Best Answer:
Air has mass just like any solid does. To move air takes energy, to move a lot of air takes a lot more energy. Just like a house fan uses 1/4 hp to move a little air, a propeller on a small airplane can absorb 300 hp to move a lot more air.

So a parachute is based on the premise that it takes energy to move air

Drag is a force that resists the motion of any object thru it. Drag is proportional to the square of the velocity. If you double velocity, you increase the drag force by 4 or 400%.

There are two styles of parachutes, the old style which relies on pure drag with lots of surface area , and the newer styles with low surface area but have an X component to the downward motion that makes the parachute generate some lift, so the chute travels down in a long decline plane in the X and Y direction both. A good chute might travel horizontally 10 feet for every foot in vertical distance it falls, and this translates from for instance of falling 100 ft /sec vertically, to 10 ft/sec vertically. So it takes your downward speed and cuts it to 1/10 th the amount.

But the standard chute based on drag force is the easier one to explain. When you first jump and you weigh say 75kg and are falling at 54 m/s (about 120 mph) you have a lot of kinetic energy. Your KE is 1/2*75kg * (54m/s)^2 = 109,350 Joules of energy.

A parachute designs in a certain fall rate that is easily survivable. Usually around 5-6 m/s. So if you are going 54 m/s the chute has to decelerate you from 54 m/s to 5 m/s. And that is the purpose of drag.

In a vacuum a stone and a feather would fall at the same rate. But in air, the stone falls faster. That is because the stone has more potential energy because of it's mass (and it's increased density) to push air out of the way than a feather does. And like the fan I spoke of earlier, it takes energy away from the stone's gravitational energy and imparts it to the air molecules in front of it to move them out of the way.

If you fall with your body parallel to the ground you fall around 54 m/s and this is because your PE is just equal to the energy you impart to the air molecules in front of you to limit your speed to 54 m/s. You are in equilibrium with the drag force at 54 m/s.

But say you do a head dive straight down with your body perpendicular to the ground. Your speed will increase to over 90 m/s, because with the decreased surface area your body is exposing to the air molecules your PE is able to move faster because it doesn't have to push as much air out of the way and give it's energy to.

But even falling in a head dive you reach equilibrium, since you are falling 90 m/s that formula for drag comes back in and since you are going 90/54 = 1.67 times faster, you have to square the drag force now, so the drag is 2.8 times greater. and equilibrium is reached at 90 m/s

So the parachute is designed with an average mass which is designed with a certain amount of surface area to coincide with your kinetic energy which came from your initial potential energy when you jumped from the plane. If you weigh 75 kg and you have a design fall speed of 5 m/s you need a drag force to exactly match that 1/2+ 75 kg * (5m/s)^2 = 938 Joules of drag needed to counter your kinetic energy of falling.

The surface area is calculated so that the energy imparted to moving all that air away from the underside of the canopy is equal to 938 Joules of drag force at 5 m/s. The air in front of the canopy is slightly compressed and their is a low pressure zone on the top side of the parachute that adds to the drag because the parachute tries to go up to fill the partial vacuum void above the chute.

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