Large calibre BB - Can someone check my maths please

[evilvet]

Hi

I am looking at going up a scale for ammo, I acquired 5000 10mm diameter pellets and want to put them to good use.

10mm diameter projectile, 0.5grams. 1.57 sq-cm hemisphere area
100PSI air (69N/cm2)
1 metre long "perfect" fit 10mm barrel

1.
Force=Pressure x (surface) area
F=69 x 1.57 = 108 newtons

2.
F=mA so A = F/m
A = 108 / .0005
A = 216,000 m/s/s (Holy Sh&^%&^% is that right ?)

3.
T= sqrt (d/A)
T = Sqrt (1 / 216000 )
T = 0.002 second

4.
V=a*t + u
V = 216,000 * .002 +0 (at rest to begin with)
V= 432 m/s

I know there is no allowance for friction etc but in a prefect machine world, do those numbers stack up ?

Thanks

[jackssmirkingrevenge]

I know there is no allowance for friction etc but in a perfect machine world, do those numbers stack up?

I'm afraid not, over mach 1 with 100 psi, not really going to happen

I modelled an "ideal" launcher on GGDT with a fast valve and large chamber and got just under 150 m/s:

[evilvet]

Thank you Jack.

The valve is this one http://www.google.com.au/url?sa=t&sourc ... 9ffAqdf1tA


which if I read it right has a 3mm orrifice and a 1/4" port. The flow Cv is given as 0.33. If I plug in the shop compressor tank volume as the chamber I get this.

Not 400+ but over 200 .

Your thoughts please ?

[jackssmirkingrevenge]

Your thoughts please?

You need to change projectile weight to 4 grams

3mm orifice is far too small for a 10mm barrel in my opinion, that's just 11% of the barrel area. If you're looking for power I would go for something bigger.

[Technician1002]

I agree that the valve is too small for the barrel. My best performer on a 2 inch valve is the 3 inch barrel. On the 1 inch valve the best performance has been the 1.25 inch barrel.

The performance on a 2.5 inch barrel on the 1 inch valve launcher while impressive, is not nearly as impressive as the 2.5 inch barrel on a 2 inch valve.

3mm is too small for a 10 mm barrel. I highly recommend at least a 7.5 mm valve seat or larger for a 10 mm barrel.

For an example of what a large valve can do, this can was filled with water and hit with a marshmallow. The valve is 1 inch and the barrel was 1.25 inch.

[al-xg]

Your calculation assumes pressure to be constant behind the projectile whereas, in reality, the pressure behind the projectile increases from 0 as the valve opens but, at the same time, starts decreasing in the chamber as it expands through the valve and barrel. As the projectile moves down the barrel the air expands and the pressure drops.

Basically this is not a constant acceleration problem so you can't use those equations.

The valve usually has a worse flow than the barrel, because of sharp edges, changes in flow direction... etc that create turbulence and shockwaves.
To get the highest possible flow through the barrel, the valve must be capable of at least the same flow. The solution is often using a larger valve to make sure the bottle neck is the barrel and not the valve.

[Technician1002]

I have found that a projectile in the barrel besides the load of air slightly lowers the requirement for the valve to be at least as large as the barrel. The larger diameter barrel provides a larger cross sectional area to the force, so a larger barrel often performs quite well.

For example, items launched from a 2 inch barrel on a 2 inch valve launched slower than the same item launched with a sabot in the 2.5 inch barrel.

The extreme test of that was pancaking AA batteries. A 1/2 inch barrel on a 1 inch valve was much lower in velocity launching batteries than a 2.5 inch sabbot driving the battery on the 2 inch valve. One was mushroomed 1/2 way. The other totaly obliterated.

[al-xg]

But then a 2.5in valve with 2.5in sabot would probably out perform both.
I guess it depends whether you want to sabot the ball bearings or not.
Other factors may come in like, bulk, or price of the valve vs performance increase.

[saefroch]

The biggest reason for your maths error is that your area is twice what it should be, so your acceleration is double what it should be. Also, what al-xg has stated already is VERY significant, especially if you don't have a massive C:B ratio.

[evilvet]

Thanks to all who replied, time to hunt for a biger valve perhaps.
Pellets due by post today

@saefroch, are you sure on that area measurement?
Surface Area of sphere = 4*Pi*R*R
So 4*3.14*.5*.5 = 3.14 (yes I know I just multiplied 4 by 1/4 to get the result)
So half that is 1.57 sq cm, yes ?

[jackssmirkingrevenge]

@saefroch, are you sure on that area measurement?
Surface Area of sphere = 4*Pi*R*R
So 4*3.14*.5*.5 = 3.14 (yes I know I just multiplied 4 by 1/4 to get the result)
So half that is 1.57 sq cm, yes ?

That's true, but you want the force vector travelling parallel to the barrel, which regardless of the shape of the projectile is pushing on an area equivalent to its widest cross section - in this case πr² = 0.785cm²

[evilvet]

Thanks JSR, as usual a correct and elegant answer. Thanks also to Saefroch for pointing out my mistake.

How does
http://www.valvesonline.com.au/products ... s_4(a).pdf

strike you for a valve, 10mm orifice and 3/8" BSP port ?

[Technician1002]

.
Force=Pressure x (surface) area
F=69 x 1.57 = 108 newtons

I agree with jack on this one..

regardless of the shape of the projectile is pushing on an area equivalent to its widest cross section - in this case πr2 = 0.785cm2

The direction vector is different than the surface area pressure trying to shrink the projectile.

A sphere in a pressure chamber has lots of force on it, but the net result is no motion as all the force vectors are equal and opposite. Only the differential pressure behind and in front of the projectile will cause motion.

@evilvet; The valve is OK. It's only good for up to 10 bar and has a minimum pressure of 0.8 bar to fully open. A small sprinkler valve may be much cheaper. Don't be afraid to use a slightly oversize valve.

The URL is causing the SF to not display your post. Try it without the tags when that happens.
http://www.valvesonline.com.au/products ... s_4(a).pdf

[jackssmirkingrevenge]

The valve is OK. It's only good for up to 10 bar and has a minimum pressure of 0.8 bar to fully open. A small sprinkler valve may be much cheaper. Don't be afraid to use a slightly oversize valve.

Agreed - a 3/4" or 1" valve will cost you very little $$$, will operate safely up to 10 bar at least and there is nothing wrong with overkill in the valve department