Most Efficient Projectile Shape

[Ragnarok]

Maybe a bit embarassing, but you got it the wrong way around...change it before people see it...

Oh crap, you're right. I've fixed it.

[jimmy101]

You have to be careful when using bullets (and other projectiles) as your model for the optimal shape for a round. Bullets are generally supersonic and the optimal supersonic shape is not the optimal subsonic shape. (Cd's are very dependent on the speed domain that the object operates in.)

Take a look at aircraft. A 747 (subsonic) has a nose that looks about like the side of a barn. No point.

Look at a supersonic aircraft (like the SST), they have sharp noses.

Look at supersonic rifle ammo, typically a fairly sharp tip. Supersonic ammo with a blunt tip doesn't carry well and the blunt tip is there for other reasons (such as mushrooming on impact).

So, what is the best shape for a 500 FPS (very subsonic) round? I suspect the answer is not the obvious "same as a high speed, high density kinetic round designed to penetrate 6 inches of depleted uranium armour at a range of 1,000 yards."

This would make a great science fair question, especially since the answer probably isn't "sharp point is best". The tricky part is making a fair comparison between shapes. For one thing, the mass of the rounds would all need to be the same. Furthermore, you have both nose and tail affects. Easiest thing to do would be to use a consistent tail on al the ammo.

Spudguns aren't all that reproducable. I would build a homemade chrono and get muzzle velocity for every firing.

Range is a bit of a problem. You need the impact point, not the roll out point, of the ammo. Perhaps fire into a lake and use spotters with transits set out a few hundred feet on either side of the launch point?

Or, probably easier, redefine the question into a Cd (coefficient of drag) question. All other things being equal the shape with the lower Cd will carry the farthest. You can get at the Cd by firing the round straight up. Measure the muzzle velocity and the hang time. From that you can calculate the Cd for the round. A homemade chrono using a pair of photogates and a push button switch plugged into the MIC input of a laptop would work great. The photogates record the muzzle velocity. When the round hits the ground push the switch, that'll give you the hang time data in the same recording as the muzzle velocity.

[rp181]

a great way to test this is eaither:

1) a wind tunnel with smoke injected, people do this all the time to get a visable flow
2) a high speed camera and water. This would probably be different then it is in air, and harder to shoot, but it would be interesing with caviation and all.

Rag: about your comment about people's scientific knowlege, i disagree. People have there different expertise. While you may be good at mechanical engineering, i doubt you know enough about neurology (or some other field) to do brain surgery.

Brian: I find it funny you say to change it before someone see's, but you quote it so everyone can see it =p

[Ragnarok]

Rag: about your comment about people's scientific knowlege, i disagree. People have there different expertise.

It's entirely true. If you were to take all the people in the UK, most of them wouldn't even be able to make even the poorest of pass grades on the lowest qualification the the school system here offers for science.

While you may be good at mechanical engineering, i doubt you know enough about neurology (or some other field) to do brain surgery.

Yes, but I'm not pretending that I know the answer. They are.

If you ask me about engineering(/aerodynamics/spudding/wargaming/another area of my expertise), if I know the answer, I'll tell you. If you ask me about neurosurgery(/skateboarding/singing/business management), I'll tell you I don't know and not make any pretence at bluffing.

[jackssmirkingrevenge]

Look at supersonic rifle ammo, typically a fairly sharp tip. Supersonic ammo with a blunt tip doesn't carry well and the blunt tip is there for other reasons (such as mushrooming on impact).

So, what is the best shape for a 500 FPS (very subsonic) round? I suspect the answer is not the obvious "same as a high speed, high density kinetic round designed to penetrate 6 inches of depleted uranium armour at a range of 1,000 yards."

Fair comments, most pistol rounds are subsonic and either flat or round nosed, while most rifle bullets have a pointed "spitzer" shape. I don't think however that this automatically means that the round nose is better at subsonic speed.

Take a look at the plan view of a racing yacht, definitely a subsonic vehicle but doesn't it look awfully like a supersonic rifle bullet?



Also, look at these cartridges made for silenced sniper rifles and designed to be subsonic at the muzzle. In the interest of as flat a trajectory as possible and therefore greater accuracy, they need to be optimised for velocity retention, and almost all of them are spitzer shaped.

[Rokmonkey]

Tear drops are the most aerodynamic shape...make that?

[jackssmirkingrevenge]

Tear drops are the most aerodynamic shape

Clearly you haven't followed the debate

Further to my previous post, this is from the article on subsonic cartridges which is the point I was trying to make:

Even this was not the ultimate answer as the bullet was still round-nosed and therefore quickly lost velocity and effectiveness at long range. Enter the current "Whisper" range of cartridges, designed to obtain the best ballistic performance possible within the constraint of subsonic velocity. The first to come to notice was the .30" Whisper (now known as the .300 Whisper), a .221" Remington Fireball cartridge (a short version of the standard 5.56 mm NATO case) necked out to 7.62 mm calibre to take a 210 grain boat-tailed spitzer match bullet.

[Ragnarok]

Now, instead of speculating and making unproven statements, I've decided to demonstrate I actually know what I'm on about, and bring some hard data for aerodynamic performances at different Mach numbers for different shapes so I can lecture at you.

So, what is the best shape for a 500 FPS (very subsonic) round? I suspect the answer is not the obvious "same as a high speed, high density kinetic round designed to penetrate 6 inches of depleted uranium armour at a range of 1,000 yards."

You would be right... but not by much. I shall explain.

Different head shapes are ideal at different Mach numbers, but they are all largely pointy - and the differences made by head shape usually only show up in the supersonic range.
Here's a graph of the Drag co-efficent of the standard "G" projectile shapes (used to give Ballistic coefficients, but this is the raw Cd data - as such, higher is worse) vs. Mach number:

The shapes those curves relate to are aptly described here.
Sorry, there are a couple of places in the graph where I had to interpolate the data in some of the sequences, because I wasn't always able to find the data over the whole Mach range, but it should be more or less correct.

That table is the one I've put into the LRC ...if I ever get it finished... to allow more accurate range predictions where ammo that is reasonably stable over the flight path concerned is used. That is of course assuming the person using the program applies the right drag model, but I can't deal with that. It should be noted that all of these are normalised in the LRC's data sheets and as such, are used as a correction factor on top of a user provided Cd, not to provide the Cd themselves.
This might prove a problem if the user doesn't understand the purpose of the drag models - for example, using the normalised curve of the normally poor GL for a drag co-efficent inconceivably good to go with it would provide an over optimistic answer for most subsonic calculations, given the large fall in Cd in the mid subsonic range. As such, there is also an auto tool which can use the Cd₀ to generate an appropriate drag model for users who don't understand the system. Those that do understand can select themselves, but the auto tool is often still the best option.
For most purposes G1, GI and GL are a reasonable estimate of supersonically inefficient rounds - which roughly conform to modern pistol bullets in shape.
And as you can see, these shapes tend to have fairly poor subsonic and transonic performance too, with Cd values in the range of 0.2 to 0.3 between Mach 0 and Mach 0.8 or so - not appalling, but compare that to the 0.12 of the G7 round in the same region.

Note also that G7 is largely immune to Cd changes in the subsonic range, and very efficent in the supersonic range - if not the outright winner, close to it.

The clear leaders in this match are the long nosed rounds, particularly the boat tailed ones - except at velocities between Mach 2 and 4.2, where G2, a boat tailless round beats G7 by a small amount, and velocities above about Mach 3 to 3.5 where G6 is the winner. (Sorry, not all of this is clear on that picture, I'm looking at my Excel original at 4x zoom)

However, as far as we are concerned, as spud guns are seldom known to beat Mach 2, we can essentially consider long noses and boat tails to be the ideal in ballistics.

Now, to expand a little, we can see the top line, which represents GS (the sphere) is clearly very poor, and would be the worst shape - but only because this graph is missing GC, the cylinder, because if I included that, everything else on the graph would be squashed and almost unreadable.

Back to Jimmy's point, at the approximate mile per second velocities involved with anti tank kinetic penetrators, there IS a different ideal for that velocity range, but not an ideal by any great amount, and the shape isn't that far separated anyway - it's still a long nosed projectile.

Teardrops fired tail last, as we are talking about, fall in a similar range to GL in the subsonic range, and that of GI in the supersonic range - so from that, it's clearly no winner.
Teardrops fired tail first - essentially a spitzer shape - make an approximate parallel to G5. Not bad, but again, no leader.

It should noted that G7 can be bested, I haven't entered the table for that into that chart yet. Not sure I'm going to, as once normalised for use by the LRC, it's performance shows little difference from G7, making it kinda moot to have in there.

[jimmy101]

Fair point Jack. But a yacht moves through a very high density medium. Water is about 1000 times denser than air and is orders of magnitude more viscous, and that has a large affect on the drag forces and the optimal shape.

I still think a 747 nose is the best model. I figure that if a pointy nose helped something moving at a couple hundred MPH then commercial jets would have pointy noses. The reduced drag would be a significant fuel saving feature.

Heck, modern cars are designed to have the lowest possible drag that their basic shape allows at a speed of something like 65MPH. Many low Cd car designs have basically flat fronts. If sharpening up the front helped then we would have pointy nosed cars. Even if the pointy nose only dropped the Cd by 0.05 that would be more than enough to justify the shape since that would represent a significant fuel savings at 65 MPH, where a heck of a lot of the engines power is dong nothing except overcoming air drag.

This would make an excellent science fair project. You can collect replicate data, do the statistics, make some nice graphs ... it would wow the heck out'a judges.

[Ragnarok]

I still think a 747 nose is the best model. I figure that if a pointy nose helped something moving at a couple hundred MPH then commercial jets would have pointy noses. The reduced drag would be a significant fuel saving feature.

There's a good reason that a 747 hasn't got a pointy nose.
Concorde's pointed nose had to be designed to fold down slightly to allow the pilots to see past it for landing.

This adds manufacture and maintenance expense to the excess of the subsonic fuel savings, which is why it's not been taken up elsewhere.

Even if the pointy nose only dropped the Cd by 0.05 that would be more than enough to justify the shape since that would represent a significant fuel savings at 65 MPH, where a heck of a lot of the engines power is dong nothing except overcoming air drag.

Petrol cars are a very bad example - they need a radiator (best positioned at the front) to help supply the air through the radiator or cooling ducts, and in a lot of cases, downforce features which add drag.
The windscreen is also a source of a lot of drag, as it needs to be reasonably wide, and moderately vertical, as extending it backwards would make a very long car - not to mention the wheels.

As such, the ideal shape for a petrol car is not a good aerodynamic shape.

A car like the Porsche 911, pretty decent as far as things go aerodynamically, has a CD of around 0.28, which is far from being ideal.
At the same speeds, round in the shape of G7, is less than half that drag.

Now take a look at Nuna - a solar car, and being electric, without the need for cooling radiators. When that it's world challenge run, it averaged about 64 mph, so fits slap bang in the range you're talking about.
It looks like a knife - it's that pointy. Drag co-efficent? 0.07 - a mere quarter of the 911.

Pointy is good in ANY mach range. Blunt can pass muster (but not as good) at low enough speeds, but in the transonic to supersonic range, it's horrible.

[jackssmirkingrevenge]

There are practical considerations to cars - a long pointy nosed car would be impossible to park, plus it would never pass a vehicle roadworthiness test on account of being a pedestrian skewer.

When they build land vehicles for speed however...

[psycix]

Now take a look at Nuna - a solar car, and being electric, without the need for cooling radiators. When that it's world challenge run, it averaged about 64 mph, so fits slap bang in the range you're talking about.
It looks like a knife - it's that pointy. Drag co-efficent? 0.07 - a mere quarter of the 911.

Im having lunch every day right next to a Nuna. The car is now just decorating the entrance hall of the faculty.
Most of the awesome projects made by students of the TU Delft stand in the hallways of our Mechanical Engineering faculty. Quite awesome.


Back on the discussion:
So could we conclude that pointy is best (especially in supersonic velocities), even though many products of today are not manufactured with a pointy tip.
Which is because the disadvantages (weight, cost, length, etc.) of a pointy tip weigh up too much against the relatively small change of CD of when using a blunt nose. (This only applies to subsonic, ofcourse)

Besides aerodynamics, shape of the projectile also plays a role on impact.
I can imagine pointy tips penetrating further then blunt tips.

[Ragnarok]

So could we conclude that pointy is best (especially in supersonic velocities), even though many products of today are not manufactured with a pointy tip.

It's not just that. You can get good subsonic aerodynamics with a blunt nose, but it's very expensive to develop it - the 747 has a very specific shape which cost many millions to develop , and what most people don't know is that there are lots of tiny fins across its surface to help with drag, directing air to help save fuel.

And even then, what we're forgetting is that the 747's nose is actually pretty pointy anyway:


But yes - pointy is good, and cheap - not requiring much in the way of thought. Where things aren't pointy, there's usually a good reason why not.

As far as I'm concerned though, for spudgun ballistics, we're best off looking at bullets and projectiles, as just about everything else has other considerations which force compromises - planes need lift, cars need downforce and engine cooling.

Not to mention that people need to fit inside both with some comfort.

[jimmy101]

AHhhhh, it ate my response.

I'm not sure I agree with your analysis of the pointy nose on aircraft. The SST had a pointy nose that could be lowered because its wings had such crappy lift characteristics at landing speeds that it had to land at a very steep angle. A 747 (or other modern airliner) lands darn near horizontal. There would be no need to pivot a long pointy nose since it wouldn't be in the pilots sight line during landing.

It would be trivially cheap to put a pointier nose on a 747. Given the huge number of hours that that aircraft is designed to operate, it would be easy to justify a couple million dollars per aircraft for a pointier nose (that doesn't have to move). Even a small decrease in drag would result in huge fuel savings over the life of the air frame.

I believe a typical long haul airliner frame is expected to last more than 20 years and 50,000 to 100,000 hours flying time. At 350 MPH (?) that is a distance of about 26 million miles. A 747 burns ~5 gallons of fuel per mile (according to Boeing). Cost to fly 26 million miles at 5gal/mi assuming $3/gal is $390 million. Save 1% in fuel cost, save $3.9 million dollars over the life of the aircraft. Spend $2M on a better nose shape and you still save ~$2M dollars.

I'm trying to figure out your Cd graph. Looking at the MACH 0.5 region (which is what we're talking about) the GL and G5 shapes looks about as good as anything else. The best, Gs is significantly better, and G5 is the second best? (Can you better annotate the MACH 0.5 region?) If I'm assigning the shapes to the curves correctly "pointy" is not always better in this speed domain. Gs always sucks but various degrees of pointy behave differently and bluntish/pointy (747 nose) point looks pretty good. Indeed, it looks better than many of the sharper points. (Again, not sure if I'm mapping the shapes to the line colors correctly, the graph really should have the shapes marked directly on the lines or the lines should have larger variations besides just color.)

Edit: "the" should be "that"

[jackssmirkingrevenge]

I don't think the 747 is good analogy in this case, let's stick to optimum subsonic bullets. Here's something from the corbin pageon the subject:

A sharp spitzer point brings the jacket material toward the tip in a strong tapered column, which tends to prevent or delay expansion. Since most of the drag on a subsonic bullet is on the base, rather than the tip, the nose can be as blunt as possible (to still permit reliable feeding). The more blunt (round) the tip, the more easily it can be expanded on impact (with a hollow point design). The 1-E elliptical ogive typically gives good feeding in most rifles. The 3/4-E ogive works in nearly all handguns

Note how expansion is a consideration here - ie, the reasons why a blunter nose is being considered . While the article suggests that a pointy nose might not be significantly better at subsonic speeds, there's no suggestion whatesoever that a blunter nose is actually a better thing.