.16
.99
1.13
1.00
.13
140
1.02
.98
.83
.94
.82
.12
150
.55
.45
.34
.45
.34
.11
160
-.14
-.36
-.39
-.30
-.32
.02
170
.09
-.07
-.21
-.06
.08
.02
180
0
.02
.01
.01
.01
0
Table 8. — The y components
of the force coefficients
Angle of
wind
(degrees)
From pressure distribution data
From
over-
Differ-
Elevation
A
Elevation
B
Elevation
C
Mean
turning
moments
ence
90
0.00
0.02
0.02
0.02
-0.01
0.03
100
-.21
-.28
-.35
-.28
-.20
.08
110
.29
.07
.04
.13
.21
.08
120
.84
.67
.57
.69
.65
.04
130
1.11
1.05
.93
1.03
.91
.12
135
1.26
1.20
1.02
1.16
1.01
.15
140
1.29
1.27
1.17
1.24
1.07
.17
150
1.44
1.40
1.31
1.38
1.16
.22
160
1.52
1.47
1.36
1.45
1.17
.28
170
1.57
1.56
1.42
1.52
1.27
.25
180
1.57
1.57
1.42
1.52
1.24
.28
3. DISCUSSION
In order to compare the pressure observations with the measure-
ments of the overturning moment, the pressures were integrated by a
process of numerical integration, namely, by multiplying the pressure
at each hole by the distance between the midpoints of the distances
to the two adjacent holes or to the edge of the face for the outer holes.
The resulting sums for the X and Y components were divided by the
width of the model in the Y and X directions and by the velocity pres-
sure to give coefficients corresponding to those computed from the
overturning moments. The coefficients for the three sections and the
various angles are given in Tables 7 and 8, columns 2 and 4, inclusive,
and the mean values are given in column 5. Since there are no pres-
sure stations on the tower which is of a different shape or on the lower
part of the building which is in a region of reduced speed, the mean
values in column 5 can not reasonably be expected to give a value
representative of the entire building. Moreover, the coefficient from
the overturning moment is truly representative only if the pressure is
uniformly distributed. Nevertheless, the coefficients determined
from the overturning moment are but 0.1 less than the mean value
from the pressures measured at three levels for the X direction and
but 0.3 less for the Y direction.
From a consideration of the values in the tables, we believe that for
design purposes a coefficient of 1.5 is not unreasonable.
Dryden
Hill
Wind Pressure on Model of Empire State Building 521
IV. REMARKS ON THE METHOD OF COMPARING MODEL
RESULTS WITH FULL-SCALE MEASUREMENTS
Although this paper is concerned mainly with the model tests, it
appears desirable to indicate the method of application of the results
for comparisons with full-scale results and to explain one supplemen-
tary measurement made on the model. It has already been pointed
out that in measurements in natural winds the wind speed and di-
rection are not under control but vary continuously. Moreover it
is certain that in a vertical distance of 1,250 feet there may be great
variations of speed and direction at any instant. The only provision
at present for measuring the wind speed on the actual building is an
anemometer mounted about 15 feet above the top of the mooring
tower. A little consideration shows that the indications of this
instrument do not
give the true speed
of the wind ap-
proaching the build-
ing.
If the anemome-
ter were placed on
the windward side
of the building on a
median line not far
from the wall of the
building, it is easily
seen that the read-
ings would be too
low, because the air
is slowed up as
it approaches the
building. Moreover,
if the anemometer
15 0
1.40
>.
\°
\
\g
>l>
\o
N^p
1.10
•
I.CO
05 1.0 |.5 1.0 1.5
6 S II 15 18
Height kbove Model-Inches
3.0
Figure 20. — Distribution of wind speed above the model
F'=local speed; F=speed at the same place when the model is absent.
Were placed at the The fact that the speed V does not fall to Fis due to the blocking of the
side of the building, tunnel cross section by the model
it would read too high because the air blocked by the building
must escape at higher speeds around the sides. A similar inter-
ference effect above the tower has been measured on the model.
Figure 20 shows the variation of speed above the top of the tower.
From this curve it is estimated that the anemometer on the building
gives a speed about 23 per cent greater than the true speed of
the approaching wind. When the anemometer reads 100 miles per
hour (after correction for purely instrumental errors), the true speed
of the approaching wind is 81 miles per hour. This correction must
be applied to the readings of the anemometer on the building before
comparison with the model tests.
In measurements in natural winds, it is practically impossible to
secure a fixed reference pressure. In the case of the installation on
the Empire State Building, it is not feasible to measure the pressures
at the three levels with respect to the same base pressure. At each
level, the base pressure is the pressure at some point within the
building at the manometer location on that floor. The model re-
sults are expressed in terms of the static pressure and hence the
161641—33 7
522
Bureau of Siandards Journal oj Research
[Vol. 10
pressures at the individual stations are not directly comparable with
those observed on the building.
Because of this fact and the previously noted variation of wind
speed and direction at the different levels on the actual building, it
is suggested that the comparison be made by assuming the model
results to apply to the building and noting whether this assumption
leads to inconsistencies. The procedure recommended is based on
the fact that it is possible to choose stations such that certain ratios
L.U
_ _ _
""■"■""H
- .. _ ^
f\
'•s.
, "* ,
1-1
_
~"~ -i
c
1.0
0.5
0
a-
0 5
t """"
W — - — -i
1
04
0.3
0.2.
O.i
in
,-j
i4
1
rj
■^»*^
*
t
s **
>
<*-
90 =
110s
-.20"
I30v
140'
Figure 21. — Diagrams to show method of determining wind speed and
direction at various levels on the full-scale building
The curves are from the model results. 2-5 stands for the difference in pressure between
stations 2 and 5, etc.
of pressure differences are very sensitive to changes of wind direction
whereas other ratios are insensitive.
The procedure is illustrated for wind directions lying between 90°
and 135° in Figure 21. It is found that the ratio of the difference
in pressure between stations 2 and 5 to that between stations 2 and
22 varies rapidly with wind direction. This ratio does not depend
on the base pressure (if it is the same for the three stations) or on the
nmden] Wind Pressure on Model of Empire State Building 523
wind speed (since all pressures vary in the same ratio with the speed).
On the other hand, the ratio of the difference in pressure between
stations 2 and 22 to the velocity pressure varies very slowly with the
angle. Suppose that observations on the building at elevation B
2-5
give a value of 0.36 for the ratio 2_ oo' From the lower curve of Fig-
ure 21, the wind direction is found to be 120° and from the upper
2 — 22
curve is found to be 1.7. From the value of 2 — 22, q may be
found and thence from Table 2 the speed. The value of the speed
and direction can be compared with that obtained for the other two
levels and the top of the building. Likewise, since the maximum
increase in pressure should be equal to q, the difference between the
base pressure and the static pressure can be evaluated, the diagrams
reduced to the same base pressure, and the shape of the distribution
curves compared. If no inconsistencies appear, it may be concluded
that the full-scale and model tests are not inconsistent, No better
procedure appears possible without an elaborate installation of ane-
mometers at different levels on the building and an expensive inter-
connection of the reference pressure sides of the manometers by pipes
of large diameter.
V. CONCLUSION
To summarize, a reasonable value of the force coefficient for use in
the design of tall buildings appears to be 1.5 corresponding to a wind
pressure equal to 0.0038 V2 (in lbs. /ft.2) where V is the true speed of
the approaching wdnd in miles per hour.
Data are given for the detailed distribution of pressure at 102 sta-
tions for wind directions varying by steps of 10°.
A suggested method of comparison with full-scale measurements
is outlined.
Washington, February 13, 1933.
f
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