(12C Platinum) Parabola - arc length

[Gamo]

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

Answer: 100.7376 feet

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

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

[Domino]

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

[Gamo]

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

Answer: 100.7376 feet

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

[Gamo]

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

[StephenG1CMZ]

(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

Answer: 100.7376 feet

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

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.

[Domino]

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

[Gamo]

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

[PedroLeiva]

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

[Albert Chan]

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