You know from the discussion of Drag Force that frontal area influences the drag a body experiences in an air stream. A bicyclist who is standing up in her seat experiences more drag force because her frontal area is greater than when she is crouched on the same bicycle in a racing position. Surface area affects the drag force a parachute produces.

There are two types of surface area that could be relevant: the flattened area of the canopy when it is laid out on a table, and the inflated area when the parachute is descending. In fact, with a circular parachute design, the diameter of an inflated parachute is only about 2/3 that of the canopy laid out flat. Figuring out ways to keep the parachute most fully opened when deployed leads some to use a frame in their designs.

When a parachute falls, you can imagine that it will interact with a column of air below it. The inflated area better predicts the drag force because its size is the effective frontal area, determining how large a column of air the parachute interacts with by moving it aside, creating friction with it as it passes, and making turbulence behind it.

One of the drawbacks of adding more surface area, which can increase the drag force and help the parachute achieve a slower terminal speed, is that it usually involves adding more coffee filters, and thereby more weight. Spreading out filters so that they overlap less can increase the chute's surface area without adding to the mass.

Without regard to size, the 3-D shape of the parachute, and its orientation, affects the drag coefficient of the body, which affects the drag force. Studies have shown that a half-circle or hemisphere, with its open end facing the flow of air, has the highest drag coefficient (1.42). If you rotate the cup so that its rounded end faces the wind, that number drops to 0.38.

Parachute Design Tip: When students are thinking of whether to orient their coffee filters so that their openings points upwards or downwards, they will get more stability when it points up, but less drag.

The parachute's shape also determines how the direction and force of airflow as the chute passes by. A flat canopy will exert less drag than a cupped canopy (though either will exert far more drag than the cupped shape facing upward).

Parachute Design Tip: Having a stiff, flat canopy does not work as well as one that inflates during descent, which results in more drag force as the air flow is caught by it.