Expert: Paul Soderman - 12/13/2009

Question
QUESTION: I have noticed that when  calculating the perimeter of rectangular parachute canopies
with different side proportions the one with the least amount of perimeter
is the most like a square which is the also the most symmetrical object. Because of thaqt
I'm wondering why the shape that is the most symetrrical will spill the
least amount of air or have the most amount of drag.In other words why does the shape with the least
perimeter spill the least air, and why is that shape the most symmetrical
shape.For the question please include the involved laws or principles of
geometry, aerodynamics, and or physics. If you know any other sources about
this please tell me so I can read more.


ANSWER: Scott
I don't understand your question.  Why would a rectangle with the least amount of perimeter be most like a square ?  Perhaps you can rephrase your question and include a sketch if possible.
Paul

---------- FOLLOW-UP ----------

QUESTION: for example you have 4 rectangles with a 1 to 1, 1 to 1.33, 1 to 1.66, and 1 to 2, base to height ratio. All of the rectangles have the same amount of surface areas. I have figured out the lengths, and it turns out that the 1:1 has the least amount of perimeter.
From another expert, i learned that parachutes with less perimeter have more drag since there is less area for air to spill out (e.g. 1:1 and 1:500).

Answer
OK Scott - now I understand though I am unsure of your definition of air spillage.  Here is the way I think about parachutes.  When airflow hits a flat surface a stagnation point near the center is created where the flow stops and builds a high pressure region. Flow approaching the high pressure region senses the pressure, curves and hits the surface farther away at an angle.  For maximum drag you want the high pressure region to be as far from the edge of the parachute as possible so more flow contacts the surface instead of curving past the edge.  The best shape would be a circle or square.  A long skinny rectangle would allow the flow the curve around easier.  In the limit, a very long thin line would have little drag.

What I have been describing is the flow field effects that determine drag coefficient.  For the same descent speed and air density, the drag only depends on cross sectional area and drag coefficient.  So if the area is constant, only the drag coefficient changes with parachute geometry.  Drag coefficient is nothing more than a constant in the drag equation that allows us to account for geometry effects.  Squares must have a greater drag coefficient than rectangles.  A more important factor would be the chute curvature.  If the flow enters a bag shape, it has to come back out at the same rate as it entered and spill around the edges.  That would interfere with the incoming air to cause much turbulence and drag.  All these things are complex in detail and have been the subject of much experimental study.
Paul