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Homework Help: Parachuting inside bales of hay

  1. Jan 15, 2015 #1
    1. The problem statement, all variables and given/known data
    During World War II the Russians, lacking sufficient
    parachutes for airborne operations, occasionally dropped soldiers
    inside bales of hay onto snow.
    The human body can survive an average pressure on impact of
    30 lb/in2 . Suppose that the lead plane drops a dummy bale equal
    in weight to a loaded one from an altitude of 150 ft, and that the
    pilot observes that it sinks about 2 ft into the snow. If the weight of
    an average soldier is 144 lb and his effective area is 5 ft2 , is it safe
    to drop the men?

    2. Relevant equations
    energy conservation

    3. The attempt at a solution

    For clarity, I set h1 = 150ft, h2 = 2ft, mg = 144lb, and S = 5lb/ft^2.

    Using conservation of energy, the paratrooper's speed just before impact is ##v_i = \sqrt{2gh_1}##.

    If ## E_r## is the mechanical energy once the paratrooper is at rest 2ft under snow, ##E_i## the mechanical energy at impact, and ##\vec N## the force of snow on man, then:

    E_r = 0\\
    E_i = mg (h_1+h_2) \\
    E_r - E_i = \int_{\vec r_{impact}}^{\vec r_{rest}} \vec N.d\vec r

    And, because the force of the snow is vertical,

    ## mg(h_1+h_2) = \int_{0}^{h_2} N(y) dy \approx h_2 N_{av} ##

    So the average pressure the paratrooper must resist is

    ##\frac{N_{av}}{S} = 144*152/(2*5) \ lb/ft^2 = 152/(2*5) \ lb/in^2 = 15.2 \ lb/in^2 < 30 \ lb/in^2##

    So yes it is 'safe' (non lethal). Is it correct ?
    Last edited: Jan 15, 2015
  2. jcsd
  3. Jan 15, 2015 #2


    User Avatar
    2017 Award

    Staff: Mentor

    Under the (problematic) assumption that the force is constant over the whole length, and if the airplane magically stops in the air, yes.
    I'm sure the Russians used a better unit system.
  4. Jan 15, 2015 #3
    I agree it is not very realistic :-)
    Thank you for the reply !
  5. Jan 15, 2015 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, two good points. The horizontal speed might not be a big deal if the bales are round, though of course that leads to the separate question of how great a rotational acceleration is tolerable.
    For the constancy of vertical force, I suspect that depends largely on snow depth. For very deep snow it could be fairly constant.
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