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### Calculations related to pneumatic cannon.

Posted: **Tue Jun 02, 2020 2:49 am**

by **valir05**

I am doing a school project regarding a pneumatic cannon which able to shoot baseballs. Unfortunately, i could not find any starting calculations to it. My teacher asked me to do the calculations looking at Bernouli's equation but other than that , he is not helping much. Can you guys help ? Thank you.

### Re: Calculations related to pneumatic cannon.

Posted: **Tue Jun 02, 2020 6:45 am**

by **jackssmirkingrevenge**

Welcome to the forum!

We typically use

Gas Gun Design Tool to predict performance but I am afraid that will not help you much if you need to show your working...

### Re: Calculations related to pneumatic cannon.

Posted: **Tue Jun 02, 2020 9:45 am**

by **mark.f**

valir05 wrote: ↑Tue Jun 02, 2020 2:49 am

I am doing a school project regarding a pneumatic cannon which able to shoot baseballs. Unfortunately, i could not find any starting calculations to it. My teacher asked me to do the calculations looking at Bernouli's equation but other than that , he is not helping much. Can you guys help ? Thank you.

Relatively easy to solve roughly with numerical integration (splitting the launch into time "steps" and using a computer to solve for force/acceleration, speed, and position at each step progressively). You'd be ignoring a number of things involved in gas flow and just looking at force at a certain position (easy gas law problem) and integrating that over the length of the barrel (minus friction) to get speed and position.

It'll also give you some insight into why we design air cannons the way we tend to do.

### Re: Calculations related to pneumatic cannon.

Posted: **Tue Jun 02, 2020 6:28 pm**

by **Moonbogg**

It seems that Bernoulli's equation is typically used with incompressible fluids such as water, or gases where a constant density can be maintained which allows Bernoulli's equation to remain valid and useful. How can Bernoulli's equation be useful for a compressed air system where the potential energy of the gas is transferred to a baseball? I'm no physics major, but I just got that from some googling. During the lecture, what was the context for discussing Bernoulli's equation? What examples were given where your professor applied Bernoulli's equation?

### Re: Calculations related to pneumatic cannon.

Posted: **Thu Jun 04, 2020 10:29 pm**

by **jimmy101**

The teacher isn't a "professor", it is a high school teacher so expertise in this area is probably limited.

Mark.f gave a reasonable answer. Don't need much of a "computer", you can do it an Excel spread sheet. Wont be super accurate but were talking a high school project, not a DARPA project. Just Force=Mass*Acceleration and F=Pressure*Area and pressure drops in proportion to the change in volume behind the ammo (chamber + barrel). Ignore temperature changes, friction, mass of air in front of ammo, gas flow constriction through valve etc. I think that for a low power gun the calculation with be at least in the ball park of the correct answer.

### Re: Calculations related to pneumatic cannon.

Posted: **Tue Jul 14, 2020 12:59 pm**

by **kunkmiester**

The ideal gas law is probably more relevant to this, as it considers changes in pressure, volume, and temperature, all of which happen.

You'll probably have to do it the same way I'm looking at when I someday get to more complicated projects--you measure your velocity, calculate your pressures and volumes, and then correlate. You'll get a theoretical chart showing how changing "chamber" pressure relates to velocity for that gun setup. It might cross over to other designs/sizes, but not well. It will also take some calculus to do well.

There are several papers out there about this, the impression I got is turbulence plays such a big part there's no way to connect a purely theoretical "ideal" model with reality, at least not without really big computers. A graph of how range and velocity change with pressure for a particular gun is easily spreadsheet stuff though.

### Re: Calculations related to pneumatic cannon.

Posted: **Wed Jul 15, 2020 6:40 pm**

by **jimmy101**

The ideal gas law is not usable in the situation of a pneumatic spud gun. Three state variables (pressure, volume and temperature)n al change. You need to do more complex stuff, like take in to account the heat capacity of the air. There are very nice tools for both pneumatics and combustion guns developed by D. Hall; "gas gun design tool" (GGDT) pneumatics and "hybrid gun design tool" (HGDT) for combustion guns.

### Re: Calculations related to pneumatic cannon.

Posted: **Fri Jul 17, 2020 12:30 am**

by **Doc j**

Maybe Just do a vacuum cannon.

Be simplest.

Plunger, Aluminium foil for burst disk.

Use a ping pong ball or tennis ball.

Be more in the "high school" theme.

Safer for demonstration.

Just my two bobs.

### Re: Calculations related to pneumatic cannon.

Posted: **Tue Jul 21, 2020 7:53 am**

by **kunkmiester**

I was a little off. I was looking more at the combined law, as here:

https://en.wikipedia.org/wiki/Ideal_gas_law
My vague memories of chemistry had them the same.

### Re: Calculations related to pneumatic cannon.

Posted: **Sun Jul 26, 2020 1:30 am**

by **D_Hall**

Probably the quickest/easiest hand calcs you can do for potato gun prediction....

EndPressure = StartPressure * ChamberVolume / (ChamberVolume + BarrelVolume)

MuzzleEnergy = (StartPressure + EndPressure) / 2 * BarrelLength * PI/4 * BarrelBoreDiameter^2

MuzzleVelocity = sqrt (2 * MuzzleEnergy / ProjectileMass )

Note that care should be taken to use consistent units.