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17 February, 03:44

A payload is to be delivered by airdrop. The vertical velocity at landing has to be less than 7m/s. The total weight of the payload and parachute system is 400kg. Determine the minimum diameter of the open parachute, assuming a drag coefficient Cd 1.20.

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  1. 17 February, 04:34
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    The minimum diameter of the open parachute = 11.77 m

    Explanation:

    For the open parachute + payload setup to drop, its weight must at least match the drag force so that the load+parachute can drop with its constant terminal velocity without accelerating.

    Drag force = CρAv²/2

    C = drag coefficient = 1.2

    ρ = density of fluid = density of air = 1.225 kg/m³

    A = Area of the body (falling through the fluid) facing the fluid = ?

    v = velocity of Body falling through a fluid = 7 m/s

    Weight = mg = 400 * 9.8 = 3920 N

    (CρAv²/2) - 3920 = 0

    (CρAv²/2) = 3920

    A = (2*3920) / (Cρv²) = 7840 / (1.2 * 1.225 * 7²)

    A = 108.84 m²

    The open parachute is assumed to be circular

    A = πD²/4

    108.84 = πD²/4

    D² = (4 * 108.84) / π

    D = 11.77 m
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