How and why shape stabilised projectiles work

[Bronezhilet]

*cracks fingers*

Something that has interested me for a while, are shape stabilised projectiles. As in, projectiles that are stable due to their shape. Everybody has heard of rotation stabilised and fin stabilised projectiles, but shape stabilised is kind of different. I guess most of you here have seen shape stabilised projectiles without actually knowing how and why they work.

Geek sidenote: Fin stabilised projectiles are actually fin and rotation stabilised.

As I said, shape stabilised projectile have a stable flight path due to their unique shape.

Figure 1: A 84mm Carl Gustav shape stabilised HEAT-round

Note the slightly ogive front and the stand-off, which are characteristic of shape stabilised projectiles (SSP). Both features are absolutely crucial for the SSP to work.
I'm going to throw you guys into the deep end by showing a .gif of the airflow in front of an SSP.
Here's a link because I can't embed .gifv apparently
The first thing you should notice is the air circulating in some-sort of pocket, and that this airflow is subsonic. Before I continue, here's the airflow in front of a blunt projectile: Clicketyclick
While that projectile has a subsonic airflow in front of it as well, it is not circulating.

Here's the airspeed of both projectiles as a normal picture:

Figure 2: Airspeed in front of an SSP


Figure 3: Airspeed in front of a blunt projectile

It's clear that an SSP has a ogive-shaped subsonic airpocket in front of the projectile. This basically emulates the ogive of a normal rotation stabilised projectile. In other words, it makes it more aerodynamic. But does that airpocket stabilise the projectile?
No it does not.

So why is this projectile stabilised? The key is in what happens when it starts to tumble. Right now, there is nothing stopping the projectile from tumbling, and that's the interesting thing. There is literally nothing stopping the projectile from tumbling, except...


the projectile itself.

Lets take a look at what happens when an SSP starts to tumble. (If I remember correctly, I rotated the projectile 10 degrees)
First off, the airflow in front of the projectile. It's fairly obvious that the airflow has changed. Lets check that again, but this time as a picture.

Figure 4: Airflow in front of a tumbling SSP

Again, it's obvious that the airflow has changed. The subsonic pocket has mainly shifted to one side and the air itself isn't really circulating in the pocket. This change causes a huge change in the Cd of the projectile. Let me show you why.

Figure 5: Pressure in front of a tumbling SSP

Next, the pressure in front of an SSP flying straight.

Figure 6: Pressure in front of an SSP flying straight

Please note the approximate pressure in front of both projectiles. The tumbling projectile has, on one side, twice the pressure as the projectile that's flying straight. Very interesting. What's even more interesting is that the pressure occurs on the opposite of the side it's turning to! The projectile is turning upwards, but the pressure builds up at the bottom. This pressure forces the projectile to start turning down again, forcing the projectile in a state where the pressure on all sides is equal.

Voila, a shape stabilised projectile.


But... why does it work?

The subsonic airpocket is created by the stand-off and that little flange, or whatever you want to call it. The dimensions and placement of both are equally important. The stand-off and its side create the airpocket and the flange give the airpocket the required shape. The stand-off size can vary, but the flange size and placement is very important. If the flange is too far forward or too far back, the airpocket will be either too small or too big. Why does the size of the pocket matter? Because of this:

Figure 7: Subsonic pocket in front of an SSP

I changed the parameters slightly and made all airflow above Mach 1 red. Whatever is not red, is trans- or subsonic. The interesting thing to note here, is the pocket extends to the edge of the projectile (if I made the projectile better it should be exactly on the edge). (Sidenote: Here's the same picture of an SSP at a 10° angle)
While the airpocket does not start at the flange, the flange determines where the pocket starts. If, at this velocity, the flange was further back, there would be supersonic flow hitting the front of the projectile, massively increasing drag. If the flange was further forward, the airpocket would be further forward too. This would mean the airpocket would not end at the edge of the projectile, but further out. Creating an airpocket which is wider than the projectile. This would allow the projectile to tumble a bit, because pressures wouldn't change much unless there is supersonic flow hitting the projectile.

It is also possible to change the size of the airpocket by changing the front of the projectile itself. If the radius connecting the front and the stand-off is too big, the airflow inside the pocket would disrupt the circulation. The same would happen if the radius is too small. The angle of the front is important as well, but I haven't expermented that much with it so I don't know how important it exactly is, but it has an effect on the airflow.

By the way, if the flange did not exist at all, the airpocket would start at around a third to half of the stand-off. Which would completely ruin the airpocket. Without a flange, the stand-off itself would have to be way bigger and longer to create the same kind of airpocket.

But Bronezhilet, I hear you cry, if the airspeed changes, the pocket changes as well!

I'm glad you brought that up, because you are right.

A shape stabilised projectile only works properly within a certain flight envelope. If the projectile is moving too fast, the airpocket would compress allowing supersonic flow to hit the front of the projectile. Which in turns increases drag. By a lot. If the projectile is moving too slow the airpocket widens, allowing the projectile to tumble a bit before it would stabilise.

I've been brainstorming with Colli a bit, and we've come to the conclusion that is why some projectiles are both shape stabilised and fin stabilised. When the projectile is moving too slow for shape stabilisation, the fins would keep it pointing in the right direction.



And that concludes today's lesson. Thank you for reading.

[Belesarius]

Interesting stuff. 

[Bronezhilet]

Forgot to add, it has about 20% more drag than a rotation stabilised projectile.

But considering a rotation stabilised HEAT projectile is about as useful as an AR or AK (only good for throwing it away as far as possible), a shape stabilised HEAT projectile is clearly the better choice.

[LostCosmonaut]

Out of curiosity, what software are you using to generate these plots?

[Bronezhilet]

Out of curiosity, what software are you using to generate these plots?

Solidworks Flow Simulation

[Sturgeon]

>informative post on something nobody knew about

>thorough analysis

>teensy bit of trolling

Oh yeah, SH is definitely the place for you.

[Sturgeon]

Also, that makes me wonder if those Tres Haut Vitesse bullets are using the same virtual nosecone effect. It would make sense if they were, as a spindly design like that would be a good way to reduce bullet mass as much as possible, giving you the highest possible velocities.

 

[Priory_of_Sion]

Also, that makes me wonder if those Tres Haut Vitesse bullets are using the same virtual nosecone effect. It would make sense if they were, as a spindly design like that would be a good way to reduce bullet mass as much as possible, giving you the highest possible velocities.

To a layman, it seems that you'd want flechettes if you want reduced mass & high velocity. 

[LoooSeR]

But can you make 6.8 mm flechettes that can kill better than those small 5.45 and 5.56 not-really-bullets?

 

Anyway, why nobody have flechette gun/sniper rifle/carabine in service? What are limitations?

[Bronezhilet]

Also, that makes me wonder if those Tres Haut Vitesse bullets are using the same virtual nosecone effect. It would make sense if they were, as a spindly design like that would be a good way to reduce bullet mass as much as possible, giving you the highest possible velocities.

 

It looks like they are indeed some form of shape stabilisation. But I have my doubts on how effective the stabilisation actually is.

 

 

To a layman, it seems that you'd want flechettes if you want reduced mass & high velocity. 

Yes, but then your accuracy goes to shit.

 

But can you make 6.8 mm flechettes that can kill better than those small 5.45 and 5.56 not-really-bullets?

 

Anyway, why nobody have flechette gun/sniper rifle/carabine in service? What are limitations?

You cannot rotation stabilise flechettes. If you do try, your shot pattern at a few meters will look like this:

Not every effective at longer ranges.

 

So you're stuck with a more elegant version of your every day shot.

[Tied]

[Collimatrix]

Hmmmm...

 

So we ought to be able to figure out what mach number range a shape-stabilized projectile is optimized for from the equation given here:

 

The angle from the feature that produces the strong mach cone to the very leading edge of the stabilizing disc of the projectile relative to the long axis of the projectile will represent the minimum mach number at which the projectile will be stable.  Below this mach number the mach cone will not contact the flat leading edge feature of the projectile and the projectile will tumble within the mach cone.

 

But that's just theorizing!  This needs to be tested against real-world data!

 

This is a picture of a 105mm M456 HEAT round in flight.  This is what it looks like unfired:

 

We can see the small "top-hat" feature at the end of the standoff probe.

 

 

Using the highly scientific methodology visible above (the picture looks perpendicular enough that I'm basically discounting any foreshortening), I get that the maximum mach angle Θ at which M456 will shape stabilize is 13.17 degrees.  So 13.17°=Sin^-1(1/M), which translates to a mach number of 4.40, or nearly 1500 M/S at sea level.  But M456 is credited with a muzzle velocity of below 1,200 M/S.

 

 

 

So it would appear that either M456 is primarily fin-stabilized, or the mach cone doesn't actually need to touch the flat bit.

[Bronezhilet]

Sidenote, the Mach wave doesn't, for some reason, start at the flange. The design in my post has it, and I assume a bigger model has it as well. But with a bigger model the Mach wave might start at a different place. It all depends on the size and shape of the flange.

Interesting to note, the tail section of the HEAT shell more or less follows the subsonic pocket behind my projectile.

 

Also note that in my simulation and your photograph the Mach wave isn't a nice cone, but rather a slightly inverted ogive. It's also a bit difficult to see where the Mach wave ends in the photograph because of the airflow around the edges of the flat bit.

[Collimatrix]

The fact that the mach cone is somehow distorted into that not-quite-straight-sided shape really complicates things.  Also, it looks like the mach cone doesn't need to actually touch the flat feature; just the high pressure zone behind it.  With that in mind, I tried again:

 

This corresponds with a mach number of 3.09, which is significantly slower than what the round actually does.  That makes much more sense.

[Bronezhilet]

The fact that the mach cone is somehow distorted into that not-quite-straight-sided shape really complicates things.  Also, it looks like the mach cone doesn't need to actually touch the flat feature; just the high pressure zone behind it.  With that in mind, I tried again:

 

This corresponds with a mach number of 3.09, which is significantly slower than what the round actually does.  That makes much more sense.

This is quite interesting, because it would in theory mean that the round experiences a massive amount of drag during the first part of the flight. But only if the cone is straight. But the sub/transonic area in front of the flat part will most likely bend the lower part of the mach wave towards the edge of the flat face. Of course the higher the velocity the smaller the sub/transonic area so at some point the mach wave will more or less hit the flat face. So the flight envelope is actually bigger than I thought it was, because the mach wave isn't a simple function of the airspeed. Edit: Basically the sub/transonic pocket has a bigger effect on the stabilisation capabilities than the velocity itself.

Edited November 18, 2015 by Bronezhilet

[Collimatrix]

Here is some interesting work in this field from the University of Tokyo:

 

This is a mach wave stabilized projectile, but instead of having a single wave generator that creates a high-pressure cone that gets caught by a single shoulder, it has multiple shoulders, each of which produce a mach wave that is caught by the next shoulder.  In theory this should produce less drag.



Additionally, if the shoulders are spring-loaded then the arrangement can in theory be self-adjusting and maintain optimal geometry over a wide range of mach numbers.

[Bronezhilet]

I got really mad when I found out about this concept a few months ago, because I had the exact same idea. But of course someone else had the same idea as me, but earlier. 

 

I've done a bunch of simulations on it and it actually works really well.