If you search the internet for the most aerodynamic shape, you will find a couple pages saying it's a teardrop. This seems pretty reasonable. It's about the shape of a wing, although wings aren't designed only for minimal drag.

But nothing really authoritative. No indication that any college kid ever spent thousands of hours with a wind tunnel trying all possible permutations. Why not?

So then you scour the web for some kind of mathematical definition of a teardrop, and you eventually come across someone suggesting a sphere and a sin wave. I was familiar enough to know that the math for the two objects are very closely related, and quickly created a model that satisfied me.

While I understand that the tail end is more aerodynamically significant, I wondered why more of a point on the nose wouldn't help. I wondered what a full sin wave would do. That looked pretty good. I thought maybe if you took a sphere or cylinder and used the flow paths around that, you would get the perfect shape.

Then I watched a couple excellent videos of flow paths around a cylinder and a plank, and realized that if the plank's flow paths weren't similar to those of the sphere, I would need to build this shape in an iterative process, using the new shape's flow paths to calculate the next shape. Looks like that would turn out like a sin wave.

This thought process was all based on the air particles very close to the object. Surely the air particles farther away would also appreciate a sin wave? I was disappointed that a shape more complex than a sin wave would probably be necessary. Then I contemplated the flow paths of those particles. They would get something nicely close to a sin wave.

I don't think a full sin wave would be practical often, because a small change in angle of attack could be bad. So perhaps an average between a sphere and a sin wave?

Also, the sin wave comes to an extremely thin and long end. I suspect it would be more practical to chop off the bottom 5% or so of the sin wave.

I hope to build a wind tunnel out of cardboard and box / window fans, and a drag balance and do some testing with clay.

The aerodynamic differences between a sphere and a cylinder would be interesting. Particles around a sphere get spread out as they're cramped over the object. Around a cylinder they all take the same parallel path.

There is an interesting page on boat hulls which mentions that no matter how lovely your shape, Osborne Reynolds says if it's long enough, your laminar flow will turn turbulent. I'm very curious how far that is in air. I'm hoping far.

Finally found an equation defining airfoils: http://en.wikipedia.org/wiki/NACA_airfoil#Equation_for_a_symmetrical_4-digit_NACA_airfoil

Yup, "Aerofoils with pointed noses have cost several lives because they stall totally and suddenly." So that appears to be the only reason wings are teardrop shaped and not pointy: They suddenly fail to cause lift. This page also implies that airfoils are based on parabolas.

2010-01-20, more stuff showed up on google:

What's the Most Aerodynamic Shape?

Sears-Haack body

2012-06-07

The images at the top of this page are 2 dimensional sine waves that are then rotated. For some time I wondered (although I didn't have these words for it) if it would be better if the *volume* of the object followed a sine wave. The Sears-Haack body makes me think that it has to at least be better than the shapes I modelled above. It's "the aerodynamic body shape with the lowest theoretical wave drag" - and wave drag is what you're concerned with as you approach super-sonic speeds, not what I'm interested in for cars. I'm not convinced it's not still ideal at 65mph. An important point, and the breakthrough that made super-sonic flight feasible, was the realization that this distribution has to apply to the entire object, for example wings and all, not just the fuselage. So include tires.

Another important point that took a while for it to sink in for me: Make sure your flow remains attached in typical cross-winds. This is why the leading edge of wings aren't pointed - it would cause them to suddenly lose flow attachment at higher angles of attack, which means stalling.

I believe the most important points we know are: 1) Maintain attached flow (which doesn't necessarily need to be laminar - turbulence can aid in retaining attachment), 2) Minimize surface area (because after detachment, skin friction drag is the biggest problem). Of course at low speeds, maybe 30mph, rolling resistence (weight, LRR tires) is more significant.

Sears-Haack body rendering from Wikipedia:

Cross-sectional area of a Sears-Haack body from aerospaceweb.org - a great page:

Also, up to 0.3 times of the speed of sound in a fluid (mach 0.3, ~220mph in air), flow can be accurately modelled as non-compressible. That means at driving speeds, air isn't springy. Most of the time I was thinking about these things, I assumed what happened to air as it went around a car was that it got squished, and then unsquished. But if it's non-compressible at these speeds, then what happens is it has to accelerate (and then decelerate) as it goes around a car - and the energy required for this acceleration is much of the cause of drag (other than skin friction). Meaning, among other things, that at the widest cross-section, air is going fastest. Also it makes more sense for air to go under a car.

Compressibility and Incompressibility, U.S. Centennial of Flight Commission

Incompressible flow, CFD-online.com

Images were created in blender which is open source (free).

Sun May 16 09:15:13 EDT 2010