Re: which shapes falls the slowest

Hi Susan,

That's a good question. The answer can be either simple or complicated, depending on how much detail you want.

The simple answer is the "biggest" object will create the most drag, and make the shape fall slowest.

That said, here's the complex answer. Drag is dependent on air resistance. Air resistance is dependent on the speed of the object and the cross sectional area (the surface that feels the oncoming air). If an object must be 10 inches all around (I take this to mean the perimeter of the cross section) then the most area you can get for the same perimeter would be in a circular cross section. Therefore, the sphere should fall slower than the cube. However, shape will affect your air resistance too. As air travels along the surface, the roughness of the surface and the angle of the surface to the oncoming air will affect the air resistance. The density of the air (altitude) and the humidity will also have an effect. So a rough sphere will fall slower than a smooth one, the cube could fall slower depending on how it is aligned, and everything will fall slower at sea level in Hawaii than on top of Mount Kilimanjaro.

The bottom line is that the difference between the cube, the sphere, and the tetrahedron is going to probably be so small, you won't be able to measure it.

However: if the rules are that the object has to be ten inches around, and there are no limits on height, a parachute is going to be your best bet. A hemispherical shape with a small hole in the center anchored to the weight by the edges of the parachute will give you the most air resistance for the smallest cross-section with the least amount of weight, and ALSO be stable (maintain it's shape).
Also, the lighter the object, the lower the terminal velocity will be. A very light object (coffee filter) will reach terminal velocity in a few inches. A wooden ball with a circumference of 10 inches will take several stories.

I hope this answers your question, and that it helps! The best method is to just try it out.

Jeff Yap
Mad Scientist

PS: If one parachute works well, then two should be better, right? Nope. Try take three coffee filters, and drop one from eye level, and count how many seconds it takes to reach the ground. (Drop it with the bottom at the bottom, so it looks like a bowl. You won't be able to get it to stay like a parachute.) Next, drop two filters, one above the other, with a space of 2-3 inches between them. What did you see?

References:
Physlink - Physics of Skydiving
Physics Classroom - Freefall and Air Resistance
NEWTON Argonne National Laboratory - Air Pressure and Resistance