That is, for minimizing drag?
I think it’d be a classic teardrop- ie., a falling drop of water- but I vaguely recall somebody once saying that surface tension prevents a drop of water from becoming as aerodynamic as it otherwise would.
Otherwise, I would have assumed that it was something pointy on both ends.
Followup: if the teardrop does have the lowest drag coefficient, why aren’t planes shaped like tears with wings and a tail?
A falling drop of water is a sphere, isn’t it?
First of all, a falling drop of water isn’t teardrop-shaped (that is, with a cusp on the top). Second of all, I don’t think there’s any reason to assume that it would form into a particularly aerodynamic shape. Third, precisely what shape is most aerodynamic depends on the speed, the viscosity of the fluid, and other factors.
Follow-up, airplanes are more-or-less teardrop-shaped, with a rounded front and a pointy back, but they also have other constraints on them, like that they have to have room inside for people or cargo or whatever, they have to be practical to manufacture, and they have to hold in a pressure difference. The cylinder-with-endcaps shape that most planes have represents a compromise of these factors.
An infinitely long, thin line. Real world requirements don’t allow this however. Tear drops are not particularly good aerodynamically, nor are water drops actually tear-shaped.
Wikipedia is your friend.
Nope. It’s sort of lens-shaped with a rounded top and a bottom flattened by aerodynamic forces. Like this.
Does it become more spherical as the drop gets smaller, due to surface tension?
This thing has a fairly efficient shape to it.
Yes, because the strength of surface tension scales down linearly with radius but the upward aerodynamic force drops off with its square. Additionally, smaller drops experience a larger drag with respect to its surface area and have a smaller terminal velocity–that is, they don’t fall as fast.
But when you are talking about supersonic speeds, you need a whole new set of efficient shapes (right?).
That’s what I was thinking. What about the principle of constant cross-sectional area?
Thanks all!
I guess the “pointy at both ends” thing is closest, then.
It depends on how fast you’re going. As mentioned, a cigar shape with points on both ends is best at trans-sonic speeds. However, a “streamlined body” will be best at subsonic speeds. This is a shape with a rounded front and a pointy back, similar to an airplane wing. It is also quite similar to the iconic teardrop shape (although I’d argue that it shouldn’t have any concave sections, while a teardrop might). The exact shape would be a function of expected velocity and viscosity of the fluid.
The purpose of a streamlined body is to get proportionally as much of the fluid drag as possible to be wind shear, because it’s much easier to slide a plate along a fluid (parallel to flow) than it is to push it through the fluid (perpendicular to flow).
Wiki explains that “wave drag” occurs between Mach 0.8 and 1.2. Does it stop at 1.2, and does it occur at all below 0.8, or are these more like one standard deviation?
Wave drag is the drag produced by a shock wave (M = 1.0). Between .8M and 1.2M you may have some shock waves on some edges due to local flow speed differences. As a rule of thumb, below .8 M you shouldn’t have any local supersonic flow, and above 1.2M it is all supersonic.
So no, it doesn’t go away at 1.2M
Zeppelins and fish and birds come close to ideal shapes, but it depends of course on the speed, viscosity, density, and dimensions of the things involved. You also have to be careful to say “for an object of volume X” or “…area Y” or “…width Z”.
It seems to be a surprise to most that tapering the back is more important than tapering the front. Many cars look like they would be more aerodynamic going backwards. Perhaps the shape of rockets has helped confuse this. Rockets can’t be very tapered at the rear if they are dominated by engine size at their very last diameter.
I suspect people also tend to imagine moving through air as similar to cutting through a soft substance with a knife. The front of the blade is sharp and the back is blunt.
How about Flash Gordon’s spaceship?
But aren’t there cases in cars where a blunt end is used to reduce drag?
Here’s a car that is tapered at the back with an excellent drag coefficient:
J.
