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Length of a helix

  1. Jul 22, 2009 #1
    Given the radius and pitch , how can we compute the length of a helix??
     
  2. jcsd
  3. Jul 22, 2009 #2

    HallsofIvy

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    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?
     
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