Compute Length of Helix Given Radius & Pitch

In summary, the formula for calculating the length of a helix is L = sqrt(r^2 + p^2), where r is the radius and p is the pitch. The radius of a helix can be measured as the distance from the center of the helix to the center of the cylinder it wraps around, and the pitch is the distance between each complete turn of the helix. The length of a helix cannot be negative as it is a physical measurement, but it can approach infinity as the radius and pitch increase. The practical application of the length of a helix includes calculating the volume and surface area of objects and designing helical structures.
  • #1
zd1899
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Given the radius and pitch , how can we compute the length of a helix??
 
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  • #2
If the helix has radius R and pitch a, meaning that the helix rises a distance a with each loop, parametric equations for the helix are [itex]x= Rcos(t)[/itex], [itex]y= Rsin(t)[/itex], z= at.

The length of a curve, with x, y, and z functions of t, from t= a to b, is given by
[tex]\int_a^b\sqrt{\left(\frac{dx}{dt}\right)^2+ \left(\frac{dy}{dt}\right)^2+ \left(\frac{dz}{dt}\right)^2}dt[/tex]
Can you get it from there?
 
1)

What is the formula for calculating the length of a helix?

The formula for calculating the length of a helix is L = sqrt(r^2 + p^2), where r is the radius and p is the pitch.

2)

How do I find the radius and pitch of a helix?

The radius of a helix can be measured as the distance from the center of the helix to the center of the cylinder it wraps around. The pitch of a helix is the distance between each complete turn of the helix.

3)

Can the length of a helix be negative?

No, the length of a helix cannot be negative as it is a physical measurement and cannot have a negative value.

4)

Can the length of a helix be infinite?

Technically, the length of a helix can approach infinity as the radius and pitch increase, but in practical terms, the length of a helix is limited by the size of the object it is wrapping around.

5)

How can I use the length of a helix in scientific research?

The length of a helix can be used to calculate the volume and surface area of objects such as DNA molecules, protein structures, and other helical structures. It can also be used in the design and construction of helical objects, such as screws and springs.

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