Hybrid Equations

[mega_swordman]

So I have been doing my homework, but there are some things in Hybrid cannon design that I cannot seem to find. Could someone kindly provide the equations and/or explanation as how to find:

The amount of energy required to ignite propane at different mixes.
-and-
The amount of energy produced by the combustion reaction in the chamber.

Quick responses would be greatly appreciated. Thanks.

[inonickname]

So I have been doing my homework, but there are some things in Hybrid cannon design that I cannot seem to find. Could someone kindly provide the equations and/or explanation as how to find:

The amount of energy required to ignite propane at different mixes.
-and-
The amount of energy produced by the combustion reaction in the chamber.

Quick responses would be greatly appreciated. Thanks.

1. I believe the energy required to ignite it remains the same, BUT the thicker atmosphere requires either a more powerful arc OR a smaller gap. Of course a 20x ix if you use a spark gap with 1/20th the length you would be fine. If the mix gets so high you can't get an arc across then there's always things like glow plugs, steel wool and shock combustion.

2. (your mixture) x energy of a 1x mix. If your calculating total energy add in pre-ignition (I think). As for a measurement in joules or anything such, no clue. Perfect 1x combustion can generate a pressure spike of 108 psi (was tested on uksgc I believe), though you'd be lucky to have that accurate a mix.

Good luck

[starman]

Have you loaded up HDGT....? It can answer much of what you are looking for.

[Biopyro]

1. I believe the energy required to ignite it remains the same, BUT the thicker atmosphere requires either a more powerful arc OR a smaller gap. Of course a 20x ix if you use a spark gap with 1/20th the length you would be fine. If the mix gets so high you can't get an arc across then there's always things like glow plugs, steel wool and shock combustion.

The reaction will have the same amount of energy, but more force. Because it's under pressure the reaction will proceed faster, so more power, which is really what interests us.

A ballvalve and a QEV in an identical gun release the same energy, but the QEV has more power which makes it preferable.

[mega_swordman]

Thanks for the information

Have you loaded up HDGT....? It can answer much of what you are look for.

I would like to make a presentation on hybrid cannons, so given the resources, I would like to be able to explain the science and the formulas behind it. It is a very handy to have HDGT around though, it helps me check some of the other work I have been doing.

[jimmy101]

1. I believe the energy required to ignite it remains the same, BUT the thicker atmosphere requires either a more powerful arc OR a smaller gap. Of course a 20x ix if you use a spark gap with 1/20th the length you would be fine. If the mix gets so high you can't get an arc across then there's always things like glow plugs, steel wool and shock combustion.

The reaction will have the same amount of energy, but more force. Because it's under pressure the reaction will proceed faster, so more power, which is really what interests us.

The same amount of energy as what?

The chemical energy in the chamber is just the number of moles of fuel times the heat of combustion of the fuel, assuming a stoichiometric mixture. At 1X, the theoretical energy from propane + air is 527 Kcal/mol (2210KJ/mol). (see the SpudWiki page on fuels for the heat of combustion of other common fuels). If you go from 1X to 2X you double the chemical energy in the chamber.

Normal firing conditions are close enough to STP so you can use STP values for calculating the number of moles of fuel in the chamber. (If you're anal you can do the gas law corrections for your actual ambient conditions but it really isn't worth the effort.)

Assuming a 1 liter chamber, STP says 22.4 liters/mole gas. Air is ~21% (volume or number of moles) oxygen and stoichiometric mixture for propane + air is 4.2% (volume or number of moles) propane.

So a 1L chamber contains 1mol/22.4L= 0.0446 moles of gas. Of that gas 4% is propane so there are (0.04)(0.0446mol)=0.00179 moles of propane. Using the heat of combustion you can calculate that there are
(527Kcal/mol)(0.00179mol)=0.941Kcal (3940J)
of chemical energy in the chamber.

At a 2X mixture you have twice the chemical energy in the chamber (3940J/Liter*2=7880J) plus the energy of the gases compressed to 2ATM. The energy in the compressed gases is pretty negligible compared to the chemical energy in the fuel+oxidizer mix so that term can be ignored unless you are going for an unrealistically accurate answer.

Combustion spud guns are pretty inefficient. Figure about 10% of the chemical energy in the chamber ends up as actual kinetic energy of the spud. Given the crappy efficiency of a combustion gun, and the uncertainty in exactly what the efficiency is, that is why it really isn't worth the effort to try to calculate a more accurate number for the energy in the chamber.

Assuming 10% efficiency our 1L 1X propane+air chamber will put 394J of kinetic energy into the ammo. If the ammo weighs 100g then the muzzle velocity would be 89m/s (290 FPS).

For the 2X mixture (same chamber size) you can pretty much ignore the pressure contribution. The chamber has twice the fuel hence twice the chemical energy so the KE of the ammo goes up by 2X. That corresponds to an increase in velocity of 1.4X (the sqrt of 2, from KE=0.5mv²).

It is possible, but non-trivial, to do a much better job of the calculations. HGDT is much more accurate (it includes the energy in the compressed gases etc) but even the HGDT numbers must be considered estimates. The absolute results are only approximately correct. Comparisons with HGDT (and most other thermodynamic models) are generally more accurate than a single calculation. That is, the accuracy of the calculated difference in performance for a modest change in one parameter of the gun are generally pretty good. So for example, the absolute accuracy of an HGDT calculation for a 1X gun is only moderate. The accuracy of the estimated percent change in performance that you would get going from 1X to 2X is probably much better.

The affect of increased pressure on the burn rate is complex. The actual flame front propagation speed decreases as the starting pressure increases. But since a unit volume of gases contains more energy the energy released per unit time may be faster with a pressurized mixture.

The efficiency of a combustion gun varies considerably with the compression (hybrid) ratio. Just as in an internal combustion engine, higher hybrid ratios tend to increase the efficiency of energy transfer to the ammo (or piston). Since combustion guns are really pretty inefficient the increase in performance of a hybrid comes from both the increased energy in the chamber and the increase in efficiency of the transfer of that energy to the ammo.

The other question was the energy required for ignition. I'm sure someone somewhere has figured it out. I wouldn't worry about it too much though for two reasons (1) the igntion energy probably doesn't change all that much with compressin ratio and (2) a decent igntion system should be putting in at least ten times more energy than is actually required. So, a good sparker for a 1X gun should be a good sparker for a 10X gun. There is the practical aspect that the breakdown voltage of the fuel mix goes up with pressure. A sparker + gap width that works well at 1X may not work at 10X since the gap will be too big. Decrease the gap width and everything should be OK. The breakdonw voltage scales pretty much linearly with the pressure so a 10X mixture would need a gap that is 1/10 as big.

The numbers I have seen concerning the actual ignition energy is generally in the range of 0.2 to 0.5millijoules for propane in air at 1X. That number is a bit misleading since it really should be an energy density and not just an energy. Smacking the chamber with your finger probably puts a couple mJ energy into the gases but it won't ignite the mixture, you need the energy concentrated in a small enough volume.

If you have 10X the minimum ignition energy in your spark that would put the spark energy at about 5mJ. Our 1L 1X chamber has about 3940J of chemical energy. The actual energy contribution of the spark to the total energy in the gun is only one one millionth the chemical energy in the chamber.

[Biopyro]

1. I believe the energy required to ignite it remains the same, BUT the thicker atmosphere requires either a more powerful arc OR a smaller gap. Of course a 20x ix if you use a spark gap with 1/20th the length you would be fine. If the mix gets so high you can't get an arc across then there's always things like glow plugs, steel wool and shock combustion.

The reaction will have the same amount of energy, but more force. Because it's under pressure the reaction will proceed faster, so more power, which is really what interests us.

The same amount of energy as what?

The chemical energy in the chamber is just the number of moles of fuel times the heat of combustion of the fuel, assuming a stoichiometric mixture. At 1X, the theoretical energy from propane + air is 527 Kcal/mol (2210KJ/mol). (see the SpudWiki page on fuels for the heat of combustion of other common fuels). If you go from 1X to 2X you double the chemical energy in the chamber.

Normal firing conditions are close enough to STP so you can use STP values for calculating the number of moles of fuel in the chamber. (If you're anal you can do the gas law corrections for your actual ambient conditions but it really isn't worth the effort.)

Didn't have time to read past here, but I assume you're saying that the extra pressure won't really affect the reaction speed? If so then yeah I guess the power is double a 1x mix.

[rcman50166]

my god Jimmy

[mega_swordman]

Thank you Jimmy for your contribution, this is exactly the kind of informatio I was looking for. You're a lifesaver.

[Moonbogg]

Dude, I think Jimmy kind of has an understanding of how a hybrid works.

[starman]

Anyone who hasn't been over to Jimmy's website should go over and peruse around some....some good info.