Any theories for Latke's data collapse?

[ammosmoke]

Wow, I feel like an idiot now...

[starman]

Wow, I feel like an idiot now...

It is nice to have David's modeling and programming prowess on the job. Thanks David for sharing your prodigious skills with the everyone.

[D_Hall]

Thanks, but right now I'm not sure how useful HGDT is. I don't mind being shifted a bit to the left or right or up or down. But I want my curves to have the right features, damnit, and I can't figure out what that nose dive of Latke's represents. It shows up in all his data. I don't doubt that it's real. But what is it? Without knowing that, I don't have much chance of modeling it.

[starman]

Being an audio engineer, I tend to think of things in those terms so bare with me a second.

There's a property of air called compliance or its springiness in a closed or ported box (tube in our case) and is related to the volume and mass of something else working against it. Speaker driver and cabinet builders use this value to optimize speaker cabinet designs. So, air has a compliance value (springiness) based on the volume it resides in. I'm sure you're probably aware of this already.

What if the volume of air in the barrel becomes so large or overcomes some equilibrium barrier, that air-compliance begins to affect performance... the actual act of having to work against this air-compliance or having to compress and move the air-mass ahead of the projectile?

Imagine a barrel 100 miles long...the mass of air in front of the projectile would dominate the calculation...and that unless you had a sufficient force, ie huge building sized chamber, loads of fuel, etc, etc. you would be doomed to having the projectile try to push and thus compress an overwhelming mass of air and would only be pushed back to the breech or be stuck mid barrel somewhere in pressure equalization state.

I am ruminating here, just theorizing, maybe way off base...you may already have barrel air-compliance factored in. I thought I would throw it out there.

[psycix]

Appereantly the friction and vacuum effect are more powerful then HGDT thinks.
You should note that when the gasses enter the (too long) barrel, the surface area to give off heat increases enormously. And thus the hot gasses cool down in milliseconds.

[D_Hall]

you may already have barrel air-compliance factored in. I thought I would throw it out there.

I don't call it that, but yes, I take some of that into effect although in my world it's primarily a function of Mach number.

[D_Hall]

Appereantly the friction and vacuum effect are more powerful then HGDT thinks.

Clearly. But why the sudden knee in the curve? It's not like the friction and vacuum are slowly building. It's like one instant they're negligable and the next instant they're heavy duty.... This instant happening at about CB of 0.5.

You should note that when the gasses enter the (too long) barrel, the surface area to give off heat increases enormously. And thus the hot gasses cool down in milliseconds.

This is already ccounted for in the model.... SurfaceArea = PI / 4 * Bore * ProjectilePosition.

[psycix]

Rereading and rethinking the previous posts, I think it surely has something to do with the air in front of the projectile.

The vacuum gives no more then 1 bar backwards (probably less, never more) but the air that is compressed in front of the projectile will smack it back as soon as the pressure behinds the projectile falls off.

Is the frontal pressure calculated in your model?
If it is, re-check your calculations.

[boilingleadbath]

Yeah, it's odd.

Phase transitions don't make any sense, considering that the temperature at a c:b ratio of .8:1 is about 650k. (PV=NrT, P=1atm)

The water vapor-liquid phase transition at 10 psi is about 355k...

Further, phase transitions take considerable amounts of energy, don't they?

[D_Hall]

Rereading and rethinking the previous posts, I think it surely has something to do with the air in front of the projectile.

The vacuum gives no more then 1 bar backwards (probably less, never more) but the air that is compressed in front of the projectile will smack it back as soon as the pressure behinds the projectile falls off.

Is the frontal pressure calculated in your model?
If it is, re-check your calculations.

Well, you may have something. I got thinking about this.....

Is the frontal pressure calculated? Absolutely. But those pressures are calculated assuming steady state conditions. IE, at Mach 1, the pressure may be [whatever], but I've made no allowances for what it takes to acclerate the air BEYOND Mach 1 (or whatever current velocity is).

I took a stab at it and tacked on the mass of the air in the barrel. IE...

Code: Select all

Acceleration = Force / (projectilemass + airmass) 

I saw some interesting things but nothing really unexpected. Velocities dropped a bit; disproportionately so for longer barrels. But it was still a very smooth curve. No knee in it!

But then it dawned on me that even this would only be true while the projectile was accelerating. It would NOT be true while the projectile was declerating. So this effect would slow acceleration, but it would speed decleration. Now THAT is interesting as it could explain the knee in the curve. So then I moved to....

Code: Select all

If (Force > 0) then
  Acceleration = Force / (projectilemass + airmass) 
  else
  Accleration = Force / projectilemass
  end if

....There's a knee in the curve. What's more, the knee in the curve is at CB = 0.53. Latke's data shows the knee at 0.5. Unfortunately, the knee in my curve isn't as dramatic as Latke's and in fact it isn't really visible to the naked eye (but it does show up when you start analyzing things rigorously). Still, I think we're on to something....

About the included plot:
The Latke 1.5" spud data (duh).
The HGDT data. The discrete data points represent muzzle velocities that directly correspond to the Latke data at the same barrel lengths.
The "one shot" data is the position/velocity curve for a single shot (360" barrel) from HGDT. Notice how the only place this curve matches the other HGDT data is at the muzzle. One can assume that this trend would also be true for the Latke tests.

[D_Hall]

Another thought I've had....

I have been treating the heat transfer coefficient between the gases and the cold gun as a constant. That is to say that the coefficient used in chamber calculations is the same as that used in barrel calculations.

HOWEVER....

If the flow in the barrel is more turbulent than the flow in the chamber (and there are several reasons to believe it might be), then the local heat transfer coefficent in the barrel would be higher.

This would have an effect of causing velocity to decay faster than one might normally expect while having little or no effect on acceleration.

[Lentamentalisk]

Another thing to keep in mind is that although Latke's graph has a big "knee", their scaling on the x axis is only tested every .1, so there could be considerable rounding of the curve if you were to test in between those points.

[D_Hall]

I haven't had time to fully explore it or document the results, but as a rough cut, the increased barrel heat transfer linked to turbulence theory is looking REALLY good. The shape of the curve is friggin' beautiful. The knee isn't horribly sharp, but as Lenta says the "real" knee may not be as sharp as indicated in the Latke data simply due to the combination of experimental error and finite data points.

The only other downside is this theory is giving me about a 10% drop in peak velocity so I'm definately shifted down. I'll have to think on that some.

Question: Does anybody know where Latke lives? Or more to the point, does anybody know what altitude those tests were run at?

[Jared Haehnel]

I would wonder if there wasn't some kind problem with their numbers. Since it seems as though they were using data from one test shot that it might not be accurate...

Weren't they using homemade rubber slugs...how much friction did they generate in the barrel? Wouldn't it make sense that if the slug was generating a high amount of friction that any pressure drop due to gas cooling would be magnified?

Those were just the thoughts I had...

[D_Hall]

I would wonder if there wasn't some kind problem with their numbers. Since it seems as though they were using data from one test shot that it might not be accurate...

Weren't they using homemade rubber slugs...how much friction did they generate in the barrel? Wouldn't it make sense that if the slug was generating a high amount of friction that any pressure drop due to gas cooling would be magnified?

Those were just the thoughts I had...

They actually took something like five shots at each barrel length. I'm using their average velocity values.

As for the rubber slugs... Yes and no. They used those, but they also used spuds and such. Currently I'm using the spud data. If I can match it, the proof will really be in whether or not I can simply change the input data and then match the rubber data.