Two Nifty Programs Shutterstock.Com ©Marekuliasz That Will Make Your HP 35S Calculator “Cry and Sing!”

Two Nifty Programs shutterstock.com ©marekuliasz That Will Make Your HP 35S Calculator “Cry And Sing!”

often think of this line when it comes to programming “Check out Guitar George, he knows HP calculators. I’ve seen many a person “skin that smoke wagon” for no other reason than their fingers only go up to all the chords; but it’s strictly ten. HP RPN calculators are one of the most powerful and rhythm. He doesn’t want to make it oft overlooked tools that a surveyor can employ. The HPS make it cry or sing… 35s is comfortable, compact, readable, and approved for the NCEES ” tests. The HP 35s is a great calculator for keystroke programming. —Dire Straits “Sultans of Swing” circa 1978 “Keystroke” is the HP equivalent to Microsoft’s “macro”. The 35s has a good chunk of memory and up to 800 accessible storage registers. Enough of the good features, let’s focus on the bad! Where programs that overcome this deficiency. I’ve slightly modified the is the rectangular/polar conversion key? WHERE IS THE listing that HP provides via their website. The good folks at the HP RECTANGULAR/POLAR CONVERSION KEY? WHERE IS THE Museum of Calculators are credited with developing the programs. I RECTANGULAR/POLAR CONVERSION KEY? WHERE IN too assign credit to the “Museum” folks and note that my listings are THE HECK IS THE… okay, I’ve made my point. HP forgot that simple modifications to their outstanding work. Surveyors really enjoy the value of the traditional rectangular/polar Let’s start with some basic information about how the 35s works. conversion logic included on HP calculators for the past 30+ years. There is a “run” mode, which is the normal everyday “punch-the- The good news is that rectangular/polar conversions on the 35s are keys-and-get-an-answer” mode. Then there is “program” mode. This performed through a display setting when viewing complex num- mode enables the 35s to write and store a series of keystrokes for bers. Oh by the way, when I say “good news” I mean get ready to future use. It’s like a macro in Microsoft Excel. To access program hear something nuttier than squirrel droppings. This “new” display mode simply press the blue shift (right arrow shift) and the R/S key logic is a loser, plain and simple (if you’re a grumpy old surveyor). (most upper left key). You’ll notice “PRGM” is written in blue on the However, HP’s redemption lies in their effort to distribute two short bottom of the R/S key. To escape from program mode simply do the

» JASON E. FOOSE, PS

Displayed with permission • The American Surveyor • August 2014 • Copyright 2014 Cheves Media • www.Amerisurv.com same blue shift and R/S sequence. You can also hit the “C” clear key What do the programs do? as well. You label a program with a “letter” label. The red alpha labels Polar enables you to enter a northing (y-register) and an easting are located on the lower right area of certain keys. You are limited to (x-register) and convert them to an azimuth and a distance. The 26 labeled programs A-Z. To run a program hit the XEQ key followed steps are as follows: by your desired alpha label key. You’ll notice that several program 1. Type your easting. lines are contained in quotation marks. These lines are actually 2. Hit the enter key. equations. You must hit the EQN key to initiate the equation and the 3. Type your northing. enter key to exit the equation. REGX, REGY, REGZ, REGZ are avail- 4. Hit the XEQ key and the () key for “P”. able in program mode by hitting the roll down key then using the 5. Hit the enter key to run the program. left/right grey arrows to select. The listings are presented as you will see them in the display with the exception of the quotation marks. The azimuth will be displayed in decimal degrees in the y-register Refer to the user’s guide or go to HP’s support site and download and the distance will be displayed in the x-register. the pdf found at the link listed below for examples of the actual key Rectangular enables you to enter an azimuth and distance and strokes. The user’s guide has a listing of all keystrokes in appendix convert them to easting and northing. “G”. Feel free to email any questions to [email protected] Type your azimuth in decimal degrees. 1. Hit the enter key. POLAR PROGRAM LISTING 2. Type your distance P001 LBL P 3. Hit the XEQ key and the 7 key for “R”. P002 CF 10 4. Hit the enter key to run the program. P003 ABS The easting will be displayed in the y-register and the northing P004 CLx will be displayed in the x-register. Remember you are working with P005 LASTx Cartesian coordinate system and HP’s special azimuth circle of +/- 180°. If you find that your answers appear “almost right” then P006 R▼ double check these two items as likely culprits. You may find your P007 R▼ northing and easting are reversed or your azimuth is negative or P008 “REGZ+i*REGT” rotated 90°. P009 ENTER P010 R▼ Sample Data P011 R▼ Convert rectangular coordinates to polar values P012 “ARG(REGT)” Note: set display to fix 4 for angles but be realistic about your distance precisions! P013 “ABS(REGT)” P014 RTN 500 [ENTER] 100 [XEQ] [P] [ENTER] should yield the result of: Y: 78.6901 (azimuth-dd) X: 509.9020 (distance)

RECTANGULAR PROGRAM LISTING 600[ENTER] 200 [+/-] [XEQ] [P] [ENTER] should yield the result of: R001 LBL R Y: 108.4349 X: 632.4555

R002 CF 10 300 [+/-] [ENTER] 300 [+/-] [XEQ] [P] [ENTER] should yield the result of: R003 ABS Y: -135.0000 X: 424.2641 R004 R▼ Convert polar values to rectangular coordinates R005 R▼ R006 “LASTx*COS(REGT)+i*LASTx*SIN(REGT)” 30 [ENTER] 250 [ENTER] [XEQ] [R] [ENTER] should yield the result of: Y: 125.0000 (northing) X: 216.5064 (easting) R007 ENTER R008 R▼ 135 [ENTER] 200 [ENTER] [XEQ] [R] [ENTER] should yield the result of: R009 R▼ Y: 141.0000 X: -141.0000 R010 “ABS(REGZ)*SIN(ARG(REGZ))” Note: HP Azimuth starts with 0˚ as east or the equivalent 90˚ in R011 “ABS(REGT)*COS(ARG(REGT))” earth based units. Positive angles represent counterclockwise rotation north of the equatorial zero whereas negative angles represent R012 RTN clockwise rotation south of the equatorial zero to 180˚ or west.

This link is to HP’s support site. There’s a link to order a pdf copy of the programs at the bottom of the page: h20000.www2.hp.com/bizsupport/ TechSupport/Document.jsp?objectID=c0174 8452&prodSeriesId=3442983

Since 2012, Jason Foose has served as Arizona’s Mohave County Surveyor. He is licensed in Arizona, Colorado, and Nevada and has enjoyed a full time career in Surveying since 1993. Prior to that he worked part time as a rodman, and full time for a title insurance company running chains of title in the dusty old Victorian courthouse in Medina County, Ohio. He owned and operated a small surveying practice on the Colorado Front Range and accumulated 12 years of private HP calculators refer to a hemispherical azimuth system as illustrated on the right. Angles are sector experience before accepting a position displayed 0˚ to 179˚ 59'59" North of the equatorial zero and 0˚ to -179˚ 59'59" South of the as a staff surveyor with Mohave County. equatorial zero. [email protected]

Displayed with permission • The American Surveyor • August 2014 • Copyright 2014 Cheves Media • www.Amerisurv.com JASON E. FOOSE, PS the HP 35s calculator A Field Surveyor’s Companion Part 1—Point Storage

he August 2014 issue of The American Surveyor presented the article Two Nifty Programs that will make your HP 35S Calculator “Cry And TSing!” The article highlights my discontent towards HP’s inadvertent omission of the traditional rectangular/polar conversion keys as well as providing a remedy to address the deficiency. Accepting this enigmatic omission and simply adding it to my list of “product faux pas” (which includes Cajun Style Visine, New Coke, and the sub-prime mortgage) has empowered me to move forward and exploit the true potential of this awesome calculator. The strength of the 35s lies with its ability to digest equations ©2014 JASON E. FOOSE along with its refined keystroke programming architecture. I will present a series of “The strength of the 35s lies with its ability to articles that demonstrate how to transform your RPN adding machine into a 400 point digest equations along with its refined keystroke COGO-DOZER rivaling the usefulness of programming architecture. commercial data collector/desktop packages. ” There are very few mathematical challenges that the HP35s cannot devour however one For example is the number 1 is stored in the is represented by ×. The variable “x” is matrix operations. Matrix logic, more variable I then “recall (I)” will retrieve the data shall be delineated by italicization. BRS memory, and a key for constructing complex stored in the indirect register 1. Likewise if the and YLS refer to the blue right shift and numbers from the stack elements would be number 799 is stored in variable J then “recall yellow left shift keys accordingly. With welcomed additions to the next generation (J)” will retrieve the data stored in indirect shifted functions I will show the main key low-budget, non-graphing RPN calculator. register 799. So in effect (I) and (J) can by any function in brackets and occasionally the one of 800 indirect registers identified by the shifted function in braces for clarity. For Laying the Groundwork values stored in the variables I or J. We are example YLS ENTER {SHOW} refers to The first task at hand is to provide for a data able to store both northing(y) and easting(x) the “SHOW” command. Passive equations base from which to recall and store points. The in a single register as a complex number dis- will be delineated by EQN and quotation 35s has 32K of useable memory. I have found played in rectangular format. This realization marks around the text. Stack registers will be with my complete set of programs installed expands the opportunities for point storage delineated by regx, regy, regz, regt. These can there is room for about 400 points in variable and is a great feature of the 35s. be accessed in programming by keying R↓ storage. The 35s has 800 indirect registers There are a few conventions I’ll use to in program and equation entry modes. that are accessed through the variables I, (I), express various programming commands. Statistics menus and data are available dur- J,(J). This function is a two level operation Keys will be identified with highlights. For ing programming as well. Access statistical that assigns the value stored in variable I or example 0 means the zero key and R/S data by keystrokes BRS - {sums}, BRS + J as the objective register of the (I) or (J) key. means the run stop key. Multiplication {s,σ}, YLS - {L.R}, and YLS + {x,y }

Displayed with permission • The American Surveyor • September 2014 • Copyright 2014 Cheves Media • www.Amerisurv.com Table 1: User Instructions KEYSTROKE STEPS RESULTANT DISPLAY ACTION XEQ SIN ENTER XEQ H___ → ”POINTS” Initiates the program. Specific program line may be defined or run program from label line. R/S “0=STO 1=RCL” Passive equation asking user to key either “0” or “1” for the desired action. 0 R/S Y-reg : N? Key in the northing value. X-reg : previous default value

100.00 R/S Y-reg : E? Key in the easting value. X-reg : previous default value

200.00 R/S Y-reg : J? Prompt for point number. Key in desired point number up to 800. Max X-reg : previous default value allowable will fall between 400 & 500 with all programs installed.

1 R/S (1)= Point number 1 was stored with according values. 100.00 i 200.00 R/S “0=MORE 1=DONE” Passive equation asking user to key either “0” or “1” for the desired action.

0 R/S “POINTS” R/S “0=STO 1=RCL”

1 R/S Y-reg : J? Prompt for desired point number. X-reg : previous default value

1 R/S (1)= Recalls and displays desired point. 100.00 i 200.00 R/S “0=MORE 1=DONE”

1 R/S Default values Exits program.

Introduction To RPN in others or referred to as subroutines. a fantastic achievement for RPN keystroke Keystroke Programming This saves on memory and redundant and real thumbs up for HP! Equations can RPN keystroke programming is very programming. The first keystrokes of every be set as active or passive. This is also a straight forward and akin to Microsoft program should be BRS XEQ {LBL} and true milestone for the 35s. Flag 10 is the Macros. A program is simply a set of your letter of choice. I have selected “H” toggle that controls this feature. When flag instructions comprised of sequential list for points for no other reason than “P” was 10 is clear the equations are active and of keystrokes representing functions, my label for “POLAR”. All programs should will be evaluated to a numerical solution. equations, and variables. If you can end with the keystroke YLS XEQ {RTN}. When flag 10 is set the equation is passive perform the calculations longhand with This instruction returns to the program top whereas its only function is displaying the 35s then you can program the 35s to or runs the next program. We have defined the text of the equation in the X-register. follow the same script. Refer to Chapters a start, an end, and now we put a bunch This is demonstrated at line H002 and 13–15 in the HP 35s User’s Guide for of stuff in between. You’ll notice that the H003. This can be another source of bugs detailed information. listing is sequential and begins with the if overlooked. Simply remember to either To begin programming let’s start with a label at line 001. The 35s automatically set or clear flag 10 when dealing with any clean slate and “clear all” by keying blue prompts for the next line number. Think of equations. Again keep in mind branching right shift (see note above for BRS ) ← 3 this as a sequence number for each step as from other subroutines may have yield to clear all memory. WARNING: This well as an address for branching. The GTO a flag setting contrary to the current clears everything! Be cautious if you are prompting may become out of sequence operation. The keystrokes to set and clear unsure. Refer to the manual to remove when you edit programs. Keep this in mind flag 10 are YLS ▲ {FLAGS} 1 . 0 to individual items. Open the program mode as a likely error source when dealing with set, and YLS ▲ {FLAGS} 2 . 0 to clear. by keying in BRS R/S {PRGM}. You will GTO statements (branching and looping). Flag 10 is represented by decimal point be at “PROGRAM TOP”. This is a reference You may have to edit GTO statement desti- and zero. See the user’s guide for detailed point and the beginning of all programs. nations along with desired program modifi- information regarding flags. If you get lost in a program simply key cations. Each line generally represents one in GTO . . to return back to the program keystroke, function, command, or value. The Program top. Every program begins with a letter An exception to this would include active Key in the following instructions beginning label from A-Z. The 35s is limited to 26 equations by which a seemingly unlimited with BRS R/S {PRGM} to open program programs max however I will demonstrate amount of mathematical operations can be mode. C or BRS R/S {PRGM} will exit that certain programs can be embedded expressed as a single line element. This is program mode.

Displayed with permission • The American Surveyor • September 2014 • Copyright 2014 Cheves Media • www.Amerisurv.com H001 LBL H H002 SF10 H003 EQN “POINTS” H004 FIX 0 H005 EQN “0=STO 1=RCL” H006 x=0? H007 GTO H013 H008 INPUT J H009 FIX 2 H010 VIEW (J) H011 GTO H024 H012 FIX 2 H013 CF 10 H014 INPUT N H015 INPUT E H016 EQN N x 1i100 + E x 1θ90 —note: RCL activates variables in EQN mode. H017 FIX 0 H018 INPUT J H019 x<>y H020 STO (J) H021 FIX 2 H022 VIEW (J) H023 SF 10 H024 EQN “0=MORE 1=DONE” H025 x=0? H026 GTO H001 H027 CLRSTK H028 RTN

Example Data and Running the Program (See Table 1: User Instructions on the previous page.) Hopefully this information presented herein is clear and genuinely explanatory. Please do not hesitate to send any comments, concerns, questions, or criticism to [email protected]. Point storage and recall is prerequisite to any COGO program. We have created a good foundation to support various routines. Elements of this program will be nested in other routines. The primary function of program “H” is to provide an independent environment to store and view coordinates. The next installment will focus on azimuth traverse and embedded point recall & storage. ◾

Since 2012, Jason Foose has served as Arizona’s Mohave County Surveyor. He is licensed in Arizona, Colorado, and Nevada and has enjoyed a full time career in Surveying since 1993. Prior to that he worked part time as a rodman, and full time for a title insurance company running chains of title in the dusty old Victorian courthouse in Medina County, Ohio. He owned and operated a small surveying practice on the Colorado Front Range and accumulated 12 years of private sector experience before accepting a position as a staff surveyor with Mohave County. [email protected]

Displayed with permission • The American Surveyor • September 2014 • Copyright 2014 Cheves Media • www.Amerisurv.com JASON E. FOOSE, PS the HP 35s calculator A Field Surveyor’s Companion Part 2—A Few Inner Workings Leading Up to Traverse

I presented the article Two Nifty Programs that will make your HP 35S Calculator “Cry And program mode. C or BRS R/S {PRGM} Sing!” in the August 2014 issue of The American Surveyor. I scoured that thing for errors will exit program mode. like a polecat in a Piggly Wiggly dumpster. While I’m ecstatic to learn that our readers are getting into the subject matter, I regret to inform you of an oversight on my part. In my “polar C001 LBL C to rectangular” conversion example I included an extra ENTER keystroke after keying in C002 STO I the distance (magnitude/modulus component) in both samples. This inadvertently places C003 R▼ note: the roll down stack key the distance in both Y-reg and X-reg rather than the intended Y-reg=angle X-reg=distance. C004 STO D Special thanks goes out to reader William L. Meagher of WM Surveys, Inc. Ventura, C005 RCL I California, for the catch and a toast to our polecat of the month award winner! C006 SIN The Inner Workings You will need to refer to the August 2014 C007 x note: multiply he development of these issue and install the Rectangular and Polar C008 STO X programs has been an programs. Make sure that you label the “R” C009 R▼ evolutionary expansion of and “P” accordingly. Traverse relies on six C010 RCL I my personal knowledge subroutines or nested programs to function. C011 COS regarding programming logic. Rectangular and Polar are two of those. C012 RCL D The components of the traverse routine are T C013 x note: multiply among my earliest attempts at keystroke This Month’s Programs programming and appear rudimentary to LBL C manipulates a distance in the Y-reg C014 0i0 me now. The catalyst of improvement is with an azimuth in the X-reg into a complex C015 + the application of hindsight to foresight; number. This program was slightly modified C016 0i0 however I have elected to present the from the work by and shown with permission C017 RCL X programs as originally written while placing of Jeremy Dean. Jeremy’s original program C018 + the challenge of improvement in the readers’ can be found at sac-surveyors.org/node/22 C019 1θ90 hands. Please email your suggestions for and can run as a “stand alone” program. improvement to [email protected]. I will Thanks Jeremy for this great little ditty! C020 x note: multiply do my best to incorporate your suggestions Key in the following instructions C021 + in print as we progress through the column. beginning with BRS R/S {PRGM} to open C022 RTN

Table 1: Example Data and Running The Program as a “stand alone”

KEYSTROKE STEPS RESULTANT DISPLAY ACTION 100 Y-reg : 0 or default value Load the distance into the stack. Note display is fix 2. X-reg : 100.00

ENTER Y-reg : 100.00 Advances value to Y-reg. X-reg : 100.00 45 LYS 8 {HMS→} Y-reg : 100.00 Load azimuth in X-reg. Note DMS→ is normally required. X-reg : 45.00 XEQ XEQ ENTER Y-reg : 45.00 Executes program C. Northing is the real number and Easting is the imaginary X-reg : 70.71 i 70.71 number when entering 360˚ azimuth values. Cartesian values will be reversed.

Displayed with permission • The American Surveyor • October 2014 • Copyright 2014 Cheves Media • www.Amerisurv.com Jeremy’s program is great and I have Program LBL S is a dependent point relied on it for several years without storage subroutine. question. I recognized that the program radiated savviness beyond my stratosphere S001 LBL S of insight. Revisiting my programs in S002 SF 10 conjunction with this series yielded a grin S003 EQN “STORE PNT” anointed with posterior knowledge and S004 FIX 0 an alternative prescription for the same solution as follows: S005 INPUT J S006 FIX 2 C001 LBL C S007 RCL C C002 CF 2 S008 STO (J) C003 EQN ((SIN(REGX) x REGY) x ©2014 JASON E. FOOSE S009 VIEW (J) (1θ90))+((COS(REGX) x REGY) The program can be verified by storing S010 RCL (J) x (1i0)) the value of 100 in variables “E” and “N”. S011 ARG C004 RTN Key the complex number 100i100 into the S012 LASTx stack and ENTER then XEQ R/S (LBL A). S013 ABS Whereas Jeremy’s original version The solution in the X-reg should be 200i200. efficiently follows the syntax and This is simply random data to verify the S014 XEQ R001 architecture of traditional keystroke mechanics of your input. There’s no need to S015 STO N programming, the alternate method examine why this works at this point. S016 x<>y demonstrates the true power of the HP 35s’ Program LBL J is a dependent subroutine S017 STO E ability to digest complicated equations. utility that manipulates a complex number S018 GTO T001 This example affords a shift in logic from (coordinate pair) into its rectangular compo- traditional keystroke step programming to nents and stores the values for later use. S019 RTN equation based programming. Besides the obvious reduction in programming lines, J001 LBL J The program can be verified by storing unlocking the power of this equation logic J002 ENTER the complex number 99i120 into variable C. also patents the opportunity to expand J003 SF 10 Run the program and enter point number 1 our conventional wisdom beyond the at the J? prompt. Press R/S and you should J004 EQN “RCL PNT” established frontiers of RPN practice. After see the point number and the coordinate realizing the “wow” factor of this equation J005 FIX 0 values in complex format. Press R/S again logic, I cut a big ol’ slice of humble pie J006 INPUT J and the word “NONEXISTENT” should and understood why a rectangular/polar J007 x=0? appear. This indicates that the program was conversion key may not be such a big deal correctly entered but LBL T (traverse) has J008 GTO T011 in the larger world of mathematics and yet to been defined. That’s okay! handheld calculators. It took me a while but J009 FIX 2 This installment’s routines are I finally caught up with HP’s foresight. J010 VIEW (J) intermediate building blocks for several Program LBL A is a dependent subroutine J011 RCL (J) programs. The routines that follow will be utility that manipulates and applies the J012 ARG the actual working programs that produce traverse course to the point coordinates then tangible results. The format of the next few J013 LASTx returns to the traverse program at line T034. installments will include a programming J014 ABS routine, instructions, and sample data for A001 LBL A J015 XEQ R001 use. The next installment will focus on the A002 RCL E J016 STO N azimuth traverse routine and data entry conventions. Hopefully the information A003 RCL N J017 x<>y presented herein is clear and genuinely J018 STO E A004 XEQ P001 explanatory. Please do not hesitate to send A005 x<>y J019 RTN any comments, concerns, questions, or A006 XEQ C001 criticism to [email protected]. ◾ The program can be verified by entering A007 + coordinates for a point using program LBL A008 R▲ H. The program will recall that point and A009 CLx display the rectangular components of that Since 2012, Jason Foose has served as Arizona’s Mohave County Surveyor. He is licensed in A010 x<>y point in the X-reg and Y-reg accordingly. Arizona, Colorado, and Nevada and has been Again this is simply random data to verify practicing since the Cleveland Browns 33rd A011 RTN the mechanics of your input. anniversary of Superbowl celibacy.

This Month’s Programs So, on that bombshell this program may W011 R▼ have often wondered how the term be more appropriately labeled “Solving W012 270 “inverse” was introduced into the for a direct, two-dimensional, polar vector W013 x>y? parlance of Coordinate Geometry. of minimal magnitude defined by the I am licensed in several states to trigonometric relationship between two W014 GTO W039 identify the physical boundary of independent points on a horizontal plane”… W015 R▼ Ia bundle of ownership rights on the face or we could just stick with “inverse”. W016 +/- of the earth and represent those findings Program LBL U is a dependent W017 360 on a flat media by reporting measurements subroutine that enables an independent W018 + of horizontal distances and bearings. The point number input when branched to the function of “identification” is my service, functional portion of Program LBL J at W019 >HMS obligation, and thus my profession, line J009 (See November 2014 “A few inner W020 x<>y whereas “reporting” is merely a mechanical workings” program listing). W021 SF 10 expression employed to demonstrate my W022 EQN “NW” opinion. A geodesist on the other hand, U001 LBL U W023 RTN does not offer an opinion, but rather reports U002 FIX 0 W024 R▼ a scientifically derived estimate of the size U003 INPUT J and shape of the earth, or portions thereof, W025 >HMS U004 FIX 2 dependent upon mathematic expressions. W026 x<>y According to Wolf and Ghilani’s Eleventh U005 RCL J W027 SF 10 Edition of Elementary Surveying (©2006) U006 RTN W028 EQN “NE” “Geodetic position computations involve W029 RTN two basic types of calculations, the direct Program LBL W is a dependent ▼ and inverse problems.” In a nutshell, subroutine that evaluates an azimuth and W030 R the Geodesist’s direct problem resolves outputs the appropriate quadrant bearing W031 +/- a new position given a known position, designator. To test your data entry simply W032 180 a direction, and a distance, whereas his enter a sample of 360° North oriented W033 + inverse problem resolves the direction and azimuth value and XEQ W. You should W034 >HMS distance between two known points. From return the according quadrant bearing W035 x<>y this it is apparent that the term “inverse” designator (i.e. 135°=SE). is derived from the geodetic component W036 SF 10 of surveying which involves spherical W001 LBL W W037 EQN “SE” geometry, elliptical gyrating, some crazy W002 CF 10 W038 RTN science hairdo and a smoking slide rule to W003 x<>y W039 R▼ determine a physical relationship between W004 90 W040 180 two points. Meanwhile, back at the ranch, we just want to keep friendly terms W005 x>y? W041 - between our neighbors so we measure W006 GTO W024 W042 >HMS everything flat with right triangles. I’ll offer W007 R▼ W043 x<>y a resolution that the term “inverse” broadly W008 180 W044 SF 10 encompasses a host of geodetic applications W009 x>y? W045 EQN “SW” that include more than just my 3-4-5 rope W010 GTO W030 stretched between a couple of old rocks. W046 RTN

I006 SF 10 ©2014 JASON E. FOOSE I007 EQN “1ST POINT” Example Data and Running the Program I008 XEQ U001 Use program H “POINTS” to enter our sample points as follows: I009 FIX 2 1. N-5000.00, E- 5000.00 2. N-5210.00, E-5204.12 I010 XEQ J009 3. N-4872.00 E-5101.00 I011 Σ+ I012 SF 10 KEYSTROKE RESULTANT DISPLAY ACTION STEPS I013 EQN “2ND PNT” XEQ COS ENTER Y-reg : Executes program {I} and displays I014 XEQ U001 X-reg : INVERSE program annunciator. I015 XEQ J009 R/S Y-reg : Annunciator for origin point. I016 - Σ X-reg :1st PNT I017 FIX 4 I018 Σx R/S Y-reg : J? Prompt for input point. X-reg : default value I019 Σy I020 XEQ P001 1 R/S Y-reg : (1)= Displays point coordinates. I021 180+REGY X-reg : 5000.00 i 5000.00 I022 x<>y R/S “RUNNING” then Annunciator for terminus point. I023 XEQ W001 Y-reg : nd I024 STOP X-reg : 2 PNT I025 GTO I001 R/S Y-reg : J? Prompt for input point. X-reg : default value I026 RTN 2 R/S Y-reg : (2)= Displays point coordinates. X-reg : 5,210.00 i 5,204.12 INVERSE: noun 4. an inverted state or condition. R/S “RUNNING” then Quadrant Bearing annunciator. 5. something that is inverse; the Y-reg : direct opposite. X-reg : NE 6. Mathematics. R/S Y-reg : 44.1111 The Quardant Bearing value (DMS) is a. an element of an algebraic X-reg : 292.8655 displayed in the Y-reg and the distance is system, as a group, correspond- displayed in the X-reg. Display fix value ing to a given element such that is set to 4 places to resolve the angular its product or sum with the given precision to seconds. The solution is element is the identity element. N44°11'11"E 292.87 (distance units) b. inverse function. R/S Y-reg : Annunciator and return to program top. c. a point related to a given point X-reg : INVERSE so that it is situated on the same radius, extended if necessary, of Inverse Check Data a given circle or sphere and so Points 1 to 3=S 38°16'32" E 163.05 distance units thatthe product ofthe distances Points 2 to 3=S 16°57'59" W 353.38 distance units of the two points from the center equals the square of the radIus of the circle or sphere. Hopefully the information presented herein is clear and genuinely explanatory. Please do d. the set of such inverses of the not hesitate to send any comments, concerns, questions, or criticism to [email protected]. ◾ points of a given set, as the points on a curve. Jason Foose is the County Surveyor of Mohave County Arizona. He has been licensed since SOURCE: DICTIONARY.COM 11111010000 and believes there are 10 types of people in the world, those that understand binary and those who don’t.

“But no longer to light candles to see the sun by, let me come certain quantity of acres has been given to be laid out five or to my business, which is to speak something concerning the six times as broad as long. This I know is to be taught by a following book; and if you ask, why I write a book of this mathematician; yet to such as have no more of this learning, nature, since we have so many very good ones already in than to know how to measure a field, it seems a difficult our own language? I answer, because I cannot find in those question: and to what book already printed of Surveying shall books, many things, of great consequence, to be understood they repair to, to be resolved?” by the Surveyor. I have seen young men, in America, often nonplus’d so, that their books would not help them forward, —John Love, Geodaesia: The Art of Surveying and particularly in Carolina, about laying out lands, when a Measuring of Land Made Easie circa 1688 A.D.

ohn Love’s observations distinguish associated with software keystrokes. It is T014 RCL E the Professional Surveyor in in this light that our beloved HP calculator T015 RCL N America from the singular technical becomes a positive augmentation to our act of measurement. Love identifies individual professional knowledge. T016 XEQ P001 J the natural cause for professional T017 x<>y development and through his work he This Month’s Programs T018 XEQ C001 championed that cause on the American Traverse is a “point and direction” style T019 FIX 0 Continent. Rather than entrusting his program. Traverse azimuth entry is based on profession to European Academia he a 360˚ north oriented zero circle accepted in T020 INPUT J asserted his own undivided professional decimal degrees. I have included an option T021 x<>y discretion towards the development of oth- to key in p.o.b. coordinates or recall point T022 STO(J) ers and openly apportioned his knowledge. coordinate values from storage. T023 FIX 2 Love truly recognized that the Art of Surveying cannot be wholly conveyed from T001 LBL T T024 VIEW(J) the confined walls of any Institution. I have T002 SF 10 T025 FIX 4 found that Love’s presentation in 1688 is T003 EQN “AZIMUTH TRAVERSE” T026 INPUT A archetypical of the following references sit- T004 FIX 0 T027 FIX 2 ting on my bookshelf: Davies 1870 Elements of Surveying and Leveling; the 1913 I.C.S. T005 SF 10 T028 INPUT D Civil Engineer’s Handbook; Davis, Foote, T006 EQN “0=INP 1=RLC” T029 FIX 2 and Rayner’s 1928 Surveying; Bouchard T007 x=0? T030 RCL D and Moffit’s 1969 Surveving Fifth Edition; T008 GTO T011 T031 RCL A and Wolf and Ghilani’s 2006 Elementary Surveying. Geodaesia is relevant 326 years T009 XEQ J001 T032 XEQ C001 later because it shares a true professional T010 GTO T025 T033 XEQ A001 understanding of Land Surveying. Imbibing T011 FIX 2 T034 STO C that knowledge recorded in Geodaesia is T012 INPUT N T035 XEQ S001 more binding to professional development than any Pavlovian memorization exercise T013 INPUT E T036 RTN

“I answer, because I cannot find in those books, many things, of great consequence, to be understood by the Surveyor.” —John Love 1688

Example Data and Running the Program

KEYSTROKE STEPS RESULTANT DISPLAY ACTION XEQ 9 ENTER Y-reg : Executes program {T} and displays program annunciator. X-reg : AZMTH TRAVERSE R/S Y-reg : Prompt for INPUT or POINT RECALL.(See below for POINT X-reg : 0=INP 1=RCL RECALL instructions in green) 0 R/S Y-reg : N? Prompt for Northing. X-reg : default value 5000 R/S Y-reg : E? Enter Northing. Prompt for Easting automatically appears. X-reg : default value 7000 R/S “RUNNING” then Enter Easting. Prompt for point storage number automatically Y-reg : J? appears. X-reg : default value 1 R/S Y-reg : (1)= Enter point number for storage. Stored point is displayed as X-reg : 5,000.00 i 7,000.00 complex number. R/S Y-reg : A? Prompt for 360˚ North oriented Azimuth in decimal degrees. X-reg : default value 180 ENTER 45.3030 YLS 8 Y-reg : A? This is an intermediate step demonstrating the ability to {HMS→} - X-reg : 134.4917 use the functioning stack during input. The input bearing is S 45˚30’30” E. The active stack permits the user to freely convert quadrant bearings to 360˚ azimuth. S 45˚30’30” E = 180-45.3030 converted to Decimal Degrees or 134.4917˚ (See ATB conversion table below). The user may also take the liberty of programming the HMS→ conversion by inserting the following lines T026 as follows: T026 INPUT A T027 RCL A T028 HMS→ T029 STO A T030 will be the old T027 FIX2 function as the lines advance after insertion. R/S Y-reg : D? Prompt for distance. Again the stack is functional. For example X-reg : default value you could add up a series of lot distances along a block line to determine an overall 100 R/S “RUNNING” then Prompt for point storage. Y-reg : X-reg : STORE POINT R/S “RUNNING” then Prompt for point number. Y-reg : J? X-reg : default value 2 Y-reg : J? Input desired point number. X-reg : 2 R/S Y-reg : (2)= Stored point is displayed as complex number. X-reg : 4929.92 i 7,071.34 R/S “RUNNING” then Program returns to it’s top for additional input. AZMTH TRAVERSE

Displayed with permission • The American Surveyor • November/December 2014 • Copyright 2014 Cheves Media • www.Amerisurv.com POINT RECALL INSTRUCTIONS Use program H “Points” to store Point 1 with N:5000 E:7000, then run TRAVERSE through step 2 as listed above and continue with the listing below.

R/S Y-reg : Prompt for INPUT or POINT RECALL. (The program is initiated X-reg : 0=INP 1=RCL and run as shown above to this point) 1 R/S Y-reg : Recall annunciator. X-reg : RCL POINT R/S Y-reg : J? Prompt for point number input automatically appears. X-reg : default value 1 R/S Y-reg : (1)= Enter point number for recall. Recall point is displayed as X-reg : 5,000.00 i 7,000.00 complex number. R/S Y-reg : A? Prompt for 360˚ North oriented Azimuth in decimal degrees. X-reg : default value (The program continues as above from this point)

Azimuth to Bearing Conversion Table QUADRANT BEARING ARITHMETIC AZIMUTH Remember to convert to decimal degrees YLS 8 Converted to decimal degrees YLS 8 N 45˚00’00” E NONE 45.0000

S 45˚00’00” E 180˚-THE BEARING IN DECIMAL DEGREES 135.0000

S 45˚00’00” W 180˚+THE BEARING IN DECIMAL DEGREES 225.0000

N 45˚00’00” W 360˚-THE BEARING IN DECIMAL DEGREES 315.0000

This Month We Have a Bonus Equation! RMD((450-REGX),360) Polecat of Add this equation to your EQN library. It converts azimuth values from the Argand the Month Plane into a 360˚ North based system. The Argand Plane is HP’s angular reference The Polecat of the Month Award goes plane in which zero is east and the angles to Mark Leasure, L.S. I. of GMS, INC. progress either left (counterclockwise, located in Colorado Springs, Co. Mark positive, north) or right (clockwise, negative, dug up a grub worm in line H016 of south) of the latitudinal axis to 180°. This the “Points” listing located on page 15 is apparent when complex coordinates are ©2014 JASON E. FOOSE of the September 2014 issue. The line both negative (The southwest quadrant to should read us rope stretchers, right?) and the argument “H016 EQN N x 1i0 + E 1θ90”. function (or a polar display conversion) desires a sample data and/or any additional yields a modulus (azimuth) for example of instructions should not hesitate to contact My apologies to the readers and staff -135°. Simply run this equation with the me. In the next installment I will present an for my oversight and as well as my undying gratitude to Mark Leasure. argument of the Argand value (-135°) in inverse program. Hopefully the information Thanks for the catch and a toast to our the X-reg. The result being 225°. There’s a presented herein is clear and genuinely polecat of the month as he dons his similar function in Excel named MOD. It explanatory. Please do not hesitate to send orange vest to swim in the melee of follows this form: any comments, concerns, questions, or traffic that the locals refer to as I-25! criticism to [email protected]. ◾ =MOD(450-the Argand value,360)

So far we have a pair of tools to create, Jason Foose is the County Surveyor of Mohave County Arizona. He has been licensed store and review coordinates. Traverse since 11111010000 and believes there are should be somewhat self-explanatory to 10 types of people in the world, those that most folks familiar with COGO. Anyone that understand binary and those who don’t.

Displayed with permission • The American Surveyor • November/December 2014 • Copyright 2014 Cheves Media • www.Amerisurv.com JASON E. FOOSE, PS the HP 35s calculator A Field Surveyor’s Companion Part 5—Inverse to a Line or Perpendicular Offset

This Month’s Program O026 .EQN. “OFFSET PNT” O059 .EQN. “RPT LINE=0” his program is comparable O027 RCL B O060 x=0? to “inverse to line” and “station/offset” routines. O028 FIX 0 O061 GTO O026 The user enters a base point O029 INPUT J O062 GTO O002 and defines a direction by O030 RCL (J) O063 RTN point or azimuth, then selects a third point O031 x<>y for reference. I use this routine frequently ▼ when evaluating rights-of-way lines. O032 R Example Data and Running O033 x<>y the Program STA-OFFSET O034 - Use program H “POINTS” to enter our O001 LBL O O035 ARG sample points as follows: 1: N-5000.00, E- 5000.00 O002 FIX 2 O036 STO Y 2: N-5210.00, E-5204.12 O003 SF 10 O037 LASTx 3: N-4872.00 E-5101.00 O004 .EQN. “STA-OFFSET” O038 ABS O005 .EQN. “BASEPOINT” O039 STO Z KEYSTROKE RESULTANT ACTION STEPS DISPLAY O006 FIX 0 O040 RCL X .XEQ. .E. Y-reg : Executes O007 INPUT J O041 RCL Y .ENTER. X-reg : program {O} O008 RCL (J) O042 - STA-OFFSET and displays program annun- O009 STO B O043 STO W ciator. .E. is 2 O010 .EQN. “DIRECTION” O044 SIN keys right of O011 .EQN. “RCL PT=1 INP=0” O045 RCL x Z (see “recall arithmetic” .ENTER. O012 x=0? User Manual 3-6) .R/S. Y-reg: Annunciator O013 GTO O021 O046 SF 10 X-reg: for Basepoint BASEPOINT input. O014 INPUT J O047 .EQN. “OFFSET -LT RT+ .R/S. Y-reg : J? Prompt for O048 +/- O015 RCL (J) X-reg : input point. O016 R▲ O049 STO O default O017 - O050 FIX 2 value O018 ARG O051 VIEW O .1. .R/S. Y-reg : Annunciator for X-reg : Direction input. O019 STO X O052 RCL W DIRECTION O020 GTO O026 O053 COS .R/S. Y-reg: Annunciator O021 .EQN. “AZIMUTH” O054 RCL x Z X-reg: RCL asking user to O022 FIX 4 O055 STO L PT=1 INP=0 key either “0” or “1” for the O023 INPUT A O056 FIX 2 desired action. O024 RCL A O057 .EQN. “LINE DIST” SEE BELOW FOR O025 STO X O058 VIEW L INPUT OPTION.

Displayed with permission • The American Surveyor • February 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com KEYSTROKE RESULTANT ACTION STEPS DISPLAY .1. .R/S. Y-reg : J? Prompt for X-reg : input point default defining line value direction. .2. .R/S. “RUNNING” Annunciator for then offset point. ©2014 JASON E. FOOSE Y-reg : X-reg : Input Option OFFSET PNT Run program as above to prompt

.R/S. Y-reg : J? Prompt for KEYSTROKE RESULTANT ACTION X-reg : input point. STEPS DISPLAY default of .R/S. Y-reg: Annunciator Polecat value X-reg: RCL asking user to the .3. .R/S. “RUNNING” Annunciator PT=1 INP=0 key either “0” Month then reminder that or “1” for the Y-reg : negative values desired action. The Polecat dumpster is awfully full X-reg : are left of line .0. .R/S. Y-reg: Annunciator this month. My undying gratitude is OFFSET –LT and positive X-reg: reminder to presented to a Lobo, a Buckeye, a RT+ values are right AZIMUTH enter Azimuth Duck, and a Terrapin. My appreciation of line. (decimal goes out to Jeff Richter of Truth or Consequences, New Mexico, Doug .R/S. Y-reg : O= Point 3 is degrees). Crawford of Wapakoneta, Ohio, Al X-reg : 161.64 units .R/S. Y-reg: A? Prompt for Skeesick of Oregon, and Adam Rook 161.64 right of the X-reg: Azimuth of Burtonsville, Maryland. Thank you line from Point default in decimal for your participation, comments and 1 to Point 2. value degrees. concern towards making things better .R/S. “RUNNING” Annunciator .1. .0. Y-reg: Enter sample for the readers! then reminder that .R/S. X-reg: azimuth of 10 Y-reg : line distance OFFSET PNT degrees and A retrospective observation X-reg : LINE will follow. continue the from the readers: DIST Negative program as “Line H016 of program H “Points” is a values fall listed above. bit confusing as printed”. The screen perpendicular The offset for shots below show the full line scrolled before the Point 3 holding left and right. p.o.b. and Line Point 1 in positive values the direction of intersect after 10 degrees is the p.o.b. 121.69 right and -108.52 (behind .R/S. Y-reg : L= Point 3 is or backwards) X-reg : 21.39 units from Point 1. -21.39 behind the Point 1 in the STA-OFFSET is a great tool for evaluating direction of lines and perpendicular offsets. Your Point 2. interest and feedback is greatly appreciated. .R/S. Y-reg: Enter 0 to Hopefully the information presented herein X-reg: RPT hold the is clear and genuinely explanatory. We’ve Wapako-whatta??? LINE=0 existing line covered some basic tools and operations so Doug Crawford of Wapakoneta, Ohio, information far. In the future I will present intersections, kindly pointed out that the “Bonus and compare areas, translate/rotate, stake out, and areas Equation” from the December issue another point. with curves. Please do not hesitate to send should refer to the command “RMDR” Otherwise press any comments, concerns, questions, or rather than “RMD”. The RMDR command .R/S. to escape criticism to [email protected]. ◾ is found on the INTG menu accessed or define a new through keystrokes YLS .TAN. .3.. line. Jason Foose is the County Surveyor of .R/S. Y-reg: Returned to top Mohave County Arizona. He has been licensed X-reg: of program. since 11111010000 and believes there are STA-OFFSET 10 types of people in the world, those who understand binary and those who don’t.

Displayed with permission • The American Surveyor • February 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com JASON E. FOOSE, PS the HP 35s calculator A Field Surveyor’s Companion Part 6—Curve Traverse

This Month’s Program solved by the formula “two times the radius D006 INPUT J his program is a curve times the sine of half Delta”. This establishes D007 FIX 2 traverse routine based upon our “stakeout” distance from the occupied the traditional methods of point to the point on the curve. D008 VIEW (J) laying out a curve with a So, all of this collectively applied yields D009 .EQN. “TAN AZ FWD” transit and tape. I assure the the following process: D010 FIX 4 users of radial layout equipment and GPS T D011 INPUT T that using this program is 100% compatible 1. Set on p.c. and sight p.i. with 0°. with all current land survey measuring 2. Make a data table of Delta, Half Delta, D012 .EQN. “RADIUS” systems, as well as any electronic survey Chord Distance, Arc, and Radius for D013 FIX 2 data collector/total station developed after each point relative to the p.c. January 1, 1959. Those who understand why 3. Turn Angle Right or Left to equal the D014 INPUT R may take a moment to bask in a jocular glow Half Delta for a given point. D015 .EQN. “DEFL θ -L R+” of professional enlightenment and those 4. Set the point at the Chord distance. note: θ is BRS .i. finding comfort in my assurances may wish 5. Repeat for all inter-visible points. D016 FIX 4 to attend my “How to make a jillion dollars D017 INPUT D by giving me $99.99+shipping and handling” The program functions with and through seminar at the Thunderbird Conference this logic. It is set up to return to the AZ D018 CF 10 Center in Granger Township on the 23rd of TRAVERSE program after completion. This D019 .EQN. T+D this month. is a nice segue from leaving a full curve and note: this is an active equation. going through the tangent out. This can be RCL activates variables. Background modified to the user’s preference at line D034. D020 .EQN. R*2*SIN(D) Prior to total stations, electronic data collec- Generally your “tangent in” is going to be the tion, and GPS, the basic method for laying same as the previous bearing leading up to D021 ABS out a curve was to physically occupy the p.c. the P.C. So at the “TAN AZ FWD” prompt you D022 x<>y and sight a point on the back tangent, or the can simply manipulate the bearing into the D023 XEQ C001 p.i, or the p.t. The “Delta” or central angle 360° azimuth using the active stack under D024 RCL + (J) was computed for the each of the desired the prompt. The results are applied by the points on the curve along with the chord .R/S. key. The ability to crank numbers with D025 STO C distance from the occupied point (p.c.). To the stack during an open prompt is one of D026 SF 10 solve for Delta, I simply divide the desired my favorite features of the 35s. Please do not D027 .EQN. “STORE PT” arc length by the radius. This produces the hesitate to send any comments, concerns, delta in radians. The HP 35s keystrokes questions, or criticism to [email protected] D028 FIX 0 BRS .9. converts radians to decimal D029 INPUT J degrees. In the days of yore this conversion The Program D030 RCL C could have been done by hand through the D031 STO (J) formula Decimal Degrees=Radians x 180/π D001 LBL D or simply pulled from a table. The deflection D002 SF 10 D032 FIX 2 angle from the tangent line is equal to D003 .EQN. “CURVE TRAVERSE” D033 VIEW (J) one-half of Delta for any given curve. This D004 .EQN. “PC PNT” D034 GTO T001 establishes our “stakeout” angle or direction from the instrument. The chord distance is D005 FIX 0 D035 RTN

Displayed with permission • The American Surveyor • March 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com Example Data and Running the Program Curve Retracement Use program H “POINTS” to enter our Comment sample point as follows: The examples herein are being offered 1. N-5000.00, E- 5000.00 to demonstrate a generalized method of curve layout. Understanding the CURVE DATA fundamentals of curve layout is a defin- Tangent Bearing in=S87°15’32”E ing circumstance of our legal function as Radius=500.00 retracement surveyors. Suppose we are Delta=-26°53’56”(negative is curve to left) ©2014 JASON E. FOOSE employed to identify the boundaries of a curvilinear tract of land originally subdi- KEYSTROKE STEPS RESULTANT DISPLAY ACTION vided prior to recording laws, electronic .XEQ. .MODE. .ENTER. Y-reg : Executes program {D} equipment, or formal recognition of X-reg : CURVE TRAVERSE and displays program monumentation standards. Utilizing GPS annunciator. .MODE. is to collect a positional attribute provides 1 key right of .XEQ. only two bits of info for analysis. .R/S. Y-reg: Annunciator for Point of X-reg: PC POINT Curvature/Occupied point 1. An independent position of the input. evidence itself; and, .R/S. Y-reg : J? Prompt for input point. 2. A string of text or photo to demon- X-reg : default value strate the physical characteristics of the remaining evidence. .1. .R/S. Y-reg : (1)= Displays point coordinates. X-reg : 5000.00 i 5000.00 Negligently dispatching a field crew to .R/S. Y-reg: Annunciator for the Tangent simply “collect” the positions of bound- X-reg: TAN AZ FORWARD Azimuth input in 360° dd ary corners narrows the Surveyor’s azimuth format. analysis to the singular function of .R/S. Y-reg : T? Prompt for input direction comparing a collection of independent X-reg : default value of forward tangent azimuth. data points against platted geometry Convert the tangent bearing under the assumption that the plat to azimuth with the active exactly matched the work in the field. stack like so: 87.1532 This method begins to discolor in a .YLS. .8. +/- 180 + Your shade of fraud as the Land Surveyor is azimuth should be 92.7411 presumed to know that some impreci- displayed in decimal degrees sion and tolerance is appropriately and ready for use. applied between the original ground {92.7411 from previous Y-reg : Annunciator for radius. markings and the original plat calls. conversion steps} then .R/S. X-reg : RADIUS The unprofessional tendency to .R/S. Y-reg : R? Prompt for radius input. simply perform a comparative analysis X-reg : default value of precise GPS positions against a 500.00 .R/S. Y-reg : Annunciator for half-delta geometric depiction of a lineal survey X-reg : DEFL θ –L +R input. Negative values reflect offers but one analytical element. That curve to the left and positive being the difference between reported values are curve to the right. relationships on the plat vs. indirect .R/S. Y-reg : D? Using the active stack enter positional relationships observed by X-reg : default value 26.5356 .YLS. .8. 2 ÷ +/- the GPS. This unprofessional approach Your half delta in decimal provides zero accountability for the degrees should be -13.4494 allowable tolerances and imprecisions {-13.4494 from previous “RUNNING” then Annunciator for point derived on the ground at the time of the conversion steps} then .R/S. Y-reg : storage. original survey. X-reg : STORE POINT A true retracement survey would .R/S. Y-reg : J? Prompt for point number. better serve its purpose through X-reg : default value application of the original techniques 2 .R/S. Y-reg : (2)= Point 2 is 43.22 north of expected from the original surveyor. For X-reg : 5043.22 i 5228.54 and 228.54 east of Point 1. example physically occupying a pipe Seems reasonable and is the at the P.C. with a modern total station position of the P.T. or a point and observing the deflection angles and on the curve.

Displayed with permission • The American Surveyor • March 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com chord distances to the points on the curve A purely geometric comparison can only may reveal the following: produce the statistical insecurity of non- conformance with the plat. Conversely, 1. The deltas were only calculated practicing the instruction “to follow in the to a precision consistent with the footsteps” provides professional insight original transit. applicable to the evaluation of bona fide 2. All curve points look pretty good evidence. The ability to understand and from the P.C. and landed where replicate the methods employed by the the original surveyor said they original surveyor imparts the retracement would, but none fall precisely on my surveyor with the opportunity to assess the computed overall curve. original imprecision between the original 3. An object obstructed the line of sight points set on the ground vs. the reported along a calculated deflection angle calls of the original plat. This essential so the point was “eased in” around aspect of boundary analysis nourishes our the limited sight line. acceptance and perpetuation of bona fide 4. All the points fit the deflections very evidence. Whereas, the statistical compari- well but the distances were loose. son of positions only establishes an artificial 5. Acceptable limitations of precision rejection parameter without providing any related to the use of slide rules and positive attribute to support the position. tables. Logic employed in the Curve Traverse Program follows in the tradition of transit/ None of these conditions listed above tape methods. You’ll notice that the term demonstrate any legal concern promulgat- “Radius Point” is not mentioned nor is ing the rejection of a monument placed in necessary to the function of laying out a its original position. However, every one of curve. The “radius point” was normally not the conditions reinforces, if not proves, the a part of the field operation and therefore is positive identification of original evidence mostly irrelevant to successful retracement or the perpetuation thereof. and perpetuation of original evidence. ◾

Jason Foose is the County Surveyor of Mohave County Arizona. He has been licensed for ≈ 441,504,000 seconds…no wait, 441,504,001 seconds…no wait, 441,504,002 seconds… adindex

Advanced Geodetic Surveys 50 Microsurvey 41 www.agsgps.com www.microsurvey.com Advanced Graphics Technology 3, 50 Ocean Science 51 www.agtcad.com www.oceanscience.com Berntsen 39 Optech 21 www.berntsen.com www.optech.com Champion Instruments 5 Pacific Crest 55 www.championinstrument.com www.pacificcrest.com CHC Navigation 53 Satlab Geosolutions IBC www.chcnav.com www.satlabgps.com Certified Survey Technician 11 Seiler 50 www.nsps.us.com solutions.seilerinst.com Dunham & Morrow 39 Sokkia BC www.magneticlocator.com www.sokkia.com Curt Brown Chronicles 13 Surv-Kap 54 www.amazon.com www.Surv-Kap.com Eastern Drafting 51 Topcon IFC-1 [email protected] www.topconpositioning.com JAVAD 33-40 (Wingfold) Trimble 7 www.javad.com www.trimble.com Leica 19 VR Mesh 51 Gnss.leica-geosystems.us www.vrmesh.com

he current price range of the HP35s is $50-$60 in the United States. In 1972 a new HP35 cost $395. Adjusting $395 to 42 years of inflation Tequates to about $2,200 according to internet fodder. Going backwards, $60 in 2014 bucks equates to about $10.75 in 1972. It’s no big secret that electronics are really cheap now-a-days and who really cares? Well, I do! I’m teaching you how to wring every single dime out of a $60 dollar black box that is really worth $2,200. Our next few programs require your elbow grease to squeeze the lemonade out of the old black box. Figure 1

This Month’s Program mark to us dirt surveyors. I can assure you They measured linearly and thus they that NGS marks are very static and don’t adjusted measurements linearly. According Background “move”! However, when introducing NGS to “Surveying” by Davis, Foote, and Rayner Why do we even bother to adjust our surveys control into a network, the expectation is to circa 1928, “Many surveyors, however, rely if our modern measuring capabilities are adjust the physical measurement between upon their own judgment, in large measure ridiculously precise to begin with? Least control points to the known adjusted control disregarding any established rule, and squares network adjustment will resolve the values. That is somewhat contrary to our arbitrarily distribute the error in accordance most probable statistical value of measure- expectations as boundary retracement with their estimation of the difficulties met ments and positions. That type of adjustment surveyors. We most often and comfortably in the field. Manifestly, if certain courses truly improves consistency of expectations report varying measurements between are over rough ground, the error of chain- when comparing positional values. Positive legal corners and place our emphasis on the ing these courses would be expected to be applications include baseline networks evidentiary value of a position as controlling relatively large, and the correction to the and level networks. Contrary to our judicial rather than the mathematically derived observed distance should be correspond- function as boundary retracement surveyors, coordinate. {If you feel any challenge to my ingly great; also when sights are steep and the objective of control work is resolving last statement please unsubscribe from The visibility is poor, larger angular errors the most absolute positional value for a American Surveyor. You are not practicing would be expected than where conditions of particular station. For example as in the NGS Land Surveying. You are engaging in some observing are more nearly ideal, and hence case the station mark itself is subordinate sub professional measurement exercise and in balancing the survey it is fair to assume to the values assigned, adjusted, published, you are a FRAUD!!!}. that the larger changes in direction should be updated, and republished as the geodesy Our predecessors did not necessarily seek in the courses where conditions surrounding is refined. I really don’t think that Michael to resolve the most probable statistical value the observations were relatively unfavorable.” Dennis and Dave Minkel sneak out at night of a position but rather aimed to accurately It should be apparent that the quest for the with a hammer and bang every mark on the identify the location of legal evidence. Their absolute mechanical position of a point continent over a smidge. Of course not, they purpose for adjusting measurements was is of little relevance in retracement work. simply report the updated adjustment values to promote consistency for retracement However, employing the compass rule which lend the appearance of a “floating” rather than a truly “most probable value”. adjustment simply provides a consistent

Displayed with permission • The American Surveyor • April 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com method to distribute error through your Example Data and Running measurements. The Program Compass Rule can logically be applied Create a traverse sketch and use field to aid in recovery of evidence when a notes to construct a data table like the consistent difference is noted between plat examples below. Raw coordinate values reports and observed measures. Where are listed to demonstrate differences but original subdivision lines were physically are not apparent while running the routine. run the difference between the physical Raw coordinates are computed by simply end points and the platted positions could assuming the backsight azimuth of N35E be prorated through the line points. The between points 4 and 5 and simply running thought being that accumulated field around the polygon. The program uses the error was accepted on the ground but not statistical accumulator and registers. Access accounted for on the plat. This computa- Ʃ registers through keystrokes BRS - for tion may lead the retracement surveyor the “SUMS” menu. ©2014 JASON E. FOOSE closer to the original evidence of the work as laid out on the ground. Frederick W. SETUP INTERIOR ANGLE Boreman P.S. 6855 (Ohio) used to say “Jase, BACKSIGHT OCCUPIED FORESIGHT ANGLE RIGHT FORESIGHT LEG they’re like clams. When one coughs, it COUNTER DISTANCE gives them all away.” (see Figure 1) CLOCKWISE The benefits of least squares adjustments 4 5 1 159-32-25 330.25 1 are negligible if not perhaps misleading 5 1 2 76-31-45 600.23 2 (too good for the intended purpose) when 1 2 3 89-01-01 598.21 3 applied to modern retracement survey work. The compass rule method is well suited to 2 3 4 89-58-46 330.43 4 retracement efforts because of its simplicity 3 4 5 125-00-48 325.89 5 and repeatability. It is quite a simple premise: any error is proportionally distributed to every measurement in a lineal set according to each measure’s magnitude. Traversing is linear and stations are generally physically dependent upon only the adjoining stations. When measurements are made with consistency they are considered equal in weight so there’s little if no need to apply any sort of arbitrary or statistical weighting. Please do not hesitate to send any comments, concerns, questions, or criticism to [email protected].

The Program

Program B: Compass Rule Traverse Adjustment This program is very dependent on the order and format of the traverse entry. The objective is to get the foresight point number to match the input leg number. The reasoning is that the program operates on a loop counter and requires sequential addressing with the order of the legs as entered. Traverse legs will be overwritten by the values of the computed coordinates as they are addressed to the same register. This may take some rearranging on your part or a change in field numbering discipline. Remember to enter azimuths/ angles in decimal degrees. Final report of angles and azimuths is in DMS format.

Displayed with permission • The American Surveyor • April 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com KEYSTROKE RESULTANT ACTION KEYSTROKE RESULTANT ACTION STEPS DISPLAY STEPS DISPLAY .XEQ. GTO Y-reg : Executes program {B} 2 .R/S. Y-reg : Annunciator to end loop. .ENTER. X-reg : COMPASS and displays program X-reg : END 1=Y Enter 1 to complete the RULE annunciator. 0=N loop or 0 to enter another “B” is for Bowditch. leg. .R/S. Y-reg: Annunciator/reminder to 0 .R/S. Y-reg : Annunciator/reminder. This is X-reg: ANGL RT enter angles right, going X-reg : ANGL RT the beginning of the next leg INTRNL counterclockwise, internal INTRNL and follows the same steps. angles (as in “N-2x180”). .R/S. Y-reg : A? Prompt for angle. .R/S. Y-reg : A? Prompt for first angle. This X-reg : default value X-reg : default value is important because your first angle is actually your 89.0101 YLS Y-reg : D? (89.0169 DD) then Prompt closing angle. Your occupied 8 .R/S. X-reg : default value for distance. point is actually your last point in the traverse 598.21 .R/S. “RUNNING” then Annunciator for foresight/ whereas your foresight (1st Y-reg : leg number. leg) is the measurement X-reg : LEG NUMBER to your P.O.B. and closing .R/S. Y-reg : J? Prompt for point number. point. Creating a sketch X-reg : default value and table help to sort this out. You may find simply 3 .R/S. Y-reg : Annunciator to end loop. assuming a sequential X-reg : END 1=Y Enter 1 to complete the point numbering scheme 0=N loop or 0 to enter another to be helpful. I can provide leg. a simple “renumbering” 0 .R/S. Y-reg : Annunciator/reminder. This program” upon request that X-reg : ANGL RT is the beginning of the enables you to reassign INTRNL next leg and follows the values consistent with your same steps. original point numbering schematic. .R/S. Y-reg : A? Prompt for angle. X-reg : default value 159.3225 YLS Y-reg : D? Enter angle in DMS then 8 .R/S. X-reg : default value convert to DD (159.5403) 89.5846 YLS Y-reg : D? (89.9794 DD) then Prompt Prompt for foresight (leg) 8 .R/S. X-reg : default value for distance. distance appears. 330.43 .R/S. “RUNNING” then Annunciator for foresight/ 330.25 .R/S. “RUNNING” then Annunciator for the Y-reg : leg number. Y-reg: foresight/leg number. This X-reg : LEG NUMBER X-reg: LEG NUMBER must begin with 1 and follow sequentially. .R/S. Y-reg : J? Prompt for point number. X-reg : default value .R/S. Y-reg : J? Prompt for leg number. X-reg : default value 4 .R/S. Y-reg : Annunciator to end loop. 1 .R/S. Y-reg : Annunciator to end loop. X-reg : END 1=Y Enter 1 to complete the X-reg : END 1=Y Enter 1 to complete the 0=N loop or 0 to enter another 0=N loop or 0 to enter another leg. leg. 0 .R/S. Y-reg : Annunciator/reminder. This 0 .R/S. Y-reg : Annunciator/reminder. This X-reg : ANGL RT is the beginning of the X-reg : ANGL RT is the beginning of the next INTRNL next leg and follows the INTRNL leg and follows the same same steps. steps. .R/S. Y-reg : A? Prompt for angle. .R/S. Y-reg : A? Prompt for angle. X-reg : default value X-reg : default value 125.0048 YLS Y-reg : D? (125.0133 DD) then Prompt 76.3145 YLS Y-reg : D? (76.5292 DD) then Prompt 8 .R/S. X-reg : default value for distance. 8 .R/S. X-reg : default value for distance. 600.23 .R/S. “RUNNING” then Annunciator for foresight/ 325.89 .R/S. “RUNNING” then Annunciator for foresight/ Y-reg : leg number. Y-reg : leg number. X-reg : LEG NUMBER X-reg : LEG NUMBER .R/S. Y-reg : J? Prompt for point number. .R/S. Y-reg : J? Prompt for point number. X-reg : default value X-reg : default value

Displayed with permission • The American Surveyor • April 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com KEYSTROKE RESULTANT ACTION KEYSTROKE RESULTANT ACTION STEPS DISPLAY STEPS DISPLAY 5 .R/S. Y-reg : Annunciator to end loop. .R/S. Y-reg : Annunciator for adjustment X-reg : END 1=Y Enter 1 to complete the X-reg : ADJUSTMENT routine. 0=N loop or 0 to enter another .R/S. Y-reg : Annunciator for point leg. We have returned to our X-reg : STORE POINT storage loop. This process first occupied station and requires user keystrokes but have completed the loop of could be automated. The 5 traverse legs. Select “1” at user can review coordinates the next prompt to complete during the routine. (end) the traverse. .R/S. Y-reg : J? Prompt for 1st point 1 .R/S. Y-reg : Annunciator for the sum of X-reg : default value number and Point Number X-reg : SUM OF the angles in the polygon. 1. Sequential order must be ANGLES observed or the coordinates .R/S. Y-reg : default value Sum in X-reg DMS format. generated within the routine X-reg : 540.0445 could be overwritten. .R/S. Y-reg : Annunciator. 1 .R/S. Y-reg : (1)= Point 1 adjusted coordi- X-reg : PERIMETER X-reg : 4,680.20 i nates. This is generated 4,917.12 from point 5 coordinates .R/S. Y-reg : 540.0445 Perimeter distance in X-reg. 5000i5000, the backsight X-reg : 2,185.01 Sum is bumped up to Y-reg. azimuth of N35E, the .R/S. Y-reg : Annunciator for the angular adjusted angle of the 1st X-reg : PER ANGLE surplus/deficiency required leg, and dispersed error. to balance angles. .R/S. “RUNNING” then Annunciator/reminder. .R/S. Y-reg : In DMS. Negative values Y-reg : X-reg : -0.0057 represent excess to be X-reg : STORE POINT subtracted.. .R/S. Y-reg : J? Prompt for sequential store X-reg : default value point. .R/S. Y-reg : Annunciator beginning the X-reg : RUN closure function. 2 .R/S. Y-reg : (2)= Point 2 adjusted coordinates. CLOSURE X-reg : 4,669.13 i 5,517.15 .R/S. Y-reg : N? Prompt for POB northing X-reg : default value coordinate. POB is point .R/S. “RUNNING” then #5 in this scenario and the Y-reg : same as the first occupied X-reg : STORE POINT point on our table. .R/S. Y-reg : J? 5000 .R/S. Y-reg : E? Prompt for POB easting X-reg : default value X-reg : default value coordinate. 3 .R/S. Y-reg : (3)= Point 3 adjusted coordinates. X-reg : 5,267.15 5000 .R/S. “RUNNING” then Annunciator for the i 5,517.46 Y-reg : backsight azimuth of the X-reg : BACKSIGHT first setup. In this scenario .R/S. “RUNNING” then AZ it is an assumed direction Y-reg : between points 5 and 4. X-reg : STORE POINT The BACKSIGHT AZ is always .R/S. Y-reg : J? an assigned direction X-reg : default value between the last two points 4 .R/S. Y-reg : (4)= Point 4 adjusted coordinates. of the traverse. X-reg : 5,267.06 i .R/S. Y-reg : A? Prompt for 360 degree north 5,186.98 X-reg : default value azimuth in DD. YLS 8 .R/S. “RUNNING” then added below for emphasis. Y-reg : 35 YLS 8 “RUNNING” then Annunciator for misclosure. X-reg : STORE POINT .R/S. Y-reg : The sceen may display .R/S. Y-reg : J? X-reg : MISCLOSURE “running” for an extended X-reg : default value period of a minute or so. 5 .R/S. Y-reg : (5)= Point 5 adjusted coordinates .R/S. Y-reg : Annunciator for precision X-reg : 5,000.00 i and closure. X-reg : 1 UNIT IN X ratio. 5,000.00 .R/S. Y-reg : 1 1 unit in 2,762 units. .R/S. Y-reg: .R/S. to exit. X-reg : 2,762 Y-reg=1 X-reg=2,762. X-reg: DONE

Displayed with permission • The American Surveyor • April 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com Program Listing B044 .EQN. 1+0 STO J B088 RCL E Note: STO appears as a right B089 RCL N B001 LBL B arrow in .EQN. B090 XEQ P001 B002 SF 10 B045 INPUT N B091 x<>y B003 .EQN. “COMPASS RULE” B046 INPUT E B092 XEQ C001 B004 CLΣ B047 RCL E B093 +/- B005 CLVARS B048 RCL N B094 STO + C B006 FIX 4 B049 XEQ P001 B095 RCL C B007 .EQN. “ANGL RT INTRNL” B050 x<>y B096 ABS B008 INPUT A B051 XEQ C001 B097 Σx B009 INPUT D B052 STO C B098 FIX 0 B010 Σ+ B053 STO B B099 SF 10 B011 RCL D B054 SF 10 B100 .EQN. “MISCLOSURE” B012 RCL A B055 .EQN. “BACKSIGHT AZ” B101 x<>y B013 XEQ C001 B056 INPUT A B102 ÷ B014 .EQN. “LEG NUMBER” B057 RCL A B103 1 B015 FIX 0 B058 RCL F B104 SF 10 B016 INPUT J B059 RCL (J) B105 .EQN. “1 UNIT IN X” B060 ARG B017 R▼ B106 x<>y B061 + B018 STO (J) B107 STOP B062 RCL A B019 FIX 0 B108 .EQN. B063 + “ADJUSTMENT” B020 .EQN. “END 1=Y 0=N” B064 RCL (J) B109 CF 10 B021 x=0? B065 ABS B110 .EQN. 0.001*(J-2) B022 GTO B006 B066 x<>y B111 STO L B023 FIX 4 B067 STO A B112 .EQN. 1+0 STO J B024 .EQN. “SUM OF ANGLES” B068 XEQ C001 B113 .EQN. 1+0 STO G B025 Σy B069 STO (J) B114 RCL (J) B026 >HMS B070 RCL C B115 FIX 2 B027 STOP B071 + B116 RCL C B028 FIX 4 B072 STO C B117 Σx B029 .EQN. “PERIMETER” B073 RCL A B118 ÷ B030 x Σ B074 180 B119 RCL (J) B031 STOP B075 ENTER B120 ABS B032 FIX 4 B076 R▼ B121 x (multiply) B033 .EQN. “PER ANGLE” B077 xHMS B081 +/- B126 + B038 STOP B082 + B127 RCL B B039 SF 10 B083 STO A B128 + B040 .EQN. “RUN CLOSURE” B084 1 B129 STO B B041 CF 10 B085 STO + J B130 SF 10 B042 .EQN. 0.001*(J-1) B086 ISG L B131 .EQN. “STORE PNT” B043 STO L B087 GTO B057 B132 FIX 0

Displayed with permission • The American Surveyor • April 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com B133 INPUT J B134 RCL B B135 FIX 2 B136 STO (J) Did You Polecat of B137 VIEW (J) Know? the Month B138 CF 10 B139 1 Do you actually know the name of Mark E. Hummel, hailing from a B140 RCL + G the division symbol? You know, the certain un-named city holding six minus sign wedged between a colon? B141 STO G Superbowl titles and the rings to Well apparently Bill Gates forgot to prove it, pointed out that Line I021 B142 STO J put it in my Microsoft Office Suite so of the January 2015 Inverse Routine B143 ISG L I set sail in that ocean of knowledge should include the keystroke .EQN.. B144 GTO B115 we call the internet. I found that the Mark Hummel’s great catch is second B145 SF 10 division symbol is named “obelus” only to Franco Harris’ Immaculate and is available in MS Windows B146 .EQN. “DONE” Reception in Iron City lore. Thanks through keystrokes Alt+0247 on the Mark for pointing it out! B147 RTN keypad ÷ there, see I just did it! I’ll do it again ÷ this is fun ÷ oh, BTW, sorry Bill I stand corrected! Jason Foose is the County Surveyor of Mohave County Arizona. He has been licensed for ≈ 441,504,000 seconds…no wait, 441,504,001 seconds…no wait, 441,504,002 seconds…

ccording to Brown, This Month’s Program 7 5,153.02 5,039.66 Robillard, and Wilson’s Program K: The Area program simply CRV Δ 75˚27'19" RAD 152.2316* “Boundary Control and resolves the “area by coordinates” of a Legal Principles” third flat sided polygon then adds or subtracts *Follow consistent rules when computing to edition, area is the second the area of a segment of a circle for curve a level of precision. “Four decimal places” is well beyond my reasonable ability to Aleast controlling factor in the order of con- areas. Segments are added or subtracted measure as well as beyond the quality of any flicting title elements and followed only by accordingly dependent on if the curve computed value in this example. Using the coordinates. However in the public’s eye area is an “outie” or an “inny” to the polygon. radius value carried out to 152.2316 yields is a most important factor in identifying land. Curve segment area formulae can be a square footage of 308,261.82 whereas the value of 152.23 yields the value of 308,261.73 I believe that the simple description “Jason’s easily wrangled up on the fruited prairie which equates to .09 of a square foot or the 10 acres in Mohave County, Arizona,” could of information we call “the internet”. area of a classroom ruler. I honestly don’t serve to effectively and legally convey land. “Area by coordinates” can be referenced measure land that well, nor do you! However, I’d be willing to bet that the PLSS guys are in many land surveying texts including you may want to expend some attention when large highway curves are encountered. already thinking “660' x 660' ”, the Colonial “Elementary Surveying” Eleventh edition Understanding the effects of computations Boys are on their way to the courthouse to by Wolf and Ghilani. I find my oldest is important in a mechanical sense but get my neighbor’s deeds, and the Texans reference in “Surveying” by Davis, ultimately the varying computations should don’t count anything under 40. Land owner- Foote, and Rayner copyright 1928. A collectively net consistent and tolerable results. Society is not interested in the claim ship seems to be commonly associated with boundary retracement surveyor is well that your answer is “more righter” than quantity. I suppose that’s because quantity served by pole-catting through the used mine. They simply expect us to agree…and is an easy metric to scale with currency. book stores. Historic Engineering and another thing, please kindly round up those The irony of that concept is that folks will Surveying textbooks demonstrate the decimally inordinate “nines” for the Planning and Zoning folks. You have professional the fight over pennies, and real estate escrow techniques used by our predecessors. It discretion to round and interpret, whereas accounts must balance at exactly $0.00, stands to reason that knowing how your they most likely don’t. but the surveyor has been graced with the predecessor measured is requisite expectation of expressing quantities “more to successful retracement surveying. Use the data from the previous “Compass or less”. Count your blessings and recognize Rule Adjustment” routine. In addition to the imprecision of your measurements when the five existing points I have introduced a expressing significant digits. curve with P.I. #6 and the P.T. #7 to show *A 1.4 square foot difference (308,263.21) Please do not hesitate to send any should show between last month's the complete function of the routine. I will comments, concerns, questions, or criticism computed coordinates and the two place demonstrate how to construct the curve and to [email protected]. decimal values presented herein. solve for the p.i. and p.t. in at a later date.

Displayed with permission • The American Surveyor • May 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com KEYSTROKE RESULTANT ACTION KEYSTROKE RESULTANT ACTION STEPS DISPLAY STEPS DISPLAY XEQ √X Y-reg : Executes program {K} R/S Y-reg : J? Prompt for point number. ENTER X-reg : AREA and displays program X-reg : default value annunciator. 7 R/S Y-reg : (7)= Display point info for review. R/S Y-reg: Annunciator/reminder to X-reg : 5,153.02 i X-reg: CNTR CLKWSE enter coordinate points 5,039.66 going counterclockwise around the polygon. R/S “RUNNING” then Prompt for additional point Y-reg : entry. R/S Y-reg: Annunciator/reminder that X-reg : 1=END ST X-reg: END W 1 PNT you must close the polygon 0=ADD by ending on the first point. Unlike “COMPASS RULE” 0 R/S Y-reg : Annunciator. points can be selected X-reg : RCL POINT regardless of order and are R/S Y-reg : J? Prompt for point number. not dependent upon any X-reg : default value sequential order. R/S Y-reg : Annunciator. 1 R/S Y-reg : (1)= Display point info for review. X-reg : RCL POINT X-reg : 4,680.20 i 4,917.12 R/S Y-reg : J? Prompt for first point X-reg : default value number. R/S “RUNNING” then Prompt for additional point Y-reg : entry. Point 1 is our closing Y-reg: (1)= Display point info for review. 1 R/S X-reg : 1=END point and P.O.B. of the X-reg: 4,680.20 i 0=ADD polygon 4,917.12 1 R/S Y-reg : Annunciator to begin curve R/S “RUNNING” then Annunciator. X-reg : CURVE INPUT data entry. Each curve is Y-reg : entered separately in a X-reg : RCL POINT typical loop sequence. R/S Y-reg : J? Prompt for point number. X-reg : default value R/S Y-reg : Prompt to skip curve entry. X-reg : 1=YES 0=NO 2 R/S Y-reg : (2)= Display point info for review. X-reg : 4,669.13 i 1 R/S Y-reg : Annunciator/reminder for 5,517.15 X-reg : DELTA delta and radius input RADIUS values. R/S “RUNNING” then Annunciator. Y-reg : R/S Y-reg : D? Prompt for delta in decimal X-reg : RCL POINT X-reg : default value degrees.(75.4553 DD)

R/S Y-reg : J? Prompt for point number. 75.2719 Y-reg : R? Prompt for radius. X-reg : default value YLS 8 R/S X-reg : default value

3 R/S Y-reg : (3)= Display point info for review. 152.2316 Y-reg : Prompt to add the segment X-reg : 5,267.15 i R/S X-reg : ADD=1 area (“outie”) or subtract 5,517.46 SBTRCT=0 segment area (“inny”). R/S “RUNNING” then Annunciator. 1 R/S Y-reg : Prompt to continue loop Y-reg : X-reg :0=MORE (add curves) or end. X-reg : RCL POINT 1=END R/S Y-reg : J? Prompt for point number. 1 R/S Y-reg : Annunciator/reminder that X-reg : default value X-reg : Y REG=SQ FT Square Feet value will be 4 R/S Y-reg : (4)= Display point info for review. displayed in Y-reg. X-reg : 5,267.06 i 5,186.98 R/S Y-reg : Annunciator/reminder X-reg : X REG=ACRES that Acreage value will be R/S “RUNNING” then After the minimum 4 points displayed in X-reg. Y-reg : are entered the program X-reg : 1=END prompts for additional point R/S Y-reg : 308,261.82 308,262 square feet and 0=ADD entry. X-reg : 7.08 7.08 acres. 0 R/S Y-reg : Annunciator. R/S Y-reg: Return to top of program. X-reg : RCL POINT X-reg: AREA

K001 LBL K K045 EQN “1=YES 0=NO” K002 SF 10 K046 x=0? Bonus K047 GTO K077 K003 EQN “AREA” Equations K048 EQN “DELTA RADIUS” K004 EQN “CNTR CLKWSE” K049 CF 10 HMS+ HMS- K005 EQN “END W 1ST PNT” K050 EQN 0►X K006 XEQ J001 Open the EQN library EQN ; K051 EQN 0►W K007 STO A Below 3X3 (linear solver) enter the K052 EQN 0►V K008 x<>y following equations; K053 CF 10 K009 STO B K054 FIX 4 Addition HMS+ K010 XEQ J001 K055 INPUT D BRS 8 YLS 8 R↓ ENTER K011 EQN B*REGX B ► GREY RIGHT ARROW-(advances K056 EQN D/2►C K012 EQN A*REGZ►A 1 space right) + YLS 8 R↓ K057 FIX 2 K013 RCL(J) GREY LEFT ARROW –(selects the K058 INPUT R X-reg) ENTER ENTER K014 XEQ J012 K059 CF 10 K015 STO D K060 EQN (D/360)*SQ(R)*π►Z Subtraction HMS- K016 x<>y K061 EQN BRS 8 YLS 8 R↓ ENTER K017 STO C (R*SIN(C))*(R*COS(C))►Y GREY RIGHT ARROW (advances K018 XEQ J001 K062 SF 10 1 space right) - YLS 8 R↓ GREY LEFT ARROW (selects the K019 EQN C*REGX►C K063 EQN “ADD=1 SBTRCT=0" X-reg) ENTER ENTER K020 EQN D*REGZ►D K064 x=0? K021 CF 10 K065 GTO K070 Screen Shot K022 EQN A+D►H K066 CF 10 3*3 LIN. SOLVE K023 EQN B+C►I K067 EQN Z-Y →HMS(HMS→(REGY)+HMS→(REGX)) →HMS(HMS→(REGY)–HMS→(REGX)) K024 RCL(J) K068 STO+ W K025 XEQ J012 K069 GTO K073 Notes: BRS and YLS are right and left K026 STO D K070 CF 10 with colors; the grey arrows left and K027 x<>y K071 EQN Z-Y right are the arrow keypad in the K028 STO C K072 STO+ V upper right portion of the keyboard. They indicate moving the cursor. K029 XEQ J001 K073 SF 10 The “Roll down” key pulls up the K074 EQN “0=MORE 1=END” K030 EQN C*REGX►C addressing for the x & y registers. K031 EQN D*REGZ►D K075 x=0? K032 EQN H+D►H K076 GTO K053 To run: K077 EQN Set display to fix 4; K033 EQN I+C►I “Y REG=SQ FT” HMS+ exit from EQN mode; K078 EQN “X REG=ACRES” K034 EQN (H-I)/2►K Enter an azimuth in HMS; 45.3030 K079 CF 10 K035 SF 10 Enter another azimuth in HMS; K080 EQN ABS(K+W-V) K036 EQN “1=END 0=ADD” 90.3050 K081 EQN ABS(K+W-V)/43560 Hit the EQN K037 x=0? K082 STOP Select the HMS+ equation K038 GTO K024 Hit ENTER to run. K083 GTO K001 K039 CF 10 The solution 136.0120 will be in the K084 RTN K040 EQN 0►X X-reg in HMS. Follow the same steps and select the K041 EQN 0►W Jason Foose is the County Surveyor of Mohave subtraction equation if desired. K042 EQN 0►V County Arizona. He has been licensed for ≈ 441,504,000 seconds…no wait, 441,504,001 K043 SF 10 seconds…no wait, 441,504,002 seconds…

Displayed with permission • The American Surveyor • May 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com JASON E. FOOSE, PS the HP 35s calculator A Field Surveyor’s Companion Part 9—Intersections

e can calculate This month we will focus on Azimuth/ anything and Azimuth(Direction/Direction) and create everything under the curve referenced in the AREA program the sun or the dismal installment. The Direction/Distance and grey Cleveland skies Distance/Distance examples will follow ofW FirstEnergy Stadium, however, a decision next month. I encourage all readers to to set aside previously fixed local survey legal try the routines preemptively and send subdivision corners must be supported by evi- feedback. I promise a speedy response and dence that goes beyond mere demonstration I’ll do my best to include your comments in of technical error, reasonable discrepancies the next installment. I think the good folks between former and new measurement, and of the campus bookstore bevy refer to that less than strict adherence to restoration and ©2015 JASON E. FOOSE as “an interactive reader experience”. subdivision rules. Were (we) obliged to open the question as to the location of a particular defining the act of subdividing lands gestat- Example Data and Running tract or tracts over technical differences ing within the prenatal title of a sovereign. The Program or reasonable discrepancies, controversies The fabric of the non-federal arena is on the We will reference our previous data set as would constantly arise, and resurveys and other hand a series of bona fide conveyances follows: readjudication would be interminable. The referencing protracted division lines within a PNT NORTH EAST law gives these activities repose. section. The weight of conveyancing coupled 1 4,680.20 4,917.12 “Oh, what’s this pile of meadow muffins?” with occupation and local surveys is whole- you say. Well, save the dismal grey non- heartedly acknowledged in numerous places 3 5,267.15 5,517.46 Superbowl rubbish, it is a direct quote from throughout the 2009 Manual. So, before 4 5,267.06 5,186.98 the summary of Chapter III section 137 of you open up to page 68 and intersect those 5 5,000.00 5,000.00 the 2009 BLM Manual of Instruction located straight lines to fire another salvo into the 1-5 N 14°31’45” E 330.36 on page 74. The instructions to establish center quarter, remember that retracement 3-4 S 89°59’04” W 330.48 the center of section in the vacuum of title surveying is an evaluation of evidence, not known as the public domain are clearly a pop quiz in geometry class. Consequently If you have carried coordinates through acknowledged as being out of character in “intersection” is a tool not an answer! from the compass rule adjustment article the fruited and colorful non-federal arena. Please do not hesitate to send any you may find insignificant differences in Where States like Colorado have provided comments, concerns, questions, or criticism solutions as noted in the last month’s area the Manual of Instruction as a statutory to [email protected] listing. The source of the error is the differ- reference (CRS 38-51-103.1) they cite “such ence between hand entering coordinates professional land surveyor shall proceed This Month’s Program to two decimal places versus the computed according to the applicable rules contained Program L: Intersections includes routines (adjusted) values that are carried out to the in the current “Manual of Instructions for for Direction/Direction, Direction/ full 12 digit precision of the HP 35s. This is the Survey of the Public Lands of the United Distance, and Distance/Distance. The a great example toward accepting tolerance States” published by the United States…” program operates by assuming a base line in measurement through the assessment rather than “Place the center one-quarter from the first point to the second point. of the source data. The amount of these corner in accordance with Chapter III Section Direction/Distance and Distance/Distance differences is insignificant, however the 114 of the Manual of Instruction”. The States naturally have 2 solutions. The preferential reason they exist must be identified before and their Honorable Courts understand that solution may be defined as being left or considering the impact. I will be reporting the Manual contains a set of instructions right of the line facing the second point. will the 2 decimal coordinates listed above.

Displayed with permission • The American Surveyor • June 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com KEYSTROKE RESULTANT ACTION KEYSTROKE RESULTANT ACTION STEPS DISPLAY STEPS DISPLAY XEQ yX Y-reg : Executes program {L} R/S Y-reg : A? Prompt for azimuth in ST ENTER X-reg : and displays program X-reg : default decimal degrees from 1 INTERSECTIONS annunciator. value point. The objective is to note: the “L” key is between intersect lines 1-5 with 3-4 the square root and recipro- to create the P.I. of the curve cal keys. It is the “Y” raised used in the previous AREA to “X” function key. routine. The inverse can be computed beforehand as R/S Y-reg: Annunciator/reminder. RCL found on the data table. Line X-reg: RCL POINT input to follow. 1-5 bears N14°31’45”E and is converted to14.5292 decimal R/S Y-reg: J? Prompt for first point degrees. The northeast X-reg: default value number. quadrant bearing is a direct expression of azimuth. 1 R/S Y-reg : (1)= Display point info for review. X-reg : 4,680.20 i 14.3145 YLS “RUNNING” then Annunciator/reminder. 4,917.12 8 R/S Y-reg : Azimuth input to follow. X-reg : 2ND R/S “RUNNING” then Annunciator/reminder. RCL AZIMUTH Y-reg : input to follow. R/S Y-reg : A? Prompt for azimuth in deci- X-reg : RCL POINT X-reg : default mal degrees from 2nd point. value Line 3-4 is in the southwest R/S Y-reg: J? Prompt for second point quadrant. Convert to decimal X-reg: default value number. degrees (89.9844) and add 3 R/S Y-reg : (3)= Display point info for review. 180°. Azimuth=269.9844 X-reg : 5,267.15 i 89.5904 YLS “RUNNING” then The “RUNNING” may take a 5,517.46 8 Y-reg : minute then annunciator for 180 + R/S X-reg : STORE point storage. R/S “RUNNING” then Prompt for Azimuth/Azimuth POINT Y-reg : intersection. Directly press R/S Y-reg : J? Prompt for point number. X-reg : AZ-AZ 0 R/S to proceed to X-reg : default PRESS 0 AZ-AZ or hit any key(except value zero) R/S to continue menu choices. 6 R/S Y-reg : (6)= Display point info for review. X-reg : 5,267.03 i 0 R/S Y-reg : Annunciator/reminder. 5,069.20 X-reg : 1ST AZIMUTH Azimuth input to follow. R/S Return to program top.

Program Listing L009 EQN (J)►K L022 CF 10 NOTES: The algebraic symbology for L010 1 L023 EQN Z-Y►T multiplication * and division / are used during L011 SF 10 L024 EQN entry. L118 begins with +/- to make “2” EQN Z-Y►U negative. The negative sign will be displayed a L012 EQN “AZ-AZ PRESS 0” L025 FIX 4 fuzz higher than a minus sign. L013 x=0? L026 SF 10 L001 LBL L L014 GTO L022 L027 EQN “1ST AZIMUTH” L002 SF 10 L015 1 L028 CF 10 L003 EQN “INTERSECTIONS” L016 EQN “DS-DS PRESS 0” L029 INPUT A L004 XEQ J001 L017 x=0? L030 RCL A L005 EQN [REGY,REGX] ►Y L018 GTO L086 L031 STO M L006 EQN (J) ►L L019 EQN “AZ-DS” L032 1 L007 XEQ J001 L020 GTO L112 L033 XEQ R001 L008 EQN [REGY,REGX] ►Z L021 STOP L034 x<>y

L036 RCL U L078 EQN “STORE PNT” L119 EQN ABS(V)►V

L037 RCL V L079 FIX 0 L120 EQN SQ(ABS(K-L))-SQ(D)►W

L038 x (multiplication) L080 INPUT J L121 EQN (SQ(V)-(4*W)►R

L039 RCL U L081 x<>y L122 EQN SQRT(R)►R

L040 ABS L082 STO(J) L123 EQN (V+R)/2►S

L041 RCL V L083 FIX 2 L124 EQN (V-R)/2►T L042 ABS L084 VIEW (J) L125 SF 10

L043 x (multiplication) L085 GTO L001 L126 EQN “DIST A-AZ PNT” L044 ÷ (division) L086 EQN “DIST-DIST” L127 RCL T L045 ABS L087 EQN “1ST DIST” L128 STOP

L046 ACOS L088 INPUT D L129 EQN “DIST B-AZ PNT” L047 STO W L089 CF 10 L130 RCL S L048 SF 10 L090 EQN D►U L131 STOP

L049 EQN “2ND AZIMUTH” L091 SF 10 L132 EQN “SAVE A=0 B=1” L050 INPUT A L092 EQN “2ND DIST” L133 x≠0? L051 1 L093 INPUT D L134 GTO L139 L052 XEQ R001 L094 CF 10 L135 RCL T L053 x<>y L095 EQN RCL D►V L136 RCL A L054 EQN [REGY,REGX] ►R L096 CF 10 L137 XEQ C001 L055 RCL T L097 EQN K-L►Y L138 GTO L142 L056 RCL R L098 EQN ABS(Y)►W L139 RCL S L057 x (multiplication) L099 EQN ACOS((SQ(W)+SQ(U)-SQ(V))/ L140 RCL A (2*W*U))►Z L058 RCL T L141 XEQ C001 L100 FIX 4 L059 ABS L142 RCL L L101 EQN K-L L060 RCL R L143 + (add) L102 ARG L061 ABS L144 EQN “STORE PNT” L103 RCL Z L062 x (multiplication) L145 FIX 0 L104 SF 10 L063 ÷ (division) L146 INPUT J L105 EQN “-LT OR +RT” L064 ABS L147 x<>y L065 ACOS L106 RCL U L148 FIX 2 L066 STO S L107 x<>y L149 STO(J) L067 L108 XEQ C001 EQN 180-W-S►P L150 VIEW(J) L109 RCL L L068 EQN ABS(U)*(SIN(S)/SIN(P))►O L151 STOP L110 + (add) L069 RCL M L152 GTO L001 L111 GTO L077 L070 RCL O L151 RTN L071 XEQ R001 L112 EQN “AZ FRM 1ST PNT” L072 XEQ P001 L113 INPUT A L073 x<>y L114 EQN “DIST 2ND PNT” Jason Foose is the County Surveyor of Mohave County Arizona. He originally hails L074 XEQ C001 L115 INPUT D from The Connecticut Western Reserve Township 3, Range XIV West of Ellicott’s Line L075 RCL L L116 CF 10 Surveyed in 1785 but now resides in Township 21 North, Range 17 West of the Gila & Salt L076 + (add) L117 EQN ((ARG(K-L)-A)►U River Base Line and Meridian.

Displayed with permission • The American Surveyor • June 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com JASON E. FOOSE, PS the HP 35s calculator A Field Surveyor’s Companion Part 10—Distance Dependent Intersections

istance dependent intersections are com- plimentary tools for the retracement surveyor. When contemplating Dintersection methods one should consider whether or not the values were actually measured in the field. Such might be the case with a radius point for example. Last month we covered direction/ direction intersection which is a well suited application for retracing linear measurements. Curve data is a derivative of the intersections of the tangent lines. ©2015 JASON E. FOOSE Holding the bearing/bearing intersection of the monumented lines recreates a p.i. that places you very close to the position of A Few Thoughts On This Month’s Program the transit man during the original survey. Constructing Radius Points Program L: Intersections includes routines The observed deflection between these Distance/distance intersections often yield for Direction/Direction, Direction/ intersected tangents IS THE REAL DELTA! inconsistency among the ground evidence Distance, and Distance/Distance. The Both ends of the curve are either found or affixing curvilinear boundaries and create program operates by assuming a base line replaced as originally set on these inter- tension in the opinions of the paper minded from the first point to the second point. sected lines. The retracement function is surveyor. Considering the legacy knowledge Direction/Distance and Distance/Distance fulfilled through a recapitulation of physical that curves were originally placed on the naturally have 2 solutions. The preferential evidence presented on the ground. ground by measuring the deflection angle, solution may be defined as being left or A strong application of distance/distance the tangent length, and the chord distance, right of the line facing the second point. intersection is found among swing ties or evidentiary weight of a calculated radius This month we will focus on Direction/ cross ties physically measured from reference point is severely disjointed from those Distance and Distance/Distance examples marks to monuments or from property implicit facts of conventional measurement. corners to building corners. These are direct The original surveyor measured along the Example Data And Running measurements from known points and a great curve naturally shedding imprecision and The Program demonstration of rope stretching to the Courts. error linearly through the curve. Neither his We will reference our previous data set I don’t think much in terms of direction/ path nor measurements extended to a radius as follows: distance intersections in retracement work. point. A computed radius offers zero contra- There is a platted mirage at the “end lots” of dictory evidence to upset the original work PNT NORTH EAST a block that can appear like the intersection measured ALONG the line. The retracement 1 4,680.20 4,917.12 of a directional right-of-way line and an end surveyor will find more comfort in working 3 5,267.15 5,517.46 lot distance. Exhaust without doubt every lineally through the curve holding bona fide 4 5,267.06 5,186.98 shred of physical evidence before using a evidence found on the ground. 5 5,000.00 5,000.00 direction/distance intersection. If itching Please do not hesitate to send any 1-5 N 14°31’45” E 330.36 and rash persist induce vomiting and call comments, concerns, questions, or criticism your physician immediately. to [email protected]. 3-4 S 89°59’04” W 330.48

Displayed with permission • The American Surveyor • July 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com DISTANCE/DISTANCE KEYSTROKE RESULTANT ACTION STEPS DISPLAY KEYSTROKE RESULTANT ACTION STEPS DISPLAY 600.34 R/S “RUNNING” then Annunciator/prompt selecting Y-reg : the appropriate solution XEQ yX Y-reg : Executes program {L} and X-reg : -LT OR +RT relative to the baseline. Left ENTER X-reg : displays program annunciator. of the line is minus key - INTERSECTIONS note: the “L” key is between and right is plus key + . A the square root and reciprocal default value will be displayed keys. It is the “Y” raised to “X” between keying + or - and function key. R/S . R/S Y-reg: Annunciator/reminder. RCL - R/S Y-reg : Annunciator for point storage X-reg: RCL POINT input to follow. X-reg : STORE PNT

R/S Y-reg: J? Prompt for first point number. R/S Y-reg : J? Prompt for store point. X-reg: default X-reg : default value value 1 R/S Y-reg : (1)= Display point info for review. 8 R/S Y-reg : (8)= Display point info for review. X-reg : 4,680.20 i X-reg : 5,267.15 i *This is the left - solution as 4,917.12 4,917.12 selected above. The right + solution is 4,666.96 i 5,503.92 R/S “RUNNING” then Annunciator/reminder. RCL Y-reg : input to follow. R/S Return to program top. X-reg : RCL POINT R/S Y-reg: J? Prompt for second point DIRECTION/DISTANCE X-reg: default number. value KEYSTROKE RESULTANT ACTION STEPS DISPLAY 3 R/S Y-reg : (3)= Display point info for review. XEQ yX Y-reg : Executes program {L} and X-reg : 5,267.15 i ENTER X-reg : displays program annunciator. 5,517.46 INTERSECTIONS note: the “L” key is between R/S “RUNNING” then Prompt for Azimuth/Azimuth the square root and reciprocal Y-reg : intersection. Directly press 0 keys. It is the “Y” raised to X-reg : AZ-AZ R/S to proceed to AZ-AZ or “X” function key. PRESS 0 hit any key(except zero) R/S R/S Y-reg: Annunciator/reminder. RCL to continue menu choices. The X-reg: RCL POINT input to follow. routine is set up with a default value that permits simply R/S Y-reg: J? Prompt for first point number. hitting R/S to continue. X-reg: default ANY KEY Y-reg : Prompt for Distance/Distance value R/S X-reg : DS-DS intersection. Directly press 0 1 R/S Y-reg : (1)= Display point info for review. PRESS 0 R/S to proceed to DS-DS or X-reg : 4,680.20 i hit any key(except zero) R/S 4,917.12 to continue menu choices. The R/S “RUNNING” then Annunciator/reminder. RCL routine is set up with a default Y-reg : input to follow. value that permits simply X-reg : RCL POINT hitting R/S to continue. R/S Y-reg: J? Prompt for second point 0 R/S Y-reg : Annunciator DIST-DIST X-reg: default number. X-reg : DIST-DIST value R/S Y-reg : Annunciator/reminder. 1st 3 R/S Y-reg : (3)= Display point info for review. X-reg : 1ST DIST point distance input to follow. X-reg : 5,267.15 i R/S Y-reg : D? Prompt for distance from first 5,517.46 X-reg : default point. R/S “RUNNING” then Prompt for Azimuth/Azimuth value Y-reg : intersection. Directly press X-reg : AZ-AZ 0 R/S to proceed to AZ-AZ 586.95 R/S “RUNNING” then The “RUNNING” may take a PRESS 0 or hit any key(except zero) Y-reg : minute then annunciator for R/S to continue menu X-reg : 2ND DIST 2nd point distance. choices. The routine is set R/S Y-reg : D? Prompt for distance from up with a default value that X-reg : default second point. permits simply hitting R/S value to continue.

Displayed with permission • The American Surveyor • July 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com KEYSTROKE RESULTANT ACTION KEYSTROKE RESULTANT ACTION STEPS DISPLAY STEPS DISPLAY ANY KEY Y-reg : Prompt for Distance/Distance R/S Y-reg : 589.72 1st solution distance along R/S X-reg : DS-DS intersection. Directly press 0 X-reg : 589.72 azimuth line from POB. PRESS 0 R/S to proceed to DS-DS or R/S Y-reg : hit any key(except zero) R/S X-reg : DIST B-AZ to continue menu choices. The PNT routine is set up with a default value that permits simply R/S Y-reg : 589.72 Y-reg is 1st solution distance. hitting R/S to continue. X-reg : 1,089.36 X-reg is 2nd solution distance. R/S Y-reg : Annunciator AZIMUTH-DIST R/S Y-reg : Annunciator/prompt to save X-reg : AZ-DS X-reg : SAVE A=0 “A” solution or “B” solution. R/S Y-reg : Annunciator/reminder. 1st B=1 X-reg : AZ FRM point azimuth input to follow. 0 R/S Y-reg : Annunciator for point storage 1ST PNT The first point is always and X-reg : STORE PNT only the azimuth point. R/S Y-reg : J? Prompt for store point. R/S Y-reg : A? Prompt for azimuth from first X-reg : default X-reg : default point. value value 9 R/S Y-reg : (9)= Display point info for review. 45.0000 YLS Y-reg : Annunciator for 2nd point X-reg : 5,097.20 I The 1st solution is shown. 8 R/S X-reg : DIST 2ND distance. The second point is 5,334.12 The 2nd solution is 5,450.49 i PNT always and only the distance 5,687.41. point. R/S Return to program top. R/S Y-reg : D? Prompt for distance from X-reg : default second point. value 250 R/S “RUNNING” then Annunciator for resulting Jason Foose is the County Surveyor of Mohave County Arizona. He originally hails from The Connecticut Western Reserve Township 3, Y-reg : distance along azimuth line. Range XIV West of Ellicott’s Line Surveyed in 1785 but now resides in X-reg : DIST A-AZ Township 21 North, Range 17 West of the Gila & Salt River Base Line PNT and Meridian.

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This Month’s Program Example Data And Running Program E: Fieldwork contains the The Program functions of Stakeout and Sideshot. We will reference our previous data set Stakeout generates an angle/distance as follows: to a known coordinate position from an PNT NORTH EAST occupied point/backsight setup whereas 1 4,680.20 4,917.12 Sideshot generates a coordinate position with an observed angle/distance. Please 3 5,267.15 5,517.46 do not hesitate to send any comments, 4 5,267.06 5,186.98 concerns, questions, or criticism to 5 5,000.00 5,000.00 [email protected] 1-5 N 14°31’45” E 330.36 ©2015 JASON E. FOOSE 3-4 S 89°59’04” W 330.48

KEYSTROKE RESULTANT ACTION KEYSTROKE RESULTANT ACTION STEPS DISPLAY STEPS DISPLAY XEQ R↓ Y-reg : Executes program {E} 2 R/S “RUNNING” then With the instrument at point ENTER X-reg : FIELDWORK and displays program Y-reg :76.3140 1 backsighting point 5 the annunciator. X-reg : 600.1321 angle right to point 2 is R/S Y-reg: Annunciator/reminder. 76°31’40” and the horizontal X-reg: OCCUPY PNT Occupy point input distance is 600.13 feet. to follow. R/S Y-reg : Menu prompt for more or end R/S Y-reg: J? Prompt for occupy point X-reg : 0=MORE Key in 0 or 1 then hit R/S . X-reg: default value number. 1=END More returns to the program to the FORESIGHT prompt R/S Y-reg : Annunciator/reminder. 1 and holds the occupied/ X-reg : BACKSIGHT Backsight point input backsight setup info for PNT to follow. radial staking. END returns R/S Y-reg: J? Prompt for occupy point to program top. X-reg: default value number. OBS Option-continued from above: 5 R/S Y-reg: Menu prompt for sideshot 5 R/S Y-reg: Menu prompt for sideshot X-reg: OBS=0 (obs) or stakeout. Key in 0 X-reg: OBS=0 (obs) or stakeout. Key in 0 STAKE=1 or 1 then hit R/S . STAKE=1 or 1 then hit R/S . See below for OBS option. 0 R/S Y-reg : Annunciator/reminder. Angle R/S Y-reg : Annunciator/reminder. 1 X-reg : ANGLE RT right input to follow. X-reg : FORESIGHT Foresight point input PNT to follow. R/S Y-reg: A? Prompt for angle right X-reg: default value in DD.DDDD format R/S Y-reg: J? Prompt for foresight point (45.5083 dd). X-reg: default value number. 45.3030 YLS Y-reg : Annunciator/reminder. 8 R/S X-reg : DISTANCE Horizontal distance input to follow.

Displayed with permission • The American Surveyor • October 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com KEYSTROKE RESULTANT ACTION KEYSTROKE RESULTANT ACTION STEPS DISPLAY STEPS DISPLAY R/S Y-reg: D? Prompt for horizontal R/S Y-reg : Menu prompt for sideshot or X-reg: default value distance. X-reg : SIDE=0 traverse. Key in 0 or 1 then 200.00 R/S “RUNNING” then Annunciator/reminder. Store TRAV=1 hit R/S . Sideshot returns Y-reg : point input to follow. to “ANGLE RT” prompt above X-reg : STORE PNT and holds the occupied/ backsight setup info for R/S Y-reg: J? Prompt for point storage. radial observations. Traverse X-reg: default value returns to the occupied 10 R/S Y-reg: (10)= Observed point coordinate point prompt above. Press 0 X-reg: 4,780.09 i solution. or 1 R/S accordingly. 5,090.39

Program Listing E036 RCL L E001 LBL E E037 ABS This month’s programs are rudimentary E002 SF 10 E038 STOP and about as dry as vulture pemmican baking on old Route 66. I’ll take E003 EQN “FIELDWORK” E039 SF 10 this opportunity to memorialize an E004 EQN “OCCUPY PNT” E040 EQN “0=MORE 1=END” important influence on our craft. We E041 x=0? E005 FIX 0 owe a professional debt of gratitude E006 INPUT J E042 GTO E021 Nathaniel Bowditch (1773-1838), for E007 RCL (J) E043 GTO E003 his realization and development of a E008 STO O E044 EQN “ANGLE RIGHT” technique we rely upon in our work. E009 EQN “BACKSIGHT PNT” E045 FIX 4 The Compass Rule Adjustment (Part E010 INPUT J E046 INPUT A 7) featured in the April 2015 issue of The American Surveyor Magazine E011 RCL (J) E047 CF 10 is the product of Mr. Bowditch’s E012 x<>y E048 EQN A+B STO A mathematic contribution to society. E049 SF 10 E013 R▼ Mr. Bowditch was an important figure E014 x<>y E050 EQN “DISTANCE” in navigation mathematics in the late E015 - E051 INPUT D 18th century and through that work E016 ARG E052 RCL D gave us the method sometimes known E017 STO B E053 RCL A as “Compass Rule Adjustment”. I was E018 EQN “OBS=0 STAKE=1” E054 XEQ C001 remiss to neither mention Bowditch E019 x=0? E055 RCL O nor associate his name as the honorable title of the method. E020 GTO E044 E056 + E021 EQN “FORESIGHT PNT” E057 STO C E022 FIX 4 E058 EQN “STORE PNT” E023 INPUT J E059 FIX 0 E024 RCL(J) E060 INPUT J E025 RCL O E061 FIX 2 El Mapache E026 - E062 RCL C Este Mes E027 STO L E063 STO (J) The pole cat of the month club E028 ARG E064 FIX 2 welcomes Daniel Pedro Leiva of E029 RCL B E065 VIEW (J) Argentina. Daniel spotted these E066 EQN “SIDE=0 TRAV=1” E030 - “descuidos” from the other side E031 x>0? E067 x=0? of the equator. E032 GTO E035 E068 GTO E044 “STEP L117...the last parenthesis is E069 GTO E004 E033 360 missing…((AGR(K-L)-A))>U E034 + E070 STOP And then... E035 >HMS E071 RTN STEP L153...is shown as L151 RTN” ¡Muchiso Gracias hermano medición! Jason Foose is the County Surveyor of Mohave County Arizona. He originally hails from The Connecticut Western Reserve Township 3, Range XIV West of Ellicott’s Line Surveyed in 1785 but now resides in Township 21 North, Range 17 West of the Gila & Salt River Base Line and Meridian.

Displayed with permission • The American Surveyor • October 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com JASON E. FOOSE, PS the HP 35s calculator A Field Surveyor’s Companion Part 12—Resection

ost of the programming work we’ve experienced thus far is no more than reliable math being indisputable as to its singular solution. This multiple point Resection should offer a good solution but not an exact solution in planar geometry. Statistics tells us that there’s always a better answer. I have incorporated a method that favors simplicity over the pursuit of an absolute or finite solution. The solution is derived from a series of overlapping Collin’s Point Resections and the simple linear average of the aggregate x ©2015 JASON E. FOOSE & y values of the solutions. The Collins Method or Bessel’s Method Example Data and Running of the source data. The amount of these considers the occupied point and the two of the Program differences is insignificant, however the three control points on a circumference. A We will reference our previous data set as reason they exist must be identified before fourth point is projected on the circumfer- follows: considering the impact. I will be reporting ence from the occupied point through the will the 2 decimal coordinates listed above. third point. The relationship between all PNT NORTH EAST points is trigonometrically defined. For 1 4,680.20 4,917.12 OBSERVATION DATA more information regarding resection 2 4,669.13 5,517.15 BS-STA-FS ANGLE CO-CURRENT methods and Collins Point refer to this link 3 5,267.15 5,517.46 1-PNT-5 49°30'20" A B www.mesamike.org/geocache/GC1B0Q9/ 4 5,267.06 5,186.98 5-PNT-4 76°10'01" B A resection-methods.pdf 4-PNT-3 52°55'02" B A Program X and Program Y are quick 5 5,000.00 5,000.00 utility programs that compose a complex 6 5,267.03 5,069.20 3-PNT-2 91°48'42" B A number in and from rectangular coordi- 7 5,153.02 5,039.66 2-PNT-1 89°35'07" B A nates (LBL X) and decompose a complex Ʃ 359°59'12" number in rectangular coordinates to polar If you have carried coordinates through coordinates (LBL Y). from the compass rule adjustment article Observation data contains a simulated I currently have all of the previously you may find insignificant differences in natural error of -0°00’48" to the horizon. published routines along with Resection on solutions as noted in the May 2015 “AREA” These values will be impacted by the linear my 35s. I am able to store points ranging from column. The source of the error is the dif- averaging of the interim solutions. Your com- single digit point numbers to some where in ference between hand entering coordinates fort level can be ascertained by comparing the mid 400’s. This is the just about the limit of to two decimal places versus the computed raw angles to post solution values. Differences practical balance between program memory (adjusted) values that are carried out to the may be apparent by fixing the display to a and data storage allocation. Please do not full 12 digit precision of the HP 35s. This is greater precision. The solutions are accumula- hesitate to send any comments, concerns, a great example toward accepting tolerance tive therefore any inclusive interim solution questions, or criticism to [email protected]. in measurement through the assessment should vary from any given singular solution.

Displayed with permission • The American Surveyor • November 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com The solution requires the input of adjoining (co-current) angles as R/S Y-reg : J? Prompt for third point number. delineated by “A” & “B”. Note that angle 1-PNT-5 is the overlapping X-reg : default angle. Entry should run clockwise using angle right. value 4 R/S Y-reg : (4)= Display point info for review. X-reg : 5,267.06 i 5,186.98

R/S Y-reg : Annunciator for the first angle X-reg : ANGLE (A-B) in decimal degrees (DD) A-B(DD) of the Collins Solution.

R/S Y-reg : E? Prompt for 1st angle. In this X-reg : default case it’s the measured angle value occupying the resection point back sighting Point 1 and measuring to Point 5 (49.5056 DD). There’s no significance to the variable “E” other than it is a conveniently available variable.

49.3020 YLS “RUNNING” then Annunciator for the second 8 R/S Y-reg : angle (B-C) in decimal degrees X-reg : ANGLE (DD) of the Collins Solution B-C(DD)

R/S Y-reg : F? Prompt for 2nd angle. In this X-reg : default case it’s the measured angle value occupying the resection point back sighting Point 5 and measuring to Point 4 (76.1669 KEYSTROKE RESULTANT ACTION DD). Again, there’s no STEPS DISPLAY significance to the variable “F” XEQ 3 Y-reg : Executes program {Z} and other than it is a conveniently ENTER X-reg : RESECTION displays program annunciator. available variable.

R/S Y-reg : Annunciator/reminder. RCL 76.1001 YLS “RUNNING” then You make hear grinding and X-reg : RCL 1ST input to follow. 8 R/S Y-reg : N= see smoke while “RUNNING” PNT X-reg : annunciator is displayed. 4,976.7106 Ensure that you change the R/S Y-reg : J? Prompt for first point number oil every 5000 computations X-reg : default of known control. All initial or less in hotter operating value input points are the knowns. temperatures. The Interim northing solution presented 1 R/S Y-reg : (1)= Display point info for review. with fix 4 precision to demon- X-reg : 4,680.20 i strate floating solution. 4,917.12 R/S Y-reg : E= Interim easting solution R/S “RUNNING” then Annunciator/reminder. RCL X-reg : presented with fix 4 precision to Y-reg : input to follow. 5,227.7579 demonstrate floating solution. X-reg : RCL 2ND PNT R/S Y-reg : X-reg : 0=MORE R/S Y-reg : J? Prompt for second point 1=STORE X-reg : default number. value

5 R/S Y-reg : (5)= Display point info for review. X-reg : 5,000.00 i 5,000.00 Interim/Final Solution Notes: At this time the solution could be accepted and stored as point 10. A R/S “RUNNING” then Annunciator/reminder. RCL single three point solution may yield sufficient results. Observations Y-reg : input to follow. can be added by repeating the steps through “MORE”. Continue RD X-reg : RCL 3 around the observation horizon clockwise until the “B-C” angle PNT of the last observation is the same as the “A-B” angle of the first observation. In this case it’s 49°30'20" between Points 1 & 5.

Displayed with permission • The American Surveyor • November 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com Continue data input for additional observations R/S Y-reg : E= Interim easting solution 2nd Observation Set X-reg : 5,227.7459 presented to fix 4 precision to 0 R/S Y-reg : Executes program {Z} and demonstrate floating solution. X-reg : RESECTION displays program annunciator. R/S Y-reg : R/S Y-reg : Annunciator/reminder. RCL input X-reg : 0=MORE X-reg : RCL 1ST PNT to follow. 1=STORE R/S Y-reg : J? Prompt for first point number of X-reg : default value known control. All initial input 3rd Observation Set points are the knowns. 0 R/S Y-reg : Executes program {Z} and 5 R/S Y-reg : (5)= Display point info for review. X-reg : RESECTION displays program annunciator. X-reg : 5,000.00 i This series will include the R/S Y-reg : Annunciator/reminder. RCL input 5,000.00 angles between 5-P-4 and 4-P-3. X-reg : RCL 1ST PNT to follow. R/S Y-reg : J? Prompt for first point number of R/S “RUNNING” then Annunciator/reminder. RCL input X-reg : default value known control. All initial input Y-reg : to follow. points are the knowns. X-reg : RCL 2ND PNT 4 R/S Y-reg : (4)= Display point info for review. R/S Y-reg : J? Prompt for second point number. X-reg : 5,267.06 i This series will include the X-reg : default value 5,186.98 angles between 4-P-3 and 3-P-2. 4 R/S Y-reg : (4)= Display point info for review. R/S “RUNNING” then Annunciator/reminder. RCL input X-reg : 5,267.06 i Y-reg : to follow. 5,186.98 X-reg : RCL 2ND PNT R/S “RUNNING” then Annunciator/reminder. RCL input R/S Y-reg : J? Prompt for second point number. Y-reg : to follow. X-reg : default value X-reg : RCL 3RD PNT 3 R/S Y-reg : (3)= Display point info for review. R/S Y-reg : J? Prompt for third point number. X-reg : 5,267,15 i X-reg : default value 5,517.46 3 R/S Y-reg : (3)= Display point info for review. R/S “RUNNING” then Annunciator/reminder. RCL input X-reg : 5,267.15 i Y-reg : to follow. 5,517.46 X-reg : RCL 3RD PNT R/S Y-reg : Annunciator for the first angle R/S Y-reg : J? Prompt for third point number. X-reg : ANGLE (A-B) in decimal degrees (DD) of X-reg : default value A-B(DD) the Collins Solution. 2 R/S Y-reg : (2)= Display point info for review. R/S Y-reg : E? Prompt for 1st angle. In this X-reg : 4,669.13 i X-reg : default value case it’s the measured angle 5,517.15 occupying the resection point R/S Y-reg : Annunciator for the first angle back sighting Point 5 and X-reg : ANGLE (A-B) in decimal degrees (DD) of measuring to Point 4 (76.1669 A-B(DD) the Collins Solution. DD). There’s no significance R/S Y-reg : E? Prompt for 1st angle. In this to the variable “E” other than X-reg : default value case it’s the measured angle it is a conveniently available occupying the resection point variable. back sighting Point 4 and 76.1001 “RUNNING” then Annunciator for the second measuring to Point 3 (52.9172 YLS 8 Y-reg : angle (B-C) in decimal degrees DD). There’s no significance to R/S X-reg : ANGLE (DD) of the Collins Solution the variable “E” other than it is a B-C(DD) conveniently available variable. R/S Y-reg : F? Prompt for 2nd angle. In 52.5502 “RUNNING” then Annunciator for the second X-reg : default value this case it’s the measured YLS 8 Y-reg : angle (B-C) in decimal degrees angle occupying the resection R/S X-reg : ANGLE (DD) of the Collins Solution point back sighting Point B-C(DD) 4 and measuring to Point 3 R/S Y-reg : F? Prompt for 2nd angle. In this (52.9172 DD). Again, there’s no X-reg : default value case it’s the measured angle significance to the variable “F” occupying the resection point other than it is a conveniently back sighting Point 3 and mea- available variable. suring to Point 2 (91.8117 DD). 52.5502 “RUNNING” then Interim northing solution Again, there’s no significance to YLS 8 Y-reg : N= presented to fix 4 precision to the variable “F” other than it is a R/S X-reg : 4,976.7016 demonstrate floating solution. conveniently available variable.

Displayed with permission • The American Surveyor • November 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com 91.4842 “RUNNING” then Interim northing solution R/S Y-reg : F? Prompt for 2nd angle. In YLS 8 Y-reg : N= presented to fix 4 precision to X-reg : default value this case it’s the measured R/S X-reg : 4,976.7136 demonstrate floating solution. angle occupying the resection R/S Y-reg : E= Interim easting solution point back sighting Point X-reg : 5,227.7396 presented to fix 4 precision to 2 and measuring to Point 1 demonstrate floating solution. (89.5853 DD). Again, there’s no significance to the variable “F” R/S Y-reg : ***Slight variations begin to other than it is a conveniently X-reg : 0=MORE show up. Hand entered coordi- available variable. 1=STORE nates may yield something like N=4,976.7006 & E=5,227.7392 89.3507 “RUNNING” then Interim northing solution YLS 8 Y-reg : N= presented to fix 4 precision to R/S X-reg : 4,976.7165 demonstrate floating solution. 4th Observation Set R/S Y-reg : E= Interim easting solution 0 R/S Y-reg : Executes program {Z} and X-reg : 5,227.7363 presented to fix 4 precision to X-reg : RESECTION displays program annunciator. demonstrate floating solution. R/S Y-reg : Annunciator/reminder. RCL R/S Y-reg : ***Variations show X-reg : RCL 1ST PNT input to follow. X-reg : 0=MORE N=4,976.7067 & E=5,227.7360 1=STORE R/S Y-reg : J? Prompt for first point number of X-reg : default value known control. All initial input th points are the knowns. 5 Observation Set 0 R/S Y-reg : Executes program {Z} and 3 R/S Y-reg : (3)= Display point info for review. X-reg : RESECTION displays program annunciator. X-reg : 5,267.15 i This series will include the 5,517.46 angles between 3-P-2 and R/S Y-reg : Annunciator/reminder. RCL 2-P-1. X-reg : RCL 1ST PNT input to follow. R/S “RUNNING” then Annunciator/reminder. RCL R/S Y-reg : J? Prompt for first point number of Y-reg : input to follow. X-reg : default value known control. All initial input X-reg : RCL 2ND PNT points are the knowns. R/S Y-reg : J? Prompt for second point 2 R/S Y-reg : (2)= Display point info for review. X-reg : default value number. X-reg : 4,669.13 i 5,517.15 R/S Y-reg : (2)= Display point info for review. 2 R/S “RUNNING” then Annunciator/reminder. RCL X-reg : 4,669.13 i Y-reg : input to follow. 5,517.15 X-reg : RCL 2ND PNT R/S “RUNNING” then Annunciator/reminder. RCL R/S Y-reg : J? Prompt for second point Y-reg : input to follow. X-reg : default value number. X-reg : RCL 3RD PNT 1 R/S Y-reg : (1)= Display point info for review. R/S Y-reg : J? Prompt for third point number. X-reg : 4,680.20 i X-reg : default value 4,917.12 1 R/S Y-reg : (1)= Display point info for review. R/S “RUNNING” then Annunciator/reminder. RCL X-reg : 4,680.20 i Y-reg : input to follow. RD 4,917.12 X-reg : RCL 3 PNT R/S Y-reg : J? Prompt for third point number. R/S Y-reg : Annunciator for the first angle X-reg : default value X-reg : ANGLE (A-B) in decimal degrees (DD) A-B(DD) of the Collins Solution. 5 R/S Y-reg : (5)= Display point info for review. X-reg : 5,000.00 i R/S Y-reg : E? Prompt for 1st angle. In this 5,000.00 X-reg : default value case it’s the measured angle R/S Y-reg : Annunciator for the first angle occupying the resection point X-reg : ANGLE (A-B) in decimal degrees (DD) back sighting Point 3 and mea- A-B(DD) of the Collins Solution. suring to Point 2 (91.8117DD). st There’s no significance to the R/S Y-reg : E? Prompt for 1 angle. In this variable “E” other than it is a X-reg : default value case it’s the measured angle conveniently available variable. occupying the resection point back sighting Point 2 and 91.4842 “RUNNING” then Annunciator for the second measuring to Point 1 (89.5853 YLS 8 Y-reg : angle (B-C) in decimal degrees DD). There’s no significance to R/S X-reg : ANGLE (DD) of the Collins Solution the variable “E” other than it is B-C(DD) a conveniently available variable.

Displayed with permission • The American Surveyor • November 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com 89.3507 “RUNNING” then Annunciator for the second 10 R/S Y-reg : (10)= The Average of the Collins Point YLS 8 Y-reg : angle (B-C) in decimal degrees X-reg : 4,976.71 i Solutions. This example is a small R/S X-reg : ANGLE (DD) of the Collins Solution 5,227.74 scale project and the differences in B-C(DD) solutions are negligible. Comparing single solutions and progressive R/S Y-reg : F? Prompt for 2nd angle. In this results would be strongly advised X-reg : default value case it’s the measured angle especially when measuring on a occupying the resection point larger scale. Any error in control back sighting Point 1 and mea- and/or measurements will rear suring to Point 5 (49.5056 DD). its ugly head in short order. This Again, there’s no significance to routine is intended to present the variable “F” other than it is a a reasonable resection solution conveniently available variable. in the realm of local boundary 49.3020 “RUNNING” then Interim northing solution retracement surveying. YLS 8 Y-reg : N= presented to fix 4 precision to Slight variations most likely will appear in insignificant doses. R/S X-reg : 4,976.7181 demonstrate floating solution. The object of this routine is to resolve a consistent value closely R/S Y-reg : E= Interim easting solution approximating the most probable or true value of the resection point. X-reg : 5,227.7370 presented to fix 4 precision to Solutions may vary between individual hardware. I use a very early demonstrate floating solution. 2007 model. The Museum of HP Calculators identifies a bug with R/S Y-reg : ***Variations show cosine function. See www.hpmuseum.org/cgi-sys/cgiwrap/hpmu- X-reg : 0=MORE N=4,976.7103 & seum/archv017.cgi?read=123814 Understand the problem, assess the 1=STORE E=5,227.7368 impact, then file it in the nuisance bin with the mosquitoes, poison 1 R/S Y-reg : J? Point Storage Input Prompt. ivy, and exploded paint cans. Please email me [email protected] X-reg : default value with any concerns whatsoever!.

Program Listing Z024 x<>y Z048 EQN 360-(180-(D-B))-E-F►G

Z001 LBL Z Z025 STO B Z049 EQN ((C*SIN(E)*SIN(G)) / ((A*SIN(F))+(C*SIN(E)*COS(G)))) Z002 CLΣ Z026 RCL (J) Z050 EQN ATAN(REGX)►H Z003 SF 10 Z027 EQN “RCL 3RD PNT” Z051 EQN ((A*SIN(F)*SIN(G)) / Z004 EQN “RESECTION” Z028 FIX 0 ((C*SIN(E))+(A*SIN(F)*COS(G)))) Z005 EQN “RCL 1ST PNT” Z029 INPUT J Z052 EQN ATAN(REGX)►I Z006 FIX 0 Z030 STO Y Z053 EQN (SIN(180-H-E)*A) / SIN(E) Z007 INPUT J Z031 RCL (J) Z054 EQN B+H Z008 STO Z Z032 FIX 2 Z055 x<>y Z009 RCL(J) Z033 VIEW (J) Z056 XEQ R001 Z010 FIX 2 Z034 x<>y Z057 x<>y Z011 VIEW (J) Z035 R▼ Z058 XEQ X001 Z012 EQN “RCL 2ND PNT” Z036 x<>y Z059 EQN Z►J Z013 FIX 0 Z037 - Z060 RCL (J) Z014 INPUT J Z038 XEQ Y001 Z061 x<>y Z015 RCL (J) Z039 STO C Z062 R Z016 FIX 2 Z040 x<>y ▼ Z017 VIEW (J) Z041 STO D Z063 + Z018 x<>y Z042 EQN “ANGLE A-B (DD)” Z064 XEQ Y001 Z019 R▼ Z043 FIX 4 Z065 XEQ R001 Z020 x<>y Z044 INPUT E Z066 x<>y Z021 - Z045 EQN “ANGLE B-C (DD)” Z067 ∑+ Z022 XEQ Y001 Z046 INPUT F Z068 EQN (SIN(180-I-F)*C) / SIN (F) Z023 STO A Z047 CF 10 Z069 EQN 180+D-I

Displayed with permission • The American Surveyor • November 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com Z070 x<>y Z071 XEQ R001 Z072 x<>y Z073 XEQ X001 Z074 EQN Y►J Z075 RCL(J) Z076 x<>y Z077 R▼ Z078 x<>y Z079 + Z080 XEQ Y001 Z081 XEQ R001 Z082 x<>y Z083 ∑+ Z084 EQN ȳ►N note: the mean value of the Y summation register YLS + Z085 EQN x̄ ►E note: the mean value of the X summation register YLS + Z086 VIEW N Z087 VIEW E Z088 SF 10 Z089 EQN “0=MORE 1=STORE” Z090 x=0? Z091 GTO Z003 Z092 GTO H017 Z093 RTN X001 LBL X X002 i note: 4th key 2nd row X003 x -multiplication X004 + X005 RTN Y001 LBL Y Y002 ARG Y003 LASTx Y004 ABS Y005 RTN

Jason Foose is the County Surveyor of Mohave County Arizona. He originally hails from The Connecticut Western Reserve Township 3, Range XIV West of Ellicott’s Line Surveyed in 1785 but now resides in Township 21 North, Range 17 West of the Gila & Salt River Base Line and Meridian.

HP35s Sliding Predetermined Area

Eq3: Computes the line distance along the the lengths of the side lines. Begin by storing right side the referenced algebraic equations in the EQN R=INV(COS(Y))×B library. The equation academically considers two “outie” wings that are both added to the Eq4: Computes the line distance along the main rectangle area. Other combinations opposite parallel side of “innies” and “outies” exist, however this (O)PPOSITE (P)ARALLEL (S)IDE = example will not sufficiently address the math TAN(X)×B+TAN(Y)×B+F involved with those solutions.

Basically you are manipulating a solution It’s apparent that the basic form is: of the area of a rectangle and two triangular Area = main rectangle + the left wing wings. However, in this case you know the

BIG TIME DISCLAIMER! This is an academic exercise. The solution method is not inclusive of all possible scenarios but rather limited to just that which is shown.

arting off a tract of land with a parallel line sliding along two sidelines can be accomplished by storing a few equations. The basic concept is predetermining a desired area then solving distances along the sidelines to place corners. The sliding line is set parallel A = 20,000 SQ. FT. with a chosen baseline. The following F = 100.00' formulas are presented in the HP 35’s X = 18º equation entry format. Y = 15º L = SOLVE FOR X Y Computes the total area. Since we R = SOLVE FOR Eq1: L R know the area and certain other variables B = SOLVE FOR we’ll use the solver to compute “B” the B B perpendicular distance to baseline A=B×(TAN(X)×B)÷2+(B×F)+B×(TAN(Y)×B)÷2

Eq2: Computes the line distance along the left side

L=INV(COS(X))×B

Displayed with permission • The American Surveyor • February 2016 • Copyright 2016 Cheves Media • www.Amerisurv.com CLOSURE REPORT Set description: (No description) Area: 19,999.56 0.46 Perimeter: 577.9143 Closure: 0.0000 Point # Direction Distance Northing Easting Elevation Station 1 90°00'00" 100.0000 5,000.0000 5,000.0000 100.00 0+00.0000 2 15°00'00" 146.0100 5,000.0000 5,100.0000 100.00 1+00.0000 3 269°59'57" 183.6143 5,141.0348 5,137.7902 100.00 2+46.0100 4 162°00'00" 148.2900 5,141.0322 4,954.1759 100.00 4+29.6243 1 5,000.0000 5,000.0000 100.00 5+77.9143

Using the supplied data I get the following thousand square feet. I could waste my .ENTER. to initiate either. They are in the antici- results: client’s dime by manipulating the data to a pated form and the variables are previously perceivably “exact” amount but face facts stored so you can blow through them quickly. B=141.035874878 or 141.04' on the meridian. here. Unless you’re working in Aspen, Los Feel free to send any questions or L=148.293894697 or 148.29' up the left side. Altos, or on the Las Vegas strip, let’s keep comments to [email protected] ◾ R=146.011081844 or 146.01' up the right side. O=183.615782401 or the same 183.61' on the things to the square foot and in round zeros closure sheet. for the Planning and Zoning folks. Jason Foose is the County Surveyor of The “A=” formula is actually used to solve for Mohave County Arizona. He originally hails The coordinates of the closure report “B”. Queue it up then press BRS .EQN. .GTO. from The Connecticut Western Reserve Township 3, Range XIV West of Ellicott’s Line were entered to a precision of 0.01'. Bwahhh, to set the solver to “B”. You will be prompted to Surveyed in 1785 but now resides in Township so I’m a realist! Get over yourself and realize input the remaining variables. Simply queue up 21 North, Range 17 West of the Gila & Salt that 19,999.56 sq. ft. is the same as twenty the left and right side equations then press River Base Line and Meridian.

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BerntSrvMkgLayoutsAppalaSPRING.inddDisplayed with permission 3 • The American Surveyor • February 2016 • Copyright 2016 Cheves Media • www.Amerisurv.com 9/29/15 6:43 PM JASON E. FOOSE, PS the HP 35s calculator Linear Equations and a Land Development Scenario inear equations are powerful and a half” acre lots. Begin by aligning the We now have enough to form a system solving tools especially when units into acres (6000 sf=0.1377 acres) then of linear equations. It is imperative that unleashed from classroom phrase an equation that relates both lot we organize our x, y, and z variables all on confines of counting the sizes to the overall area. It sounds like this: the same side of the equation and it simply number of legs on chickens “The sum of a certain number of 1.5 acre lots flows well with the HP solver to collect Land cows. We can utilize systems of linear and .1377 acre lots plus a certain amount of them on the left side alphabetically. equations for many applications like solving roadway is equal to 10 acres.” intersections, estimating project supplies, Forming The System 1.5x + .1377y + z = 10 and in this case land development potential. 1.5x + .1377y + z = 10 The numbers used herein are merely pre- We have assigned “x” to be the number of 2x - y = 0 sumptuous attempts at reasonable values. big lots, “y” to be the number of small lots, (20 x 255.62)1.5x + (20 x 60).1377y - z = 0 The objective of this exercise is to estimate and “z” to be the amount of roadway. Next how many lots a client could expect to net let’s establish the relationship between small There is no ‘z’ in the second equation. from a given parcel of land. lots and big lots. We want twice as many However we need to accommodate ‘z’ to small lots as big lots “so two times “x” number square up the system. This is accomplished Client Request of lots should equal “y” number of lots.” by giving ‘z’ a value of zero in the second The client inherited 10 acres of relatively equation. We also must represent solo 2x = y flat and easy vacant ground. She would like variables with 1 or -1 depending upon the Re-arrange by subtracting “y” to know how many lots she can offer in leading operator of “+” or “-“. The function- from both sides order to do a cost analysis for development 2x - y = 0 ing system looks like this: and improvements. 1.5x + .1377y + 1z = 10 The relationship between roadways and 2x - 1y + 0z = 0 Constraints lots can be expressed by assuming that a (20 x 255.62)1.5x + (20 x 60).1377y - 1z = 0 Local Zoning Code permits 6,000 square length equal to the frontage of each lot will foot lots with 60’ minimum frontage. Local be reserved for half of the prescribed road’s Zoning Code permits 1.5 acre residential/ width. Local zoning guides us to consider THE HP 35s 3x3 SOLVER agricultural. Local roadways are required to all 6,000 square foot lots as being 60’ wide The solver uses the linear form of be a minimum 40’ right-of-way. and 100’ deep. Having no other reason, we Ax+By+Cz=D. The complete system looks will assume that 1.5 acre lots are 255.62 feet like this: Initial Concept square. So we need to form an equation that Ax+By+Cz=D Our objective is to present the client with expresses half of the road width times each Ex+Fy+Gz=H an initial concept and open the floor for frontage then apply it to every lot accord- Ix+Jy+Kz=L discussion, feasibility, and alternatives. ingly. It sounds like this (read it aloud): Our professional experience hints that a “Twenty feet times two-hundred fifty-five The letters A thru L are the coefficients blend of high density and low density lots point sixty two feet, times one point five and x,y, and z are the solution variables. intermingled at a 2:1 ratio provides a solid acres, times “x” number of lots, plus 20 feet The 3x3 routine will request input for the opportunity for the incidental land developer times 60 feet, times .1377 acres, times “y” coefficient registers A thru L. Our particular in our post-apocalyptic housing market. number of lots equals “z”.” It looks like this: coefficients are as follows:

Forming Equations (20 x 255.62)1.5x + (20 x 60).1377y = z A: 1.5 Re-arrange by subtracting “z” from both sides B: 0.1377 We propose a division of 10 acres with twice (20 x 255.62)1.5x + (20 x 60).1377y - z = 0 C: 1 as many 6,000 square foot lots as “one

Displayed with permission • The American Surveyor • January 2016 • Copyright 2016 Cheves Media • www.Amerisurv.com D: 10 Five 1-1/2 acre lots are 7.5 acres; E: 2 Ten small lots or 60,000 square feet equals F: -1 1.4 acres; G: 0 An acre of 40 foot road is about 1,100 !OYE COMO VA! H: 0 feet long on both sides for a total of I find that verbalizing a problem then I: 20 x 255.62 ÷ 43,560 x 1.5 (or 0.1760) 2,200 feet; Ten 60’ lot frontages plus five restating it aloud helps me to “hear J: 20 x 60 ÷ 43,560 x .1377 (or 0.0038) 250’ lot frontages equals about 1850 feet. how it goes”. The rules of arithmetic K: -1 Hmmmm, ballpark. and algebra are rigid whereas the art L: 0 of problem solving is the application The solutions seem reasonable in this of those rules in a world made of silly The stack is active within the 3x3 solver. light. Although this is an appropriate putty. Solving a problem requires the Utilize the operators to combine (multiply/ occasion to loosely apply measure, great ability to describe the problem, identify divide) the numbers for variables “I” and consideration should be taken toward the the variables, and then check solution! “J” then hit [R/S] to store the result and client’s understanding of your estimates. continue. Negative numbers are entered in Your lot design proposal impacts the typical HP fashion with [+/-]. financial yield of the client’s property and Run the solver as shown on page 7-6 of thus should be considered as a tenant of the HP 35s User’s Guide. Chapters 6 and 7 liability. both explain the use of equations. I get the Feel free to email me at rls43185@gmail. following results: com with any questions. ◾

X = 5 large lots (1-1/2 acre) Y = 10 small lots (6,000 square foot) Jason Foose is the County Surveyor of Mohave County Arizona. He originally hails Z = Almost an acre in roadway (.9374) from The Connecticut Western Reserve These are cursory estimates rounded Township 3, Range XIV West of Ellicott’s Line Surveyed in 1785 but now resides in Township to practical units. They reasonably add up 21 North, Range 17 West of the Gila & Salt

Elgin 911-Reverse Curve Problem

There is something we need to understand point oh-oh feet equals six-hundred thirty- along with this simple curve data. With six point seventy-nine feet”. Done! reverse curves the tangent direction out of C1 736.79-100=636.79 is the same as the tangent direction into C2, or a “straight line” to us hill folk. Consequently We have 636.79 feet of tangent to the distance between P.I.’s in a reverse curve distribute among each side of the 100.00 is simply the sum of their tangent distances. tangent. Keep in mind that after the dust That’s very convenient because we can solve settles our final tangent values should equal both tangent values by simply multiplying the this number. The challenge of this whole TAN of one-half Δ by the radius. problem lies in writing an equation that will express our given Δ’s, equal radii, and maintain 100.00 feet of tangential separa- ©2015 JASON E. FOOSE tion. Hmmmmmm… Let’s start by recognizing the facts. Our r. Elgin, The American Δ’s are fixed and our unknown radii values Surveyor Staff, and I collective- are constrained by the condition of being ly strive to educate our peers equal. That leaves us with elastic tangent and readers of this publication. values, right? So another table: DI have continually enjoyed Dr. Elgin’s effort to advance knowledge through problem C1 DATA C2 DATA solving. The HP 35s is a true problem solver Δ=120°57 Δ=104°37 and I find great honor in demonstrating how to solve one of Elgin’s enigmas with this tool. R=? but equal R=? but equal The goal is for everyone to appreciate the T=Elastic and most T=Elastic and most mechanics of problem solving and instill the likely ≠ likely ≠ necessary logic to tackle larger problems. There is no digital witchcraft or ghost in the So the distance between the P.I.’s on a machine here, nope. Just logic, brain cells, straight line could be expressed verbally Ultimately we are solving for “R” which and two CR2032 batteries. You may find as “the tangent of half of one-hundred and according to Dr. E must be the same several approaches to solving any given twenty degrees fifty-seven minutes times value in both curves. So, if we can form a problem. The more the merrier, I say! three-hundred plus the tangent of half of statement from C1 that equals “R” and the Let’s refer to TAS October 2015 issue. Dr. one-hundred and four degrees thirty-seven same statement applied to C2 also equals E’s ultimate request is to “Compute the radii minutes times one-hundred and sixty.” “R” then doesn’t it stand to reason that both of the replacement curves” so that a 100.00 Or statements are equal? Yes, it’s true and we foot tangent separates them. This problem can form a larger statement by substituting is all about the tangents. First, let’s organize smaller statements into singular variables. our given information. That’s handy because the HP 35s EQN In our case the solution equals 736.79 feet Library and solver also will do just that. C1 DATA C2 DATA between points. Dr. E. wants 100.00 feet of Let’s jot down equations that express some Δ=120°57 Δ=104°37 tangent to separate P.T. #1 and P.C. #2 and common elements between each curve: we shall deliver. “Seven-hundred thirty six We’ve already figured out distance between R=300 R=160 point seventy-nine feet minus one-hundred P.I.’s minus Dr. E’s requested hundred feet.

Displayed with permission • The American Surveyor • December 2015 • Copyright 2015 Cheves Media • www.Amerisurv.com equal to the tangent of half delta of curve one times its radius plus the half delta of curve two times its radius”. It looks like this: And, the tangent length divided by the tangent of one-half delta equals the radius of each curve. Or

And, the radii of Curve 1 and Curve 2 are equal. This yields an equation with a singular unknown which can be rearranged to If the radii are equal, then couldn’t we just say that all the things that make up each radius are equal too? Yes, we can and Where I will just like this: “The tangent length of A=120°57’ (HMS→) the first curve divided by the tangent of B=104°37’ (HMS→) one-half delta is equal to the tangent length C=100.00 of the second curve divided by the tangent of D=736.79 one-half of its delta”. It looks like this: Written for the EQN Library in algebraic form it looks like this:

(TAN(A÷2)xR)+(TAN(B÷2)xR)+C=D This equation helps us to understand Solve the equation for R and fill in the the relationship defining an equal radius prompts. If you wish to automate the HMS→ but we still have to resolve the tangent conversion then enter the equation as follows: lengths to produce a solution. There are (TAN(HMS (A)÷2)xR)+(TAN(HMS (B)÷2) three unknowns which is way too many for → → xR)+C=D us to work a solution. They are TL1, TL2, and of course the solution itself. Let’s try At this point you should be able to deliver something else. Remember when I said this the goods to Dr. E! problem “is all about the tangents”? Well, Feel free to email me at rls43185@gmail. we have already summarized and know com with any questions. ◾ the distance between P.I.’s and also know that subtracting one hundred feet leaves Jason Foose is the County Surveyor of us with a balance equal to both half delta’s Mohave County Arizona. He originally hails times the radius and we are solving for that from The Connecticut Western Reserve same radius value. Let’s verbalize and form Township 3, Range XIV West of Ellicott’s Line Surveyed in 1785 but now resides in Township another equation like this: “The distance 21 North, Range 17 West of the Gila & Salt between P.I.’s minus Dr. E’s one-hundred is River Base Line and Meridian.

a series of progressive equations and Equations carry variable solutions, or better yet write the equation itself incorporating & Solver the sub-equations for the variables. For The HP SOLVER and EQN Library are very example Y=mX+b represents how many powerful tools. Simply queue up any “Y’s” are equal to a certain number of equation and BRS EQN initiates “X’s” where X progresses from a known the SOLVER. You will be prompted to point (b) at a certain rate (m). select a variable to solve for and input “m” (slope) is equal to (the differences the remaining variables. You can solve in your sample points). So instead of for any variable residing within the hand computing “m” by itself, why not equation regardless of its location. just substitute “m’s” equation in place Variables are stored so you may resolve of the “m” variable? Get it?