How can I calculate the length of wire needed to make a helix?

[drkirkby]

I'm trying to make a helical antenna. I know the number of turns (N=7), diameter (D=39 mm) and the spacing between each turn (S=27 mm), but how can I calculate the total length of material needed for the helix given N, D and S? Clearly if the spacing was infintesimally small, it would simply be Pi*D*N, since Pi*D is the circumference of a circle.

 

[_Eduardo_]

Developing the cylindrical surface becomes a triangle whose cathetus are pi*D*N and p*N (p : pitch , 27mm )

Then L = N √(Π²D²+p²)

 

[drkirkby]

Developing the cylindrical surface becomes a triangle whose cathetus are pi*D*N and p*N (p : pitch , 27mm )

Then L = N √(Π²D²+p²)

Thank you. That's certainly easier to understand than what I think Wikipedia is trying to say:

https://en.wikipedia.org/wiki/Helix#Arc_length.2C_curvature_and_torsion

My own attempts started with 3 parametic equations but I was getting nowhere useful after trying to integrate things using Mathematica!

Dave

 

[nashm999]

May I ask what length of wire your calculations resulted in to make sure I am equating the answers correctly.

Thanks

 

[nashm999]

May I ask what length of wire your calculations resulted in to make sure I am equating the answers correctly.

Thanks

Use pythagoras theorem C=PI*D, S = spacing L = sqrt(C^2 + S^2)
L = length of one full rotation
L*N = total length
Height of helix = S*N