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Force calculations

  1. Mar 27, 2013 #1
    I'm not sure this is the best forum but I'm trying to work out how to do the math
    for a problem -

    Imagine a small private jet of weigtht about 6000kg flying at about 850kph
    If a constant force was applied to the nose of the aircraft - how much force would it take
    to force it down to the ground (assuming engine thrust is constant)?

    I've looked at this and suspect there may be attendant problems such as the angle
    of the force applied and perhaps even the altitude?

    Could someone explain how to work out such a problem and any other factors that
    would need to be considered please?

    Thanks
     
  2. jcsd
  3. Mar 27, 2013 #2

    jbriggs444

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    Science Advisor

    Since you've chosen to apply the downforce on the nose of the target aircraft, it seems that you expect to be able to force that aircraft to pitch down, ultimately causing it to fly into the ground at high speed and crash.

    The engine thrust of the target aircraft is largely irrelevant in this situation. You will be applying a torque that tends to pitch the craft down. The target pilot (or autopilot) will be pulling back on the stick, using the elevators (the horizontal control surfaces on the tail) to apply a downforce on the tail, causing a countering torque that tends to pitch the craft back up.

    If you knew the maximum force that the elevators could supply and if you knew the distance from the wings to the tail and from the wings to the nose then you could equate the two torques and solve for the required force on the nose.
     
  4. Mar 28, 2013 #3
    Thanks jbriggs444

    Yes the assumption is the craft will be forced down.
    I didn't realise the wing and tail position would be so relevant. (I hadn't thought of it as a turning force
    ... more of a straight line vector - so thanks for pointing that out - In my head I had envisioned a
    simple beam on a pivot type system - but with the forward motion and wing lift it is obviously more complex)
    To keep it simple for me to start with can we assume everything is stable and fixed
    (no pilot intervention or fly by wire response)
    Would I be right in assuming an angle would occur whereby the wings cease to provide lift?
    How could that angle be calculated?
    Could you (or anyone) point me at formulas for the likely sequence of events so that
    I can see what force is required to do this and begin to understand the math a little?
    thanks
     
  5. Mar 28, 2013 #4

    jbriggs444

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    Science Advisor

    If you are after equations, you could start with Google using a search term such as "induced drag" or "angle of attack"

    http://en.wikipedia.org/wiki/Lift-induced_drag; [Broken] http://en.wikipedia.org/wiki/Angle_of_attack

    As you force the craft's nose down the angle of attack is reduced. That means that lift is reduced. The plane starts to lose altitude. This means that the velocity vector is no longer horizontal. This tends to increase the angle of attack, thereby restoring lift.

    If you want to reduce lift to zero, you have to apply enough torque so that the plane's pitch changes fast enough that the angle of attack stays constant at near-zero while the plane describes a parabolic trajectory.

    http://en.wikipedia.org/wiki/Reduced_gravity_aircraft
     
    Last edited by a moderator: May 6, 2017
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