Key sources used to develop the physics model for this calculator
Why it was useful: The definitive reference for GGDT (Gas Gun Design Tool) - the gold standard pneumatic cannon simulator. Provided critical information about what GGDT models (valve types, blow-by, flow choking) and what it doesn't (turbulence, friction). Key insight: GGDT achieves 5-10% accuracy. Also provided the Cv formula: Cv = K × D² where K=1 for sprinkler, K=2 for QEV.
Why it was useful: Revealed the critical importance of valve opening time. Key data: for 500 fps muzzle velocity in a 3' barrel, transit time is only ~12ms. A 30ms valve loses nearly 50% of the energy compared to a fast valve. Provided GGDT comparison: 30ms valve = 172 m/s, 295.8 J vs fast piston = 236.7 m/s, 560.2 J. This was the breakthrough insight for fixing our overestimated velocities.
Why it was useful: Real-world measured data comparing valve performance. Key finding: 3/4" modded sprinkler = 388 fps vs 1/2" QEV = 517 fps under identical conditions (40 CI chamber, 5' barrel, 100 PSI). That's 33% higher velocity just from valve choice - proving valve type matters enormously.
Why it was useful: D_Hall's simplified hand calculation method. Provided the basic equations: EndPressure = StartPressure × ChamberVolume / (ChamberVolume + BarrelVolume), and MuzzleEnergy = (StartPressure + EndPressure) / 2 × BarrelLength × π/4 × BarrelBoreDiameter². Also noted limitations: these ignore valve timing, blow-by, and use isothermal instead of adiabatic expansion.
Why it was useful: Optimal C:B ratio data. Key finding: optimal ratio is 0.6-0.8:1 for potatoes, with performance within 5% across 0.5-1.2 range. Also mentioned that friction of ~5 PSI is typical for a spud in a 2" barrel, and projectile continues accelerating until chamber pressure drops below 20 PSIa (atmospheric + friction).
Why it was useful: Specific GGDT parameters for 3/4" QEV: seat diameter 1.25", dead volume 1.178 in³, piston diameter 1.75", piston mass 8.3g, pilot volume 0.98 in³. Essential for accurate GGDT comparison.
Why it was useful: Direct-acting solenoid valves have 50-60ms open/close time. This confirmed that stock sprinkler valves are very slow compared to QEVs (3-5ms), explaining a major source of performance loss.
Why it was useful: Academic paper from US Naval Academy published in European Journal of Physics. Provided rigorous physics framework: Newton's second law, ideal gas law, first law of thermodynamics. Noted that the model assumes frictionless piston and no gas leakage (appropriate for thick, wet potato slices force-fit to bore) - highlighting that golf balls with clearance behave differently.
Why it was useful: Explained that sprinkler valves have "large number of internal turns" that decrease flow by ~25% compared to piston valve of same diameter (though muzzle velocity only drops ~10%). This justified our 0.75 flow factor for sprinkler valves.
Why it was useful: Explained how blowgun pilot modification improves opening time by replacing the slow solenoid pilot with a fast-venting blowgun. This justified having separate "Sprinkler" (stock, 50-60ms) and "Sprinkler (Mod)" (20-30ms) options.