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Paper plane physics question

  1. Nov 7, 2011 #1
    Hello Guys.

    Maybe you got in the past some similiar questions :)

    I'm a game developer and I'm programming a game with a paper plane and I want to achieve a nearly real physic.

    What I got so far:

    trust = the speed when I throw the paper plane.
    drag = dragcoefficient * airdensity * trust² * surface / 2
    lift = 0.5 * airdensity * velocity² * wingarea * lift coefficient
    gravity = weight * 9.822 / (24 frames per seconds)
    velocity = trust - drag - lift + gravity

    So, my problem now is this:

    • the correct lift coefficient:
      How can I calculate the lift coefficient with aoa? Here on this forum I found the following formula:
      Cl = Cl(2d slope) * (AR/AR+2)*aoa

      But what is 2d slope, and how can I calculate the Cl when I don't have the Cl? And what is AR?
    • When I throw the paper plane, and it's moving upwards, the speed is increasing. But it must be decreasing:
      I know, that I calculate the lift into velocity. So it must be increasing. But how is it in reality?

    Greetings and thanks

  2. jcsd
  3. Nov 7, 2011 #2
    Paper airplanes (at least the ones I use) have no internal thrust; no motors, engines, or propellers. They are therefore more like gliders and less like true powered airplanes. This means that unless they hit an up-drafting air current which externally provides lift, the paper airplane can only fall over the long-term. It can momentarily ascend as part of its overall downward path, but only at the expense of its forward momentum. It momentarily exchanges kinetic energy for gravitational potential energy (like a pendulum).
  4. Nov 7, 2011 #3


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    The 2d slope is the CL versus AOA curve for a 2d (idealized) wing, which would be similar to a wing with infinite span. AR is aspect ratio, the (wing span) / (wing chord). Link to a web page about paper airplanes:

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