Water Balloon Cannon Optimization

[gblake]

Anyone feel free to correct me
...
As for air resistance and your water balloon, in order to increase the mass to add momentum that would easily overcome air resistance, you would have to increase the size of the balloon by adding more water. This would increase the surface area of the balloon, therefore making more air resistance. Hence, for air resistance purposes, size doesn't matter.

My quick hunch is that because the mass of a rigid sphere increases with the cube of its radius, and the area of the sphere increases with the square of its radius, and the effective front surface of the sphere only increases roughly in direct proportion to its radius; a large massive sphere will be affected less by air resistance than a small one made of the same materials.

This hunch ignores the sloppy oscillations and other distortions that will plague a flexible water balloon in flight.

This hunch also ignores the nonlinear behavior of air (a fluid) at various scales (sizes) and speeds. For many insects, flying through air is more like a human sized device trying to swim through oil. On the other hand, for a uranium rod shot from an M1A1's 120mm cannon, I don't think that air behaves much like oil behaves at human scales, other attributes will dominate at the rod's speeds and scales.

Because of the many difficulties involved in using "simple" physics to do more than roughly approximate a water balloon's trajectory, my suggestion is that for your wiggly water balloons, you use empirical data to predict trajectories. Make enough test shots to allow you to build up accurate heuristics and then use the heuristics. As an interesting academic exercise, figure out which of the equations folks have cited in this thread best explain the results you measure.

During the test shots, keep track of the wind at all points (at altitudes and along the ground) along your trajectory (for obvious reasons). Also track ambient air pressure, humidity, and perhaps temperature.

I suspect that the pressure and humidity will have noticeable effects on moderately light rigid spheres, I don't know if the effects will be noticeable when combined with all the wiggling a water balloon will do. If you publish your data, you can challenge us to explain it using equations derived from first principles....

Finally, big guns often use a sabot to increase muzzle velocity, not just to protect their projectiles from damage in the barrel (which is what you seem to be describing).

For a given propellant pressure (see others' advice on tank sizes, valves, etc.), with a wider barrel you get more force on the projectile than you do with a smaller diameter barrel. This is because of the increased surface area of the projectile. However if the projectile is a single isotropic lump, the increased mass of the projectile tends to cancel the advantage of wider barrels. You can try to counter this by making the projectile less dense, but then it is strongly affected by drag once it leaves the barrel.

The notion of a sabot (a shoe) offers an effective compromise. You wrap a sturdy low-density sabot around a small high-density core. The two stay together in the barrel but the sabot falls away after leaving the barrel.

At launch, the sabot fills up the wide barrel so that you get a lot of force from the propellant's pressure. The sabot falls away after the projectile leaves the barrel so that bulk of the kinetic energy of the total (core plus sabot) projectile is sent on its way to the target in the compact high-density core that was wrapped in the sabot back when the core was in the barrel.

Maybe a sabot made of stiff foam, or Styrofoam, or foam in a bigger plastic cup, would give you a good sabot of the sort I describe.

Blake