WS A KMY Wee RC Coast ee es. Cir, CETA

CETA 82-4

Hand-Held Calculator Algorithms for Coastal Engineering (Second Series)

WHO!

DOCUMENT | COLLECTION

by Todd L. Walton, Jr.

COASTAL ENGINEERING TECHNICAL AID NO. 82-4 NOVEMBER 1982

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Approved for public release; distribution unlimited. U.S. ARMY, CORPS OF ENGINEERS

a COASTAL ENGINEERING We RESEARCH CENTER

O 33 Kingman Building Fort Belvoir, Va. 22060

Reprint or republication of any of this material

shall give appropriate credit to the U.S. Army Coastal Engineering Research Center.

Limited free distribution within the United States of single copies of this publication has been made by this Center. Additional copies are available from:

Wattonal Technical Information Service ATTN: Operattons Diviston 5285 Port Royal Road

Springfteld, Virginta 22161

Contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official

endorsement or approval of the use of such commercial products.

The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents.

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UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

REPORT DOCUMENTATION PAGE |__ perce conmnenne rom —_|

- REPORT NUMBER 2. GOVT ACCESSION NO.} 3. RECIPIENT'S CATALOG NUMBER

CETA 82-4

TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED Coastal Engineering HAND-HELD CALCULATOR ALGORITHMS FOR Technical Aid

COASTAL ENGINEERING (Second Series) SID ERFORMINGIORNGJREEORTNUMEER

AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s)

odds Walktone wits.

PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK Department of the Army Coastal Engineering Research Center (CEREN-EV) €31181 Kingman Building, Fort Belvoir, Virginia 22060

AREA & WORK UNIT NUMBERS

CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Department of the Army November 1982 Coastal Engineering Research Center 13. NUMBER OF PAGES

Kingman Building, Fort Belvoir, Virginia 22060 Al 14. MONITORING AGENCY NAME & ADDRESS/(if different from Controlling Office) 15. SECURITY CLASS. (of this report)

UNCLASSIFIED

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Approved for public release; distribution unlimited.

DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report)

SUPPLEMENTARY NOTES

KEY WORDS (Continue on reverse side if necessary and identify by block number)

Calculator algorithms Wave generation Coastal engineering Wave transformations

ABSTRACT (Continue on reverse side if necessary and identify by block number)

This report provides algorithms for a number of calculator programs useful in performing coastal engineering calculations, primarily in the area of wave transformations and wave generation. Six programs are included for use with HP41CV hand-held calculators which employ the Reverse Polish Notation (RPN). These programs can be used to compute linear wave parameters, orbital veloci- ties, breaking wave height and direction, shallow-water wave forecasts, depth- limited breaking wave height, and wave transmission past a vertical barrier.

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1

PREFACE

This report provides coastal engineers a second series of algorithms for a number of hand-held calculator programs for coastal engineering, primarily in the area of wave transformations and wave generation. These algorithms were developed under the U.S. Army Coastal Engineering Research Center's (CERC) Littoral Data Collection Methods and Their Engineering Application work unit, Shore Protection and Restoration Program, Coastal Engineering Area of Civil Works Research and Development.

The report was prepared by Dr. Todd L. Walton, Jr., Hydraulic Engineer, under the general supervision of Dr. J.R. Weggel, Chief, Evaluation Branch, and Mr. N. Parker, Chief, Engineering Development Division.

The author acknowledges the assistance of J. Dean in preparing the manu- script. The review by Dr. J.R. Weggel is appreciated.

Technical Director of CERC was Dr. Robert W. Whalin, P.E., upon publica- tion of this report.

Comments on this publication are invited.

Approved for publication in accordance with Public Law 166, 79th Congress, approved 31 July 1945, as supplemented by Public Law 172, 88th Congress,

approved 7 November 1963.

TED E. BISHOP Colonel, Corps of Engineers Commander and Director

CONTENTS

Page

CONVERSTONSFACTORS 3 URSt KCUSTROMARYGeT OMEN Ret Ci (Sil) qareyare nasa mone 5

IE Pe AUN PYOIDIOGIILOMM Sic Gd Tomo Oo 0 OER oO Om) ols6 6 5.60 6b 51 a.6.0 6 6 7/ Tee PROGRAMSI yer. 6 5 0 0D 7

1. 100R41CV romeae fees eo Heelleacen (REN. igeite) BuO oo 9 2. 101R41CV Calculation of Wave Parameters from Linear

Theory (RPN Logic). .... 3 anezen. yor Se are IBD 3. 102R41CV Wave Approximation to ) Biecikine Ewe Height

and! Breaking Wave Angele (REN Molec) saan) uaennsn since nec EEEEIES 4. 103R41CV Shallow-Water Wave saga ris ae

GRIN WORSE) 5 6. 6 RE ease 5. 104R41CV Depth- amiead nection Breaking Wave Tekan: at

Structures (RENG Lo ede) ieee Bean 20)

6. 1O5R41CV Wave Transmission - Pushes! ‘Baracion (RPN Toei) Se 3g}

JNA. WANS IDINOEVAG THONG 6 6 o 56 Oo 6000000660606 00000 37

CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI) UNITS OF MEASUREMENT

U.S. customary units of measurement used in this report can be converted to metric (SI) units as follows:

Multiply inches

square inches cubic inches

feet

square feet cubic feet

yards Square yards

cubic yards

miles square miles

knots acres

foot-pounds

millibars ounces

pounds

ton, long ton, short

degrees (angle)

Fahrenheit degrees

by 254 2.54 6.452 16.39 30.48 0.3048 0.0929 0.0283 0.9144 0.836 0.7646

1.6093 259.0

1.352 0.4047

1.3558

1.0197 28.35

453.6 024536

1.0160 0.9072 0.01745

5/9

x 1002

To obtain millimeters centimeters

square centimeters cubic centimeters centimeters meters square meters cubic meters meters Square meters

cubic meters

kilometers hectares

kilometers per hour hectares newton meters

kilograms per square centimeter

grams

grams kilograms

metric tons metric tons radians

Celsius degrees or Kelvins!

1To obtain Celsius (C) temperature readings from Fahrenheit (F) readings, use formula: C = (5/9) (F -32).

To obtain Kelvin (K) readings, use formula:

K = (5/9) GP 232) cP Zi SailSo

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HAND-HELD CALCULATOR ALGORITHMS FOR COASTAL ENGINEERING (Second Series)

by Todd L. Walton, Jr.

I. INTRODUCTION

The advent of the hand-held programable calculator has led to the develop- ment of numerous programs in various fields of engineering and science. Coastal engineering is no exception. This report provides algorithms for a number of calculator programs useful in performing coastal engineering calcu- lations, primarily in the area of wave transformations and wave generation.

There are basically two types of hand-held programable calculators: those that use algebraic logic, such as Texas Instruments, Algebraic Operating System (AOS) notation, and those that use Reverse Polish Notation (RPN), such as Hewlett-Packard. The six programs presented herein are versions of RPN logic suitable for use on HP41CV programable calculators with or without accessory printer. Each program is documented, the assumptions are briefly described, and references to more detailed presentations of the theory are given. This same set of algorithms was programed for the TI-59 (AOS logic) and HP67 (RPN logic) calculators in an earlier report with the same title (Walton, Birkemeier, and Weggel, 1982)'.

Each of the RPN programs incorporates HP41 compatible print routines which print and label all input and output parameters. The user only has to enter the input parameters and the results are automatically computed and printed. Since the printing routines increase program length by as much as 25 percent, use of a magnetic card for permanent program storage is recommended. All print steps are marked with asterisks and need not be entered if printing is not desired.

II. PROGRAMS

Six programs (100, 101, 102, 103, 104, and 105) are presented in this report. Program 100, a simple program that computes linear wave theory wave- length for a given depth, is designed to be used as the basis for any program that requires wavelength; in fact, it has been incorporated into programs 101, 102, and 105.

Program 101 is another basic program which computes not only wavelength but also a number of other linear wave theory parameters. This program forms the basis for program 102 and can be adapted to other programs as well.

WALTON, T.L., BIRKEMEIER, W.A., and WEGGEL, J.R., "Hand-Held Calculator Algorithms for Coastal Engineering,'' CETA 82-1, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., Jan. 1982.

Program 102 computes linear wave parameters and breaking wave height and direction based on nearshore or deepwater wave information. Program 103 can be used to forecast wave height and period in shallow water. Program 104 and 105 address wave conditions at structures-—-program 104 predicts the depth- limited design breaking wave height at a structure; 105 uses Fuchs' equation to predict wave transmission over a thin barrier.

Each program allows either English or metric input and output. Program listings are annotated, making it possible to follow the logic of the algori- thm and to make modifications if desired.

There are undoubtedly many calculator programs not included here that have been developed on coastal engineering subjects. Practicing engineers who would like to disseminate such programs (in either AOS or RPN) to other users are encouraged to submit them to the Coastal Engineering Research Center (CERC).

If the response is great enough, additional reports presenting the programs will be prepared. Comments, programs, or suggestions for programs should be sent to:

Commander and Director

US Army Coastal Engineering Research Center ATTN: Evaluation Branch

Kingman Building

Fort Belvoir, VA 22060

These programs and future programs will generally correspond to the following nurtrering scheme:

Miscellaneous 0-99

Waves and currents 100-299 Inlets 300-499 Beaches 500-699 Geology 700-899 Structures 900-1099

In general, the documentation of programs submitted should be in a format paralleling that of the programs presented in this report. A blank set of forms which can be reproduced is included in the Appendix.

Program Description

Program Title 1OOR-41CV Linear Wave Theory Wavelength (RPN Logic) Name T.L. Walton, Jr. Datene/i82 Coastal Engineering Research Center

Kingman Building Se : Zip Code Fort Belvoir Virginia

Address ety 22060

Program Description, Equations, Variables, etc.

This algorithm takes deepwater wavelength as input and using the depth at a given site iterates to obtain wavelength by linear wave theory. Algorithm uses English or metric system of units.

REFERENCE

U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Protection Manual, 3d ed., Vol. I, Eq. (2-4), Stock No. 008- 022-00113-1, U.S. Government Printing Office, Washington, D.C., WOA Thc

Operating Limits and Warnings

100R-41CV-1

User Instruetions

100R-41CV LINEAR THEORY WAVELENGTH (RPN LOGIC) fel emcee iw [ance] or] rr [aoa PROGRAM (WAVED | __‘(ea) wen Ca] eS er a a Dimeineninnaiti os | ess eooret ores a a a Withee Ra lps

Be

[a] rotenvculaTeel lynne alll (arrseu ne

ES (sas ae 9 ee =

eee

4a Lo ee ee ee

jae Example | ana /a ee T= 10SeC , d= /oft (3.05m

ENGLISH PERION=

18.0086 #8

DEPTH=

18, 668A tr

LENGTH=

175.7738

METRIC PERI ON=

16.8604 a4

DEPTH=

LEHGTH=

100R-41CV-2

STEP KEY ENTRY

B1¢LBL “WAYEL"

B2 “E ORM 2°

AZ PROMPT

A4eLBL E

@ 32.2

A6 STO A6 3807 “ENGLISH: Rag pra

99 GTO @1

1H*LBL “Ae RAL KETRIC" Miz PRA

13 9.81

14 STO 86

1S¢LBL @i 7B 16 ~PERION="

M31 PRA 32 "DEPTH?" 33 PROMPT

R34 PRK

25 ENTERT )

* 78 P r

4A STO 85

41 RCL 81 42¢LBL *ITERAT" 43 STO 83

44 17%

435 PCL AS

46 *

47 STO a4

48 Ete

49 PCL a4

58 CHS

1 EtX

Z =

23 RCL fd 54 Ete so RCL a4 36 CHS

KEY CODE

Program Listing

COMMENTS

g(english) > Roe

g(metric)—> Rog

T= Kon

Los Ro

| etd — Ros

Laid Roz

STEP

KEY ENTRY KEY CODE

?2 GTO @5 73 RCL #2 74 GTO °ITERAT" 75¢LBL 85 76 RCL #2

R77 “LENGTH=" R7E PRA R79 PRE

28 STOP

81 END.

COMMENTS

L'+ Lold = R, =) € (error tolerance

lft ori mekr

Lin display

100R-41CV-3

% THESE STEPS MUST BE DELETED IF NO PRINTER /S AVAILABLE

Program Description

TOIR-41CV Calculation of Wave Parameters from Linear Theory Program Title (RPN Logic)

Name Wolo WeULE@INg died 1/82 Coastal Engineering Research Center

Kingman Building Fort Belvoir

Address City

imate EDD DOVE)

State

Vire

Program Description, Equations, Variables, etc. This program calculates the product of the wave number and depth, kd, the ratio of group wave speed to wave celerity, n = 0.5 (1+2kd/sinh 2kd), the group wave speed, Cg, the shoaling coefficient, Ks, the refraction coeffi- cient, K;, horizontal orbital velocity, u, and vertical orbital velocity, w.

Program input includes wave period, T, deepwater wave angle, a9, deepwater wave height, Hj, wave phase angle, 8, depth of water, d, at which results are desired, and depth from surface, z, at which velocities are calculated. This program assumes straight and parallel offshore bottom contours for

assumption of Snell's law of refraction. Algorithm uses English or metric

system of units.

REFERENCE

U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Protection Manual, 3d ed., Vol. I, Ch. 2, Stock No. 008-022-00113-1, U.S. Government Printing Office, Washington, D.C., 1977.

Operating Limits and Warnings

If printer is not used, R/S must be inserted where output values are desired (i.e., where printer output steps are deleted).

101R-41CV-1

User Instruetions

101R-41CV CALCULATION OF WAVE PARAMETERS FROM LINEAR THEORY (RPN LOGIG

Sarr al aera (See AE a eS ee [ro Compre mi enous oweb: | | Milomes cote: | ewtets Jae |

[press Ns *Y dCs _—r?

[4_|_ enter .Pekio 7 Ress FIs _[r(sec) | [ris] _|DEeTH? o D

PEAD W (vertical orbital velocity) _|

101R-41CV-2

User Instruetions

70 COMPUTE JN METRIC_U tn maine ae

= nai || sees 3a-1a pee Te SAME As| [Ses Gag eee le

STE BS i= (TE MENCE Lia

PT mer tp 2 in meres | ie maa io) ere Sse S| Rehr se |

GSC, d= SOFE (IS. 244m

ie 0° ee 3 i fet 78m) 20 Istel -detaznil, Oueo® |_| i

ENGLISH METRIC PERIN= SSS

DEPTHS

15.2448

24. BARR ie 34. HAGA

al * 5.4878

aon pi -4.9732

easite

101R-41CV-3

@ e Program Listing KEY CODE COMMENTS STEP KEYENTRY KEY CODE COMMENTS 56 STO 15 O> Eis ALOLBL “LINEAR™ ae pas az “E OR M7 > HED 08 43 PROMPT 2 ; ee 61 STO 11 gTdfy —> Ru a5 32.2 ae STO 14 pe *ENGLISH* 2 a8 es a e4 RCL 11 GTO 43 1OeLBL "K" a1 cHETRIC™ * 12 pra 13 9.91 14 $70 14 I5¢LBL #3 16 “PERIOL?" PROMPT “PERIOD=" 9 PRA A PRX STO a2

STEP KEY ENTRY

n> Ry

n>Ru

Cq> Rx

Ks > Ry

“HO=" PRA 96 A er PRY. . a9 J Kad SINK STO A Le “27 : p siInK

6 PRNMPT 7s

2 PRA A u

9 PRX 95 cost

A 37 12 He 17% "PHASE?" 147 1 52 PROMPT 18 EXTERt 2 "PHASES" 189 RCL a8 PRA 118 x42 5 PRX 11 -

4DELETE THesEe L/NES JE A PRINTER JS NOT AVAILABLE. 101R-41CVv-4 ALSO SEE ‘OPERATING LIMITS AND WARNINGS “ ON PAGE /0/R-4ICV= |.

2 e @ Program Listing STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS F168 “He W —> Rx E169 PRA £176 PRY 171 RTN — 1726LBL "kd “subrowhre | 172 RCL 8 es, 172-218 at 8 lines | 75

176

AR Lo Roz *TTERAT" ret Lord > Ru

: sinh ( Ris) > Ros ? STO @8 PCL Al

9 PCL A4 a yy? 310 a5 oe ¥EQ 82 ae eee 209 GTN *ITERAT* 5 21ASLBL 25 ete 211 RCL al ae 212 RCL Ad : 213 7 CFO a4 ¢ “¢ prides 2 ae 9K 215 *KD=" aus ¥F 216 FR kd — Rx PCL AS Ponce ¥EO Ai a 7 PCL Ag D196LBL Al subrouhne . , 228 STO A? Sera Ipeaes

5 POL 15 221 Ety

a 222 ROL 87 219-228

223 CHS

HK DELETE THESE L/NES JF A PRINTER /S NOT AVAILABLE. 1°1R-41CV-s ALSO SEE ‘OPERATING LLMITS AND WARNINGS” ON PAGE (01R-41CV~].

Program Listing

STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS

224 Etx 228. - 226 2 227 / 228 RIN 229¢LBL a2 238 STO 47 231 Ets 232 RCL 47 233 CHS 234 EtX 235 +

236 2

237 /

238 “END? 239 .END.

subroutine cosh ) lines 229-238

___ en ae | if a eee]

* DELETE THESE C/NES JF fA PRINTER IS NOT AVAILABLE, 101R-41CV-6 ALSO SEE ‘OPERATING LINITS AND WARNINGS’ ON PAGE J0I1R-4ICV-/,

Program Description

102R-41CV Linear Wave Approximation to Breaking Wave Height and Program Title Breaking Wave Angle (RPN Logic)

Name Tol) Wadltone ia. Date 1/82 AaHTORS Coastal Engineering Research Center

Kingman Building :

cy Fort Belvoir, - Stale Virginia ZipiCore 22060

Program Description, Equations, Variables, etc.

This program calculates breaking wave height, H,, and breaking wave angle, Qb, using linear wave theory approximations combined with the shallow-water breaking assumption. Input parameters are wave height, H, wave period, T, wave angle, a, and the water depth, d, where the preceding three variables are measured. An additional input parameter is nearshore beach slope, m. The ratio of the breaking wave height to the water depth at breaking is pre-

dicted using the equation m 0.22 kK = Hp/dy = 1.1677) b/"b VHg/L,

from Singamsetti and Wind (1980), where dj is the water depth at breaking, HS the deepwater wave height, and Lo the deepwater wavelength. This solution requires the assumption of straight and parallel offshore bottom contours for the application of Snell's law of refraction. Input wave parameters H, T, and a can be in any depth of water, d. Algorithm uses English or metric sys tem of units. The development of the equation is derived on the attached solution sheet.

REFERENCES

SINGAMSETTI, S.R., and WIND, H.G., "Characteristics of Shoaling and Breaking Periodic Waves Normally Incident to Plane Beaches of Constant Slope," Report No. M1371, Toegepast Onberzoek Waterstaat, July 1980.

U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Protection Manual, 3d ed., Vol. I, Ch. 2, Stock No. 008-022-00113-1, U.S. Government Printing Office, Washington, D.C., 1977.

Operating Limits and Warnings

102R-41CV-1

SOLUTION SHEET FOR PROGRAM 102R-41CV Development of the equation:

From conservations of energy

H. 2 cos a = = Cpei cos aq (1)

WEE 8 where the subscript i indicates incident wave parameters.

If left-hand side of above equation represents conditions at breaking then

Cy = C = Ch = Vedp = Vel /k (2) Hb where eo == (3) dp 622 Now assume eS LoS) //—— 4 (Fagris) "

where Hi is unrefracted deepwater wave height.

Usinem (C2); (Gi, sand (4) it can" be) found 1 2 Hp -{() ie H,? Cgi cos ai] AS (5)

From Snell's law of refraction

Sin % _ sin oj (6) CS aR

therefore,

. 9 1 sin Op = (=) Hs) a (7) Ht

102R-41CV-2

@ User Instruetions 102R-41CV LINEAR APPROXIMATION TO BREAKING WAVE HEIGHT AND a wea WAVE ANGLE eral LOGIC) a ri eer LOAD PROGRAM (ANGLE B) er "ANGLEBY EoRMZ

See See | Ae | Frees fis. fae WSS Mens Sue e Tete i pull eee

Z 5 6 :

PRESS RIS, READ % eS enicean

es ie |

EACLE tai ETN vars |—_——__>_ FOLLOW THE SAME INSTRUCTIONS As Above Excepr|

= PRESS GTO “M" AT STEP lie lel

role seer ond NAP eee a

P| Gy, te Hy ARE OUTPUT IN [Mis,m.|m KesPecribery. | ee ie ee

Se

102R-41CV-3

20

User Instruetions

a

MizG| iomise (mol yea

Di empad Iemiaiei ao (sear | |

a= a0? eee 1. aren. | aii 22 | le

H= I8ft (5.4879m)

B.1n8R

58. BAB

39, ARR 1 28, BABE

18,4468

§, 40AK M3 4, BARA

102R-41CV-4

2!

Pp 2 xs Li ~ e rogram Listing STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS

BL*LEL *ANGLEB* S7 / aay caf) Mae 58 STO 83 to? Ros

a3 PROMPT 59¢LBL *ITERAT" AdeLBL E 68 STO 11 Loid 7 Ru 61 1/% ; 62 RCL 12

a7 *ENGLISH g(English) > Rig 63s & PRA 64 STO 13 2Itd —>Rj3

a9 GTO ai 65 KEQ 82

{ASLBL =H 56 310 6 cosh (R,3)—> Roe

Wil cMETRIC: 67 R 2 PRA ,

Te nha 59 S70 85 sinh (Ris) > Ros 14 810 14 g (Metric) > Riq IS#LBL Bi

Big -SLOPES*

E17 Pra 18 “SLOPE?

19 PROMPT

HR Pex

ST 15

*DEPTH=* 2 PRE

"DEPTH?"

a> Roy

om or OW NM NINO Bane De p 0-5

WO O5

oOo a

96 GTO “ITERAT"

87¢LBL 13 2nd > Riz 38 RCL 12

89 RCL A4

>

Ao Od td hu ro no

ch)

Cn A Re

STO 89 kd = Roa *KD=* > displa Zz PRA 5P 3 94 PRX 5 STOP

| Pte OG OW co NH

‘=~ oD oO

PROMPT 96 STO 11 2kd > Ry, PRY 99 ¥EQ 83

ST) 48 AB 1/%

“PER IOD=" RCL 11

Pog {A2 *

“PER ION?"

a we 4 ~ me op NO On & GI HD

Pe oO

1 + a Jo /

STO A n= Roi 3} ER — display ag PRA f PRY STOP 2 PCL Ad

X DELETE THESE STEPS IF A PRINTER 1S NOT AVAILABLE. 102R-41CVv-5

22

e @ Program Listing STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS "R169 “HB=" Hp 19 aisplay

, *

114 RCL a2 6178 PRA

115 7 5R171 PRE

116 S70 a4 172 STOP M117 -cG=" 173 RCL a6 119 PRA 174 17% F119 PRE 175 *

128 STOP

121 17%

122 REL A2

5 x

PCL 14

a, In displa y

bax Ru

= display

sinh ( ) subrovhne

Ho In dis play

cosh( ) subroutine

2A BL

5 201 STO a? 146 POL {5 2h? EtX 147 / 263 RCL A? 148 17% 204 CHS 143.22 205 ety 158 tx one, +

1.16 * 153 RCL 14 154 7

155 $10 86 156 RCL 46 157 at2 158 RCL Ad 159 *

164 RCL 68

rns

¥ DELETE THESE STER JF A PRINTER 1S NOT AVBILABLE. 102R-41CV-6

28)

Program Description

103R-41C Shallow-Water Wave Forecasting Equations (RPN Logic) Walks Walton, LEO Date 1/82 Coastal Engineering Research Center

; Kingman Building :

Ci Fort Belvoir, irpini Ze 22060

Program Title Name

Address

Program Description, Equations, Variables, etc.

This algorithm computes the wave height, H, wave period, T, and minimum dura tion, t, from input values of the water depth, d, fetch length, F, and adjusted windspeed, Ua, using equations (1), (2), and (3) of CETN-I-6. Equa tions (1) and (2) are for constant water depth and unlimited wind duration and have been revised from equations (3-25) and (3-26) of the Shore Protec- tion Manual. Wave height and period in this algorithm are significant wave height and period. Algorithm uses English or metric system of units.

REFERENCES

U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Protectton Manual, 3d ed., Vols. I, II, and III, Stock No. 008-022-00113-1 U.S. Government Printing Office, Washington, D.C., 1977, 1,262 pp.

.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, "Method for Determining Adjusted Windspeed, Ua, for Wave Forecasting,'' CETN-I-5, Fort Belvoir, Va., 1981.

-S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, "Revised Method for Wave Forecasting in Shallow Water," CETN-I-6, Fort Belvoir, Va., 1981.

-S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, "Revised Method for Wave Forecasting in Deep Water,'' CEIN-I-7, Fort Belvoir, Va., 1981.

Operating Limits and Warnings

If a printer is not used, R/S must be inserted where output values are desired (i.e., where printer output steps are deleted).

103R-41CV-1

24

User Instruetions

103R-41CV SHALLOW WATER WAVE FORECASTING EQUATIONS (RPN LOGIC)] size: 02 |

ac as ae [ono PROGRRM (FOCAST) | ___‘eearocas

Sn fe ee ees 2 ee a tess Aig a peal Weare oer tess As [a (ee pais) Mie ao [ic ee 2 rl eee dee |4 | READ Time IN HOURS. (minimun|auranian) | e(nours)

ei ee ee

lee

| eoremar eA eae Cin el as Peaimercessmiere i ell Ree) bea BaTIa SAME AS SrePs 5-9 Aeove excepr | | Oe ee

Kilometers) and

103R-41CV-2

25

User Instruetions

ae i ee 2 ee Ses a i Sr domph rescore |S ae a oa he ee seal Unie Sis nig moe rd geal nO ee fala OCT a a ia on ee

tree Ess = al a"

64.4166 et

483.1208 rex

6, [AaB ee

~ 1, 3889 1M. #44

103R-41CV-3

26

Program Listing

STEP KEY ENTRY KEY CODE COMMENTS

SLeLBL *FOCHST* M2 “E OF M 2° AS PROMPT B4eLBL E

9 (English) > Rog

English Conversion —> Ror Conyersion

ENG lish — Ror

A STO al "ENGLISH" PRA 13 GTO Al 14@LBL “8° WS METRIC? R16 FRA 17 3.31 18 STO 49 19.2778 2h STO a? 2) {Hae 22 S70 ai 23 RUE A} “Haze 25 PROMPT “\Q=" PRA g PRR STQ 83 "FETCH?" PROMPT “FETCH=" PRO PRY. 310 #5 “DEPTH?* PROMPT “TEPTH=° PRA A PRE S10 #6 RCL 3 POL 7 * S10 #8 PEL 3 REL @ 8 at? A 310 #2 ROL Be + 2 570 Be PCL BE BOL Bi

36

(Metric) » Rog

metric Conversion oR :

metric Conversion > Ro,

HEH M Das as es ed es BY nm |] ms

tnd

ne

STEP

“IN No

Per eet ae]

DELETE JF PRINTER IS. NOT AVAILABLE

ALSO SEE ‘operating Limits and Warnings: on

27

oo O00 AY on oo) Aon

CU Ro oe

oa) WOO NEON cn oe

KEY ENTRY KEY CODE COMMENTS

9F/y,2 = Ro

a tanh[.53(3) J — Rog

8565 x RCL 44

tanh eae]

103R-41CV-4 p. 103R-AICV- |

Program Listing

STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS Woe ee ee | 115 537 ie a ae ee ee) 117 RCL 87 (ies ee ae | ee] 119 * Bean Preval eee as) 119 RCL a9 Gis DAES Cay 128 7 [aa] (es ee [iad aA 121 3688 geal (RS a | 122 / hl | ee °8123 -TIME=" ea Re Pel R124 PRA (Shope | Rees Soe 3125 PRX ee ee a | 126 RTH ieee eras SS 127¢LBL a3 ae] ie Fe see 128 STN 62 (Rae eee oar eee 129 EtX ee es [a ee 138 RCL 42 a rae [ie Sees! 131 CHS (ees ea aca FS ee 132 ERX SS a Tara a TD 132 - ee DAE fs SE 134 RCL fe (ied Lilie eee) 135 EK eee [pee IMT aa 136 RCL @2 ee | PT | ere 13? CHS ire | aSBRERS ee 1 ea 139 + Taal ee | Pee | | MT es ares ae ae ee ee ee eae ee fe es rn eee | (i ae a (Tate flere ses Hee (es =e eee Ee] ee eee Se) Bees |= eee ees ee ee eee Be (ies hee] Poa hee a. ee eee ET SS (aires Eee oe] = Rare pee aa area] ele ire el ee eae ea ae] ert Ute a ee) a aaa al ae La eee ea ee aS Ly Se ot eae ees [eae ener eee (core ayy [ee ee fe ee i ear ey eee i Pe ENE nd ie ea fee aes Pat el eee ie [eter] ars Ree] inl Rae re ee es] eee ae] [aan rervenden] ie cee) Fn Ra eS ee ee | | ae ee) eo ea ee] [ini] nek eel Se Pee Fh a) Saas es aa] (ee ee [ed ian Fee] [i Bee i ee) ae] ee ae] ae eee I raeeet Pear Rese Peer oa ee) Remes | aeenRae|

103R-41CV-5

%* DELETE IF PRINTER 15 NOT AVAILABLE. | ALSO SEE ‘Operating Limits and Warnings oN P. /03R-4ICV-1.

28

Program Description

5 an 104R-41CV Depth-Limited Design Breaking Wave Height at Structure poorer Tiee (REN oeac)

Name T.L. Walton, Jr. Date 1/82 Address Coastal Engineering Research Center Kingman Building ane Fort Belvoir,

City

Virginia 20 Core 2060

Program Description, Equations, Variables, etc. This algorithm computes the depth-limited breaking wave height at a struc- ture for design purposes. It can be used in lieu of Figure 7-4 of the Shore Protection Manual. The equation for the curves in Figure 7-4 is not given in the SPM but can be found by simultaneous solution of SPM equations (2-91), (2-92), (2-93), (7-3), and (7-4). Input is wave period, T, and water depth at the structure toe, dg. The development of the equation is derived on the attached solution sheet. Algorithm uses English or metric system of units.

REFERENCE

U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Protection Manual, 3d ed., Vols. I and II, Chs, 2 and 7, Stock No. 008- 022-00113-1, U.S. Government Printing Office, Washington, D.C., 1977.

Operating Limits and Warnings

104R-41CV-1

29

SOLUTION SHEET FOR PROGRAM 104R-41CV

The following equations are given in the Shore Protection Manual:

ih bigness (2-91) Hy, b - (aly/gT*)

a = 43 75\@ie= tem) (2-92) Sie 1.56

(1 + e719.5m) (2-93) Xp = tpHb = (4.0 - 9.25 m)Hp (7-3) Hp = = (Wey)

Equation (7-4) can be rewritten in dimensionless form as:

A

és d

Hp = =

[@ - aly) —! = mtp|

where

a

Hp = Hp/gT? and dg = dg/gT? The above equation can then be solved via the quadratic formula for Hp in terms

of ds, Tp» M, a, and b where the positive root provides useful results.

A a a XS 1 -1 fi, = {(mrpb - adg - 1) + [(mtpb-ad,-1)? + 4amtp bdg] /?\. (2amtp)

This is the equation used in the program for design breaking wave height.

104R-41CV-2

30

User Instruetions

104R-41CV DEPTH-LIMITED DESIGN BREAKING WAVE HEIGHT AT STRUCTURE (RPN LOGIC) SIZE: O2|

[7 c | 7 | coap PROGRAM. (HB) a “up” [Ee oR MZ

en aoe ee eee Fabeesicomenris 15) croc

104R-41CV-3

3|

Program Listing

STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS

a7 +

ALeLEL “HE 82 "E ORM 2 Q2 PROMPT 1.56 A4¢LBL E 7 I 32.2 STO 88 ¢ "ENGLISH" H8 PRA a9 GTO Al 16¢LBL “KR i1 "METRIC" me 12 PRA 139,81 {4 STO @8 15eL8L a! ' Wis "SLOPE" 7 a5 mJp=mm(4-9.25m) r PRA ? 4 Ree “SLOPE?” 9 PROMPT A PRY 310 aA “DEPTH=" 2 PRA re 24 * DEPTH?" : 2 25 PROMPT 2 f mIpb-ads | 6b PRE ‘ = Row 310 47 43 “PERIOD=" PRA "PERIOD?" 21 PROMPT 22 PRE 2 STO As bans

35 RCL

17%

S70 44 RCL 88 ENTERT

9.25

Hp in display

% THESE STEPS MUST BE DELETED IF NO PRINTER |S AVAILABLE 101R-41¢V-4

32

Program Description

105R-41CV Wave Transmission - Fuchs' Equation (RPN Logic) T.L. Walton, Jr. Date 1/82 Coastal Engineering Research Center

Kingman Building

Fort Belvoir

Program Title Name Address

City

Program Description, Equations, Variables, etc. This algorithm computes wavelength, L, in water depth, d, given the wave period, T. The program then computes wave transmission over a thin verti- cal barrier in water depth, d, using Fuchs' equation: 4th 4th —— + sinh L sinh 4nd 4nd = op Seljalny Se it saan where Ht is the transmitted wave height, Hj the incident wave height, and h the height of barrier. Note that this equation cannot be used when wave: transmission is by overtopping of a structure. Algorithm uses English or metric system of units.

REFERENCE

U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Protection Manual, 3d ed., Vol. II, Ch. 7, Stock No. 008-022-00113-1, U.S. Government Printing Office, Washington, D.C., 1977, p. 7-62.

Operating Limits and Warnings

105R-41CV-1

SS)

User Instruetions

10SR-41CV WAVE TRANSMISSION - FUCHS' EQUATION (RPN logic) ee get oe ao saw ee

St Res aoe | ea” a Bi hia ieee a | ENTER PERIOD T, PRESS R/s__| Tlsec) | [R/s] a | liza] REA kes M/iie) Greansmisso | 4 _sseeetceenen _} _}_____ ee ee ee Wane aa | lizallpeess) roti i ee ero || sre ps 3a-Ta ARE THE SAMELAS Srebs 3-7 agdve ExcEP er

Gl lay SINE VES

| | meur dh on merers |_| ALPS ye he whee Nghe ee ee Re a

igainge Landlia a ae || values used: d=istt (4.5732m), ht loft 3.0984m) , T= /asec ea a

PRINTOUTS :

ENGLISH ~ METRIC DEPTH= DEPTH=

15,0886 9 +e SIL HT=

19. 4688 eee PEPTOD=

16,8688 led

4.5732 ey

SIL HT=

3.0488 tax

PEPION=

19.0600 = xxx

213.6238 +a 64,9450 $a

ALT

9.5977 +4

CALPHA

8.5977 tee

105R-41CV-2

34

Program Listing

STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTAY KEY CODE COMMENTS

BLOLBL “FUCH"

Ag "ER N 2 54 a2 PROMPT i" AsOLEL E ‘1 Be 62 ae (22 a4 Lod 9 G10 Al ; 1ROLEL “He {1 °RETRIC* ae aie PRA 6 1s Fey 12 9.81 14 S19 #6 SoLBL fl 16 “DEPTH? PROMPT 8 “DEPTH=" : SHERR 76 RCL A? PRX GTO ITERAT 212 ‘ GPCL a2 3 Pl fy ee + 25 STO a 6 °SIL HT?" PROMPT “SIL HT=* 9 PRA PRY STO Ag ae 4rd —> Ros “PERION?= a a) 32 PROMPT 34 “PER IOR=" q : 5 Ppa a2 STO Rag t Sth (Ro) > Rey 76 PRY ; este ENTER? PI h * PCL a8 . r x PCL 2 i! 10 49 4th —> “TTERAT* B2 YEO 83 — Roa a3 PCL a9 + ae BCL 97 if a7 CHS AS | ie) SP . SORT Hej = Ke In display

caja PRA

PRY

LETED IF A PRINTER Zs NOT AVAILABLE, 3 THESE LINES MUST BE DELETE Hee

35

Program Listing

STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS

116 RTN Es) ee ee LI5@LBL 82 ee ere ea 116 STO a5 rane ee 117 EtX ee ae ee 118 RCL @5 a ee Pay 119 CHS RE [Ro le SRT 12 Etx ea] ee all grea) 1210= eae Ree el nT 122 2 eS ae ie ee] 123 / aes Te a 124 . END. —|—-——}—___. eal er aaa] a a

eee Cs feeders ieee eee ye Sas ieee] a] Gs ae ees Pe) a eae ee se Roe he eae et ee a eS ae | ee Ee Sl Ss eae ee ee] nan Raa er eee

(oS Ea eee] eS aes ee eee (eae | EI eis] ay ore PS See Erriag Rae an eh )] ae eee ee et (ieee pene ae [eg Sore] ae eer Se ee | oe es ee a ee SS] ere iat ee [cama ca [ipa Ea | el] Tae, | a aoe Bae | (ieee Ree a es SS iia es ier eee ees i eee ae oar ae ee (Cancel aay ial ees Sa (eee pee ee eel [SPE || Serres es | TET ee ae ee eS ee rae [ee eee 7 ae ee) a | (See Ee aa fa es | es | Se (ete enna [Pon Son i haa ee (ae ae I ee (ae eS oa (ae netted ee Ge] Ree eae (Le ERS a Bet Oe] (ee ee ell Be el Se ae ren a ees as ee Ree es ea ee a] aaa es Seat eer es ee ae ae Pe ieee | ee wan (Ee | ss ee | ee Sa RS TER A, ES] a Saar ee | (eas ea eae ad | es aes Ee ey ee Ol ee aa

105R-41CV-4 *K THESE LINES MUST BE DELETED /F A PRINTER IS NOT AVAILABLE.

36

APPENDIX

BLANK PROGRAM FORMS

37

Program Description

Program Title Name Date

Address City Zip Code

Program Description, Equations, Variables, etc.

Operating Limits and Warnings

38

User Instructions

Program Titie

OUTPUT DATA/JUNITS

HUUULICUZUUC U0 CUCU OCU C0

177) e = 55 22 ze C4 Qa

INSTRUCTIONS

Program Listing

KEY CODE

COMMENTS

KEY ENTRY KEY CODE

STEP

COMMENTS

KEY ENTRY

STEP

COMMENTS

KEY CODE

KEY ENTRY

STEP

170

COMMENTS

KEY CODE

KEY ENTRY

STEP

REEL

22!

oO =

4|

=.

~ t {

i

Sa if

a i h oe

Beale

i t

aoe

er

bev

i ee ae ae Oo Sear is as ms ee ces se z ; eee sie eee

Ey

i

!

a ee ae ee eet a

f. ra

Ge . eee: 4. Lom te ast my Te

| '

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