1. Using the HP35s For Land Surveying Computations by Jon B. Purnell, PLS ©2010 Alidade Consulting

2. Synopsis StrategiesStrategies Capabilities and LimitationsCapabilities and Limitations Operating EssentialsOperating Essentials Statistics FunctionsStatistics Functions Traverse and InverseTraverse and Inverse Memory and VariablesMemory and Variables Equation SolverEquation Solver

3. Capabilities and Limitations User programmableUser programmable –30K of memory for programs, variables and user equations 800+ storage registers800+ storage registers –For variables/data Integrated equation Solver utilityIntegrated equation Solver utility RPN or Algebraic entry modesRPN or Algebraic entry modes

4. Capabilities and Limitations 3 rd Party surveying applications are available3 rd Party surveying applications are available –http://www.softwareby dzign.com/ http://www.softwareby dzign.com/http://www.softwareby dzign.com/ Legal for LSIT examLegal for LSIT exam –http://www.ncees.org/ exams/calculators/ http://www.ncees.org/ exams/calculators/http://www.ncees.org/ exams/calculators/

5. Capabilities and Limitations No Polar-Rectangular conversion functionsNo Polar-Rectangular conversion functions HMS conversion functions cannot be used with Complex Math “conversion” functionsHMS conversion functions cannot be used with Complex Math “conversion” functions

6. Capabilities and Limitations Only 27 storage registers are directly accessible to the UserOnly 27 storage registers are directly accessible to the User A handful of Stats registers are reservedA handful of Stats registers are reserved Remainder are easily accessible only to running programsRemainder are easily accessible only to running programs

7. The Keyboard 0.00000000 GOLD  Press to power [ON] or to clear an entry Press [GOLD  ] [ON] to turn unit OFF Press [BLUE  ] + [key] to access Blue functions [GOLD  ] Gold Press [GOLD  ] + [key] to access Gold functions Press [key] alone to access“unshifted” functions Press key when prompted for “Alpha” input

8. The Keyboard Press to select operating modes: DEGrees, RADians, GRaDs, or ALGebraic and Reverse Polish Notation GOLD  ] Press [GOLD  ] + key to select DISPLAY formats: FIXed, ENGineering notation, SCIentific notation, or ALL (automatic formatting) Cursor pad—click up, down, left or right to choose menu options, or scroll amongst options 0.00000000

9. Setting and Changing Display Formats 0.00000000 GOLD  ] Press [GOLD  ] + [<] key to open DISPLAY menu Use Cursor Pad to select display mode, or press [1] for FIXed, [2] for SCIentific, [3] for ENGineering, or [4] for ALL EXAMPLE: to set display to show 4 FIXed decimal places: GOLD  ] 1.Press [GOLD  ] +[DISPLAY], then [1], then [4] EXAMPLE: to set display to show 4 FIXed decimal places: GOLD  ] 1.Press [GOLD  ] +[DISPLAY], then [1], then [4] 1 F I X2 S C I 3 E N G4 A L L FIX 4 0.0000 Options appear on menu. Underlined option = current selection

10. Setting and Changing Angular Mode Format 0.0000 Press to open MODES menu EXAMPLE: to set unit to work in DEGrees: 1.Press [MODES], then [1] EXAMPLE: to set unit to work in DEGrees: 1.Press [MODES], then [1] 1 D E G 2 RAD 3 GRD 4 ALG 5 RPN Options appear on menu. Underlined option = current selection 0.0000 Use Cursor Pad to select mode, or press [1] for DEGrees, [2] for RADians, [3] for GRaDS, or choose [4] or [5] to select between ALGebraic and Reverse Polish Notation modes

11. The Display Two lines of data Mode icons: ALGebraic, RPN and EQuatioN entry modes, GRADs and RADians angular modes Current numeric system: HEXidecimal, OCTal or BINary. Blank = Decimal HYPerbolic mode is active [Gold  ] Icons: [Gold  ] and [Blue  ] keys Program “Flag” indicators “Alpha” keys active Programming mode active ERROR! Low battery System Busy Scrolling mode is active

12. RPN: Reverse Polish Notation = Math without Parentheses Evaluate 20 / 2+3Evaluate 20 / 2+3 RPN:RPN: –20 [ENTER] 2 [ENTER] 3 [+] [/] (Result is 4) Algebraic:Algebraic: –20 [/] [(] [2] [+] [3] [)] [=] (Result is 4)

13. Order of operations and your calculator Not all of these expressions yield the same answer! Be careful how you write and enter the expression! Not all of these expressions yield the same answer! Be careful how you write and enter the expression! =4=4 =4=4 =4=4 =13=13 =13=13

14. Algebraic Mode Set up your calculator to operate in the ALG (Algebraic) mode 1. Press the [MODE] key 2. Press [4] “ALG” should appear here

15. Back to our problem… Evaluate the expression 20 / 2+3 1. Key in “20” 2. Press the [division] key 3. Key in “2” and press the [addition] 4. Key in “3” and press [ENTER] Did the calculator evaluate the expression using the rules of the order of operations? 20 20  20  2 + 20  2 + 3 13.0000

16. 20 Let’s try it again… Evaluate the expression 20 / (2+3) 1. Key in “20” 2. Press the [division] key 3. Press the [( )]key 4. Key in “2+3” Did the calculator evaluate the expression using the rules of the order of operations? Are the results the same as before? What’s different? Did the calculator evaluate the expression using the rules of the order of operations? Are the results the same as before? What’s different? 5. Press press [ENTER] 8 keystrokes! 20  20  ( ) 20  (2 +3) 20  ( 2 + 3 ) 4.0000

17. RPN: Math without parentheses Set up your calculator to operate in the RPN (Reverse Polish Notation) mode 1. Press [MODE] 2. Press [5] “RPN” should appear here

18. Using RPN Evaluate the expression 20 / (2+3) using RPN 1. Key in “20” 2. Press the [ENTER] key 3. Key in “2” and press [ENTER] 4. Key in “3” and press the [addition] key Did the calculator evaluate the expression using the rules of the order of operations? 5. Press the [division] key 8 keystrokes! 0.0000 20 20.00002.0000 2.0000 3 20.0000 5 0.0000 4.0000

19. The Stack Four “registers” (X,Y,Z and T) for temporary storage of values and intermediate resultsFour “registers” (X,Y,Z and T) for temporary storage of values and intermediate results X and Y registers visible on the displayX and Y registers visible on the display Z and T registers, not visibleZ and T registers, not visible Operations performed on values in X and Y registersOperations performed on values in X and Y registers 0.0000 0.0000 X register T register Z register Y register

20. 20 / (3+2) on the Stack Key in “20”Key in “20” Press [ENTER]Press [ENTER] Key in “3”, Press [ENTER]Key in “3”, Press [ENTER] Key in “2”Key in “2” Press [+]Press [+] Press [  ]Press [  ] 0.0000 0.0000 0.0000 0.0000 0.0000 20 0.0000 0.0000 20.0000 20.0000 0.0000 20.0000 3.0000 3.0000 0.0000 20.0000 3.0000 2 0.0000 0.0000 20.0000 5.0000 0.0000 0.0000 0.0000 4.0000 X register T register Z register Y register

21. Stack Functions “Roll Down” (values in stack drop down 1 register, value in X register goes to top (T register) “X-Y Exchange” (values in X and Y registers trade places) “Last X” (recalls last value stored in X register) Press [ENTER] to execute “Last X” (recalls last value stored in X register) Press [BLUE  ] [ENTER] to execute

22. Some Functions that Operate on Values in the X Register Key in a number, execute the functionKey in a number, execute the function “X Squared” [X 2 ] “Square root of X” [√X] “1 over X” [1/X] “Trig Functions” [SIN] [COS] [TAN] [ASIN] [ACOS] [ATAN]

23. Unit Conversions The HP35s ships with several built in unit conversionsThe HP35s ships with several built in unit conversions –Sexagesimal Units (Decimal Degrees and Degrees Minutes and Seconds) –Centigrade and Farenheit –Inches and Centimeters –Miles and Kilometers (US or International definition?)

24. Sexagesimal Units When finding the Sine, Cosine or Tangent of an angle, you must:When finding the Sine, Cosine or Tangent of an angle, you must: –Enter the value in degrees, minutes and seconds… –…then, convert the value to decimal degrees… –…then get the Sine, Cosine or Tangent

25. Finding a Sine, Cosine or Tangent Result is 20.1528 ° Convert the D.MS value to Decimal degrees: Press the [GOLD  ] key, then press [HMS  ] (think from HMS to Decimal) Key in the value in D.MS format: 20.0910 Press [COS] Find the Cosine of 20º09’10” 0.0000 20.0910 Result is 0.9388 (rounded!) 0.0000 20.1528 0.0000 0.9388

26. Sexagesimal Math When adding, subtracting, multiplying or dividing, (etc.) an angle, you must:When adding, subtracting, multiplying or dividing, (etc.) an angle, you must: –Enter the values in degrees, minutes and seconds… –…then, convert the values to decimal degrees… –…then perform the operation –…then convert the result to D.MS format

27. Sexagesimal Math Example 1 Key in the value “2.30”, press the [GOLD  ] key, then press [HMS  ] Key in the value 2, press the [  ] key Key in the value “5.2514”, press [ENTER] Convert result to D.MS format: Press [BLUE  ] key, then press [  HMS] Problem: Find the angle from a PC to a POC at 525.14 feet from the PC (degree of curvature = 2°30’) Solution: Angle = 5.2514 x (2°30’) /2 Problem: Find the angle from a PC to a POC at 525.14 feet from the PC (degree of curvature = 2°30’) Solution: Angle = 5.2514 x (2°30’) /2 5.2514 Result is 6.3351 which is 6 ° 33’51” 5.2515 2.5 5.2514 1.2500 Press the [ x ] key. Result is 6.5643 ° 0.0000 6.5643 0.0000 6.3351

28. Sexagesimal Math Example 2 0.0000 Problem: Find the Weighted Mean Azimuth of Line 1 and Line 2 Line 1 = 97 ° 05’21” – 656.89 feet Line 2 = 92 ° 56’05” -2607.00 feet Solution =

29. Sexagesimal Math Example Key in the value “656.89”…then press the [ x ] key Key in the value “92.5605”, press the [GOLD  ] key, then press [HMS  ], then press [ENTER] Key in the value “97.0521”, press the [GOLD  ] key, then press [HMS  ], then press [ENTER] 0.0000 97.0521 Key in the value “2607.00”…then press the [ x ] key ….next, press the [+] key Line 1 = 97 ° 05’21” – 656.89 feet Line 2 = 92 ° 56’05” -2607.00 feet Solution = 97.0892 97.0892 656.89 0.0000 63776.9027 63776.9027 92.9347 92.9347 2607.0000 63,776.9027 242280.8208 The result, 306,057.7235 is the numerator in the equation…. 0.0000 306,057.7235

30. Sexagesimal Math Example Press the [  ] key…the result 93.7708 ° is the weighted mean azimuth of the line in Decimal Degrees Key in the value “2607.00”…then press the [ + ] key…the result, 3263.8900 is the denominator in the equation…. Next, key in the value “656.89”,and press [ENTER] 656.8900 Convert result to D.MS format: Press [BLUE  ] key, then press [  HMS] Line 1 = 97 ° 05’21” – 656.89 feet Line 2 = 92 ° 56’05” -2607.00 feet Solution = 656.8900 2607.00 306,057.7235 3263.8900 0.0000 93.7708 0.0000 93.4615 The result is 93 ° 46’15”

31. Statistics functions Entering observationsEntering observations Getting nGetting n Getting the mean of the setGetting the mean of the set Standard deviation of a populationStandard deviation of a population Standard deviation of a sampleStandard deviation of a sample

32. Statistics Functions FunctionDescriptionKeystrokes  Enter observations into stats registers [   Delete observations from stats registers [GOLD  ] [   CLEAR Clear stats registers [BLUE  ] [CLEAR] [4] SUMS View SUMMATIONS Menu [BLUE  ] [SUMS] n Number of observations in data set Access via SUMS menu  x Sum of x values Access via SUMS menu  y Sum of y values Access via SUMS menu  x 2 Sum of squared x values Access via SUMS menu  y 2 Sum of squared y values Access via SUMS menu

33. Summary Statistics Functions FunctionDescriptionKeystrokes View MEANS Menu [GOLD  ] [ ] Mean of x values Access via MEANS menu Mean of y values Access via MEANS menu Weighted mean of x values Access via MEANS menu S,  S,  View Standard Deviation Menu [BLUE  ] [S,  Sx Sx Sample Standard Deviation of x values Access via SD menu  Sy Sample Standard Deviation of y values Access via SD menu  x Population Standard Deviation of x values Access via SD menu  y Population Standard Deviation of y values Access via SD menu

34. Statistics Example 1 0.0000 Problem: Find the Weighted Mean Azimuth of Line 1 and Line 2 Line 1 = 97 ° 05’21” – 656.89 feet Line 2 = 92 ° 56’05” -2607.00 feet Clear STATS Registers, press: [BLUE  ] [CLEAR] [4] Key in “656.89”, press [ENTER] 1 X2 VARS 3 ALL4 656.8900 Key in “97.0521”, press [GOLD  ] [HMS  ] 656.8900 97.0892 Press [  ] 656.8900 1.0000 Key in “2607.00”, press [ENTER] 2607.0000 Key in “92.5605”, press [GOLD  ][HMS  ] 2607.0000 92.9347 Press [  ] 2607.0000 2.0000 Press [GOLD  ] [+], and select 3 rd option…result is weighted mean azimuth in Decimal Degrees x y x W 93.7708 Press [ENTER], then [BLUE  ] [  HMS]…result is weighted mean azimuth in Deg.MinSec format 2607.0000 93.4615

35. 0.0000 Statistics Example 2 0.0000 20.0000 Clear STATS Registers, press: [BLUE  ] [CLEAR] [4] Key in each value from the table, press [  ] after each entry Problem: Find the 95% Standard Deviation of the following set of 20 observations: Press [BLUE  ], [S,  ] to view Sample Standard Deviation (or Sx) at the 1 Sigma level Sx Sy  x  y 1.9541 Press [ENTER] to copy the result to the X register. Key in “1.96” and press [multiply]. Result is Standard Deviation of set at 95% confidence level Press [ENTER] to copy the result to the X register. Key in “1.96” and press [multiply]. Result is Standard Deviation of set at 95% confidence level 0.0000 1.9541 1.9541 1.96 0.0000 3.8300

36. Vectors and vector addition (Traverse and Inverse) You can do these COGO computations with your hp35s (with the Equation Solver-no programming required)You can do these COGO computations with your hp35s (with the Equation Solver-no programming required) –Compute latitudes and departures, given the azimuth and length of a line –Compute azimuth and distance, given the coordinates of the end points of a line –Carry coordinates (traverse)

37. Using Equations for Problem Solving Equations are sets of instructions that the HP35 can use to perform computationsEquations are sets of instructions that the HP35 can use to perform computations Equations can use values stored in variables A though Z for their computations, or they can prompt you to supply values for the variablesEquations can use values stored in variables A though Z for their computations, or they can prompt you to supply values for the variables

38. Using Equations for Problem Solving Equations can be used to solve repetitive problemsEquations can be used to solve repetitive problems Equations can be used to solve for any unknown in the equationEquations can be used to solve for any unknown in the equation Equations can be stored for future use, or input on-the flyEquations can be stored for future use, or input on-the fly Not all functions are available, see pg. 6-16 of the Users GuideNot all functions are available, see pg. 6-16 of the Users Guide

39. Using Equations for Problem Solving Northing = Northing+(Dist x cos(Azm))Northing = Northing+(Dist x cos(Azm)) –Variable assignments: –N = Northing –D = Distance –G = Azimuth N = N + (D x cos (HMS  (G)))N = N + (D x cos (HMS  (G)))

40. Using Equations for Problem Solving Easting = Easting+(Dist x sin(Azm))Easting = Easting+(Dist x sin(Azm)) –Variable assignments: –E = Easting –D = Distance –G = Azimuth E = E + (D x sin (HMS  (G)))E = E + (D x sin (HMS  (G)))

41. Store an equation for computing Northings N = N +(D x cos (HMS  (G))) Store an equation for computing Northings N = N +(D x cos (HMS  (G))) 1. Press [EQN] 0.0000 2. Press [RCL] then [N] 6. Press [Multiply] EQN LIST TOP EQN LIST TOP N= 3. Press [GOLD  ] then [=] 5. Press [( )] then [RCL][D] 7. Press [COS] 4. Press [RCL] [N] then [+] EQN LIST TOP N=N+ EQN LIST TOP N=N+(D) EQN LIST TOP N=N+(D x) EQN LIST TOP N=N+(D x COS( )) EQN LIST TOP N=N+(DxCOS(HMS  (G))) 8. Press [GOLD  ] then [HMS  ] then [G]

42. Using a Stored Equation Use Stored Equation for finding Northing of a new point Northing 1 = 1000.0000 Distance 1-2 = 85.31 feet Azimuth 1-2 = 10 ° 38’24” Press [EQN] 0.0000 Scroll up or down if necessary to select desired equation, and press [ENTER] EQN LIST TOP N=N+(DxCOS(HMS  (G)) N? 1000.00 At the prompt “N?” key in the starting Northing, or 1000.0000, and press [R/S] At the prompt, “G” ken in the Azimuth from point1 to point2 in D.MS format or 10.3824 and press [R/S] At the prompt, “D?” key in Distance from point1 to point2, or 85.31 and press [R/S] D? 85.31 G? 10.3824 N= 1083.8432 New Northing, N is displayed

43. Selected Equation Mode Operations FunctionDescriptionKeystrokes EQN Enter and leave Equation mode [EQN] ENTER Evaluates displayed equation, stores result in variable on left of equals sign [ENTER  RUN/STOP Prompts for next variable in the equation [R/S] CLEAR Deletes displayed equation from memory [BLUE  ] [CLEAR] SOLVE Solves for a user-specified variable in an equation Select an Equation via [EQN], press [SOLVE] DELETE Deletes rightmost character in an equation [][][][] SCROLL UP / DOWN Scrolls up/down through list of stored equations Cursor pad  SCROLL TOP / BOTTOM Jumps to top/bottom of equation list [BLUE  ] + Cursor pad  SHOW View Checksum and length of equations [GOLD  ] [SHOW] Exit Exit Leaves Equation mode [C]

44. Horizontal Curve Equations Basic Coordinate Geometry NameEquationVariables Northing* N = N + (D x cos (HMS  (G))) N = Northing, D = Distance, G = Azimuth in D.MS Easting* E = E + (D x sin (HMS  (G))) E = Easting, D = Distance G = Azimuth in D.MS LatitudeN = D x cos (HMS  (G)) N = Delta N or Latitude, D = Distance G = Azimuth in D.MS Departure E = E = D x sin (HMS  (G)) E = Delta E or Departure, D = Distance G = Azimuth in D.MS Distance D = SQRT(SQ(N)+SQ(E)) D = Distance, N = Delta N or Latitude E = Delta E or Departure Bearing B = ATAN(E/N) B = Bearing of line with respect to N or S axis. Determine quadrant from sign of Latitude (N) and Departure (E) Test Data D = 630.40, G = 198 ° 30’24” N = -597.80, E = -200.10, B = 18º30’24” *Equation can also be used to find latitude and departures by setting initial Northing and Easting values to Zero at prompt.

45. Horizontal Curve Equations 100 Foot Arc Definition Horizontal Curve Equations NameEquationVariables Arc Length L = 2 x π x R x I ÷ 360 L = Arc Length, R = Raduis, I = Central Angle in Decimal degrees Semi- Tangent T = R x tan( I ÷ 2 ) T = Semi-tangent, R = Radius I = Central Angle in Decimal degrees Long Chord C = 2 x R x sin( I ÷ 2 ) C = Long Chord, R = Radius I = Central Angle in Decimal degrees External E = ( R ÷ cos(I ÷ 2 )) - R E = External distance, R = Radius I = Central Angle in Decimal degrees Middle Ordinate M = R – ( R x cos(I ÷ 2 )) M = Middle Ordinate, R = Radius I = Central Angle in Decimal degrees Degree of Cruvature D = 5729.578 ÷ R D = Degree of Curvature in Decimal degrees, R = Radius Test Data R = 818.51, I = 22 ° 50’28” L = 326.30, T = 165.35, C = 324.14, E = 16.53, M = 16.21, D = 7 °

46. Horizontal Curve Equations Triangles NameEquationVariables Area of Right triangle Q=1/2*B*H Q = Area, B = Base, H = Height Area of Oblique triangle Q=.5*A*B*sin(C) Q = Area, A = Side a, B = side b, C = Angle C in Decimal degrees CoslawT=acos((B^2+C^2-A^2)/(2*B*C)) T = Angle A in Decimal degrees, B = side b, C = side c, A = side a Hero’s Formula Q=SQRT(.5*(A+B+C)*(.5*(A +B+C)-A)*(.5*(A+B+C)- B)*(.5*(A+B+C)-C)) Q = Area, A = side a, B = side b, C = side c Pythagorean Theorem C = SQRT(A^2+B^2) A = side A, B = side B, C = side C Trapezoid Area Q=(A+B)*H/2 Q = Area, A = Base 1, B = Base 2, H + Height Test Data Right triangle: a = 60, b = 80, c = 100, A = 36 ° 52’12”, B = 53 ° 07’48” C = 90 ° Area = 2400 Trapezoid: Base 1 = 100, Base 2 = 80, Height = 95, Area = 8550

47. Sample equation documentation –Sample problem –Sketch –Variable definitions –Equation formatted for input –Explanation –Sample data –Solution

48. Memory Hp35s has 30K of memoryHp35s has 30K of memory You can storeYou can store –Numbers –Equations –Programs 27+ directly addressable27+ directly addressable –Registers A though Z, i, (plus STATS registers) –Additional storage is available via Indirect Addressing (available to running programs only) - Ask presenter to explain, or see Chapter 14 of the Users Guide

49. Storing an often used number Meters to US Survey Feet: 1 meter ≈ 3.2808333333 US Survey feet You can store this number in a storage register for later use Meters to US Survey Feet: 1 meter ≈ 3.2808333333 US Survey feet You can store this number in a storage register for later use Key in value you want to store… 3.28083333333, then press [BLUE  ] [STO] STO _ Next, choose a register in which to store the number (select a letter, from A to Z… We will store this value in register U): Press [U] to store the value in register U

50. Math with Stored numbers Using the stored Meters-to-US foot conversion, convert these metric coordinates to State Plane values: 119,521.155mN, 337,663.473mE Using the stored Meters-to-US foot conversion, convert these metric coordinates to State Plane values: 119,521.155mN, 337,663.473mE Key in 119521.155 0.0000 Press [RCL], then [U] Press [Multiply] Key in 337663.473 Press [RCL], then [U] Press [Multiply] 0.0000 119,521.155_RCL _ 119,521.1550 3.2808 0.0000 392,128.9894 392,128.9894 337,663.473_RCL _ 337,663.4730 3.2808 392,128.9894 1,107,817.5777

51. Thanks for your kind attention! Contact: Jon B. Purnell, PLSContact: Jon B. Purnell, PLS –jon.purnell@wavecable.com jon.purnell@wavecable.com 360-460-8565360-460-8565 Download this presentation atDownload this presentation at –www.lsaw-noly.org www.lsaw-noly.org