HP 35s Surveying Programs

HP 35s Surveying Programs

CLOSURE with Accuracy, Area and double-missing distance Coordinate RADIATIONS with rotation and scale Coordinate JOINS Radiations from OFFSETS RESECTION ADJUSTMENT – Bowditch and Crandall Geospatial Science, RMIT University

HP35s SURVEYING PROGRAMS

1.

The following programs have been collated for the use of students in the Surveying and Geospatial Science programs in the School of Mathematical and Geospatial Sciences, RMIT University. As always, it is the user’s responsibility to ensure that the programs are installed correctly and then checked. Also, do not alter programs unless you are aware of what LABELS are being used or whether GTO and BRANCHING label addresses will be affected; because by doing so you may dramatically affect the way they work and hence obtain incorrect answers.

2.

The following two programs under LABEL Z are critical and must be kept in your HP35s at all times. Do not delete them!

• •

RECTANGULAR→POLAR POLAR→RECTANGULAR

XEQ Z002 XEQ Z015

These programs are software replacements for the Polar  Rectangular conversion functions that were present on the HP33s and HP32s calculators and have not been implemented on the HP35s.

3.

The following are a ‘suite’ of surveying computation programs that will be useful in the field and office. Some (Closure, Radiations, Joins, Offsets) have a heritage extending back to HP desktop-computer programs from the 1970’s written by Bodo Taube of Francis O’Halloran, Surveyors. And Bodo Taube’s programs were (and are) models of efficiency. Others are more recent.

Each program has a set of User Instructions, with examples and relevant formula and HP35s Program Sheets listing the program steps (that you may key into your calculator), storage registers used and program notes.

• • • • • •

CLOSURE RADIATIONS JOINS OFFSETS RESECTION ADJUSTMENT

XEQ C001 XEQ R001 XEQ J001 XEQ O001 XEQ S001 XEQ A001

Rod Deakin, 18-Jan-2012 Geospatial Science, RMIT University

HP35s POLARRECTANGULAR CONVERSIONS The following programming code is a software replacement for the POLARRECTANGULAR conversion functions that were present on the HP33s and HP32s calculators and have not been implemented on the HP35s.

T his c o de was m ade a v a il a b le t hr ou g h T h e Mus e u m of H P C a lc u l a tor s a n d a pp e ar e d in HP F or um Ar c hi v e 1 7 ( 22- A u g- 20 0 7) ht tp :/ / www. h pm us e um .or g /c gi - s ys /c g i wr a p/ hp m us eum /ar c h v0 1 7.c g i ?r e a d = 12 2 51 9

RECTANGULARPOLAR

XEQ Z002

XEQ

3

0

0

2

POLARRECTANGULAR

XEQ Z015

XEQ

3

0

1

5

LINE

STEP

KEYSTROKES

Z001

LBL Z

Z002

CF 10

Z003

ABS

Z004

CLx

Z005

LASTx

Z006

R

Z007

R

Z008

Eqn REGZ+i*REGT



R

Z011

R

Z012

Eqn ARG(REGT)

Z013

Eqn ABS(REGT)

Z014

RTN

Z015

CF 10

Z016

ABS

Z017

R

Z018

R

0

ENTER R R

EQN

+

3

R

i

ENTER

×

ENTER

ENTER R R EQN

i

R

EQN

+/-

R

XEQ

 +/R R

1

2

.

 

Z010

.

1

 

ENTER

2

+/-

R

Z009

3

XEQ

0

ENTER

ENTER

Z019

Eqn LASTx*COS(REGT)+i*LASTx*SIN(REGT)

+



ENTER

R

SIN

ENTER

Z021

R

Z022 Z023

R Eqn ABS(REGZ)*SIN(ARG(REGZ)) EQN +/i SIN Eqn ABS(REGT)*COS(ARG(REGT)) EQN +/-

ENTER

ENTER

ENTER

R R

R

R

×

ENTER ENTER ENTER

XEQ

RTN

What do these pieces of code do?

RECTANGULARPOLAR T Z Y X

East North

XEQ

XEQ Z002 3 0 0

2

T Z Y X

Bearing Distance

5

T Z Y X

East North

POLARRECTANGULAR T Z Y X

Bearing Distance

XEQ

XEQ Z015 3 1 0

The contents of registers Z and T remain unchanged for both conversions.

2



R

3 3



R

 

i

COS

Z025

×

R

COS

ENTER

Z020

Z024

i

 

×

×

ENTER

 

EQN

×

HP35s PROGRAM

CLOSURE PROGRAM

MISSING BEARING & DISTANCE OR DOUBLE MISSING DISTANCE (BEARING INTERSECTION) WITH AREA PRESS

Notes:

XEQ C001 TO RUN PROGRAM

1.

For missing bearing and distance, the missing line must be the last line in the closure.

2.

For double missing distance, the missing distances must be on the last two lines of the closure.

3.

Missing elements must be input as zero, i.e., if the bearing is unknown then enter 0 when requested and if the distance is unknown enter 0 when requested.

4.

Bearings of lines that are 0º 00' 00" must be entered as 360º 00' 00"

2

1 Bn1

∆N

MISSING BEARING & DISTANCE

∆E

n B1n

n-1 2

Bn1

1 Bn1 − Bnn−1 = ± (180 − γ ) B1n −1 − Bn1 = ± (180 − α )

180 − α

α Bn1

180 − γ

b

DOUBLE MISSING DISTANCE c

sin (180 − γ ) = sin γ

γ

sin (180 − α ) = sin α

n

c sin α ±a = sin γ

Bnn-1

a

n-1

AREA ALGORITHM

B1n-1

β

Bnn-1

k k   ∆ Area k = − 12  ∆N k ∑ ∆Ei − ∆Ek ∑ ∆N i    = i 1 =i 1

1

n Bn-1

HP35s PROGRAM

CLOSURE PROGRAM

EXAMPLES Closure with: (i) misclose bearing and distance; (ii) misclose east and north; (iii) misclose accuracy; and (iv) area

90° 00′ 287.86

207 .53 11 7 °3 0′ 20 4 .56 D

E

C

2 0.

2 2 ° 09 00 ′

F

B

292.75

20

A

0° 00′ 20

1.

Figure ABCDEF is section of road 20 m wide that is being excised from an allotment of land.

Check that the dimensions are correct and determine the area.

Starting with the line AB and going clockwise around the figure, enter the bearing and distance of each side, remembering that the bearing of the last side FA should be entered as 360º 00'.

Enter 0 for the last bearing and 0 for the last side (you don’t have to key anything in; just press R/S at the prompts) since the last side (the misclose) is unknown.

The calculator will display: B = 136.0924 (136º 09' 24") (the misclose bearing); Press R/S The calculator will display: D = 0.0021 (the misclose distance); Press R/S The calculator will display: 0.0014 (east misclose) 001 -0.0015 (north misclose); often shown as 002 Press R/S The calculator will display: R = 502,288.7039 (this is the misclose accuracy ratio 1:502289) Press R/S The calculator will display: A = -9,926.0706 (this is the area 9926 m2) (the negative sign is due to entering the figure clockwise) Press R/S The calculator will display: B? 0.0000 Ready for the next closure.

2

HP35s PROGRAM

CLOSURE PROGRAM

EXAMPLES Closure with: (i) double missing and distance; and (ii) area

90° 00′ 287.86

E

207 .53 11 7 °3 0′ D

C

00 ′

F

B

292.75

22°

0° 00′ 20

A

20

2.

Figure ABCDEF is section of road 20 m wide that is being excised from an allotment of land.

Compute the missing distances CD and DE, and the area.

Starting with the line EF and going clockwise around the figure, enter the bearing and distance of each ‘known’ side, remembering that the bearing of the side FA should be entered as 360º 00'.

Enter the bearing of the side CD and 0 for the distance (the 1st missing distance; you don’t have to key anything in; just press R/S at the prompt).

Enter the bearing of the side ED. The calculator will now solve for the two missing distances CD and DE. The calculator will display: D = 20.0907 (the 1st missing distance); Press R/S The calculator will display: D = 204.5581 (the 2nd missing distance); Press R/S The calculator will display: A = -9,926.6036 (this is the area 9926 m2) (the negative sign is due to entering the figure clockwise) Press R/S The calculator will display: B? 0.0000 Ready for the next closure.

NOTE:

For double missing distance closures, the missing sides must be the last two sides. To achieve this, some figures may need re-casting. In such cases, the areas of re-cast figures may not be correct. See the following example

3

HP35s PROGRAM

CLOSURE PROGRAM

EXAMPLES Closure with: (i) double missing and distance; and (ii) area

207 .53 11 7 °3 0′ 2 04 .56 D

287.86

E

C

00 ′

90° 00′

22°

F

B

20

0° 00′ 20

A

Figure ABCDEF is section of road 20 m wide that is being excised from an allotment of land.

Compute the missing distances AB and CD, and the area.

Re-cast the figure so that the last two sides contain the missing distances

shifted line BC

287.86 90° 00′

E

90° 00′

11 720 4.5 °3 6 0′ shifted line AB

C

00′

F

11 207 7° 3 0 .53 ′ B′

D

2 2°

A

0° 00′ 20

3.

Starting with the line DE and going clockwise around the re-cast figure, enter the bearing and distance of each ‘known’ side, remembering that the bearing of the side FA should be entered as 360º 00'.

Enter the bearing of the side B'C and 0 for the distance (the 1st missing distance; you don’t have to key anything in; just press R/S at the prompt).

Enter the bearing of the side CD. The calculator will now solve for the two missing distances B'C and CD. The calculator will display: D = 292.7520 (the 1st missing distance); Press R/S The calculator will display: D = 20.0916 (the 2nd missing distance); Press R/S The calculator will display: A = 18,126.6222 (this is complete rubbish since the lines in the re-cast figure cross)

4

HP35s PROGRAM

CLOSURE PROGRAM AREA ALGORITHM

The algorithm for computing the area of a polygon can be derived by considering Figure A1, where the area is the sum of the trapeziums bBCc, cCDd and dDEe less the triangles bBA and AEe. The area can be expressed as

B x2 y2

b

2 A = ( x2 − x1 ) + ( x3 − x1 )  ( y2 − y3 )  + ( x3 − x1 ) + ( x4 − x1 )  ( y3 − y4 )  + ( x4 − x1 ) + ( x5 − x1 )  ( y4 − y5 ) 

c A

(A1)

− ( x2 − x1 )( y2 − y1 )

C x3 y3

x1 y1

− ( x5 − x1 )( y1 − y5 )

Expanding (A1) then cancelling and rearranging terms gives

D x4 y4

d

2 A x1 ( y5 − y2 ) =

y

+ x2 ( y1 − y3 )

e

Ex y 5 5

+ x3 ( y2 − y4 ) + x 4 ( y 3 − y5 )

x

+ x5 ( y4 − y1 )

which can be expressed as 2 A =

Figure A1 n

∑{ x ( y k =1

k

k −1

− yk +1 )}

(A2)

In Figure A2, the coordinate origin is shifted to A ′ y= ′ 0 and the area, using (A2), is where x= 1 1 2 A = y2′ x3′ + y3′ x4′ − y3′ x2′ + y4′ x5′ − y4′ x3′ − y5′ x4′

B x' y' 2 2 y'

1

(A3)

Considering each side of the polygon to have components ∆xk , ∆yk for k = 1 to 5 , (A3) can be written as

A x'1 y'1

2 C x'3 y'3

x'

2 A = ∆y1 ( ∆x1 + ∆x2 )

3

+ ( ∆y1 + ∆y2 )( ∆x1 + ∆x2 + ∆x3 ) − ( ∆y1 + ∆y2 )( ∆x1 )

5

Dx' y' 4 4

+ ( ∆y1 + ∆y2 + ∆y3 )( ∆x1 + ∆x2 + ∆x3 + ∆x4 ) − ( ∆y1 + ∆y2 + ∆y3 )( ∆x1 + ∆x2 )

4

− ( ∆y1 + ∆y2 + ∆y3 + ∆y4 )( ∆x1 + ∆x2 + ∆x3 )

E x' y' 5 5

Figure A2

HP35s Closure Program Area Algorithm.docx

1

HP35s PROGRAM

CLOSURE PROGRAM

Expanding and gathering terms gives 2 A = ∆y1 ( 3∆x1 + 3∆x2 + 2 ∆x3 + ∆x4 ) − ∆y1 ( 3∆x1 + 2 ∆x2 + ∆x3 ) +∆y2 ( 2 ∆x1 + 2 ∆x2 + 2 ∆x3 + ∆x4 ) − ∆y2 ( 3∆x1 + 2 ∆x2 + ∆x3 ) +∆y3 ( ∆x1 + ∆x2 + ∆x3 + ∆x4 )

− ∆y3 ( 2 ∆x1 + 2 ∆x2 + ∆x3 ) − ∆y4 ( ∆x1 + ∆x2 + ∆x3 )

and cancelling terms and re-ordering gives 2 A = ∆y1 ( 0 + ∆x2 + ∆x3 + ∆x4 ) +∆y2 ( −∆x1 + 0 + ∆x3 + ∆x4 )

(A4)

+∆y3 ( −∆x1 − ∆x2 + 0 + ∆x4 ) +∆y4 ( −∆x1 − ∆x2 − ∆x3 + 0 )

This equation for the area can also be expressed as a matrix equation 2A = [ ∆y1

∆y2

∆y3

∆y4 ]  0 1 1  −1 0 1  −1 −1 0   −1 −1 −1

1  ∆x1  1  ∆x2    1  ∆x3    0  ∆x4 

(A5)

By studying the form of equations (A4) and (A5), the following algorithm for calculating the k= n − 1 area components Ak for a polygon of n sides may be deduced as   ∆x 

k k 1 k i k 2 =i 1 =i 1

Ak=

∑ ∆y

− ∆y



where k ∑ ∆x  = i

1, 2, 3,  n − 1

(A6)

Equation (A6) is an efficient way to accumulate the area of a polygon given the coordinate components of the sides. By studying the algorithm, it can be seen that A= A= 0 and hence the area of a polygon is 1 n accumulated without having to deal with the last side. This makes it a very useful area algorithm for simple closure programs where the last side is often the missing side in the polygon. In addition, it can be seen that each area component Ak is a triangle with one vertex at the starting point and the line k, with components ∆xk , ∆yk , the opposite side.

Rearranging equation (A6) and expressing the components of lines as ∆E and ∆N where E and N are east and north respectively gives the area algorithm used in the HP35s Closure Program k k   where k 1, 2, 3,  n − 1 Ak = − 12  ∆N k ∑ ∆Ei − ∆Ek ∑ ∆N i  = = i 1 =i 1  

HP35s Closure Program Area Algorithm.docx

2

(A7)

HP35s PROGRAM SHEET LI N E

C001 C002 C003 C004 C005 C006 C007 C008 C009 C010 C011 C012 C013 C014 C015 C016 C017 C018 C019 C020 C021 C022 C023 C024 C025 C026 C027 C028 C029 C030 C031 C032 C033 C034 C035 C036 C037 C038 C039 C040 C041

ST E P

LBL C CLVARS CLΣ 0 STO B STO D INPUT B HMS STO B STO C INPUT D STO+R RCL B + x=0?

GTO C068 RCL D x=0?

GTO C042 XEQ C022 GTO C004 RCL B RCL D XEQ Z015 Σ+ R LASTx Σy × x<>y Σx × − 2

÷ STO+A RTN Σy Σx XEQ Z002 RTN

CLOSURE PROGRAM X

Y

Z

T

START NEW CLOSURE NEW LINE OF CLOSURE

Enter Bearing

Enter Distance accumulate distances Brg Dist Brg+Dist test to see if both Brg & Dist are zero go for missing bearing & distance test to see if Dist is zero go for double missing distance compute area contribution for line go for next line of closure AREA SUBROUTINE Brg Dist Brg ∆N ∆E n ∆E ∆E ∆N ∆E Σ(∆E) ∆N ∆E ∆N(Σ(∆E)) ∆E ∆E ∆N(Σ(∆E)) Σ(∆N) ∆E ∆N(Σ(∆E)) ∆E(Σ(∆N)) ∆N(Σ(∆E)) ∆N(Σ(∆E))−∆E(Σ(∆N)) area component accumulate area Σ(∆E) Σ(∆N) Dist

BRG & DIST SUBROUTINE Σ(∆E) Brg

SHEET 1 0F 3 SHEETS

HP35s PROGRAM SHEET LI N E

C042 C043 C044 C045 C046 C047 C048 C049 C050 C051 C052 C053 C054 C055 C056 C057 C058 C059 C060 C061 C062 C063 C064 C065 C066 C067 C068 C069 C070 C071 C072 C073 C074 C075 C076 C077 C078 C079 C080 C081 C082

CLOSURE PROGRAM

ST E P

0 STO B INPUT B HMS STO B RCL C − SIN XEQ C038 x<>y RCL B − SIN × x<>y

X

Z

T

Enter 2nd Bearing Bn1 Bn1 Bn1

Bnn−1

± (180 − γ ) ± sin γ c n −1 1

B

B1n −1

± sin γ

c

± sin γ n −1 1

1 n

± sin γ

B

B

c

± (180 − α )

c

± sin γ

± sin α ±c sin α ± sin γ

÷

±a

STO D RCL C STO B XEQ C022 VIEW D XEQ C038 STO D VIEW D VIEW A GTO C002 XEQ C038 STO D

±a Bnn−1

STO ÷ R x<>y 180 + HMS STO B VIEW B VIEW D Σy +/Σx +/STOP

Y

DOUBLE MISSING DISTANCE

c ± sin γ

± sin γ

±c sin α

(1st missing distance) ±a

compute area contribution for line 1st Missing Distance

2nd Missing Distance Area Dist

Brg

MISSING BRG & DIST

Brg Missing Bearing Missing Distance Σ(∆E) -Σ(∆E) Σ(∆N) -Σ(∆E) -Σ(∆N) -Σ(∆E) N miscl.

E miscl.

SHEET 2 0F 3 SHEETS

HP35s PROGRAM SHEET

LI N E

C083 C084 C085

ST E P

VIEW R VIEW A GTO C002

CLOSURE PROGRAM

X

Y

Z

T

Misclose Accuracy 1:x Area

STORAGE REGISTERS A B C D R

Area Bearing Bearing Distance Cumulative distance; closure accuracy

PROGRAM LENGTH AND CHECKSUM LN = 261; CK = D83C



 Length & Checksum:

2

;

ENTER

(Hold)

PROGRAM NOTES Lines C022 to C037

Lines C038 to C041

Lines C042 to C067 Lines C067 to C085

is an area subroutine that also accumulates the east and north components of lines is a subroutine to calculate a bearing and distance from east and north components of a line is the double missing distance part of the closure program is the missing line part of the closure program.

The calculator must contain LBL Z which contains the Polar to Rectangular routines

SHEET 3 0F 3 SHEETS

HP35s PROGRAM

RADIATIONS PROGRAM USER INSTRUCTIONS COORDINATE RADIATIONS PROGRAM

1.

To start program press XEQ R001

2.

Display

E? 0.0000

Enter:

East coordinate of traverse point; then press R/S

3.

Display

N? 0.0000

Enter:

North coordinate of traverse point; then press R/S

4.

Display

R? 0.0000

Enter: Rotation (±D.MMSS); then press R/S [If no rotation to be applied, press R/S and rotation = 0º]

5.

Display

S? 1.0000

Enter: Scale Factor; then press R/S [If no scale factor to be applied, press R/S and scale factor = 1]

6.

Display

B? 0.0000

7.

Display

D? 0.0000

7A

If Rotation and Scale not 0º and 1; new bearing and distance displayed at successive R/S

8.

East and North coordinate displayed at successive R/S. GoTo step 6.

Enter:

Radiation Bearing (D.MMSS); then press R/S

Enter: Radiation Distance; then press R/S [If next Instrument Point, enter distance with a negative sign.]

In the example traverse below, with rotation = 0º and scale = 1, start at A, compute the coordinates of A1 and A2; jump to B, compute coordinates of B1 and B2; then to C and the coordinates of C1, C2 and C3. The values in parentheses are for rotation = +2º 18' 35" and scale factor = 1.002515.

(Distances and coordinates are rounded to nearest mm.)

)

Scale Factor: 1.002515

E ( 539.637 553.400 N )

(

29 0 ° 13 ′ 4 4 .6 20 ′ 26 0° 15 0 5 .0 40

A1 •

)

)

(

 A

500.000 E 500.000 N

′ 25 9° 35 0 35.0 5

(

548.038 E 481.995 N 547.392 E 480.024 N

′ 35″ 26 1° 53 35.138

(

) (

1

)

585.996 E 463.264 N 584.658 E 459.727 N

)

• C2

23′ 35″ (17425° .374 )

C3 •

° 05′ 35 ″ ( 9225.364 )

582.510 E 488.332 N C 89° 47′  25.300

E ( 582.179 484.979 N )

)

E ( 564.747 546.148 N )

17 2° 05′ 25.310

(

″ 40 2′ 1 ° 0 5 2 .3 1 5″ 79 ′1 3 1 10 ° 54 79.5

″

 B 562.677 E 548.598 N

)

″ ° 33′ 35 (26240.151 )

460.529 E 493.218 N 460.187 E 494.801 N

2

283° 48′ 26.07 0 28 6° 06′ 3 26.13 5″ 6

)

4.73

E ( 583.850 566.330 N )

161

( 2942° 31′ 35

A2 •

•

(

)

458.129 E 515.419 N

580.905 E 569.481 N

5″ 05′ 3 16 4° 5 0 63.6 00″ ° 47′ 45 63.4

(

B2

(

B1 •

537.359 E 554.816 N

458.681 E 517.137 N

43 ° 27 2 5′ .7 35 90 ″ 41 ° 27 07 ′ .7 20

+2° 18 ′ 35″

Rotation:

607.810 E 488.428 N • C1 E ( 607.526 484.052 N )

HP35s PROGRAM SHEET LI N E

R001 R002 R003 R004 R005 R006 R007 R008 R009 R010 R011 R012 R013 R014 R015 R016 R017 R018 R019 R020 R021 R022 R023 R024 R025 R026 R027 R028 R029 R030 R031 R032 R033 R034 R035 R036 R037 R038 R039 R040 R041 R042 R043

ST E P

LBL R CLVARS CLΣ INPUT E INPUT N CF 2 INPUT R HMS STO R x=0?

999 STO T 1 STO S INPUT S STO×T RCL T 999 x=y?

SF 2 RCL E RCL N Σ+ CF 1 0 STO B STO D INPUT B INPUT D x<0?

SF 1 ABS STO D FS? 2 GTO R046 RCL B HMS RCL R + HMS STO B RCL S STO×D

RADIATIONS PROGRAM X

Y

Z

T

START RADIATION PROGRAM Enter Enter Clear Enter

East coordinate of Instrument Pt. North coordinate Flag 2 ± Rotation (D.MMSS)

±Rotation

Enter Scale factor rot×scale 999

rot×scale

Yes! Set Flag 2, no rotation or scale E COORDS OF I.P. N E n E RADIATION TO NEW POINT

Enter Bearing (D.MMSS) Enter Distance Test for negative distance ±Dist Yes!, Set Flag 1, radiation to new I.P. |Dist| Test for rotation and scale No rotation or scale Bearing Rotation Bearing Rotated Bearing

Scale

SHEET 1 0F 3 SHEETS

HP35s PROGRAM SHEET LI N E

R044 RO45 R046 R047 R048 R049 R050 R051 R052 R053 R054 R055 R056 R057 R058 R059 R060 R061

ST E P

VIEW B VIEW D RCL B HMS RCL D XEQ Z015 STO+N FS? 1 Σ+ x<>y STO+E VIEW E VIEW N Σx STO N Σy STO E GTO R024

RADIATIONS PROGRAM X

Y

Z

T

Rotated Bearing (D.MMSS) Scaled Distance Brg Dist Brg ∆N ∆E ∆N ∆E Test for new Instrument Point n Yes! new I.P. ∆E n ∆E East North North coord of Instrument Point East coord of Instrument Point

STORAGE REGISTERS B D E N R S T

Σx Σy

Bearing(D.MMSS); Bearing(Degree); Rotated Brg Distance; Scaled Distance East coordinate North coordinate Rotation (D.MMSS); Rotation (Degrees) Scale factor T=999 if Rotation = 0 degrees and Scale Factor = 1 T≠999 if any other Rotation and Scale Factor North coordinate of Instrument Point East coordinate of Instrument Point

PROGRAM LENGTH AND CHECKSUM LN = 191; CK = 22C1



 Length & Checksum:

2

;

ENTER

(Hold)

SHEET 2 0F 3 SHEETS

HP35s PROGRAM SHEET

RADIATIONS PROGRAM

PROGRAM NOTES Flag 1 is used to test to see if new point is to be next Instrument Point.

Flag 2 is used to test to see if Rotation and Scale Factor is to be applied.

Lines R001 to R023

Initialisation; storing coordinates of Instrument Point; storing Rotation and Scale.

If Rotation = 0 degrees and Scale Factor = 1 then register T = 999. Any other value in T means that a Rotation and Scale Factor is assumed.

Lines R024 to R033

Radiation Bearing and Distance to new point entered. If the distance is negative; Flag 1 is set and the new point will be the next Instrument Point.

Lines R036 to R045

Rotated Bearing and Scaled Distance to new point displayed.

Lines R046 to R060

Coordinates of new point computed.

Flag 1 is set then the new point becomes the next Instrument Point.

If

The calculator must contain LBL Z which contains the Polar to Rectangular routines XEQ Z015 on line R049 is the Polarâ&#x2020;&#x2019;Rectangular conversion

SHEET 3 OF 3 SHEETS

HP35s PROGRAM

JOINS PROGRAM USER INSTRUCTIONS COORDINATE JOINS PROGRAM

1.

To start program press XEQ J001

2.

Display

E? 0.0000

Enter:

East coordinate of Instrument Point; then press R/S

3.

Display

N? 0.0000

Enter:

North coordinate of Instrument Point; then press R/S

4.

Display

E? 0.0000

Enter:

East coordinate of next point; then press R/S

5.

Display

N? 0.0000

6.

Bearing (D.MMSS) and Distance displayed at successive R/S. GoTo step 4.

Enter: North coordinate of next point; then press R/S [If next Instrument Point, enter Northing with negative sign.]

In the example traverse below, start at A, compute the radiations (bearings and distances) to A1 and A2; jump to B, compute radiations to B1 and B2; then to C and the radiations to C1, C2 and C3.

(The computed bearings and distances are rounded to the nearest 5 mm and 10" respectively.)

B2

283° 4 8′ 26.07 0

A2 • 290 ° 13 ′ 44.6 20 ′ 260 ° 15 40.050

 B 562.677 E 548.598 N

0″ 47′ 0 161° 45 63.4

0″ ′4 2 °1 0 5 2 .3 1 79

458.129 E 515.419 N

A1 •

B1 •

41 ° 27 07′ .72 0

537.359 E 554.816 N

 500.000 E A 500.000 N

C3 • 548.038 E 481.995 N

′ 259° 35 35.0 50

582.510 E 488.332 N C 89° 47′  25.300 172° 05′ 25.310

460.529 E 493.218 N

•

585.996 E 463.264 N

1

580.905 E 569.481 N

• C2

607.810 E 488.428 N • C1

HP35s PROGRAM SHEET LI N E

J001 J002 J003 J004 J005 J006 J007 J008 J009 J010 J011 J012 J013 J014 J015 J016 J017 J018 J019 J020 J021 J022 J023 J024 J025 J026 J027 J028 J029 J030 J031 J032 J033 J034 J035 J036

ST E P

LBL J CLVARS INPUT E INPUT N RCL E STO Y RCL N STO X CF 1 0 STO E STO N INPUT E INPUT N x<0?

SF 1 ABS STO N RCL Y RCL E RCL X RCL N XEQ Z002 STO D x<>y 180 + HMS STO B VIEW B VIEW D FS? 1 GTO J005 GTO J009

JOINS PROGRAM X

Y

Z

T

START JOINS PROGRAM Enter East coord of Instrument Point.

Enter North coord of I.P. NEW INSTRUMENT POINT Ei Ni

Ei NEW POINT

Enter East coord of next point Enter ± North coord of next point Ek ±N k |N k | Ei Ek E i -E k Ni Nk Ni- Nk Dist Brg(k,i)

Ei E i -E k Ni E i -E k

E i -E k

Brg(k,i)

Brg(i,k)

Bearing Distance

SHEET 1 0F 2 SHEETS

HP35s PROGRAM SHEET

JOINS PROGRAM

STORAGE REGISTERS B D E N X Y

Bearing(D.MMSS) Distance E k East coordinate N k North coordinate N i North coordinate of Instrument Point E i East coordinate of Instrument Point

PROGRAM LENGTH AND CHECKSUM LN = 112; CK = A366



 Length & Checksum:

2

;

ENTER

(Hold)

PROGRAM NOTES Flag 1 is used to test to see if new point is to be next Instrument Point.

Lines J001 to J004

Initialisation; storing coordinates of Instrument Point.

Lines J005 to J008

Storing coordinates of Instrument Point in registers X and Y.

Lines J009 to J014

Entering coordinates of next point.

Lines J015 to J036

Computing Bearing and Distance from Instrument Point to new point. If Flag 1 is set then the new point becomes the next Instrument Point.

The calculator must contain LBL Z which contains the Polar to Rectangular routines XEQ Z002 on line J025 is the Rectangular→Polar conversion

SHEET 2 0F 2 SHEETS

HP35s PROGRAM

OFFSETS PROGRAM USER INSTRUCTIONS OFFSETS PROGRAM

1.

To start program press XEQ O001

2.

Display

B? 1.0000

Enter:

B1, the bearing of traverse line 1; then press R/S

3.

Display

B? 2.0000

Enter:

B2, the bearing of traverse line 2; then press R/S

4.

Display

D? 11.0000

Enter:

±d1, the offset from traverse line 1; then press R/S

5.

Display

D? 22.0000

Enter:

±d2, the offset from traverse line 2; then press R/S

6.

Radiation Bearing (D.MMSS) B3 and Distance d3 displayed at successive R/S. GoTo step 2.

Rule:

 positive   right   if point is to the   of the traverse line looking in the negative   left 

Offset distances are 

direction of the bearing.

Derivation of formula: Radiation from offsets d1 tan (90 − θ) =

d1

tan α =

tan θ

d1 d + 2 tan θ sin θ d1 sin θ = d1 cosθ + d 2

d2 sin θ



θ α

θ

d3

B1 d1

=

d2 B2

Conventions:

θ= B2 − B1  + tve   right  if point is   of line tve   left  −  B= B1 + α 3

d is 

Formula:

tan α =

sin θ cosθ −

d1

d2 d1

1

sin θ cosθ +

d2 d1

HP35s PROGRAM SHEET LI N E

O001 O002 O003 O004 O005 O006 O007 O008 O009 O010 O011 O012 O013 O014 O015 O016 O017 O018 O019 O020 O021 O022 O023 O024 O025 O026 O027 O028 O029 O030 O031 O032 O033 O034 O035 O036 O037 O038 O039 O040 O041 O042

ST E P

LBL 0 1 STO B INPUT HMS STO A 2 STO B INPUT HMS RCL A 360 x<>y x<0? + STO T 11 STO D INPUT STO C 22 STO D INPUT RCL T SIN RCL T COS RCL D RCL C ÷ ÷ ATAN STO+A SIN STO÷C RCL C 0 x>y?

180 STO+A

B

B

OFFSETS PROGRAM X

Y

Z

T

1 Enter Bearing of 1st line (B 1 ) B1

2 Enter Bearing of 2nd line (B 2 ) B2 B1 B2 ±θ=B 2 -B 1 360 ±θ 360 ±θ θ

D

D

11 Enter Offset ±d 1 from 1st line ±d 1 22 Enter Offset ±d 2 from 2nd line θ sin(θ) ±d 2 sin(θ) ±d 2 θ cos(θ) sin(θ) ±d 2 ±d 2 cos(θ) sin(θ) ±d 1 ±d 2 cos(θ) ±d 2 /d 1 cos(θ) sin(θ) cosθ-(d2/d1) sin(θ) sin(θ) tan(α) ±α B3 sin(α) ±d 3 0

±d 2 sin(θ) sin(θ) sin(θ)

±d 3

SHEET 1 OF 2 SHEETS

HP35s PROGRAM SHEET LI N E

O043 O044 O045 O046 O047 O048 O049 O050 O051 O052 O053 O054 O055

ST E P

RCL A 360 x<y?

STO-A RCL A HMS STO B VIEW B RCL C ABS STO D VIEW D GTO O002

OFFSETS PROGRAM X

Y

B3 360

Z

T

B3

B3

Radiation Bearing B 3 ±d 3

Radiation Distance d 3

STORAGE REGISTERS A B C D T

B1; B3 B 2 (D.MMSS); B 3 (D.MMSS) ±d 1 ; ±d 3 ±d 2 ; d 3 θ

PROGRAM LENGTH AND CHECKSUM LN = 181; CK = A802



 Length & Checksum:

2

;

ENTER

(Hold)

SHEET 2 0F 2 SHEETS

HP35s PROGRAM

RESECTION PROGRAM USER INSTRUCTIONS RESECTION PROGRAM (Auxiliary angles method)

1.

To start program press XEQ S001

2.

Display

E? 1.0000

Enter:

East coordinate of Point 1 (P1); then press R/S

3.

Display

N? 1.0000

Enter:

North coordinate of P1; then press R/S

4.

Display

E? 2.0000

Enter:

East coordinate of P2; then press R/S

5.

Display

N? 2.0000

Enter:

North coordinate of P2; then press R/S

6.

Display

E? 3.0000

Enter:

East coordinate of P3; then press R/S

7.

Display

N? 3.0000

Enter:

North coordinate of P3; then press R/S

8.

Display

A? 0.0000

Enter:

Angle α (D.MMSS) at Resection Point P; then press R/S

9.

Display

B? 0.0000

Enter:

Angle β (D.MMSS) at Resection Point P; then press R/S

10.

East and North coordinate of Resection Point displayed at successive R/S. GoTo step 2.

Notes: (1) Coordinates of points P1, P2, P3 must be entered left to right (clockwise direction) as seen from the Resection Point P. (2) Observed angles α and β are angles P1-P-P2 and P2-P-P3 respectively.

EXAMPLE 1100.000 E 2000.000 N

1 

1368.962 E 1943.585 N 3

1207.028 E 1882.466 N  2

α = 20° 00′ 37″ 

P

1

β = 43° 35′ 43″ 1220.471 E ( 1751.653 N)

HP35s PROGRAM

RESECTION PROGRAM RESECTION − AUXILIARY ANGLES

2 

2

γ

1



3 

ψ γ

α

ϕ

β

 P

β

α

ϕ

P



ψ

1 CASE 2

CASE 1 

3 

3

CASE 1

P is INSIDE triangle of fixed stations

CASE 2

P is OUTSIDE triangle of fixed stations; P and 2 are opposite sides of line 1−3

CASE 3

P is OUTSIDE triangle of fixed stations; P and 2 are same side of line 1−3

In each case there is a four-sided figure P123 with angles (α + β), ϕ, γ and ψ at the vertices. ϕ and ψ are unknown ‘auxiliary angles’ and ϕ + ψ = 360° − (α + β + γ). α and β are known (observed) and γ is the difference in bearings of lines 2−1 and 2−3.

ψ

1  ϕ

CASE 3

2 

γ

α

β  P

GIVEN:

1 (E1, N1), 2 (E2, N2), 3 (E3, N3)

OBSERVED:

α, β

COMPUTE:

P (EP, NP)

1.

Compute bearings and distances of lines 2−1 and 2−3

2.

Calculate angle γ as the difference between bearings B21 and B23. [BKJ means the bearing from K to J]

3.

ϕ + ψ= 360 − (α + β + γ = ) θ

4.

From sine rule:

(1)

d2P d 21 d 21 sin ϕ or d 2 P = = sin ϕ sin α sin α

(2)

d 23 d 23 sinψ d2P = = or d 2 P sinψ sin β sin β

(3)

HP35s Resection Program Auxiliary Angles.docx

1

HP35s PROGRAM

RESECTION PROGRAM

Equating (2) and (3) gives

sin ϕ d 23 sin α = = a sinψ d 21 sin β 5.

(4)

ϕ a sin (θ −= ϕ ) a ( sin θ cos ϕ − cos θ sin ϕ ) .

From (4) sin ϕ = a sinψ , but from (1) ψ= θ − ϕ ; hence sin= a sin θ and Dividing both sides by cos ϕ and re-arranging gives tan ϕ (1 + a cos θ ) = tan ϕ =

a sin θ 1 + a cos θ

(5)

6.

After computing θ [using (1)], a [using (4)] and ϕ [using (5)] then ψ can be calculated using (1).

7.

The bearing B1P (bearing of the line 1−P) is given by

B= B12 + ϕ 1P

(6)

The distance d1P (distance of line 1−P) is obtained using the sine rule in triangle 12P and

d1P = 8.

d12 sin (α + ϕ )

(7)

sin α

EP and NP obtained from E1 and N1 and the bearing B1P and distance d1P of the line 1−P.

EXAMPLE

323590.140 E 5816974.280 N

3 

γ = 151 18′ 43.18′′

ψ

sin ϕ d 23 sin α = = a= 0.695460833 sinψ d 21 sin β tan ϕ =

a sin θ = 0.935247303 1 + a cos θ

ϕ = 43 05′ 01.03′′ ; ψ = θ − ϕ = 79 09′ 57.79′′

321756.522 E 5813142.354 N

2

B1P = B12 + ϕ = 39 58′ 02.04′′ 

 γ

1956.317075 356° 53′ 01.01″

d12 sin (α + ϕ ) = d1P = 5692.379793 sin α



HP35s Resection Program Auxiliary Angles.docx

2

β



P

α

ϕ

1

24 ′2 0 .0 4″

5 2 1 692 9° .37 58 97 ′ 0 93 2.0 4″

25° 424 34′ 17 .

8. 0 362 83″ 33

ϕ + ψ = 360 − (α + β + γ ) = θ = 122 14′ 58.82′′

30 6°

325519.373 E ( 5815551.638 N)

321862.876 E 5811188.930 N

α = 17° 24′ 07.5″ β = 69° 02′ 10.5″

HP35s PROGRAM SHEET LI N E

S001 S002 S003 S004 S005 S006 S007 S008 S009 S010 S011 S012 S013 S014 S015 S016 S017 S018 S019 S020 S021 S022 S023 S024 S025 S026 S027 S028 S029 S030 S031 S032 S033 S034 S035 S036 S037 S038 S039 S040 S041 S042

ST E P

LBL S CLVARS 1 XEQ S093 RCL E STO R RCL N STO U 2 XEQ S093 RCL E STO S RCL N STO V 3 XEQ S093 INPUT A HMS STO A INPUT B HMS STO B RCL S RCL E RCL V RCL N XEQ Z002 RCL A SIN × STO C x<>y 180 + RCL S RCL R RCL V RCL U -

RESECTION PROGRAM X

Y

Z

T

START RESECTION PROGRAM Enter coordinates of Point 1 E1 E1 N1 N1 E1 Enter coordinates of Point 2 E2 E2 N2 N2 E2 Enter coordinates of Point 3 Enter angle α (D.MMSS) α Enter angle β (D.MMSS) β E2 E3 ∆E 3 2 =E 2 -E 3 N2 N3 ∆N 3 2 =N 2 -N 3 d 3 2 =d 2 3 α sin(α) d 2 3 sin( α) B32 180 B23 E2 E1 ∆E 1 2 =E 2 -E 1 N2 N1 ∆N 1 2 =N 2 -N 1

E2 ∆E 3 2 N2 ∆E 3 2 B32 d23 d23 B32 d 2 3 sin(α) B32 d 2 3 sin(α) B32 E2 B32 N2 ∆E 1 2

∆E 3 2

B32 B32

d 2 3 sin(α) d 2 3 sin(α) B32 d 2 3 sin(α)

d 2 3 sin(α) d 2 3 sin(α)

∆E 1 2 B32

B32 B32

SHEET 1 OF 4 SHEETS

HP35s PROGRAM SHEET LI N E

S043 S044 S045 S046 S047 S048 S049 S050 S051 S052 S053 S054 S055 S056 S057 S058 S059 S060 S061 S062 S063 S064 S065 S066 S067 S068 S069 S070 S071 S072 S073 S074 S075 S076 S077 S078 S079 S080 S081 S082

ST E P

XEQ Z002 STO D RCL B SIN × STO÷C R STO F 180 + x<>y 360 x<>y x<0? + RCL A RCL B + + 360 x<>y RCL C XEQ Z015 1 + XEQ Z002 x<>y STO+F RCL A + SIN STO×D RCL A SIN STO÷D RCL F RCL D XEQ Z015

RESECTION PROGRAM X

Y

Z

T

d12

B12

B32

B32

β sin(β ) d 1 2 sin(β )

d12 d12 B12

B12 B12 B32

B32 B32 B32

B12

B32

B32

d 1 2 sin(β )

180 B21 B32 ±γ

B12 B32 B21 B32

B32 B32 B32 B32

B32 B32 B32 B32

±γ

360

B32

B32

γ α β

γ α

γ

α+β +γ

θ=360-(α+β +γ) a θ a×cos(θ) a×sin(θ) 1+acos(θ) ϕ ϕ α α+ϕ sin(α+ϕ)

asin(θ) ϕ

ϕ

α sin(α) B1P d1P ∆N 1 P

B1P ∆E 1 P SHEET 2 OF 4 SHEETS

HP35s PROGRAM SHEET LI N E

S083 S084 S085 S086 S087 S088 S089 S090 S091 S092 S093 S094 S095 S096 S097

ST E P

RCL U + STO N x<>y RCL R + STO E VIEW E VIEW N GTO S002 STO E STO N INPUT E INPUT N RTN

RESECTION PROGRAM X

Y

N1 N P =N 1 +∆N 1 P

∆N 1 P ∆E 1 P

∆E 1 P E1 E P =E 1 +∆E 1 P

NP ∆E 1 P NP

Z

T

∆E 1 P

NP

E P = East coordinate of resected point N P = North coordinate of resected point 1,2,3 Enter E k (k = 1,2,3) Enter N k (k = 1,2,3)

STORAGE REGISTERS A B C D F E N R U S V

α β d 2 3 sin( α) ; a=d 2 3 sin(α)/d 1 2 sin(β ) d 1 2 ; d 1 2 sin(α+ϕ) ; d 1 P =[d 1 2 sin(α+ϕ)]/sin(α) B 1 2 ; B 1 P =(B 1 2 +ϕ) Ek ; E3 ; EP Nk ; N3 ; NP E1 N1 E2 N2

PROGRAM LENGTH AND CHECKSUM LN = 307; CK = AE78



 Length & Checksum:

2

;

ENTER

(Hold)

SHEET 3 OF 4 SHEETS

HP35s PROGRAM SHEET

RESECTION PROGRAM

PROGRAM NOTES P 1 , P 2 , P 3 means Points 1, 2 and 3.

E 1 , E 2 , etc. and N 1 , N 2 , etc. mean east and north coordinates of P 1 , P 2 , etc. ∆E 1 2 =E 2 –E 1 , ∆N 1 2 =N 2 –N 1 , etc.

B 1 2 means bearing of the line from P 1 to P 2 d 1 2 means distance from P 1 to P 2 Lines S001 to S016

Initialisation; storing coordinates of P1, P2, P3.

Lines S017 to S022

Entering and storing observed angles α and β at the Resection Point P.

Lines S023 to S029

Bearing and distance P 3 to P 2 .

Lines S034 to S036

Note here that B 2 3 = B 3 2 +180°

Lines S037 to S043

Bearing and distance P 1 to P 2 .

Lines S044 to S065

Calculation of angles γ at P 2 and θ=360°-(α+β +γ); and the ratio a=d 2 3 sin(α)/d 1 2 sin(β )

Lines S066 to S079

Calculation of auxiliary angle ϕ and the bearing and distance P 1 to the resection Point P: B 1 P =(B 1 2 +ϕ) and d 1 P =[d 1 2 sin(α+ϕ)]/sin(α).

Lines S080 to S091

Calculation and display of coordinates of Resected Point P.

Lines S093 to S097

Subroutine for entering coordinates of P1, P2, P3.

The calculator must contain LBL Z which contains the Polar to Rectangular routines XEQ Z002 on lines S067, S082 is the Rectangular→Polar conversion XEQ Z015 on lines S029, S043, S070 is the Polar→Rectangular conversion

SHEET 4 0F 4 SHEETS

HP35s PROGRAM

ADJUSTMENT PROGRAM USER INSTRUCTIONS TRAVERSE ADJUSTMENT PROGRAM

This program can perform either a BOWDITCH 1 or a CRANDALL 2 adjustment on a closed traverse (or figure). The bearings and distances of each line of the closed traverse must be entered before selecting the method of adjustment (1 = Bowditch; 2 = Crandall).

After all lines have been entered and adjustment type selected the program will display the adjusted bearings and distances and then the area of the adjusted figure.

A closed traverse must start and end at known points (east and north coordinates known); but in the case of a loop traverse the start and end points will be the same. The program requires that DE = EEND − ESTART and DN = NEND − NSTART are known. If the traverse is a loop traverse DE = DN = 0 1.

To start program press XEQ A001

2.

Display

B? 0.0000

3.

Display

D? 0.0000

4.

Repeat steps 2 and 3 until all known information is entered; then enter 0 at the Bearing prompt and 0 at the Distance prompt (just press R/S at the prompts)

5.

Display

X? 0.0000

Enter: DE; then press R/S [If loop traverse DE = 0, just press R/S]

6.

Display

Y? 0.0000

Enter: DN; then press R/S [If loop traverse DN = 0, just press R/S]

7.

Display

F? 0.0000

8.

Adjusted Bearings (D.MMSS) and adjusted Distances displayed at successive R/S. [Note that Crandall’s adjustment only adjusts distances]

9.

Adjusted Area displayed at last prompt. Press R/S and go to step 2 for new adjustment.

Enter: Bearing (D.MMSS); then press R/S [Bearing of lines that are 0° 00′ 00″ must be entered as 360° 00′ 00″] Enter:

Enter:

Distance; then press R/S

1 = BOWDITCH or 2 = CRANDALL; then press R/S

1

A mathematical adjustment of chain and compass surveys developed by the American mathematician and astronomer Nathaniel Bowditch (1773-1838). This adjustment affects both bearings and distances.

2 A mathematical ‘least squares’ adjustment of traverse distances only that assumes that observed bearings ‘close’ perfectly. Developed in 1906 by Charles L. Crandall, Professor of Railroad Engineering and Geodesy, Cornell University, New York.

Theory and examples of Bowditch’s and Crandall’s adjustments can be found in Notes on Least Squares, Geospatial Science, RMIT University, Chapter 6, pp.6-15 − 6-26.

1

HP35s PROGRAM

ADJUSTMENT PROGRAM

THEORY AND FORMULA Theory, formula and examples of Bowditch’s and Crandall’s adjustments can be found in Notes on Least Squares, Geospatial Science, RMIT University, Chapter 6, pp.6-15 − 6-26. A summary of the formula and the sequence of computation is presented below.

BOWDITCH A closed traverse of k = 1, 2,3 , n lines, sides or legs having bearings φk and distances d k (or a figure of n sides) that has a misclosure may be adjusted in the following manner.

1.

Each traverse line (having bearing and distance) has east and north components ∆Ek = d k sin φk , ∆N k = d k cos φk , and the sums of these components for the traverse are S= E

n

∑ ∆E k =1

k

and S= N

n

∑ ∆N k =1

k

n

2.

A traverse has a total length L = ∑ d k k =1

3.

A closed traverse has a start point and an end point assumed to have known east and north coordinates; ESTART , N START , EEND , N END and differences; = DE EEND − ESTART and = DN N END − N START . If the traverse is a loop traverse (starting and ending at the same point), then D = D= 0.

E N

4.

The east and north components of each traverse leg may be adjusted by adding corrections  ∆Ek   ∆Ek   dEk   DN − S N   D − SE  dEk = d k  E    +   and dN k = d k   so that ∆N= L L      k  ADJUST ∆N k OBS dN k 

5.

Adjusted bearings and distances and area are then computed from the adjusted east and north components.

CRANDALL A closed traverse of k = 1, 2,3 , n lines, sides or legs having bearings φk and distances d k (or a figure of n sides) that has a misclosure may be adjusted in the following manner.

1.

First adjust the bearings of the traverse so that they close perfectly. This may be an arbitrary adjustment.

2.

Each traverse line (having bearing and distance) has east and north components ∆Ek = d k sin φk , ∆N k = d k cos φk , and the sums of these components for the traverse are S= E

n

∑ ∆Ek and S= N k =1

n

∑ ∆N k =1

k

2

HP35s PROGRAM

ADJUSTMENT PROGRAM

THEORY AND FORMULA continued

3.

n

( ∆Ek )

k =1

dk

In addition, the traverse has the following summations: a = ∑

2

n

( ∆N k )

k =1

dk

, b=∑

2

, and

∆Ek ∆N k dk k =1 n

c=∑ 4.

5.

6.

A closed traverse has a start point and an end point assumed to have known east and north coordinates; ESTART , N START , EEND , N END and differences; = DE EEND − ESTART and = DN N END − N START . If the traverse is a loop traverse (starting and ending at the same point), then D = D= 0.

E N  b ( DE − S E ) − c ( DN − S N )    k   ab − c 2 Two ‘multipliers’ are computed:  1  =   k2   a ( DN − S N ) − c ( DE − S E )    ab − c 2

A residual vk for each traverse line is computed from vk = k1∆Ek + k2 ∆N k and added to the observed traverse distance to obtain the adjusted traverse distance: d ADJUST = dOBS + v

00 C

93° 42¢ 15² 15² 15²

8.5 25

D

6² ² 3 42 ² 30 2¢

-0 0-

268.7 86

B

Datu m 285° 00¢ 00 ²

00 -

7 156.62

03

1 5° 32

² 7¢ 18² 24 346° 3 30²

273° 42¢ 30² 40² 35²

148.650

EXAMPLE 1

-0 0A

Figure 1. Fieldnotes of traverse Figure 1 shows a traverse between points A, B, C and D. The bearing datum of the survey is the line AB 285º 00' 00". The distances are horizontal distances. Observed face-left (FL) bearings are shown along the traverse line and the seconds part of the face-right (FR) bearing is shown above.

The mean of the FL/FR seconds is shown to the right of the brace }. The angular misclose in the traverse is 20", which is revealed in the forward and reverse bearings on the line CD. 3

HP35s PROGRAM

1.

ADJUSTMENT PROGRAM

BOWDITCH ADJUSTMENT OF EXAMPLE 1

For the purpose of the exercise we assume that the angular misclose of 20″ is acceptable and that this error is apportioned equally at the four corners giving the observed traverse to be adjusted as shown in the left-columns of the table below Line

Bearing

Distance

k

φk

dk

285° 00′ 00″ 346° 37′ 29″ 93° 42′ 25″ 145° 12′ 31″ sums

268.786 156.627 148.650 258.503 832.5660

1: AB 2: BC 3: CD 4: DA

L =

n

d = ∑ k =1

k

components ∆Ek ∆N k -259.6273 -36.2322 148.3390 147.4993 -0.0212

corrections dEk dN k

69.5669 152.3786 -9.6107 -212.2917 0.0431

n

0.0068 0.0040 0.0038 0.0066 0.0212

832.5660 , S E = −0.0212 and S N = ∑ ∆Ek = k =1

-0.0139 -0.0081 -0.0077 -0.0134 -0.0431

n

∑ ∆N k =1

adjusted components ∆Ek ∆N k -259.6205 -36.2282 148.3428 147.5059 0.0000

69.5530 152.3705 -9.6184 -212.3051 0.0000

= 0.0431

k

Since this is a loop traverse D 0.0212 , DN − S N = −0.0431 = D= 0 and DE − S E = E N  DE − S E   0.0212  The corrections to the traverse components are: dEk d= = k    dk  L   832.5660    DN − S N   −0.0431  = dEk d= k    dk  L  832.5660    The adjusted traverse is Line

Bearing

Distance

k

φk

dk

1: AB 2: BC 3: CD 4: DA

284° 59′ 51″ 346° 37′ 32″ 93° 42′ 35″ 145° 12′ 33″

268.7758 156.6182 148.6543 258.5178

Using the program: press XEQ A001 (or XEQ A

ENTER

)

Enter the bearings and distances of the sides at the prompts B? and D? pressing R/S after entry When all sides have been keyed in, enter 0 at the prompt B? and press R/S; and 0 at the prompt D? and press R/S (or simply press R/S at both prompts).

At the prompt X? enter 0 and press R/S (DE = 0) and at the prompt Y? enter 0 and press R/S (DN = 0) At the prompt F? enter 1 and press R/S. The calculator will then display the adjusted bearing at B = . Press R/S and the adjusted distance will be displayed at D = . Repeat pressing of R/S will display adjusted bearings and distances.

After the last adjusted line, a final R/S will cause the calculator to display the adjusted area at A = (The area = -33,556.9387 m2)

4

HP35s PROGRAM

2.

ADJUSTMENT PROGRAM

CRANDALL ADJUSTMENT OF EXAMPLE 1

For the purpose of the exercise we assume that the angular misclose of 20″ is acceptable and that this error is apportioned equally at the four corners giving the observed traverse to be adjusted as shown in the left-columns of the table below Line

Bearing

Distance

k

φk

dk

∆Ek

∆N k

285° 00′ 00″ 346° 37′ 29″ 93° 42′ 25″ 145° 12′ 31″ sums

268.786 156.627 148.650 258.503 832.5660

-259.6273 -36.2322 148.3390 147.4993 -0.0212

69.5669 152.3786 -9.6107 -212.2917 0.0431

1: AB 2: BC 3: CD 4: DA

n

SE = −0.0212 , S N = ∑ ∆Ek = k =1

= a

( ∆Ek ) = 2

n

∑ k =1

dk

,b = 491.3526

components

n

∑ ∆N k =1

k

( ∆Ek )

dk 250.7808 8.3815 148.0286 84.1616 491.3526

( ∆N k ) = 2

dk

k =1

2

dk 18.0052 148.2455 0.6214 174.3414 341.2134

∆Ek ∆N k dk

residual

-67.1965 -35.2495 -9.5906 -121.1316 -233.1681

-0.004 -0.021 -0.002 0.027

vk

= 0.0431

n

∑

( ∆N k )

2

341.2134 and c =

∆Ek ∆N k = −233.1681 dk k =1 n

∑

Since this is a loop traverse D = D= 0 and DE − S E = 0.0212 , DN − S N = −0.0431 E N The multipliers are:

The residuals are:

b ( DE − S E ) − c ( DN − S N ) k1 = = −2.4593e − 05 ab − c 2 a ( DN − S N ) − c ( DE − S E ) k2 = = −1.4324e − 04 ab − c 2 vk = k1∆Ek + k2 ∆N k

The adjusted traverse (nearest mm) is Line

Bearing

Distance

k

φk

dk

1: AB 2: BC 3: CD 4: DA

285° 00′ 00″ 346° 37′ 29″ 93° 42′ 25″ 145° 12′ 31″

268.782 156.606 148.648 258.530

Using the program: press XEQ A001 (or XEQ A

ENTER

)

Enter the bearings and distances of the sides at the prompts B? and D? pressing R/S after entry When all sides have been keyed in, enter 0 at the prompt B? and press R/S; and 0 at the prompt D? and press R/S (or simply press R/S at both prompts).

At the prompt X? enter 0 and press R/S (DE = 0) and at the prompt Y? enter 0 and press R/S (DN = 0)

5

HP35s PROGRAM

ADJUSTMENT PROGRAM

At the prompt F? enter 2 and press R/S. The calculator will then display the adjusted bearing at B = . Press R/S and the adjusted distance will be displayed at D = . Repeat pressing of R/S will display adjusted bearings and distances.

After the last adjusted line, a final R/S will cause the calculator to display the adjusted area at A = (The area = -33,555.9331 m2)

EXAMPLE 2

33² 195° 12¢

9¢ 14

² ¢ 58² 4287.873 E 7944.574 N

8² 4¢ 140 3 ° 68 032.3 1

°

°

5248.853 E 8321.726 N

E

² 18 6¢ 4 0° 5411.746 E 13

22 559.03¢ 32² 0 163°

FIXE D

138° 18

7²

°

D

°2

2¢ 4 °0

110 °1 240 5¢ 20² 1.60 9

274

275

A

2034.785 E FIXED 8776.030 N

C ED RV E D S OB FIXE

F 7786.963 N

113 ° 156 49¢ 50 ² 4.6 83

² 48¢ 11 302°

² 01 8¢ 46² B 3 6° 7¢ 23 6° 3 6843.030 E 23 OBSERVED 7154.779 N 6843.085 E FIXED 7154.700 N

C

Figure 2 Traverse diagram showing field measurements, derived values and fixed values.

Figure 2 is a schematic diagram of a traverse run between two fixed stations A and B and oriented at both ends by angular observations to a third fixed station C. The bearings of traverse lines shown on the diagram, unless otherwise indicated, are called "observed" bearings and have been derived from the measured angles (which have been derived from observed theodolite directions) and the fixed bearing AC. The difference between the observed and fixed bearings of the line BC represents the angular misclose of 15″. The coordinates of the traverse points D, E and F have been calculated using the observed bearings and distances and the fixed coordinates of A. The difference between the observed and fixed coordinates at B represents a traverse misclosure.

6

HP35s PROGRAM

3.

ADJUSTMENT PROGRAM

BOWDITCH ADJUSTMENT OF EXAMPLE 2

For the purpose of the exercise we assume that the angular misclose of 15″ is acceptable and that this error is apportioned equally at the five traverse points giving the observed traverse to be adjusted as shown in the left-columns of the table below Line

Bearing

Distance

k

φk

dk

110° 15′ 17″ 68° 34′ 12″ 163°03′ 23″ 113° 49′ 38″ sums

2401.609 1032.340 559.022 1564.683 5557.6540

1: AD 2: DE 3: EF 4: FB

L =

n

d ∑= k =1

k

5557.65400 , S E =

components ∆Ek ∆N k 2253.1002 960.9688 162.9160 1431.3217 4808.3067 n

∑ ∆E k =1

k

corrections dEk dN k

-831.4235 377.1801 -534.7560 -632.1006 -1621.1000

-0.0029 -0.0012 -0.0007 -0.0019 -0.0067

-0.0994 -0.0427 -0.0231 -0.0648 -0.2300

adjusted components ∆Ek ∆N k 2253.0973 960.9676 162.9153 1431.3198 0.0000

-831.5229 377.1374 -534.7791 -632.1654 0.0000

n

−1621.1000 = 4808.3067 and S N = ∑ ∆N k = k =1

DE =EEND − ESTART =6843.085 − 2034.785 =4808.300 DN = N END − N START = 7154.700 − 8776.030 = −1621.330 DE − S E = −0.0067 , DN − S N = −0.2300  DE − S E   −0.0067  The corrections to the traverse components are: dEk d= = k    dk  L   5557.6540    DN − S N   −0.2300  = dEk d= k    dk  L  5557.6540    The adjusted traverse is Line

Bearing

Distance

k

φk

dk

1: AD 2: DE 3: EF 4: FB

110° 15′ 25″ 68° 34′ 20″ 163° 03′ 26″ 113° 49′ 46″

2401.6407 1032.3232 559.0439 1564.7074

Using the program: press XEQ A001 (or XEQ A

ENTER

)

Enter the bearings and distances of the sides at the prompts B? and D? pressing R/S after entry When all sides have been keyed in, enter 0 at the prompt B? and press R/S; and 0 at the prompt D? and press R/S (or simply press R/S at both prompts).

At the prompt X? enter 4808.300 and press R/S (DE = 4808.300) At the prompt Y? enter -1621.330 and press R/S (DN = -1621.330) At the prompt F? enter 1 and press R/S. The calculator will then display the adjusted bearing at B = . Press R/S and the adjusted distance will be displayed at D = . Repeat pressing of R/S will display adjusted bearings and distances.

7

HP35s PROGRAM

ADJUSTMENT PROGRAM

After the last adjusted line, a final R/S will cause the calculator to display the adjusted area at A = (The area = -357,496.7606 m2 but is meaningless since this is not a closed polygon)

4.

CRANDALL ADJUSTMENT OF EXAMPLE 2

For the purpose of the exercise we assume that the angular misclose of 20″ is acceptable and that this error is apportioned equally at the four corners giving the observed traverse to be adjusted as shown in the left-columns of the table below Line

Bearing

Distance

k

φk

dk

∆Ek

∆N k

110° 15′ 17″ 68° 34′ 12″ 163°03′ 23″ 113° 49′ 38″ sums

2401.609 1032.340 559.022 1564.683 5557.6540

2253.1002 960.9688 162.9160 1431.3217 4808.3067

-831.4235 377.1801 -534.7560 -632.1006 -1621.1000

1: AD 2: DE 3: EF 4: FB

n

components

( ∆Ek )

( ∆N k )

2

dk 2113.7748 894.5319 47.4788 1309.3270 4365.1124

2

dk 287.8342 137.8081 511.5433 255.3560 1192.5416

∆Ek ∆N k dk

resid.

-780.0106 351.1036 -155.8442 -578.2253 -1162.9764

0.057 -0.168 0.129 0.064

n

S E = ∑ ∆Ek = 4808.3067 , S N = −1621.1000 ∑ ∆N k = k =1

= a

k =1

( ∆Ek ) = 2

n

∑ k =1

dk

,b = 4365.1124

( ∆N k ) = 2

n

∑

dk

k =1

1192.5416 and c =

∆Ek ∆N k = −1162.9764 dk k =1 n

∑

DE =EEND − ESTART =6843.085 − 2034.785 =4808.300 DN = N END − N START = 7154.700 − 8776.030 = −1621.330 −0.2300 DE − S E = −0.0067 , DN − S N =

The multipliers are:

The residuals are:

b ( DE − S E ) − c ( DN − S N ) k1 = = −7.1501e − 05 ab − c 2 a ( DN − S N ) − c ( DE − S E ) k2 = = −2.6259e − 04 ab − c 2 vk = k1∆Ek + k2 ∆N k

The adjusted traverse (nearest mm) is Line

Bearing

Distance

k

φk

dk

1: AB 2: BC 3: CD 4: DA

110° 15′ 17″ 68° 34′ 12″ 163°03′ 23″ 113° 49′ 38″

2401.666 1032.172 559.151 1564.747

8

vk

HP35s PROGRAM

ADJUSTMENT PROGRAM

Using the program: press XEQ A001 (or XEQ A

ENTER

)

Enter the bearings and distances of the sides at the prompts B? and D? pressing R/S after entry When all sides have been keyed in, enter 0 at the prompt B? and press R/S; and 0 at the prompt D? and press R/S (or simply press R/S at both prompts).

At the prompt X? enter 4808.300 and press R/S (DE = 4808.300) At the prompt Y? enter -1621.330 and press R/S (DN = -1621.330) At the prompt F? enter 2 and press R/S. The calculator will then display the adjusted bearing at B = . Press R/S and the adjusted distance will be displayed at D = . Repeat pressing of R/S will display adjusted bearings and distances.

After the last adjusted line, a final R/S will cause the calculator to display the adjusted area at A = (The area = -357,597.8300 m2 but is meaningless since this is not a closed polygon)

9

HP35s PROGRAM SHEET LI N E

A001 A002 A003 A004 A005 A006 A007 A008 A009 A010 A011 A012 A013 A014 A015 A016 A017 A018 A019 A020 A021 A022 A023 A024 A025 A026 A027 A028 A029 A030 A031 A032 A033 A034 A035 A036 A037 A038 A039 A040 A041

ST E P

LBL A CLVARS CLΣ -1 STO I 2 STO+I STO+J 0 STO B STO D INPUT B HMS STO B INPUT D STO+L RCL B + x=0?

GTO A044 RCL B RCL D XEQ Z015 Σ+ LASTx STO(J) x<>y STO(I) × RCL D ÷ STO+S RCL(I) x2 RCL D ÷ STO+R RCL(J) x2 RCL D ÷

ADJUSTMENT PROGRAM X

Y

Z

T

START NEW ADJUSTMENT

START NEW LINE OF FIGURE Increment indirect storage registers

Enter Bearing (D.MMSS)

Enter Distance d k Accumulate distances Brg Dist Brg+Dist Yes! End of Data; GO TO adjustment Brg Dist Brg ∆N k ∆E k n ∆E k ∆N k ∆E k ∆E k

∆N k

∆E k ∆N k dk ∆E k ∆N k /d k

∆E k ∆N k

∆E k (∆E k ) 2 dk (∆E k ) 2 /d k ∆N k (∆N k ) 2 dk (∆N k ) 2 /d k

SHEET 1 0F 6 SHEETS

HP35s PROGRAM SHEET LI N E

ST E P

A042 A043 A044 A045 A046 A047 A048 A049 A050 A051 A052 A053 A054 A055 A056 A057 A058 A059 A060 A061 A062 A063 A064

STO+V GTO A006 INPUT X INPUT Y INPUT F RCL F 1 x=y?

GTO A056 RCL F 2 x=y?

GTO A079 GTO A046 XEQ A128 RCL L ÷ STO Y x<>y RCL L ÷ STO X XEQ A135

A065

XEQ A144

A066 A067 A068 A069 A070 A071 A072 A073 A074 A075 A076 A077 A078 A079 A080 A081 A082 A083

XEQ A151 RCL D RCL X × STO+(I) RCL D RCL Y × STO+(J) XEQ A162 XEQ A151 XEQ A177 GTO A065 RCL R RCL V × RCL S STO U

ADJUSTMENT PROGRAM X

Y

Z

T

GO FOR next line Enter D E Enter D N Enter Flag (Bowditch = 1; Crandall = 2) Flag 1 Flag Yes! GO TO Bowditch adjustment Flag 1 Flag Yes! GO TO Crandall adjustment D N -S N L (D N -S N )/L

D E -S E D N -S N D E -S E

D E -S E L (D E -S E )/L

(D N -S N )/L D E -S E (D N -S N )/L

BOWDITCH ADJUSTMENT D E -S E

(D N -S N )/L

Set registers C,I,J,A Increment counters for next line of adjusted figure Get UNADJUSTED Bearing and Distance dk (D E -S E )/L d k dE k = d k [(D E -S E )/L] = correction to ∆E k dk (D N -S N )/L d k dN k = d k [(D N -S N )/L] = correction to ∆N k Compute Area contribution of ADJ. line Get ADJUSTED Bearing and Distance View Adjusted Bearing and Distance GO FOR next line of figure CRANDALL ADJUSTMENT a = Σ[(∆E k ) 2 /d k ] 2 b = Σ[(∆N k ) /d k ] a = Σ[(∆E k ) 2 /d k ] ab ab c = Σ[∆E k ∆N k )/d k ] c ab SHEET 2 0F 6 SHEETS

HP35s PROGRAM SHEET LI N E

ST E P 2

A084 A085 A086 A087 A088 A089 A090 A091 A092 A093 A094 A095 A096 A097 A098 A099 A100 A101 A102 A103 A104 A105

x STO T XEQ A128 STO×S STO×R x<>y STO×V STO×U RCL R RCL U RCL T ÷ STO W RCL V RCL S RCT T ÷ STO T XEQ A135

A106

XEQ A144

A107 A108 A109 A110 A111 A112 A113 A114 A115 A116 A117 A118 A119 A120 A121 A122 A123 A124 A125 A126

XEQ A151 RCL(I) RCL T × RCL(J) RCL W × + STO+D RCL B HMS RCL D XEQ Z015 STO(J) x<>y STO(I) XEQ A162 XEQ A177 GTO A106 VIEW A

ADJUSTMENT PROGRAM X

Y

c2 ab-c 2

ab

D N -S N

D E -S E

D E -S E

D N -S N

Z

T

a(D N -S N ) c(D E -S E ) a(D N -S N ) a(D N -S N )-c(D E -S E ) ab-c 2 a(D N -S N )-c(D E -S E ) k 2 =[a(D N -S N )-c(D E -S E )]/(ab-c 2 ) b(D E -S E ) c(D N -S N ) b(D E -S E ) b(D E -S E )-c(D N -S N ) ab-c 2 b(D E -S E )-c(D N -S N ) k 1 =[b(D E -S E )-c(D N -S N )]/(ab-c 2 ) Set registers C,I,J,A Increment counters for next line of adjusted figure Get UNADJUSTED Bearing and Distance ∆E k k1 ∆E k k 1 ∆E k ∆N k k 1 ∆E k k2 ∆N k k 1 ∆E k k 2 ∆N k k 1 ∆E k v k =k 1 ∆E k +k 2 ∆N k

Brg Dist ∆N k

Brg ∆E k

∆E k

∆N k

Compute Area contribution of ADJ. line View Adjusted Bearing and Distance GO FOR next line of figure Area SHEET 3 0F 6 SHEETS

HP35s PROGRAM SHEET LI N E

A127 A128 A129 A130 A131 A132 A133 A134 A135 A136 A137 A138 A139 A140 A141 A142 A143 A144 A145 A146 A147 A148 A149 A150 A151 A152 A153 A154 A155 A156 A157 A158 A159 A160 A161 A162 A163 A164 A165 A166 A167 A168 A169 A170

ST E P

GTO A002 RCL X Σy RCL Y Σx RTN n STO C CLΣ -1 STO I 0 STO J STO A RTN 2 STO+I STO+J RCL C x=0?

GTO A126 RTN 360 RCL(I) RCL(J) XEQ Z002 STO D R x<0? + HMS STO B RTN RCL(I) RCL(J) Σ+ R LASTx Σy × x<>y Σx

ADJUSTMENT PROGRAM X

Y

Z

T

GO FOR new figure to adjust DE DE S E =Σ∆E k D E -S E DN D E -S E DN D E -S E S N =Σ∆N k D N -S N D E -S E n count = n

SET REGISTERS C,I,J,A

-1 0

INCREMENT REGISTERS I,J 2 Increment indirect storage reg. for ∆ E Increment indirect storage reg. for ∆ N count Yes! GO FOR Area of adjusted figure 360 ∆E k ∆N k dk

BEARING & DISTANCE SUBROUTINE 360 360 ∆E k Brg k 360

Brg k

360

Brg(D.MMSS)

∆E k ∆N k n ∆E k ∆N k Σ∆E k ∆N k Σ∆E k ∆E k Σ∆N k

AREA SUBROUTINE ∆E k ∆E k ∆E k ∆N k ∆E k ∆N k Σ∆E k ∆E k

∆E k

∆N k Σ∆E k SHEET 4 0F 6 SHEETS

HP35s PROGRAM SHEET LI N E

A171 A172 A173 A174 A175 A176 A177 A178 A179 A180 A181

ST E P

× 2 ÷ STO+A RTN VIEW B VIEW D 1 STO-C RTN

ADJUSTMENT PROGRAM X

Y

Z

T

∆E k Σ∆N k ∆N k Σ∆E k ∆N k Σ∆E k -∆E k Σ∆N k Area component Accumulate area (Adjusted) Bearing (D.MMSS) Adjusted Distance 1 Decrement count

STORAGE REGISTERS A B C D I J L R S T U V W X Y

Area Bearing count = counter for lines of figure 0 ≤ count ≤ n Distance d k ; d k +v k Indirect storage register for ∆E Indirect storage register for ∆N Cumulative distance L = Σd k a = Σ[(∆E k ) 2 /d k ] ; a(D N -S N ) c = Σ[∆E k ∆N k )/d k ] ; c(D N -S N ) ab-c 2 ; k 1 =[b(D E -S E )-c(D N -S N )]/(ab-c 2 ) c ; c(D E -S E ) b = Σ[(∆N k ) 2 /d k ] ; b(D E -S E ) k 2 =[a(D N -S N )-c(D E -S E )]/(ab-c 2 ) D E = E E N D -E S T A R T ; (D E -S E )/L D N = N E N D -N S T A R T ; (D N -S N )/L

PROGRAM LENGTH AND CHECKSUM LN = 558; CK = 68A4



 Length & Checksum:

2

;

ENTER

(Hold)

SHEET 5 0F 6 SHEETS

HP35s PROGRAM SHEET

ADJUSTMENT PROGRAM

PROGRAM NOTES Lines A021 to A042

Lines A056 to A078 Lines A079 to A125 Lines A128 to A134

Lines A135 to A143 Lines A144 to A150

Lines A151 to A161 Lines A162 to A176 Lines A177 to A181

convert bearings and distances of the figure to east and north components (∆E k ,∆N k ) and form the sums: S E = Σy = Σ∆E k ; S N = Σx = Σ∆N k ; a = Σ[(∆E k ) 2 /d k ]; b = Σ[(∆N k ) 2 /d k ]; c = Σ[∆E k ∆N k )/d k ].

Bowditch adjustment using subroutines A128, A135, A144, A151, A162, A177.

Crandall adjustment using subroutines A128, A135, A144, A151, A162, A177. is a subroutine that computes the misclosures east and north: D E -S E and D N -S N where D E = E E N D -E S T A R T and D N = N E N D -N S T A R T Note that for a loop traverse (or closed figure) D E = D N = 0 is a subroutine that sets storage registers C,I,J,A and clears Σ is a subroutine that increments indirect storage registers I,J and tests to see if count=0. If count=0 then all adjusted bearings and distances have been computed and the area will be displayed. is a subroutine that computes bearings and distances from components ∆E k ,∆N k is an area subroutine. is a subroutine for displaying Bearing (D.MMSS) and Distance and decrementing the counter.

The calculator must contain LBL Z which contains the Polar to Rectangular routines.

XEQ Z002 on line A154 is the Rectangular→Polar conversion XEQ Z015 on lines A023,A119 is the Polar→Rectangular conversion.

SHEET 6 0F 6 SHEETS