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Re: Water Balloon Cannon Optimization
I haven't worked with water balloon cannons before, but I can give a few broad tips from working with other projectiles.
Match your barrel to your projectile:
There is no ideal projectile and no ideal barrel, the two are very dependent on each other. Barrel material, diameter, and length are all effected by what you're firing. You don't want excess pressure escaping around the edge of your projectile, so for a non-uniform object such as a water balloon sabot/wadding is favorable. Remember to take your sabot/wadding into consideration when doing any calculations later (they have a mass too!). The lower the kinetic friction between your projectile/sabot the better, as less force will be acting against it. Keep in mind you need enough static friction though to allow for adequate pressure to build behind your projectile to get maximum force (quicker valves does the same). Your barrels do not have to be uniform over their entire length either, which can be used to your advantage if properly planned.
Barrel length is key:
Your object will experience a "favorable force" so long as the pressure behind it is greater than the pressure in front of it. This force will cause the projectile to accelerate (F=ma). You want to find the point where the pressure equalizes in your barrel and the outside atmospheric pressure, and that should be the (ideal) length of your barrel. Afterwards you then need to factor in other forces (such as friction, inefficiency, air resistance, etc.) and adjust your barrel length properly. As soon as your projectile leaves your barrel (or once forces resisting it's motion are greater than those aiding it) your projectile will begin to decelerate. Look at JesseK's equations for a bit more detail.
Carefully chose your projectile:
In this case it's dealing with the mass/shape/material of your balloons, as well as your sabot/wadding. With practical limitations on pressure (and thus force) created by your barrel and other components, mass becomes an important consideration. In particular the mass of your sabot/wadding, as that mass will reduce your acceleration in the barrel, but will not resist the deceleration of the projectile while in flight.
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