What would be an appropiate shape for a parachute? I'm trying to design a parachute that minimizes the descent velocity, but I'm not sure what shape I should use.
From what I've read, ellipse-shaped parachutes are too aerodynamic and minimize drag, while squares are good enough to maximize drag, but I've read this from very unreliable sources and unfortunately I've never taken a fluid dynamics course so I'm not sure if those answers are right.
 A: You want your parachute not to be a parachute, but a wing.
The difference is that it has horizontal velocity, and the air flows smoothly over the top and bottom surfaces.
In addition, you want to minimize drag, because sink rate is proportional to drag.
The main way to minimize drag is to minimize speed.
So it needs forward speed, but no more than necessary.
Check out paragliders, because that's what they do.
I've seen these things in action.
They stay up a long time.
A: Bernoulli's law. Hydrodynamic lift is created in a wing that has more (air, water, etc)but traveling under than over. This is how an airplane is lifted off the ground. Speed is just a consequence of the creation of lift. The wing does not stall from lack of speed it stalls because the air under the wing has equalized with the air flowing over the wing. I can launch a plane without starting the motor. Teather it down from the nose with a long rope, put it nose to the wind and make sure the wind speed is higher than the stall speed. As necessity we have given planes motors and propellers to reverse this idea and allow aircraft to be self propelled instead of relying on the right conditions conducive to flight....a parachute is a wing that is engineered for controlled decent instead of powered ans sustained flight. The closest to sustained unpowered flight would be a paraglider wing. The span and trim(the angle of attack) of the wing is optimised for extremely slow controlled decents. They(pilots) are able to maintain flight only when given thermals to create lift and hence maintain flight. Without mother nature helping, it will decend. Wing load is the next consideration for optimal flight. To light the wing will not inflate to full flight, to heavy and your glide slope is not optimal.......the design of paraglider canopies is that of ram air inflation, fully elliptical. The ram air "cells" inflate to create rigidity to the the wing. The suspension lines are selected by weight rating, drag, durability.....if you can find the canopy size of a pilot and get his weight, a wing load can be scaled to size for your needs. I jump a 210 sq foot sport canopy as a skydiver. My exit weight is 260the lbs. Divide 260 by 210 and you get 1.23 pounds load per sq foot of fabric. This should give you a solid start and some ideas for resources to more/better information ....  
