The document provides an overview of the capabilities and limitations of using the HP35s calculator for land surveying computations. It describes the calculator's memory, equation solving capabilities, and supported functions for operations like trigonometry, statistics, traverses, and unit conversions between different angular and distance units. Instructions are provided for basic functions like setting the display format and changing the angular mode, as well as examples of using the calculator for surveying calculations involving sexagesimal units and statistics.

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

7. The Keyboard 0.00000000 0.00000000 Press to power [ON] or to clear an entry Press [ GOLD  ] [ON] to turn unit OFF Press [BLUE  ] + [key] to access Blue functions 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 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 0.00000000

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 Icons: [Gold  ] and [Blue  ] keys Program “Flag” indicators “ Alpha” keys active Programming mode active ERROR! Low battery System Busy Scrolling mode is active

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! =4 =4 =4 =13 =13

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 [BLUE  ] [ENTER] to execute

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

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 5.2514 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 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 97.0892 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 Line 1 = 97 ° 05’21” – 656.89 feet Line 2 = 92 ° 56’05” -2607.00 feet Solution =

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 656.8900 Convert result to D.MS format: Press [BLUE  ] key, then press [  HMS] 656.8900 2607.00 306,057.7235 3263.8900 0.0000 93.7708 0.0000 93.4615 The result is 93 ° 46’15” Line 1 = 97 ° 05’21” – 656.89 feet Line 2 = 92 ° 56’05” -2607.00 feet Solution =

32. Statistics Functions Function Description Keystrokes  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 Function Description Keystrokes 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 ,  View Standard Deviation Menu [BLUE  ] [S ,  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 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 X 2 VARS 3 ALL 4  656.8900 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 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. Statistics Example 2 0.0000 0.0000 0.0000 20.0000 Clear STATS Registers, press: [BLUE  ] [CLEAR] [4] Key in each value from the table, press [  ] after each entry 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 0.0000 1.9541 1.9541 1.96 0.0000 3.8300 Problem: Find the 95% Standard Deviation of the following set of 20 observations:

41. Store an equation for computing Northings N = N +(D x cos (HMS  (G))) 1. Press [EQN] 0.0000 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 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 Function Description Keystrokes 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 Leaves Equation mode [C]

44. Horizontal Curve Equations Basic Coordinate Geometry Name Equation Variables 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 Latitude N = D x cos (HMS  (G)) N = Delta N or Latitude, D = Distance G = Azimuth in D.MS Departure 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 Name Equation Variables 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 Name Equation Variables 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 Coslaw T=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

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 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 Key in 119521.155 0.0000 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