pitch of circular helix

Discussion in 'Math' started by Muqaddas Jamil*, Nov 19, 2009.

  1. Muqaddas Jamil*

    Thread Starter New Member

    Nov 1, 2009
    8
    0
    Hi.

    can u tell me how to calculate pitch (i mean the vertical distance between two revolutions)of a helix with parametric equatios [2cost 2sint 6t]..?
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,178
    1,799
    What you wrote does not look like a parametric equation. I would expect something like:
    Code ( (Unknown Language)):
    1.  
    2. z = f(t)  ; z is some function of the parameter t
    3.  
    4. or
    5.  
    6. z = f(s,t) ; z is some function of parameters s, and t
    7.  
    what you wrote using square brackets looked like
    Code ( (Unknown Language)):
    1.  
    2. [2cost 2sin6t]
    3.  
    if that is a row vector then it only represents a figure in 2-dimensions and so the concet of "height" is meaningless in that context.
     
  3. Muqaddas Jamil*

    Thread Starter New Member

    Nov 1, 2009
    8
    0
    i mean that there are three parameters

    x=2cost [​IMG] [​IMG] [​IMG] [​IMG] [​IMG]
    y=2sint
    z=6t

    (helix is increasing along z axis)
     
  4. Papabravo

    Expert

    Feb 24, 2006
    10,178
    1,799
    OK, I see it now, it was a vector belonging to R3. I saw "sin 6t", instead of "sint 6t"

    If you start at t=0, z=0 and goto t=2*pi, then z=12*pi

    Does that make sense?
     
    Last edited: Nov 19, 2009
  5. Muqaddas Jamil*

    Thread Starter New Member

    Nov 1, 2009
    8
    0
    ok, i understand,we start from t=0,but how did u chose t=2*pi,(like i know that the circle completes its one revolution from 0-2*pi)but can you check that for this particular equation of helix
    [ tsin2t tcos2t t^2 ]
    will t still be fom 0 to 2*pi or will it be till pi only?
     
  6. Papabravo

    Expert

    Feb 24, 2006
    10,178
    1,799
    You are correct. With the parametric functions for x and y running at twice the frequency of the first example, one revolution in the xy plane will occur at t = pi
     
  7. KL7AJ

    AAC Fanatic!

    Nov 4, 2008
    2,040
    287
    This is a really interesting exercise when applied to things like helical antennas. Only in recent years have they had the formulas down for optimum pitch/gain of a helical antenna....and it was done with brute force numerical methods. The helix is deceptively simple (or complicated, depending on your point of vew!) Optimizing a pitch becomes very complicated very fast when working with electromagnetics!

    Eric
     
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