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GGDT questionI have a 3/4" cannon (ID = .811")
If I substitute a 1/2" barrel (ID = .569" ) and also reduce the projectile diameter to .569" maintaining the same weight, GGDT calculates a decrease in energy. I can't understand why?
Area is decreased.
Take a t shirt into a windstorm along with a bed sheet. Notice the bed sheet gets more pull from the wind? It has larger area. It's why my marshmallow cannon has a peak force at 100 PSI on a 1 inch gumball that is much less than my large cannon tossing a full gatoraid out the barrel at 100 PSI. The gumball area permits a force of about 78 Lbs. The Gatoraid has a 315 Lb push. All with the same 100 PSI.
OK That being the case, a sabot nail dart in a 3/4" tube would be better than a barrel fitting the smaller nail head.
Precisely the idea behind saboted projectiles
Re: GGDT questionTechnician has already explained it well enough, but I figured I'd add some details.
Muzzle energy is equal to the integral of the pressure in the barrel, multiplied by the barrel's volume. So, for the same integral of the pressure (or slightly more specifically, the effective pressure, after accounting for losses due to fluid velocity) a barrel with a greater volume will have a greater muzzle energy. It doesn't matter if this increase in volume is due to the barrel being longer, or higher in diameter  the larger the barrel volume, the higher the energy. Either way, this kind of thing is useful  with an appropriate understanding of the maths behind it, and with some analysis of various relationships, it's possible to create a series of equations which, although not quite as accurate as a full simulator, can predict muzzle velocity within a few percent with next to no computing power at all. And being able to calculate a "close enough" muzzle velocity with just a basic scientific calculator and a scrap of spare paper is rather useful.
Does that thing kinda look like a big cat to you?
These calculations are only valid if the plumbing between the tank and barrel are not high loss. This is the reason I like large fast valves with a larger barrel. A 1 inch valve feeding a t shirt or tennis ball barrel simply doesn't deliver much of the energy.
Given that you've never seen the equations, that's an assumption  and in error, because I did build variables that account for valve flow into the equation.
Does that thing kinda look like a big cat to you?
With lightweight projectiles the rate of flow from the accumulator and barrel does make a large difference in performance. We saw that first and in the t shirt competition when comparing an inch and a half sprinkler valve to the 2 inch QDV. The QDV is about double in velocity for about 4X the muzzle energy when launching shirts out a 3 inch barrel. This is not insignificant.
Technician, you're probably thinking of some simple algebraic expressions you've made. That is not what Ragnarok has in mind.
Fairly complicated equations can be found that will approximate the performance of subsonic pneumatic guns reasonably well. Subsonic interior ballistics of pneumatic guns can be represented by a system of nonlinear ordinary differential equations. I just linearized the system of ODEs BAGS uses with a few simplifying assumptions (isothermal, the gas is stationary, the flow is always choked in the valve, etc.) to see what it would take. This system can be solved (but I didn't go that far). The solved equation for muzzle velocity will be messy, but it is completely capable of being solved with a pocket calculator, a pencil, and paper. And it should be reasonably accurate in a number of situations.
All spud gun related projects are currently on hold.
Quite right. Put it this way, the full equation(s) are not something which can be remembered off the top of my head... so it's fortunate that I'm in the habit of carrying a notepad. As a better solution (if a solution is necessary at all), I'm considering the possibility of putting together a mobile version of Apocalypse that'll run on my PDA.
Does that thing kinda look like a big cat to you?
Re: GGDT question
One point worth making is that with all else being equal, the smaller diameter barrel with have a larger length:calibre ratio and lose barrel pressure at a lower rate, resulting in higher velocity even if muzzle energy is reduced. This is sometimes a desirable trait especially if greater penetration or a flatter trajectory are requires, hence the idea behind "necked down" firearm cartridges like the .17 HMR.
 
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