I know you say that you disagree that they are inversely related but you also just said they were.
"Static friction can increase the maximum pressure, which can shorten ideal barrel length"
i.e., More static friction = Less barrel length.
No, more static friction CAN EQUAL, not does equal, less barrel length. It is possible, and likely, but not necessarily true. You understand the restrictions. Just make them clear by avoiding absolute statements like "more static friction = lower ideal barrel length".
I understand this in terms of theory but for this application I really don't think it's necessary to take temp change into consideration.
You really think the temperature change of the gas in the chamber is really going to effect anything to a degree where it should even be considered?
Even if it does change to an amount that should factor in then fine, use PV=NRT. You still end up with the same effect. The pressure increase in with a tightening ring before it overcomes static friction, regardless of if the temp changes a little.
The temperature changes significantly as can be shown in both theory and experiment. The temperature must change because the thermal energy of the gas is converted into dart kinetic energy and there is no heat transfer to make up the difference. A simple calculation using an equation I linked to shows that the temperature in the gas of a Nerf gun drops to about -105 F if it starts at 80 F. That's a drop of about 33% in thermal energy (and the percent drop is the same regardless of what temp. it starts at for calorically perfect gases). That's significant. It causes the pressure to drop faster than it would under isothermal conditions, so neglecting the temperature drop results in inaccurate muzzle velocity estimates.
And you don't seem to understand my point, which was that Boyle's law is not an appropriate model, not that your understanding is entirely wrong. I never said using adiabatic process relationships show that increasing static friction can't help, for example. (I'm not sure if you are confused about what I said.)
Also, the ideal gas law can not be used alone to derive these relationships because it says nothing about heat transfer. If you read the link I posted you would have seen that the adiabatic process relationships detailed are derived from the ideal gas law and the first law of thermodynamics.
Edited by Doom, 25 December 2011 - 08:43 PM.