(12C Platinum) Parabola - arc length
06-29-2019, 10:22 AM (This post was last modified: 07-02-2019 12:30 AM by Gamo.)
Post: #1
 Gamo Senior Member Posts: 623 Joined: Dec 2016
(12C Platinum) Parabola - arc length
The Arc Length of a Parabola calculator compute the arc length (S)

of a parabola based on the distance height (H) and

the width (L) of the parabola at that point perpendicular to the axis.

----------------------------------------------------------------

The formula for determining the length of an arc of a Parabola.

----------------------------------------------------------------

Instruction: FIX 4

1. H [R/S] display Height
2. L [R/S] display Answer of the Arc Length of a Parabola

----------------------------------------------------------------

Example: H is 20 feet and L is 90 feet, what is the length of S?

20 [R/S] display 20.000
90 [R/S] display 100.7376

To check answer for difference problem or check if this program give

URL: https://www.vcalc.com/wiki/vCalc/Parabola+-+arc+length

---------------------------------------------------------------
Program: ALG mode
Code:
 [÷] [R/S] [STO] 0 [=] [STO] 1 [X^2] [+] 16 [1/x] [=] [√x] [+] [(] [(] 1 [÷] [(] 16 [x] [RCL] 1 [)] [)] [x] [(] [(] [RCL] 1 [+] [(] [RCL] 1 [X^2] [+] 16 [1/x] [)] [√x] [)] [LN] [+] 4 [LN] [)] [)] [)] [x] 2 [x] [RCL] 0 [=]  // 51 program steps //

Gamo
06-30-2019, 08:33 AM
Post: #2
 Domino Junior Member Posts: 3 Joined: May 2019
RE: (12C Platinum) Parabola - arc length
Hello,

Here is a rpl solution for the HP11C :

Code:
 LBL A STO 0 / STO 1 ENTER X2 1 6 1/x + √x STO 2 RCL 1 + 4 * LN 1 6 / RCL 1 / RCL 2 + RCL 0 * 2 * R/S //// 29 steps

Instructions : H [enter] L [A]

Regards
Dominique
06-30-2019, 11:35 AM (This post was last modified: 06-30-2019 11:38 AM by Gamo.)
Post: #3
 Gamo Senior Member Posts: 623 Joined: Dec 2016
RE: (12C Platinum) Parabola - arc length
Parabola -arc Length program in RPN mode using this formula:

---------------------------------
Instruction:

H [ENTER] L [R/S] display Answer of Parabola arc length

H is the Height
L is the distance from both end

--------------------------------
Example: FIX 4

H is 20 feet and L is 90 feet, what is the length of S?

20 [ENTER] 90 [R/S] display 100.7376

--------------------------------
Program: RPN mode (For HP-12C replace [X^2] to [ENTER] [x]
Code:
 001 STO 1 002 R↓ 003 STO 0 004 X^2 005  1 006  6 007  x 008 RCL 1 009 X^2 010  + 011  √x 012 STO 2 013 RCL 0 014  4 015  x 016  + 017 RCL 1 018  ÷ 019 LN 020 RCL 1 021 X^2 022 RCL 0 023  8 024  x 025  ÷ 026  x 027 RCL 2 028  2 029  ÷ 030  +

Gamo
07-01-2019, 09:12 AM
Post: #4
 Gamo Senior Member Posts: 623 Joined: Dec 2016
RE: (12C Platinum) Parabola - arc length
Thanks Dominique

Here is another version without using any STO registers and only use the stacks.
This can be adapted to HP-11C as well.

Procedure is the same: H [ENTER] L [R/S] display Parabola Arc Length

Program for HP-12C Platinum on RPN mode
Code:
 001  ÷ 002 LSTx 003 X<>Y 004 ENTER 005 X^2 006  1 007  6 008 1/x 009  + 010 √x ------------ 011 X<>Y 012  + 013 LSTx 014 X<>Y 015 LN 016  4 017 LN 018  + 019 X<>Y 020  1 ----------- 021  6 022 X<>Y 023  x 024 LSTx 025 X<>Y 026 1/x 027 X<>Y 028 R↓ 029  x 030 R↓ ----------- 031 R↓ 032 R↓ 033 X^2 034  1 035  6 036 1/x 037  + 038 √x 039  + 040  x ---------- 041  2 042  x

Gamo
07-02-2019, 09:18 AM
Post: #5
 StephenG1CMZ Senior Member Posts: 868 Joined: May 2015
RE: (12C Platinum) Parabola - arc length
(06-29-2019 10:22 AM)Gamo Wrote:  The Arc Length of a Parabola calculator compute the arc length (S)

of a parabola based on the distance height (H) and

the width (L) of the parabola at that point perpendicular to the axis.

----------------------------------------------------------------

The formula for determining the length of an arc of a Parabola.

----------------------------------------------------------------

Instruction: FIX 4

1. H [R/S] display Height
2. L [R/S] display Answer of the Arc Length of a Parabola

----------------------------------------------------------------

Example: H is 20 feet and L is 90 feet, what is the length of S?

20 [R/S] display 20.000
90 [R/S] display 100.7376

To check answer for difference problem or check if this program give

URL: https://www.vcalc.com/wiki/vCalc/Parabola+-+arc+length

---------------------------------------------------------------
Program: ALG mode
Code:
 [÷] [R/S] [STO] 0 [=] [STO] 1 [X^2] [+] 16 [1/x] [=] [√x] [+] [(] [(] 1 [÷] [(] 16 [x] [RCL] 1 [)] [)] [x] [(] [(] [RCL] 1 [+] [(] [RCL] 1 [X^2] [+] 16 [1/x] [)] [√x] [)] [LN] [+] 4 [LN] [)] [)] [)] [x] 2 [x] [RCL] 0 [=]  // 51 program steps //

Gamo

The formula given in your image can be optimised, unless LN is a natural log.
It includes two instances of LN: LN4 and LN().
Where N = H/L
Thus LN 4 can be optimised to LH/L = H, and similarly for LN() if that is an implied multiply and not a natural logarithm.

Stephen Lewkowicz (G1CMZ)
ANDROID HP Prime App broken offline on some mobiles
07-03-2019, 07:35 AM
Post: #6
 Domino Junior Member Posts: 3 Joined: May 2019
RE: (12C Platinum) Parabola - arc length
Hello,

This the trap ! In the formula, LN is the neperian logarithm, and not LxN !

However, you can optimize the computation : the steps sequence "ln 4 ln +" can be replace with "4 * ln".

Dominique
07-03-2019, 08:14 AM
Post: #7
 Gamo Senior Member Posts: 623 Joined: Dec 2016
RE: (12C Platinum) Parabola - arc length
Hello, thanks to StephenG1CMZ and Dominique

Yes Post#1 Formula look very tricky and thanks for the head up on that formula.
On Post#3 that formula is a good one to use.

Thanks

Gamo
07-03-2019, 10:07 PM
Post: #8
 PedroLeiva Member Posts: 167 Joined: Jun 2014
RE: (12C Platinum) Parabola - arc length
One more parameter can be calculated with the same data, the Surface:
A= 2/3 * H * L
For H= 20 and L= 90, A= 1200.00
You only need to store H in R3 and actívate LBL B with the following sequence:
LBL B
2
ENTER
3
/
RCL 0
RCL 3
x
x
RTN

Pedro
07-11-2019, 04:19 PM (This post was last modified: 07-11-2019 04:37 PM by Albert Chan.)
Post: #9
 Albert Chan Senior Member Posts: 1,242 Joined: Jul 2018
RE: (12C Platinum) Parabola - arc length
For HP-11C, code can be shortened using identity: asinh(x) = ln(x + √(x^2+1))

parabola arc length = (asinh(x)/x + √(x^2+1)) * L/2, where x=4H/L

Doing everything on the stacks, we have:

Code:
01 LBL A ; Instructions : H [enter] L [A] 02 / 03 LST-X 04 X<>Y 05 4 06 x ; x = 4H/L 07 ASINH 08 LST-X 09 / 10 LST-X 11 X^2 12 1 13 + 14 SQRT 15 + 16 x 17 2 18 / 19 R/S
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