Syntax for 4p ² R/[H²+(2 p R) ²] 1

[garvock]

How do I enter the following formula in a cell in Excel.
4p ² R/[H²+(2 p R) ²]
Where R=1 and H=10 the answer should be 3.533.
I cannot get this answer, but I am not very proficient at math.
Any help would be appreciated.
P.S. The formula is for calculating the curvature of a helix. I intend to use it for bending handrails on spiral staircases.

 

[garvock]

I have just noticed that the Pi symbol in the formula has changed to P. Sorry if this has confused anyone.

 

[Molby]

Are you sure the answer is 3.533? As you've written it the formula works out at about (4*9)/(100+36) which is about 0.3. In Excel, enter the below to get your answer. I've substituted R as 1 and H as 10.

=4*(PI()^2)*1/(100+(2*(PI())*1)^2)

 

[SkipVought]

garvock,
[tt]
=4*PI()^2*R_/(H_^2+(2*PI()*R_)^2)
[/tt]
I don't get 3.533, rather 0.2830432

???

Skip,

_{[red]Be advised:[/red]
Alcohol and Calculus do not mix!
If you drink, don't derive!}

 

[garvock]

I have copied the text from the document.
"If R is the radius of the cylinder and H is the height of one turn of the helix, then the curvature of the helix can be computed to be 4?2R/[H2+(2?R)2]. In the case of R = 1m and H = 10m, this gives us r = 3.533m."

 

[Molby]

Can you write the formula out in full, we'll have a better idea of how the calculation works.

 

[garvock]

OK here it is written out as best I can
4pi^2R/[H^2+(2PiR)^2]

 

[Molby]

We are obviously not understanding this right as that still works out at we stated earlier. Are you sure there are no other brakets in there?

 

[Philly44]

The only way that I have been able to get 3.533 as the answer is to reverse your formula to
[H^2 + (2piR)^2]/(4pi^2R)

 

[garvock]

Here is the page I got the formula from. It is in the section on "Curvature of Curves" section.

http://www.math.cornell.edu/~dwh/papers/EB-DG/EB-DG-web.htm

 

[SkipVought]

Garv,

You should real the ENTIRE document!
[tt]
curvature = 4*PI()^2*R_/(H_^2+(2*PI()*R_)^2)

r = 1 / curvature
[/tt]
VOLA!



Skip,

_{[red]Be advised:[/red]
Alcohol and Calculus do not mix!
If you drink, don't derive!}

 

[Molby]

That would explain things!!

 

[garvock]

OK my mistake, I did say I'm not very good at math.
Thanks everybody for your assistance!!

 

[SkipVought]

BTW,

This formula is not a magical as it might seem.

1) We know that the CIRCUMFERENCE of a CYLINDER is
[tt]
C₁ = 2[π]r₁
[/tt]
where r₁ is the RADIUS

2) If you take the CYLINDER and lay the side out flat, you would have a RECTANGLE with the CIRCUMFERENCE as the Length and the HEIGHT as the WIDTH.

3) A HELIX could be traced on this RECTANGLE as one of the DIAGONALS.

4) This DIAGONAL would be the CIRCUMFERENCE of the HELIX
[tt]
C₂² = (2[π]r₂)² = H² + (2[π]r₁)²
[/tt]
5) It is then a simple step to solve for r₂, the RADIUS of the HELIX.
[tt]
r₂ = [√]((H² + (2[π]r₁)²)/(2[π])²)
[/tt]


Skip,

_{[red]Be advised:[/red]
Alcohol and Calculus do not mix!
If you drink, don't derive!}

 

[bluedragon2]

no wonder you are in squaring the circle forum Skip

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