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Algorithm for acceleration of projectile undergoing squared velocity drag?

  1. Jan 11, 2012 #1
    I am trying to write a java program to simulate the motion of a projectile undergoing a drag proportional to the velocity squared, but i am having some issues writing the acceleration part. This is my attempt, not sure if its right though;

    a=g-kv^2
    da/dt=-k dv^2/dt
    since dv^2/dt=2vdv/dt;
    da/dt=-2vkdv/dt
    da=-2vkdv
    and
    a=dv/dt
    dv=adt inserting;
    da=-2vkadt
    trying to incorporate some indexes; (bear with me, first prog. algorithm :)
    a_(n+1)-a_n=-2vka_n Δt
    a_(n+1)=a_n-2vka_n Δt

    Is this all wrong ?
     
  2. jcsd
  3. Jan 11, 2012 #2

    rcgldr

    User Avatar
    Homework Helper

    wiki already worked out a direct solution for free fall with air resistance (for constant air density which matches your original equation):

    wiki_falling_with_air_resistance.htm

    Wiki doesn't show the math. To get there, you start with

    a = dv/dt = g - k v2

    dv / (g - k v2) = dt
     
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