Most Efficient Projectile Shape

[ALIHISGREAT]

For spud gunning purposes, unless you want to achieve crazy range (like Rag's ~400m target) a stable shape that promotes accuracy will always be better, if you can achieve that with a low Cd, well thats good, but i would got for accuracy over range everyday..

so i think that we shouldn't just be looking at range as the OP asked, i think the overall performance of the round should be taken into account to provide an overall efficiency, because after all, what use is a bullet that can travel XXXm with no accuracy?

[jackssmirkingrevenge]

I think that we shouldn't just be looking at range as the OP asked, i think the overall performance of the round should be taken into account to provide an overall efficiency, because after all, what use is a bullet that can travel XXXm with no accuracy?

Horses for courses, if you want range above all else then projectile consistency, ease of manufacture etc. are of little concern. However if you're concerned with hitting targets and manufacturing projectiles in quantity, there are other considerations.

[Ragnarok]

Ah yes, I see, Excel 2007 has picked stupid indistinct line colours, so it's hard to differentiate some of the lines.

OK - redo in rainbow bright colours, and with a higher quality JPEG:


And a zoomed in section on the Mach 0 to 1 range:


I've deliberately removed GI from the second picture (GS is way off the chart), as it's an older version of G1 that was incomplete in the subsonic range, so I've taken it out to get rid of clutter.
I've also put in the data points and more grid lines to make it clear. There's a data point at every 0.05 Mach up to Mach 0.7, and one every 0.025 after that.

Also, note that the lines for G7 and G8 are not completely flat, although they may appear it. We're not dealing with interpolated data here to fill in between other points - their Cd really is that constant below the transonic range.

Now, this is actually quite an interesting chart, if you're a boring engineer like me.
Somewhat contrary to what you might expect, all the rounds, save the missing GS and GC, which consistently worsen (until approxmiately Mach 1.6 in GS. GC continues to increase) have Cd reductions of varying magnitudes towards at some point in the subsonic range. It's large in GL, a fall of around 38% at 0.5-0.55 Mach, and about 0.5% in G7 and G8.

Now, there are sections where GL, the blunt nosed bullet beats G6 and even G8. This is because of a similar phenomenon to supercavitation (which we've discussed before), and it only exists because the rounds are flat tailed, an inefficiency in itself.
The brute force of the flatter nose smashes it's way through the air, producing something of a bubble of vacuum in which the round flies, which reduces the vortices produced by the hard edges on the round's tail - essentially giving it a boat tail it doesn't have.
If you added boat tails to the designs of G6, G8 and GL, GL would gain significantly less benefit than the other two.

But anyway, G7 is still the winner by a long shot.

[jimmy101]

Ah! (assuming I've got the traces mapped to the correct shapes.)


So, lets say we ignore the boat tailed rounds G2, G5 and G7 for the moment and just compare the rounds with blunt butts; GL, G1, G6 and G8. Otherwise it's an apples to oranges comparison.

At typical spudgun velocities of say 300 - 700 FPS, the GL nose (a hemisphere) is as good as or better than the three pointier tips.

That pretty well matches 747's noses, mostly just a hemisphere, no real point to speak of.

It also matches what "Design of Aerodynamically Stabilized Free Rockets" says for subsonic rounds. The most important feature of the nose is that the surface area is minimal, at least down to the point where you start to approach a flat front (i.e., a right cylinder).

Nose cone drag characteristics
For aircraft and rockets, below Mach .8, the nose pressure drag is essentially zero for all shapes. The major significant factor is friction drag, which is largely dependent upon the wetted area, the surface smoothness of that area, and the presence of any discontinuities in the shape. For example, in strictly subsonic rockets a short, blunt, smooth elliptical shape is usually best. In the transonic region and beyond, where the pressure drag increases dramatically, the effect of nose shape on drag becomes highly significant. The factors influencing the pressure drag are the general shape of the nose cone, its fineness ratio, and its bluffness ratio.

From the Wiki on nose cone design (emphasis added) which references the Department of Defense's "Design of Aerodynamically Stabilized Free Rockets".

So, I don't see G7 as the "winner by a longshot" if we are talking about this speed domain and just the nose shape, not the nose + tail shape. For the nose shape only, a hemisphere is about as good as you can do with a blunt butt.

If you can change both the nose and butt then G5 and G7 are really good but neither is really all that pointy, certainly neither shape would be considered a sharp tip. At lower speeds G2, even with the non-blunt tail, is only slightly better than a blunt tailed hemisphere nose.

[jimmy101]

Oh ya, one more thing. Without a stabilized round (either via rifling or fins or hollow tail) none of this aredynamic stuff really matters all that much. Once the round starts to tumble, which is just about the instant it leaves the barrel, the Cd is going to go way up. For a tumbling round a sphere is probably the best shape.

[jitup]

what type of software, and math course, should I use to be able to figure this stuff out?

I am considering building a miniature wind tunnel with a smoke stream, can any one suggest a good cheap software that can analyze a video feed and plot the information? Am I getting in over my head with this project? (I want it for more than just figuring out cannon stuff)

I want to take my cannon building to the next level and want to actually figure out and build something and know its cappabilites and the amount of a load it could handle.

[Ragnarok]

At typical spudgun velocities of say 300 - 700 FPS, the GL nose (a hemisphere) is as good as or better than the three pointier tips.

GL is a good shape in that range, yes, but other things have to be taken into consideration. Like you said:

The major significant factor is friction drag, which is largely dependent upon the wetted area, the surface smoothness of that area, and the presence of any discontinuities in the shape.

The brute force of the nose produces a relative vacuum around the projectile, reducing friction drag. This vacuum also reduces tail eddies (like a boat tail).

It should be noted that these traits are highly dependent on the round's length. Using a blunt nose on a longer round would show less beneficial traits with regards tail eddies, and on a shorter round with regards friction drag. As such, GL's success is a bit like the Ballmer peak, it's very dependent on a specific variable being in the right range.

This is also why the GL shape has a very specific velocity range in which it fairs well. It's poor Cd at lower and higher velocities is when the advantages conferred by these traits start to die down - as can be seen by comparing it to the similar, but pointier noses G1 (which I feel better represents the 747 if I'm honest) - which shows performance within 3% of GL essentially between Mach 0.3 and Mach 1 - but a very drastic improvement below that range, which we have to consider that lobbed spudgun shots are likely to fall into, mostly due to velocity traded for height.

Simulating a 150 m/s 100 gram projectile of 1.5" diameter being launched at 35 degrees (usually roughly the "ideal launch" angle when drag is applied) and applying the exact drag characteristics of all the blunt tailed rounds (assuming stable flight), with all else the same.
Full drag integration active, 1 ms timebase, altitude air density variation, 1013 mb, 20 C, 60% RH and no wind.

G1 - Minimum flight speed: 51.6 m/s - Range: 759 m.
G6 - Min flight speed: 51.2 m/s - Range: 747 m.
G8 - Min flight speed: 53.9 m/s - Range: 786 m.
GL - Min flight speed: 49.8 m/s - Range: 741 m.

(The numbers may seem high to some people, but consider the cannon is pretty powerful, and these results are assuming stable projectiles, which most spudgun shots aren't)

There's clearly no huge amount in these figures, but it demonstrates how low a projectile's speed can fall. Now, clearly, at those low velocities, drag is much reduced, but notice the advantage of G8, which flies around 3% further than the other rounds.
That low drag at lower velocities really benefits it.

Now, for fun let's simulate GC, the 3 diameter cylinder... Min flight speed: 33.7 m/s - Range: 402 m.
Ouch. That shows what a really blunt nose does for you.

~~~~~

Now, back to the friction vs. pressure drag, what I would be interested to see however is how all those shapes faired if the friction drag were reduced - i.e. the rounds were all polished smooth and perhaps coated. (I'm currently experimenting with Teflon coating materials.)

~~~~~

@Jitup: There is no such software that analyses video feeds. If you really want to find the sort of data we're throwing around at the moment for a certain projectile, expect to pay around $250,000 for the radar based equipment.

I spent some time finding the data we're using at the moment on the internet. It's information the firearms community uses regularly, and it relates to very specific shapes. It's possible to use the data here for predicting how similar shapes will act, but it's still a bit imprecise.

[jitup]

Oops! I read an add I found wrong! I thought it was for wind tunnel analysis, but it was a virtual wind tunnel. I think a virtual wind tunnel might work well for what I want to use it for. dose any body know of any good cheap/ free virtual wind tunnels?

P.S would video analysis software be of any use to any one? if it is I will ask my friend who is a programmer if it is possible.

[Ragnarok]

If it is I will ask my friend who is a programmer if it is possible.

It won't be possible unfortunately.

[jitup]

oh well it was worth a try, maybe one day some one will figure it out, my coding skills are poor at best so it won't be me!

I don't mean to pull this topic to off course, but can some one shoot me a link to a good resource for cannon math and design?

[jackssmirkingrevenge]

'nuff said

[jitup]

wow thanks for the great tool! 8)

[jimmy101]

G1 - Minimum flight speed: 51.6 m/s - Range: 759 m.
G6 - Min flight speed: 51.2 m/s - Range: 747 m.
G8 - Min flight speed: 53.9 m/s - Range: 786 m.
GL - Min flight speed: 49.8 m/s - Range: 741 m.

So, from a practical standpoint there is no difference in these four shapes at this initial velocity. The average of the group is 758m, the standard deviation is 20m (3%), the range 45m (6%). You would have a heck of a time actually measuring any difference in the performance of the three rounds.

[Ragnarok]

So, from a practical standpoint there is no difference in these four shapes at this initial velocity.

Exactly... those variations would be lost in natural errors - environmental changes, wind, muzzle velocity, projectile weight.
Still, it also points out that we mustn't disregard low velocity performance, because projectile speed can fall very drastically near the apogee of the flight path. As such, GL is the worst of the performers - not by a long shot, but it's there.

Now, as you say "At this initial velocity" - with a more moderate velocity of 100 m/s, which is about what should be expected from a moderate size cannon - say a sprinkler valve and a 4' long 1.5" barrel running on around 100 psi, the differences would show up slightly more. A velocity of 150 m/s would require a fairly beefy cannon.

You would have a heck of a time actually measuring any difference in the performance of the three rounds.

Yes. However, for comparison to show the importance of a boat tail for aerodynamic performance, here's G7's results at 150 m/s:
Min flight speed: 67.5 m/s - Range: 1049 m.

[jimmy101]

Ragnarok: How accurate are your Cds and velocity and range calculations? How acurately do you thing they predict actual performance? My understanding was that precise ab initio calculations for the aerodynamic performance of shape is basically impossible. In practice, the calculations are always tweaked by experimental data. Hence the need still for wind tunnel testing, range testing etc.

Even for artillary shells, the range tables are all based on many actual firings. The model is then calibrated with that data and used to fill in additional points between the values that were experimentally measured. I don't believe the range tables are ever based soley on calculations.