# Most aerodynamic shape?

yrjosmiel73
I mean aerodynamic as in least air resistance.

Just curious.

Simon Bridge
Homework Helper
Consider: what causes air resistance? How would you go about minimizing it?
Do you have other constraints? (I.e. a geometric point has zero air resistance.)

Have you looked for objects that are engineered for low air resistance to see what shapes they tend to have?

berkeman
russ_watters
Mentor
Generally, for the same cross-sectional area, a teardrop shape is most efficient.

yrjosmiel73
typically the "most" aerodynamics shape sis dictated by constraints...and finding it is very difficult (this is why aerospace engineers are involved with it), with no constraints a point have zero drag so...a point is the answer.

cjl
Most aerodynamic given what constraint? Lowest drag for a given cross sectional area? Lowest drag for a given volume? In general, the shape will tend to be somewhat similar to a teardrop, but it will vary depending on your constraints.

yrjosmiel73
Most aerodynamic given what constraint? Lowest drag for a given cross sectional area? Lowest drag for a given volume? In general, the shape will tend to be somewhat similar to a teardrop, but it will vary depending on your constraints.
Let's say lowest drag for a given volume.

The shape of the Hindenburg Zeppelin hull gives you the lowest drag coefficient-to-volume ratio if you extend the tail cone to a sharp point. (The tail cone was rounded off to fit the hangar in Lakehurst NJ.) I'm assuming incompressible flow (speed << transonic). At very low Reynolds numbers it might be necessary to modify the fineness ratio.

cjl
While the Hindenburg isn't a bad shape for low drag, it isn't quite the ideal. Here's an interesting paper exploring the optimization problem: http://cafefoundation.org/v2/pdf_tech/Drag.Reduction/5.AIAA-48131-445.pdf

You can see in Fig. 5 that the optimum is somewhat like a teardrop with an elongated nose (the labeled "Body X-35"), though a wide variety of teardrop-like shapes do pretty well (for example the labeled "Dolphin" profile).

David Lewis
Simon Bridge
Homework Helper
... although this is for incompressible flow.
Looks somewhat like a half-deflated balloon - you know, as it propels itself through the air.

cjl
True. If you start introducing compressibility, it becomes an entirely different problem. That shape should work well up to a couple hundred miles per hour though (~100m/s), at least as far as standard atmospheric conditions are concerned.

Dr. Courtney
Gold Member
2020 Award

This is a common bullet shape which is very close to optimizing (low) drag for supersonic spin stabilized projectiles.

Last edited by a moderator:
cjl
It's not bad, though it would be better with a more complete boat tail (which it does not have because of the requirements of barrel launching as well as spin stability concerns).

Dr. Courtney
Gold Member
2020 Award
It's not bad, though it would be better with a more complete boat tail (which it does not have because of the requirements of barrel launching as well as spin stability concerns).

Yes, there is potential to reduce the drag by about 5% more by a more complete boat tail. The longer bullets that result would require a faster twist rate to maintain gyroscopic stability. The longer base would also reduce powder capacity by extending further into the cartridge case. These effects tend to combine to increase peak operating pressures in the barrel without increasing muzzle velocity. There is also the additional challenge of keeping such a design cylindrically symmetric. Imperfections in the overlap between the geometric center and the center of mass create significant inaccuracies as the bullet leaves the barrel. Resulting pitch and yaw also contribute to aerodynamic drag and tend to cancel out the small advantage gained with the longer boat tail.

We measure a lot of supersonic drag coefficients. In addition to the above practical challenges, a fundamental challenge of supersonic bullet design is that the shape that is ideal at the launch speed (usually close to Mach 3) is not ideal as the speed decays down through Mach 2.0 and then toward Mach 1.0. In long range applications, the compromise is to try and optimize the average drag over the supersonic range.

256bits
Gold Member
Nose cone shape is of importance.
As usual wiki is a primer.
https://en.wikipedia.org/wiki/Nose_cone_design
which gives the mathematical equations for several types.

Above graph shows the drag with 1 being favourable to 4 unfavourable versus speed.

If you are really intersted in this topic just get Fluid Dynamic drag by Hoerner :)

rcgldr
Homework Helper
Speeds in the range 300kph to 700kph or so are achieved by land speed record vehicles run at places like Bonneville Salt Flats or El Mirage Lake. Most have long tail sections.

http://en.wikipedia.org/wiki/Bonneville_Salt_Flats#Land_speed_events

http://en.wikipedia.org/wiki/El_Mirage_Lake

List of land speed records, some with links to vehicles including images:

http://en.wikipedia.org/wiki/List_of_vehicle_speed_records#Land_vehicles

Example wheel driven vehicle with long tail section:

http://www.teamvesco.com/vesco111.html

Example motorcycle with a long tail section, 360 view option:

http://top1ackattack.com

Nose cone shape is of importance.
As usual wiki is a primer.
https://en.wikipedia.org/wiki/Nose_cone_design
which gives the mathematical equations for several types.

Above graph shows the drag with 1 being favourable to 4 unfavourable versus speed.

Some of these appear to flux, like a sine wave. Ie. at Mach 0.9 it has low drag, then at Mach 1 it has high drag, but at mach 1.1 it has low drag again. Is this the natural order of things, or are your statistics incorrect? If your statistics are correct, this would seem to indiciate that air has some kind of inherent frequency, causing wave phase cancellation effects.

The concept is similar to music, timbre, where the air (instrument) has a wide range of frequencies, and when you get close to the concentrated parts, things become either more or less harmonious.

Whoops. I can see why you'd draw that conclusion from the sample set I typed in my post. (The article talks about the effects of subsonic vs. supersonic.)

But if you look at the chart it seems to continue even after sonic boom...it goes 0.9 low then 1 high then 1.1 low then 1.25 high then 1.4 low and so forth.
The von Karman almost seem to be symetrrical, with drag highest at 1.5 and then low drag at 1.0 and 2.0. Which the possibilities in my mind makes this seem to be some kind of phase timbre effect, being analogous to sound theory, or the results in the chart are inaccurate.

What Im trying to say is Wikipedia provides a chart like this, implying a simple drag related to the sonic boom.

I'm saying its not so simple, I think its more analogous to this video below.
(can't find it just think of a crazy looking video with sine waves and eq frequencies and such.)

Last edited:
cjl
Whoops. I can see why you'd draw that conclusion from the sample set I typed in my post. (The article talks about the effects of subsonic vs. supersonic.)

But if you look at the chart it seems to continue even after sonic boom...it goes 0.9 low then 1 high then 1.1 low then 1.25 high then 1.4 low and so forth.
The von Karman almost seem to be symetrrical, with drag highest at 1.5 and then low drag at 1.0 and 2.0. Which the possibilities in my mind makes this seem to be some kind of phase timbre effect, being analogous to sound theory, or the results in the chart are inaccurate.

What Im trying to say is Wikipedia provides a chart like this, implying a simple drag related to the sonic boom.

I'm saying its not so simple, I think its more analogous to this video below.
(can't find it just think of a crazy looking video with sine waves and eq frequencies and such.)

I don't see any video, but one thing to keep in mind is that those numbers aren't telling you absolute drag, they're telling you the relative suitability of the shape for that speed regime. All of those shapes will have an absolute drag profile that looks pretty much like the Wiki chart, but the VK happens to be a bit below most of the others at mach 1, and a bit above the others at 1.5, dropping back down below the others at 2. That doesn't mean that the drag quantity is oscillating however.

The most aerodynamic shape is typically known as the teardrop - it's the shape water forms when it runs down a window because it's been pushed into that position by the air flowing over it on the way down. The idea is to start with a nice rounded front - air naturally makes its own 'knife edge' point with a curved front without the need of an excessively pointy front end - making the front too pointy ends up forcing air in directions it doesn't want to go - producing good downforce but increasing overall resistance. The tip at the end should be relatively pointed to follow the air back smoothly through without a massive drop-off creating low pressure sucking stuff in (causing drag). The fine tuning of what exact teardrop you want to use depends on what it's being used for - you can adjust where the peak circle radius is for different uses, of which I can't really link up to its own scenario, although especially with formula one parts like above the drivers head they often have an elliptical front rather than an exact circle with a triangle on the end. The half teardrop proves to work just as well as the normal teardrop, as the underside just carries on as normal.

I hope I didn't bore you to death, or patronise you with stuff you already knew, but there aren't many situations people let me go into as much detail as that

berkeman
Mentor
known as the teardrop - it's the shape water forms when it runs down a window because it's been pushed into that position by the air flowing over it on the way down
Welcome to the PF.

I think you may have made a typo here, and also have a misconception about raindrop shapes. When you said the teardrop shape is formed by airflow as the water runs down a window, there is no airflow when water is running down a window. I think you meant to say that the teardrop shape develops because of airflow when in freefall (like rain). However, that also turns out to be a popular misconception...

http://water.usgs.gov/edu/raindropshape.html
USGS said:
The common raindrop is actually shaped more like a hamburger bun

cjl
Welcome to the PF.

I think you may have made a typo here, and also have a misconception about raindrop shapes. When you said the teardrop shape is formed by airflow as the water runs down a window, there is no airflow when water is running down a window. I think you meant to say that the teardrop shape develops because of airflow when in freefall (like rain). However, that also turns out to be a popular misconception...

http://water.usgs.gov/edu/raindropshape.html

The most aerodynamic shape does happen to be fairly close to a stereotypical "teardrop" shape though (with a longer nose - see the paper I linked in my earlier post for a full analysis), despite the fact that raindrops arrange themselves into a very different shape.

Levi Partridge and berkeman
Yeah
that's more or less what I meant - when a bead of water runs down the wall of the shower it forms into a shape similar to the 'teardrop' with the bulky front, although it is more of a sphere as it doesn't have a very significant tail. With vehicles (or drops of water) it is basically the object moving and the air moving out of the way, I don't know if that's what you were picking up by mentioning airflow in freefall.

I've probably misunderstood your point again- tell me how if I did

berkeman
Mentor
I've probably misunderstood your point again- tell me how if I did