Hi Everyone, Here in this discussion, i will talk about doing X- sections of road beds and days gone by of using a planimeter and miles and miles of road beds, this meant sheet after sheet of X-sections, that was first plotted and drawn, then the templates of the design road beds are then drawn, this includes Cut and Fills. your road must have drainage ,so it must have a ditch, Stop right there. This was a lot of work, also a lot of work for your Planimeter and you. A lot of adding and subtracting and dividing and multiplying. so who needs a Computer, somebody Does and did. But there was none where i worked ,not at this time,Finally it did come, But not before we got the next best Thing. What you ask ?, A Calculator, and not just a Calculator , but one you could program, Notice i said one that YOU can, not one that has a program. Because, that is what first came, one's with programs came later. But using a planimeter all day, well this is a ART in itself. If you never used one, how does it work, I will just say it calculates by following the outline of a figure,to determine how much Area is in this figure. I will leave it at that for now. Because all of us who have done this was glad to see a calculator , that would do this. Planimeters are only as good as the person following the outline of the figure, if you are off the area is off. The method i am talking about was used by Surveyors / or Surveying Engineers Firms that built and design Roads and Highways. This little planimeter is also used by surveyors to calculate Area and other things. But lets move on to when we got our Calculators, that we had to program.Why, i told you the others were not made yet, that's one reason, the main reason, because they did not have a constant memory. when you turn it off, and then turned them back on, you have no program, in fact all the memory was cleared. So before you begin your day of calculations, the first thing you had to do ,was to re-program your calculator. So i Guess you know what this means, If you couldn't then you didn't. Now we are lucky, entering a program today you will have it tomorrow and until the battery goes dead. So now back to X- section and one of the reason they were drawn. It is called Volume by Average End Area. The word Average has a big meaning here .This program i wrote ,is a whole lot better than the ones we first used, First this is for the HP 35s. It Is a HP in every way , but every HP calculator programs are a little different, more memory, different storage system, Labels , titles, keys, they all are different. This is a RPN Program, but you have simple to complex programmimg. This program is in it's simple forum, i have not made it complex yet. This is one of the most advance RPN calculators, made today, in fact it is the only Scientific programmable RPN calculator made today. And you will find, not every Surveyor knows how to program Reverse polish Notation, and may not care to know, but some might, and you will find, not all Students care to learn this also, again you will find those who do. So for those who Do, Surveyors and Students , and for those with a HP 35s RPN calculator. The Hp 35 program works just like you using a planimeter, you go around the template in Clock Wise or counter CW. Either way you must stay in that motion that you chose thru out the program until that section of calculation is completed. Who would want to do this, it can be done on a computer. PE and PLS students, cannot use a computer in a Exam Room. Plus it must be done on a Hand Programmable calculator. Not a calculator with a program. So there is a NEED for IT. And they may not even ask to do this on your test or they might. This is also one of those see how it was Done. You can search the internet, and you may not find a program like this. But you got this one FREE. What a Deal.
This Content Originally Published by a land surveyor to Land Surveyors United Network
Rather than Average End Area try this modification using the geometric mean.
V = L/3(A1 + SQRT(A1*A2) + A2)
L is distance3 between sections at stations 1 and 2.
A1 is the cross-sectional area at station 1.
A2 is the cross-sectional area at station 2.
Gives the correct volume for a pyramidal shape.
Hi Barry, thanks for the reply, Great equation, I know i seen it somewhere before, but thanks for sharing it. A1 and A2 are still unknown, The purpose of what i am showing is for students,who use a RPN hand programmable calculator, to use on their PE or PLS Exams.Only certain calculators can be used. My other purpose was to show how it was done years ago using these programs, before pre- program devices came out. In these test you must program or use key stroke programs. Nothing else is allowed. This is also to show how it was done before computers. And how Average by End Area was used. Can you show me this in RPN, that would be great.
How about this, G ( a1,a2) = √ a1 a2
G (a1,a2,a3) = (a1 a2 a3 ) 1/3
I would have to write yours as
V = L / 3 ( A + √ ( A * B ) + B) ,in my HP 35 that is the calculator in this discussion, It can be used on the test.
I also seen a program for this , i will have to look, but that is why i used Average by end Area.
Thanks on any math or programs.
But this is how my HP 35s Program works to do X-Sections.So lets begin. Sta 1 is 0+00, the next Sta 2 is 0+25. your Center line is the Baseline that equals 0+00 right and left, to the right is positive + to the left - is negative.And that is how the program knows what is left and what is right from the CL center line of the Road Bed,or center line of the cut.You will Enter the Elevations and key in the Distance and R/S on a beginning point. What point it does not matter,but you have to end on this point,clockwise or counterclockwise, but whatever it must be done the same thru the program.
I used the center line,As a starting point,as a Rule, easy to start and end and easy to remember.And this is the place where the X-Sections starts. Just like you would use a planimeter. so Sta 1,0+00 Begins the cuts your second Sta 2 , could be at 0+01 if you like, This makes the area of 0+01 and the interval of 1, 1 x the Area ,but this example starts at Sta 2@0+25 and it is the same as Sta 1@0+00, so you will be multiplying by 25 times Sta 2 of 0+25, so this area will be between 0+00 to 0+25, using 0+01 can be done if there is a big difference in the stations template Elevations, or natural ground so the first X-Section is @STA 2,0+25. starting at 0+00 CL @ 0+25 we are going RIGHT, in this example, Using the elevation of 0.0,to show the program can use negative values,both in Elev. and Dist.
V 001 is the routine.
V 021 is a calling subroutine for interval input.
V 003 is a nested subroutine, it can not be called.
0+00 CL Rt. + / Lt. -
STA 1 is 0+00, Note: First sta has 0 intervals
XEQ V 021, display = 0.0000 ,
STA 2 IS 25+00
XEQ V ,ENTER, V001
(Road Sta.2,0+25 ,and 0+00 CL Rt.+/Lt.-)
Volume by Average End Area
CounterClockWise Motion to the Rt.
( as above )
XEQ V 021, display 0.0000, STARTS PROGRAM
XEQ V ENTER, V001,run
0.0 ENTER 0.0 R/S ..........AS ELEV. ENTER, DIST,R/S
0.0 ENTER 10.0 R/S.........AS """"""""""""""""""""
2.0 CHS+/- ENTER 12.0 R/S... AS -2 ENTER 12 R/S
7.0 ENTER 20.0 R/S......... AS ELEV. ENTER, DIST,R/S
6.0 ENTER 3.0 +/- R/S..... AS 6 ENTER,-3 R/S
7.0 ENTER 18.0+/- R/S.... AS 7 ENTER,-18 R/S
2.0+/- ENTER 12.0+/- R/S... AS -2 ENTER-12 R/S
0.0 ENTER 10.0+/- R/S........ AS 0 ENTER-10 R/S
0.0 ENTER 0.0 R/S.....AS 0 ENTER 0 R/S....... Back at starting point
X-section complete,Now you want to calculate this section
and 25 ft . back to 0+00 Sta1 for the area in that 25 ft. so
Key in 25,
XEQ V021 ENTER...... interval subroutine of V001
your answer = 100.0000............Total Vol.(cu.yds.)
RCL E =100.0000.......................Int. Vol.(cu yds.)
RCL D=216.0000........................Area (sq.ft.)
Initialize for next Sta.
[ R/S ]
( RD.STA.3,0+75,AND 0+00 CL Rt.+/Lt.-)
0.0 ENTER 0.0 R/S..........ELEV. ENTER,DIST,R/S
0.0 ENTER12.0 R/S.........""""""""""""""""""""
1.0+/- ENTER 14.0 R/S....-1 ENTER 14 R/S
1.0+/- ENTER 15.0 R/S ....AS -1 ENTER 15 R/S
10.0 ENTER 30.0 R/S.......ELEV. ENTER,DIST,R/S
8.0 ENTER 6.0 R/S...........""""""""""""""""""""
7.0 ENTER 21.0+/- R/S.....7 ENTER -21 R/S
4.0 ENTER 17.0+/- R/S......AS 4 ENTER -17 R/S
1.0+/- ENTER 10.0 +/- R/S ...AS -1 ENTER -10 R/S
0.0 ENTER 8.0+/- R/S..........AS 0 ENTER -8 R/S
0.0 ENTER 0.0 R/S......... AS 0 ENTER 0 R/S....... Back at starting point
X-section complete,Now you want to calculate this section
and 50 ft. back to 0+25 STA 2 for that area in that 50 ft.
so key in 50,
XEQ V021..........interval subroutine of V001
your answer =597.6852...............Total Vol.( cu. yds. )
RCL E=497.6852.........................Int. Vol. ( cu.yds.)
RCL D= 321.5000............................Area (sq. ft.)
As you see it can be done, Little or Big projects. no it's not as fast
as a computer program. but your doing it ,this way,because you don't have one.
And you can not take them to a test. This can be used on any X-Section
System for Volume by Average End Area.
And that's how it is done on a HP 35s calculator.
This is my Program,I have sole rights to it.
This program was written by Billy Brooks,
prior to this Date of 09-18-2016 .
for the HP 32s,33s and 35s.
all three have different programs.
Volume by Average End Area, HP 35s
1.LBL V...................21.RCL D
2.CLx..................... 22.RCL C
4.STO x A................24.STO D
5.RCL A...................25. +
6.STO - B.................26. 54
7.R ↕ dn...................27.÷
9.STO x Z.................29.STO E
10.RCL Z..................30.STO + F
11.STO + B...............31.RCL F
13.STO A..................33. CLx
14.R↕ dn...................34.STO C
15.STO Z..................35.STO B
16.RCL B..................36.STO A
17. 2.........................37.STO Z
18. ÷.........................38.GTO V003
As you can see this program is simple and short, so it can be programed Quick.
And is simple to use, I will later add labels and instruction line in the program lines.
To make it a little more complex and more user friendly.
But for now it serves it purpose
Today in Modern surveying and Engineering, large computer programs took over all this math and calculations. But just think how much work was put into just a small project for these Volume Average End Area's. That does not include all the math of running levels ,them being reduced and the X- section plotted on X-section paper. But today's students have to take on this task of knowing how to do this and others like it. That is called Foundation.
Hi Everyone, I like to add a little more info on this program.
First the Formulas i used:
Vol =( AREA í + AREA 1 - 1 ) INT / 2
AREA = 1/2 [ EL 1 ( D2 - Dn ) +... + ELn ( D1 - Dn - 1 ) ]
where : VOL =Average volume between two stations .
............AREA =Cross-sectional area at a station.
............INT =Interval between stations.
............EL = Elevation at a point on a cross- section.
............D =Horizontal distance ( offset ) from centerline.
............i =Subscript referring to current point.
............n = Subscript referring to the last point
............Numeric subscript refers to point or station number
Note: Volumes are calculated in cubic yards, areas in square feet.
If you like to have volumes calculated in cubic feet, then do this.
Delete 54 on line 26 and replace it with 2 in it place.
Hope all this helps.
Thanks again Survenator for the FAV., I can always count on you.
Hi Charlie, This Topic, is about how it was done,and how students or surveyors today who are taking their test will have to do it today on a Exam . There is no option for using a Computer. these are not computerized Exam. You can not also have a pre-program card, or module or a downloaded program in memory. In fact you must be a key stoke program Calculator. This program is to help them Before not After. No matter what anyone's opinion is about using a computer, it does not apply here. I am not trying to promote this as a everyday solution. I use a computer everyday and write programs in them. This is to help those who must do it on a calculator, they have no other choice. This is not what is Best to use. This is what they have to use. And how does Units fit into all of this, I do not recall saying anything about Units, and what is the meaning of this statement. Was it Billy that hit on units?. just what exactly are you saying. I would like to know. I only showed this in the Units we used. meters are no problem. but i do not know if that is the issue here so please clarify yourself.
No need to apoligise.
Didn't see a thing wrong with your replies Charlie.
Volume by Average End Area is the topic heading - nothing else.
well maybe i just stop using them and put a Big ?????? marks. then everyone can guest what the discussion is about, That's is why books have titles, But i forgot you can not judge a book by it's Cover, well i guess that means the title's too.
Have a great day, and Barry thanks for the equation, but i am still waiting on the RPN program to it. That would be great ,like i said.
Dear Charlie, That reply was not to you, all is well between me and you. your friend ship means a lot to me. Why do we have topic headings, are they just for looks are to get someone attention. This site is to share and help your fellow surveyors, that's is why it's Title has United in it. We at times may have a different opinions, but to disrespect someones opinion or to put them or their idea down,this is not in the cards. I respect everyone here and in return I expect the same. The best thing is everyone try to get alone. If someone does not want to be a friend with someone else ,that is your right, but just keep it to yourself and everything will be find. To you Charlie I hope this explains that I was not talking to you. And there is never nothing wrong with a apology, even when it is not needed and if i have ever done anything wrong to you I apologize for it also. You are a Great contributor to this community.