Parachute hole, drag coefficient, surface area?

Question

When a parachute hole is made in a parachute, why does the size of the parachute hole not affect surface area, but only the drag coefficient?

Answer 1

You have to analyze the flow pattern to answer this question which is a little vague in what "surface area" means, so I'll assume it means the diameter and basic shape of the "airfoil" or parachute.

The flow from below to above means the air captured by a solid 'chute will rotate around the edges and try to come back together above it, but it can't do this completely so there is a zone above the middle of the 'chute where a pressure differential builds up.

When it does this it creates a zone of turbulence rotating back down onto the top of the chute, trying to collapse it to equalize the pressure differential and making collapse more likely since it can move a solid top down far enough to cause unintended flows that can move an edge toward the center of the 'chute, and if the wind pushes on this it will be forced by its angle of attack even more toward the center allowing a full collapse to occur.

To overcome this a hole is made in the top to allow flow through to equalize this zone and prevent the canopy from collapsing. This flow alters the drag coefficient, but doesn't change the overall "frontal area" of the object in the wind, which is what I assume is meant by "surface area".