Calculate the air pressure needed for a projectile to travel X distance

[DrPython]

TL;DR

I'm trying to build an air cannon to launch a projectile but I need to know the pressure that is needed to launch it a certain distance so then I can buy the appropriate items.

Hello! I'm brand new to the physics forum so please excuse any mistakes I make. I'm not even sure if I'm in the right forum section lol.

My goal is to create a air cannon to launch a piece of dog food (super overkill) and I have pretty much 0 background in anything post-high school physics. I'm still a junior in high school so I've only taken the non-calculus physics class, however I do understand a tiny bit of calculus if that is necessary for an explanation. I would really appreciate any simplification of concepts or explanations if that would be possible.

Anyways, continuing on to the launching apparatus. It would consist of a few main things. An air tank of some sort with a certain pressure, a solenoid release valve to be controlled electronically and a release pipe of some kind. Depending on what kind of pressure is needed I would change the dimensions/material of the pipe, but for now I'm thinking of 2 cm diameter pvc pipe. All the connections between components would use flexible rubber tubing that is rated for around 2.5Mpa. The dimensions of the dog treat are about 1.5 by 1.8 by 0.6 cm. I don't have the mass of the treat since I don't have a precise scale so feel free to use any number. I don't have many specifics on the materials since I'm trying to figure out what my project requires so I can save some money.

My main goal is to calculate how much I need to pressurize the system in order to shoot a treat about 150 feet max from it's starting position. I've done some research already but I'm still feeling very lost. Any help would be welcome.

https://www.physicsforums.com/threads/velocity-of-air-coming-out-of-a-nozzle.694656/
https://en.wikipedia.org/wiki/Mass_flow_rate
https://en.wikipedia.org/wiki/Choked_flow
https://www.engineersedge.com/wwwboard/posts/15354.html

https://en.wikipedia.org/wiki/Pressure#Formula

Once I figure out the force on the treat I assume this just becomes a normal projectile problem; however, I don't know how to account for air drag if it's going really fast. If someone could point me in the direction of how to account for drag that would be great.

Thanks in advance!

 

[jedishrfu]

There's some DIY projects on potato guns that may be of help:

Please be aware though that this project uses hairspray combustion and it could be dangerous. Notice the warnings on the video and the use of proper safety procedures including safety goggles.

To figure out the treat force, you could use a bow to launch the treat and measure the force needed to pull back the bow a certain distance (assuming a standard recurve or long bow not the mechanical ones). Alternatively you could use a sling shot to do your measurements.

NASA has a nice writeup on baseballs that would give a good approximation:

https://www.grc.nasa.gov/WWW/K-12/airplane/balldrag.html

 

[Baluncore]

It would consist of a few main things. An air tank of some sort with a certain pressure, a solenoid release valve to be controlled electronically and a release pipe of some kind.

The problem will be turning on the air very rapidly, and I don't think a low cost solenoid will do it. There are two other ways.
The first is to use a ball valve with the same size bore as the tube. That will need to turn quickly through 90°. You could turn it by hand, hit it with a hammer, spring load then trigger it, or drive it with a motor.
The second technique is to insert a foil diaphragm at a clamped flange joint in the tube. The pressure is built up in the closed chamber end until the foil bursts. The bolt of compressed gas then expands along the open end of the barrel at a supersonic velocity, carrying the projectile with it.

My goal is to create a air cannon to launch a piece of dog food (super overkill) ...

I can't help wondering why you want to deliver a bait to a dog 150 feet away.
Is it your dog? Is the bark really that loud?

 

[Nik_2213]

Need it be an air-gun ? Skeet shooting and batting practice use other approaches to launch issues...

And, IIRC, there's a centrifugal method for distant dispersal.
Due Care as rapidly rotating machinery...

 

[Dullard]

In order to get repeatable results, you'll need a projectile that completely fills the barrel. That may be accomplished by:

modifying the treat
using some 'wad' between the chamber and the treat
creating a 'sabot' for the treat (a shell which is shed as the projectile leaves the barrel)
some combination of these

Any of these will make the calcs for accelerating the projectile pretty simple.

The required muzzle velocity, not so much.

If I had to do this, I would obtain a sling-shot and a reasonably fast camera (phones are pretty good these days). Shoot the treat your required distance (while recording). Repeat multiple times. You should be able to estimate the required initial velocity.

Wear safety glasses when operating your device. Every PVC manufacturer on Earth says not to use PVC with compressible fluids (like air)- The failure mode for PVC involves shrapnel.

Do not exceed (or even approach) the pressure rating of your PVC parts.

Glue thoroughly.

 

[DrPython]

I can't help wondering why you want to deliver a bait to a dog 150 feet away.
Is it your dog? Is the bark really that loud?

The original purpose was to use this in a huge field but if you're wondering, yes, his bark is really that loud (and annoying)

 

[DrPython]

Need it be an air-gun ? Skeet shooting and batting practice use other approaches to launch issues...

And, IIRC, there's a centrifugal method for distant dispersal.
Due Care as rapidly rotating machinery...

Yeah I'm considering other methods of launching the treat now. A really big slingshot is probably more practical and easier to deal with.