BASIC PROGRAMS AND EQUATIONS INHP 33s FOR PE CIVIL SURVEYING EXAMJoselito I. de Paula, E.I.T.
TABLE OF CONTENTS:ABOUT THE AUTHOR …………………………………………………………………1PREFACE ………………………………………………………………………………..2ACKNOWLEDGEMENT ………………………………………………………………..3INTRODUCTION ………………………………………………………………………...4REFERENCES …………………………………………………………………………..5DISCLAIMER …………………………………………………………………………….6 A. LIST OF SURVEY EQUATIONS ……………………………………………..7 B. LIST OF SURVEY PROGRAMS: …………………………………………….14 • TRIGONOMETRY ……………………………………………………………… 15 • TRAVERSE ………………………………………………………………………23 • INVERSE …………………………………………………………………………25 • AREA BY COORDINATES ……………………………………………………..27 • AREA BY DMD METHOD ………………………………………………………30 • HORIZONTAL CURVES ………………………………………………………..35 • VERTICAL CURVES …………………………………………………………….40 • RIGHT TRIANGLES……………………………………………………………...41 • AZIMUTH AND BEARING……………………………………………………….44 C. SAMPLE PROBLEMS……………………………………………………………46-58
ABOUT THE AUTHORJoselito Intia de Paula was born in Centro, Oas, Albay, Philippines, son of Cesarand Corazon de Paula and finished his college degree at Bicol University,College of Engineering, Legazpi City with a degree of Bachelor of Science in CivilEngineering in the year 1992. On the same year where he finished his collegedegree at the age of 21 he passed the Board Examination for Civil Engineeringand Geodetic Engineering in the Philippines.He works abroad for 8 years in the Middle East as a Survey/Site Engineer invarious foreign European companies such as ABV Rock Group, NorconsultTelematics, and Archirodon Construction Company.He and his family immigrated to the United States in the state of Californiain the year of 2006. After a month of his arrival in the United States he landed ajob in Mark Thomas and Company, a Transportation Engineering Consulting firmat Walnut Creek, California. He passed the Engineer-in-Training (EIT)examination of the Board of Professional Engineers and Land Surveyors andGeologist (BPELSG). He later joined the San Francisco Public UtilitiesCommission – Engineering Management Bureau year 2012 up to present.He has two sons named Cesar Henry, 13 years old and Andrei Joselito, a newborn whose birth was around the time of this book’s creation. His wife ElizabethMorante is a Registered Nurse who works as an Operating Room Nurse in theContra Costa Regional Medical Center in Martinez, Ca. USA.Joselito loves to play golf and tennis. 1
PREFACETHE CONTENTS OF THIS BOOK ARE PROVIDED TO GUIDE THE USER OF HP 33s ONHOW TO STORE SURVEY EQUATIONS AND PROGRAMS AND HOW TO SAVE TIME INSOLVING PROBLEMS THAT HAVE LENGTHY SOLUTIONS BY HAVING THIS KIND OFTOOL. THIS HP33s IS INCLUDED IN THE LIST OF OFFICIAL CALCULATORS ALLOWEDDURING THE TEST.IN REGARDS TO THE PROBLEMS THAT NEED MORE TIME TO SOLVE , IT IS BETTER TOANTICIPATE THOSE SURVEY PROGRAMS AND EQUATIONS AND STORE THEM IN THECALCULATOR BEFOREHAND. AN EXAMPLE OF A PROBLEM THAT MIGHT NEED A FEWMORE MINUTES TO SOLVE IS ONE OF CALCULATING AN AREA BY COORDINATEMETHOD OR DETERMINING AN AREA USING DOUBLE MERIDIAN DISTANCE (DMD)METHOD.IN THIS BOOK YOU WILL FIND THOSE EQUATIONS AND PROGRAMS THAT CAN HELPYOU SAVE TIME IN SOLVING A PROBLEM THAT HAS A LONG SOLUTION.I HOPE YOU FIND THIS BOOK A USEFULL TOOL TO PASS THE PE CIVIL SURVEYINGEXAM. 2
ACKNOWLEDGEMENTI WOULD LIKE TO THANK GOD FOR GIVING ME THE STRENGTH AND WISDOM TOREALIZE THIS BOOK; TO MY FAMILY WHO SERVES AS MY INSPIRATION, ESPECIALLYMY TWO SONS NAMED CESAR HENRY AND ANDREI JOSELITO AND MY LOVING WIFEELIZABETH WHO GAVE ME A LOT OF SUPPORT IN EVERYTHING. 3
INTRODUCTION: THE CONTENTS OF THIS BOOK EXPLAIN HOW TO STORE BASIC PROGRAMS ANDEQUATIONS FOR SURVEYING IN HP33s. THIS BOOK WILL GIVE YOU CONSTANTPRACTICE USING A CALCULATOR’S PROGRAM MODE OR EQUATION MODE ANDSOLVE FUNCTIONS. YOU CAN SAVE A LOT OF TIME BY USING THIS APPROVEDCALCULATOR OF NCCS DURING THE TEST FOR PE CIVIL SURVEYING EXAM. THE BOOK CONTAINS THREE PARTS, NAMELY “LIST OF SURVEY EQUATIONS”, “LISTOF SURVEY PROBLEMS”, AND “SAMPLE PROBLEMS.” ALSO, THERE ARE MORE THANTHIRTY STORED BASIC SURVEY EQUATIONS ON THIS CALCULATOR. YOU MAY REFERTO HP33s HANDBOOK MANUAL FOR QUICK AND EASY STORING OF THOSEEQUATIONS. YOU SHOULD FAMILIARISE YOURSELF WITH THE VERY BASIC METHODOF USING THE CALCULATOR IN REVERSE POLISH NOTATION (RPN). ALL THE BASICPROGRAMS AND EQUATIONS USED HEREIN ARE IN RPN MODE. IF YOU HAVE ANYQUESTIONS OR CONCERNS YOU MAY EMAIL ME AT [email protected] 4
REFERENCES:CALTRANS, “SAMPLE PROBLEMS FOR BASIC SURVEYING MATH”HEWLETT PACKARD COMPANY, “HANDBOOK MANUAL FOR HP33s CALCULATOR”VENANCIO I. BESAVILLA, “SURVEYING FORMULAS FOR COMPUTERIZED LICENSUREEXAMS” 5
DISCLAIMER: THE HEWLETT-PACKARD COMPANY AND ITS AFFILIATES ARE IN NO WAY INVOLVEDWITH THIS BOOK. THE CALCULATOR IS ONLY A TOOL FOR YOU TO SAVE TIME INSOLVING LENGTHY PROBLEMS ON THE PE CIVIL SURVEYING EXAM. PASSING THISTEST WILL DEPEND ON THE EFFORTS OF EACH INDIVIDUAL TAKING THE TEST, ANDARE NOT THE RESPONSIBILITY OF THE AUTHOR. 6
LIST OF SURVEY EQUATIONS 7
LIST OF USEFUL SURVEY EQUATIONS I-TAPE CORRECTION SLOPE EQUATION H = LcosαWHERE: A = ANGLE α L = SLOPE DIST. H = HORIZONTAL DIST.1 EQ001SLOPE H = L x cosA C=(6.45 x 10-6)x(T – A)xL 2- TEMPERATURE C = 6.45 x 10-6 (T – TS)L where: C = CORRECTION A = TS (STD TEMP. @ 68° F) T = GIVEN TEMP. L = MEASURED DIST.2 EQ002TEMP 3 - PULL CORRECTIONS CP = [(P1 – PS)/AE]L where: C = CP, CORRECTION A = A, CROSS SECTIONAL ARE OF THE TAPE E = E, MODULUS OF ELASTICITY OF THE STEEL TAPE X = P1, APPLIED PULL Y = PS, STANDARD PULL L = L, MEASURED DISTANCE3 EQ003PULL C = ((X - Y) ÷ (A x E)) x L 4 - SAG CORRECTION: C = - (W^2)LS÷24P12 where: C = CS, SAG CORRECTION W = W, TOTAL WEIGHT OF STEEL TAPE P = P1, APPLIED PULL L = LS, UNSUPPORTED TAPE LENGTH4 EQ004SAG C= -((W^2)xL)÷((24)x(P^2)) 8
B – LEVELLINGi) DIFFERENTIAL LEVELLINGELEVATION @ ANY POINT = INITIAL EL. + (ΣBS –ΣFS)Where:E = ELEV. @ ANY POINTI = INITIAL ELEV.B = ΣBS, SUM OF ALL THE BACKSIGHTF = ΣFS, SUM OF ALL THE FORESIGHT5 EQ005LEVELLING E = I+(B - F)HI = ELEV. BENCHMARK + BACKSIGHTWhere:H =HI, HEIGHT OF INSTRUMENTE = BM, BENCHMARK ELEVATION (KNOWN)B = BS, BACKSIGHTF = FS, FORESIGHTU = UNKNOWN ELEV.6 EQ006HI H = E +B7 EQ007UNKELEV U=H–FMISCLOSURE = OBSERVED EL. – ESTABLISHED EL. where: M=O–E M = MISCLOSURE DIFFERENCE O = OBSERVED EL. E = ESTABLISHED EL.8 EQ008MISCLOSURECORRECTION = MISCLOSURE/No. of SETUPS x CUMULATIVE No. of SETUPS where: C = (M ÷ N) x Z C = CORRECTION TO EACH PT. M = MISCLOSURE N = No. of SET-UPS Z = CUMULATIVE9 EQ009CORRMISC C – STADIAwhere:S = S, NORMALIZED ROD INTERVALT = S, ROD INTERVALD = D, DISTANCE LINE OF SIGHT 9
H = H, HORIZONTAL DIST.V = V, VERTICSL CURVEA = ANGLE, ӨS = S'COSӨ10 EQ010RODINTERVAL S=TxCOS(A)11 EQ011DISTLOS D=100xTxCOS(A)12 EQ012HORDIST H=100xTx(COS(A))^213 EQ013VERTDIST V=100xTxCOS(A)XSIN(A)D - SLOPES =( ( ELEV.B - ELEV.A )÷( STA.B - STA.A))x100 WHERE: S=((B-A)÷(X-Y))x100 S = SLOPE IN % A = ELEV. A S = (A+B+C)÷2 Y = STA. A P=SQ.RT√Sx(S-A)x(S-B)X(S-C) B = ELEV. B X = STA. B14 EQ014SLOPE E - AREAS P = √S(S-A)(S-B)(S-C) WHERE: P = AREA OF A 3 GIVEN SIDES15 EQ015SIDES16 EQ016AREA3SIDES17 EQ017AREASAS P=0.5xAxBxSIN(X) WHERE: A=SQ.RT(B^2+C^2)-2xBxCxCOS(X) P = AREA A = SIDE B = SIDE X = INCLUDED ANGLE18 EQ018COSLAWWHERE:A = SIDEB = SIDEC = SIDEX = INCLUDED ANGLE 10
F - HORIZONTAL CURVESFORMULAS: T = R TAN (I/2)WHERE:T = TANGENTR = RADIUSI = CENTRAL ANGLE19 EQ019TAN T=RxTAN(I÷2) L = Rx Ix (∏ )÷ 180 L = R I (∏ ) / 180 WHERE: L = LENGTH OF CURVE R = RADIUS I = CENTRAL ANGLE20 EQ020LCURVE LC = 2RSIN(I/2)WHERE:C = LC, LONG CHORDR = RADIUSI = CENTRAL ANGLE21 EQ021LONGCHORD C = 2xRxSIN(I÷2) M = R(1-COS (I/2)WHERE:M = MIDDLE ORDINATER = RADIUSI = CENTRAL ANGLE22 EQ022MIDORD M=Rx(1-COS (I÷2)E=R((1÷COS(I÷2))-1)WHERE:E = EXTERNAL DISTANCER = RADIUSI = CENTRAL ANGLE23 EQ023EXTDIST E=Rx((1÷COS(I÷2))-1)G - DEFLECTION ANGLE METHOD FORMULAS: D = (I÷L)x£ WHERE: D = SUB-CENTRAL ANGLE L = LENGTH OF CURVE 11
I = CENTRAL ANGLE D = (I÷L)x£ F = £, SUB-LENGTH OF CURVE24 EQ024DEFANGMENOTE: IN PLUGGING IN THE VALUES OF THE GIVEN CENTRAL ANGLE IN HP33s CALCULATOR IT MUST BE CONVERTED FROM DEGREES TO RADIANS. EX. 65DEG 45'35\" DEGREESKEY RADIANS65.4535←┐→HR65.7597 H - VERTICAL CURVESSYMBOLS:G = G1 IN %H = G2 IN %L = L, LENGTH OF VERTICAL CURVERESULTS:R = RATE OF CHANGEX = HIGH OR LOW POINT LOCATION FROM BVCM = MIDDLE ORDINATESYMBOLS:B = BVC STATIONC = BVC ELEVATIOND = DISTANCE FROM BVCRESULTS:Y = ELEVATION AT ANY POINT AT DIST. DS = SLOPE AT ANY POINT AT DIST. DO = OFFSET FROM GRADE LINE TO CURVEZ = ELEVATION OF HIGH OR LOW POINTI = STATION OF HIGH OR LOW POINT25 EQ025RATEOFCH R= (G-H)÷L26 EQ026HILO X= (GxL)÷(G-H)27 EQ027MIDORD M= ((G-H)xL)÷ABS(G-H)28 EQ028ELEVANYPTD Y= C+(GxD)+(0.5xRxD^2)29 EQ029ELEVANYPTX Z= C+(GxX)+(0.5xRxX^2) 12
30 EQ030SLOPEANYPT S= ((GxL)-(Dx(G-H)))÷L31 EQ031OFFSET O= (4xMxD^2)÷L^2EXAMPLE OF HOW TO INPUT SURVEY EQUATIONS INTO HP33s.31 EQ031OFFSET O= (4xMxD^2)÷L^2FIRST SEE TO IT THAT YOUR CALCULATOR IS IN RPN (REVERSEPOLISH NOTATION) MODEGB GREEN BUTTONPB PURPLE BUTTONSTART GB RPN PB EQN RCL E RCL Q 31 RCL O RCL F RCL F RCL S RCL E RCL T ENTER RCL O = (4xMxD^2)÷L^2 ENTER 13
LIST OF SURVEY PROGRAMS 14
TRIGONOMETRY INVOLVING ELEMENTS OF TRIANGLES 15
TRIGONOMETRY GENERAL SYMBOLS USED FOR THE ELEMENTS OF A TRIANGLEFIGURE 1.0 FNOTE: SS D E S S = SIDE S = SIDE S = SIDE D = ANGLE E = ANGLE F = ANGLE THE FIGURE 1.0 ONLY APPLIES TO THE FOLLOWING PROGRAM: 1 XEQ A - SIDE SIDE SIDE 2 XEQ B - SIDE ANGLE SIDE 3 XEQ C - SIDE SIDE ANGLE 4 XEQ D - ANGLE ANGLE SIDE 5 XEQ E - ANGLE SIDE ANGLE 16
1 SIDE SIDE SIDE A001 F A002 SS A003 A004 D E A005 S A006 A007 XEQ A A008 LBL A A009 INPUT S A010 STO A A011 INPUT S A012 STO B A013 INPUT S A014 STO C A015 EQN ACOS ((A^2-B^2-C^2) ÷ (2 x B x Cx(-1))) A016 →HMS A017 STO D A018 EQN ACOS ((A^2-B^2-C^2) ÷ (2 x A x C)) A019 →HMS A020 STO E A021 EQN ACOS ((C^2-A^2-B^2) ÷ (2 x A x B)) A022 →HMS A023 STO F A024 →HR A025 STO Z A026 EQN 0.5 x A x B x sin(z) A027 STO G A028 43560 A029 ÷ A030 STO H A031 VIEW D VIEW E VIEW F VIEW G VIEW H R/S GTO A RTN 17
2 SIDE ANGLE SIDE B001 F B002 SS B003 B004 D E B005 S B006 B007 XEQ B B008 LBL B B009 INPUT S B010 STO L B011 INPUT A B012 STO F B013 INPUT S B014 STO B B015 RCL F B016 →HR B017 STO Z B018 EQN SQRT((L^2+B^2) - (2 x L x B x cos(z))) B019 STO C B020 EQN Asin[(L x sin(z)) ÷ C] B021 →HMS B022 STO D B023 EQN Asin[(B x sin(z)) ÷ C] B024 →HMS B025 STO E B026 EQN 0.5 x L x B x sin(z) B027 STO G B028 43560 B029 ÷ B030 STO H B031 VIEW D B032 RCL C B033 STO S VIEW S VIEW E VIEW G VIEW H R/S GTO B RTN 18
SIDE SIDE ANGLE F SS D E SC001 XEQ CC002 LBL CC003 INPUT SC004 STO AC005 INPUT SC006 STO BC007 INPUT AC008 STO DC009 RCL DC010 →HRC011 STO ZC012 EQN Asin((B x sinZ) ÷ A)C013 →HMSC014 STO EC015 RCLEC016 →HRC017 STO YC018 EQN (180 - Z - Y)C019 STO XC020 EQN ((A^2+B^2)-(2xAxBxCOS(X)))C021 STO CC022 EQN 0.5 x A x B x sinXC023 STO GC024 43560C025 ÷C026 STO HC027 RCL XC028 →HMSC029 STO FC030 RCL CC031 STO SC032 VIEW SC033 VIEW EC034 VIEW FC035 VIEW GC036 VIEW HC037 R/SC038 GTO C RTN 19
ANGLE ANGLE SIDE F SS D ED001 SD002D003 XEQ DD004 LBL DD005 INPUT AD006 STO FD007 INPUT AD008 STO DD009 INPUT SD010 STO BD011 RCL FD012 →HRD013 RCL DD014 →HRD015 +D016 180D017 -D018 +/-D019 →HMSD020 STO ED021 RCL DD022 →HRD023 STO YD024 RCL ED025 →HRD026 STO XD027 RCL FD028 →HRD029 STO ZD030 EQN (B x sinY) ÷ sinXD031 STO LD032 EQN (B x sinZ) ÷ sinXD033 STO CD034 EQN (0.5 x L xB x sinZ)D035 STO GD036 43560D037 ÷D038 STO HD039 VIEW ED040 RCL CD041 STO SD042 VIEW S RCL A STO S VIEW S 20
D043 VIEW GD044 VIEW HD045 R/SD046 GTO DD047 RTN 21
ANGLE SIDE ANGLE F SS D E SE001 XEQ EE002 LBL EE003 INPUT AE004 STO DE005 INPUT SE006 STO LE007 INPUT AE008 STO EE009 RCL DE010 →HRE011 STO YE012 RCL EE013 →HRE014 STO XE015 EQN (L x SIN(X)) ÷ SIN(Y)E016 STO BE017 EQN (180 - X - Y)E018 STO ZE019 EQN SQRT((L^2+B^2) - (2 x L x B x COS(Z)))E020 STO CE021 RCL ZE022 →HMSE023 STO FE024 EQN (0.5 x A x B x sinZ)E025 STO GE026 43560E027 ÷E028 STO HE029 RCL CE030 STO SE031 VIEW SE032 VIEW FE033 RCL BE034 STO SE035 VIEW SE036 VIEW GE037 VIEW HE038 R/SE039 GTO E RTN 22
TRAVERSE 23
SYMBOLS: TRAVERSET001 N = NORTHING COORDINATEST002 E = EASTING COORDINATEST003 A = AZIMUTHT004 D = HORIZONTAL DISTANCET005T006 XEQ TT007 LBL TT008 INPUT N (BEGINNING NORTHING)T009 INPUT E (BEGINNING EASTING)T010 INPUT A (AZIMUTH)T011 INPUT D (HORIZONTAL DISTANCE)T012 RCL AT013 →HRT014 RCL DT015 O, r -> y, xT016 RCL + NT017 STO NT018 x <>yT019 RCL + ET020 STO ET021 RCL XT022 RCL ET023 =T024 RCL YT025 RCL NT026 -T027 y, x -> 0, rT028 STOPT029 x <> yT030 180T031 +T032 →HMS STO Q RCL P RCL Q R/S (STOP) GTO T RTN 24
INVERSE 25
SYMBOLS: INVERSEI001 N = NORTHING OCCUPIEDI002 E = EASTING OCCUPIEDI003 Y = NORTHING ENDI004 X = EASTING ENDI005I006 XEQ II007 LBL II008 INPUT NI009 INPUT EI010 INPUT YI011 INPUT XI012 RCL EI013 RCL XI014 -I015 RCL NI016 RCL YI017 -I018 y,x →Ө,rI019 R/S (STOP)I020 STO DI021 x<>yI022 180I023 →HMS STO A VIEW D VIEW A R/S (STOP) GTO I RTN 26
AREA BY COORDINATE METHOD 27
SYMBOLS: AREA BY COORDINATESF001 N = NORTHINGF002 E = EASTINGF003F004 XEQ FF005 LBL FF006 CLVARSF007 INPUT NF008 STO YW001 STO CW002 INPUT EW003 STO XW004 STODW005 LBL WW006 INPUT NW007 INPUT EW008 RCL YW009 xW010 RCL NW011 RCL XW012 xW013 -W014 RCL FW015 +W016 STO FW017 RCL EW018 RCL XW019 -W020 RCL NW021 RCL YW022 -W023 y,x →Ө,rW024 RCL PW025 +W026 STO PW027 RCL NW028 STO YW029 RCL EW030 STO XW031 RCL DW032 x≠y?W033 GTO WW034 RCL NW035 RCL CW036 x≠y?W037 GTO W RCL P VIEW P RCL F 2 28
W038 ÷W039W040 plus/minus signW041 STO FW042 VIEW FW043 43560W044 ÷W045W046 STO A VIEW A RTN 29
AREA BY DOUBLE MERIDIAN DISTANCE (DMD) METHOD 30
AREA BY DMD METHODSYMBOLS: A = BEARING OF LINE 1 B = HORIZONTAL DISTANCE OF LINE1 C = BEARING OF LINE 2 D = HORIZONTAL DISTANCE OF LINE 2 E = BEARING OF LINE 3 F = HORIZONTAL DISTANCE OF LINE 3 G = BEARING OF LINE 4 H = HORIZONTAL DISTANCE OF LINE 4 I = BEARING OF LINE 5 J = HORIZONTAL DISTANCE OF LINE 5NOTE: 1 NORMALLY IN THE GIVEN PROBLEM OF A CLOSED POLYGON IS CONSIST OF 5 SIDES BUT IF IT IS LEES THAN 5 SIDES JUST MAKE THE BEARING AND DISTANCE OF THE LAST SIDES EQUALS TO ZERO WHEN INPUTING THE DATA INTO HP33s 2 CONVERT ALL THE BEARINGS INTO AZIMUTH NE = ANGLE = AZIMUTH SE = 180 - ANGLE SW = 180 + ANGLE NW = 360 - ANGLE 3 PLUGGING IN THE AZIMUTH IS THE SAME AS PLUGGING IN A NUMBER WITH A DECIMAL POINT. EX. AZIMUTH = 125º 35' 45\" HP 33s = 125.3545RESULT: Z = AREA IN SQUARE FEET (SQ.FT) Q = AREA IN ACRES (AC)BONUS RESULT: A = DEPARTURE OF THE MISSING SIDE B = LATITUDE OF THE MISSING SIDE C = DISTANCE OF THE MISSING SIDE D = ANGLE OF THE MISSING SIDE HP 33s PROGRAM FOR DMD METHODO001 XEQ OO002 LBL OO003 INPUT AO004 INPUT BO005 RCL AO006 →HRO007 RCL B O, r --> y, x 31
O008 STO YO009 X<>YO010 STO XO011 INPUT CO012 INPUT DO013 RCL CO014 →HRO015 RCL DO016 O, r --> y, xO017 STO WO018 X<>YO019 STO VO020 INPUT EO021 INPUT FO022 RCL EO023 →HRO024 RCL FO025 O, r --> y, xO026 STO SO027 X<>YO028 STO UO029 INPUT GO030 INPUT HO031 RCL GO032 →HRO033 RCL HO034 O, r --> y, xO035 STO TO036 X<>YO037 STO RO038 INPUT IO039 INPUT JO040 RCL IO041 →HRO042 RCL JO043 O, r --> y, xO044 STO OO045 X<>YO046 STO PO047 RCL XO048 2O049 xO050 RCL VO051 +O052 STO KO053 RCL KO054 RCL VO055 +O056 RCL UO057 +O058 STO LO059 RCL LO060 RCL UO061 +O062 RCL R 32
O063 +O064 STO MO065 RCL PO066 +/-O067 STO NO068 RCL XO069 RCL YO070 xO071 RCL KO072 RCL WO073 xO074 +O075 RCL LO076 RCL SO077 xO078 +O079 RCL MO080 RCL TO081 xO082 +O083 RCL NO084 RCL OO085 xO086 +O087 2O088 ÷O089 ABSO090 STO ZO091 VIEW ZO092 RCL ZO093 43,560O094 ÷O095 ABSO096 STO QO097 VIEW QO098 RCL XO099 RCL VO100 +O101 RCL UO102 +O103 RCL RO104 +O105 RCL PO106 +O107 +/-O108 STO AO109 VIEW AO110 RCL YO111 RCL WO112 +O113 RCL SO114 +O115 RCL TO116 +O117 RCL O 33
O118 +O119 +/-O120 STO BO121 VIEW BO122 RCL AO123 RCL BO124 O, r --> y, xO125 STO CO126 X<>YO127 180O128 +O129 STO DO130 RCL CO131 VIEW CO132 RCL DO133 VIEW DO134 STOPO135 GTO OO136 RTN 34
HORIZONTAL CURVES 35
HORIZONTAL CURVESSYMBOLS: R - RADIUSOPTIONAL: I - DELTA B - BEGINNING OF CURVE (BC) P - POINT OF INTERSECTION (PI)RESULTS: T - TANGENT C - LONG CHORD L - LENGTH OF CURVE M - MIDDLE ORDINATE E - EXTERNAL DISTANCEZ - AREA SHADED (SQUARE FEET) Y - AREA SHADED (SQUARE FEET) X - AREA SHADED (SQUARE FEET) W - AREA SHADED (SQUARE FEET) U - AREA SHADED (SQUARE FEET) 36
OPTIONAL: V - AREA SHADED (SQUARE FEET)IF B IS GIVEN K - POINT OF INTERSECTION (PI) G - END OF CURVE STATIONIF P IS GIVEN F - BEGINNING OF CURVE STATIONQ001 N - END OF CURVE STATIONQ002Q003 HP33s PROGRAM FOR HORIZONTAL CURVESQ004Q005 XEQ QQ006 LBL QQ007 INPUT RQ008 INPUT IQ009 INPUT BQ010 INPUT PQ011 RCL RQ012 RCL IQ013 →HRQ014 2Q015 ÷Q016 TANQ017 xQ018 STO TQ019 VIEW TQ020 RCL RQ021 RCL IQ022 →HRQ023 2Q024 ÷Q025 SINQ026 xQ027 2Q028 xQ029 STO CQ030 VIEW CQ031 RCL R RCL I →HR x pi x 37
Q032 180Q033 ÷Q034 STO LQ035 VIEW LQ036 RCL RQ037 RCL IQ038 →HRQ039 2Q040 ÷Q041 COSQ042 ±Q043 1Q044 +Q045 xQ046 STO MQ047 VIEW MQ048 RCL IQ049 →HRQ050 2Q051 ÷Q052 COSQ053 1/xQ054 1Q055 -Q056 RCL RQ057 xQ058 STO EQ059 VIEW EQ060 RCL PQ061 RCL TQ062 -Q063 STO FQ064 VIEW FQ065 RCL FQ066 RCL LQ067 +Q068 STO NQ069 VIEW NQ070 RCL BQ071 RCL TQ072 +Q073 STO KQ074 VIEW KQ075 RCL BQ076 RCL LQ077 +Q078 STO GQ079 VIEW GQ080 RCL TQ081 RCL RQ082 xQ083 STO ZQ084 VIEW ZQ085 RCL RQ086 RCL L 38
Q087 xQ088 2Q089 ÷Q090Q091 STO YQ092 VIEW YQ093 RCL RQ094 x2Q095 RCL IQ096 →HRQ097 SINQ098 xQ099 2Q100 xQ101 STO XQ102 VTEW XQ103 RCL YQ104 RCL XQ105 -Q106 STO WQ107 VIEW WQ108 RCL ZQ109 RCL YQ110 -Q111 STO UQ112 VIEW UQ113 RCL ZQ114 RCL XQ115 -Q116 STO VQ117 VIEW VQ118 R/S (STOP)Q119 GTO Q RTN 39
VERTICAL CURVES 40
1 SYMBOLS: VERTICAL CURVES RESULTS: G = G1 IN %2 SYMBOLS: H = G2 IN % RESULTS: L = L, LENGTH OF VERTICAL CURVE3 SYMBOLS: R = RATE OF CHANGE RESULTS: X = HIGH OR LOW POINT LOCATION FROM BVC M = MIDDLE ORDINATE4 SYMBOLS: RESULTS: B = BVC STATION NOTE: C = BVC ELEVATION D = DISTANCE FROM BVC Y = ELEVATION AT ANY POINT AT DIST. D S = SLOPE AT ANY POINT AT DIST. D O = OFFSET FROM GRADE LINE TO CURVE Z = ELEVATION OF HIGH OR LOW POINT I = STATION OF HIGH OR LOW POINT P = PVI STATION Q = PVI ELEVATION B = BVC STATION C = BVC ELEVATION E = EVC STATION K = EVC ELEVATION E = EVC STATION K = EVC ELEVATION P = PVI STATION Q = PVI ELEVATION B = BVC STATION C = BVC ELEVATION LENGTH OF CURVE AND ALL STATIONS MUST BE IN DIVISIBLE BY 100 WHEN PLUGGING INTO HP33s. EX. STA. 45+12.36 PLUG-IN = 45.1236 XEQ V 41
V001 LBL VV002 INPUT GV003 INPUT HV004 INPUT LV005 EQN (G-H)÷LV006 ABSV007 STO RV008 EQN (GxL)÷(G-H)V009 STO XV010 EQN ((G-H)Xl)÷ABS(G-H)V011 STO MV012 VIEW RV013 VIEW XV014 VIEW MV015 R/SV016 INPUT BV017 INPUT CV018 INPUT DV019 EQN C+(GxD)+(0.5xRxD^2)V020 STO YV021 EQN C+(GxX)+(0.5xRxX^2)V022 STO ZV023 EQN ((GxL)-(Dx(G-H)))÷LV024 STO SV025 EQN (4xMxD^2)÷L^2V026 STO OV027 EQN B+XV028 STO IV029 VIEW YV030 VIEW SV031 VIEW ZV032 VIEW IV033 VIEW OV034 R/SV035 INPUT PV036 INPUT QV037 EQN P-(0.5xL)V038 STO BV039 EQN Q+(0.5xLxG)x(-1)V040 STO CV041 EQN P+(0.5xL)V042 STO EV043 EQN Q+(0.5xLxH)x(-1)V044 STO KV045 VIEW BV046 VIEW CV047 VIEW EV048 VIEW KV049 R/SV050 INPUT EV051 INPUT KV052 EQN E-(0.5xL)V053 STO PV054 EQN K+(0.5xLxH)x(-1)V055 STO Q 42
V056 EQN E-LV057 STO BV058 EQN Q+(0.5xLxG)x(-1)V059 STO CV060 VIEW PV061 VIEW QV062 VIEW BV063 VIEW CV064 R/SV065 GTO VV066 RTN 43
RIGHT TRIANGLE 44
RIGHT TRIANGLE FUNCTION: SIN COS TAN Y C A Z B SYMBOLS: A = SIDE B = SIDE C = SIDE Z = ANGLE Y = ANGLE T = AREAP001 XEQ PP002 LBL PP003 INPUT AP004 INPUT ZP005 RCL ZP006 →HRP007 STO LP008 EQN A ÷ sin(L)P009 STO CP010 EQN A ÷ tan(L)P011 STO BP012 EQN 90 -LP013 STO YP014 EQN 0.5 x B x AP015 STO TP016 VIEW BP017 VIEW CP018 VIEW YP019 VIEW TP020 R/SP021 INPUT BP022 EQN B x tan(L)P023 STO A EQN B ÷ cos(L) 45
P024 STO CP025 VIEW AP026 VIEW CP027 VIEW YP028 R/SP029 INPUT CP030 EQN C x sin(L)P031 STO AP032 EQN C x cos(L)P033 STO BP034 VIEW AP035 VIEW BP036 VIEW YP037 R/S STOPP038 GTOPP039 RTN 46
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