how does the shape of a parachute effect its time of landing?

Answer 1

In general drag forces, which are those forces opposing the force of gravity, are found by 1/2 rho Cd A v^2; where rho is the air density, Cd is a coefficient of drag, A is the cross sectional area of the falling body, and v is its velocity through the air.

The shape of a falling body determines the value of Cd and its aspect relative to the velocity determines the cross sectional area. The more steamlined shapes have lower Cd's than the less streamlined shapes. Further, the shape can be oriented so its area perpendicular to the velocity is maxium A.

The time to landing varies according to t = S/v; where S is the distance to the ground and v is the termiinal velocity of the parachutist with the parachute open. From, the terminal velocity (with chute) is found when the weight (W = mg) of the parachute and parachutist equals the drag force; so we have 1/2 rho Cd A v^2 = mg; where m is the mass of the chute and person combined. Thus, we have v^2 = 2mg/(rho Cd A) and v = sqrt(2mg/(rho Cd A)).

Put v into t = S/v and we have t = S/sqrt(2mg/(rho Cd A)). So we see decreasing Cd from streamlining the shape or decreasing A from orienting the parachute off the velocity vector will shorten the time (t) of landing.

(NB: The velocity in these equations is strictly the vertical velocity of the fall from a height S with the parachute deployed. So t starts with the chute open; not when the person bails out into a free fall. Also, there is no accounting here for lift due to lift forces from a wing shaped parasail type chute.)

Answer 2

the shape defines the air resistance which influences the rate of descent or time of landing.

Think of all the physics equations that neglect air resistance as an example. You will recall that if a brick and a feather are dropped from the same height in a vacuum, both will hit the ground instantaneously.

On earth there is air and hence the brick will hit the ground first, but dont due to its weight, but rather due to the fact that that the air resistance is far greater than that of the feather.