Author Topic: What Does the Air Weigh?  (Read 1448 times)

rsterne

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What Does the Air Weigh?
« on: June 08, 2017, 11:36:48 AM »
Ever wondered how much of the energy in a PCP goes into accelerating the air along with the bullet?.... Lloyd just added that calculation to his Internal Ballistics Spreadsheet, and it's quite an eye-opener.... I'll just give you a few of examples....

.25 cal with a 20" barrel, running regulated on 2000 psi, 25.4 gr. pellet at 900 fps, with an efficiency of 1.5 FPE/CI.... Weight of air in barrel = 9.15 gr. (36% of pellet weight)....

Same gun, but keep the valve open until the pellet reaches the muzzle.... Velocity 1079 fps, efficiency drops to 0.66 FPE/CI.... Weight of air in barrel = 29.9 gr. (more than the pellet)....

.308 cal with a 24" barrel, running on 3000 psi, 120 gr. bullet at 900 fps, with an efficiency of 1.0 FPE/CI.... Weight of air in barrel = 64.7 gr. (54%)....

If you wonder why Helium makes such a big difference in velocity.... take the last example, and replace the air with Helium (no other changes)....

.30 cal with a 24" barrel, 3000 psi of Helium.... That 120 gr. bullet will now hit 1033 fps, at an efficiency of 1.22 FPE/CI.... because the mass of He is only 9.62 gr. (8%)...

Bob
« Last Edit: June 08, 2017, 11:43:36 AM by rsterne »


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oldpro

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Re: What Does the Air Weigh?
« Reply #1 on: June 08, 2017, 12:39:09 PM »
Ever wondered how much of the energy in a PCP goes into accelerating the air along with the bullet?.... Lloyd just added that calculation to his Internal Ballistics Spreadsheet, and it's quite an eye-opener.... I'll just give you a few of examples....

.25 cal with a 20" barrel, running regulated on 2000 psi, 25.4 gr. pellet at 900 fps, with an efficiency of 1.5 FPE/CI.... Weight of air in barrel = 9.15 gr. (36% of pellet weight)....

Same gun, but keep the valve open until the pellet reaches the muzzle.... Velocity 1079 fps, efficiency drops to 0.66 FPE/CI.... Weight of air in barrel = 29.9 gr. (more than the pellet)....

.308 cal with a 24" barrel, running on 3000 psi, 120 gr. bullet at 900 fps, with an efficiency of 1.0 FPE/CI.... Weight of air in barrel = 64.7 gr. (54%)....

If you wonder why Helium makes such a big difference in velocity.... take the last example, and replace the air with Helium (no other changes)....

.30 cal with a 24" barrel, 3000 psi of Helium.... That 120 gr. bullet will now hit 1033 fps, at an efficiency of 1.22 FPE/CI.... because the mass of He is only 9.62 gr. (8%)...

Bob
That is far beyond anything I could have imagined I would have never guessed the air had that much weight to volume

int3man

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Re: What Does the Air Weigh?
« Reply #2 on: June 08, 2017, 04:13:18 PM »
Yes we run into that with hydraulics all the time.  The good news we are usually running in a closed circuit and keep it moving once we get it started.

We had an issue when I first started. after sitting all night, in the cold,  the back pressure (Caused by the cold thick oil) in the return lines at start up exceeded the pilot pressure for the check valves.  So every time they started the coach they would let some oil out.  The product would fail on first operation.  Stronger springs in the check valves solved the issue.

Thanks for the education Bob.
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Christopher

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Re: What Does the Air Weigh?
« Reply #3 on: June 08, 2017, 07:26:48 PM »
That's very interesting....So one cubic inch of air weighs 0.3 grains and helium weighs 0.04 grains per cubic inch....or air is 7.5 times heavier than helium and helium weighs 13.3% of what regular air weighs.

Kind of gives me a better idea of why Bob's lofty goal of 50% of theoretical maximum (bore volume x pressure) is so "lofty". Quite a bit of drag going on and weight to push with the air itself, besides the energy that is expended on the projectile.

Huh, who da thunk it? (Not counting Bob and Lloyd :) )

I'll repeat what int3man said:
Quote
Thanks for the education Bob.

Chris



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rsterne

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Re: What Does the Air Weigh?
« Reply #4 on: June 08, 2017, 07:42:00 PM »
The weight depends on the pressure, of course....

Bob
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Christopher

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Re: What Does the Air Weigh?
« Reply #5 on: June 08, 2017, 07:51:46 PM »
The weight depends on the pressure, of course....

Bob
Care to expand? I was calculating the weight at one bar of pressure, but I may be, more like probably, wrong. I'm kind of like HPA......dense.

Thanks,
Chris
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rsterne

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Re: What Does the Air Weigh?
« Reply #6 on: June 08, 2017, 09:17:24 PM »
At STP, one MOLE of a gas ( 6 x 1023 atoms/molecules) occupies 22.4 litres (22,400 cc) = 1366 CI.... One mole of a gas has a weight in grams that is exactly it's atomic/molecular weight.... Nitrogen (N2), weighs (14x2) = 28 MW, and Oxygen (O2) weighs (16x2) = 32 MW.... Air, which is a mixture, is about MW = 29.... However, it has a bit less density than that would predict.... Air has a density at STP of 1.225 g/L.... which works out to 0.31 grains per CI at 1 bar....  Helium weighs 4 AW, so 4 grams for 1366 CI.... which is (4 x 15.43 / 1366) = 0.045 grains per CI at 1 bar.... Air, at STP, is 6.9 times as heavy as He....

If the pressure is 100 bar, then the weight per CI is 100 times greater.... Air would weigh 31 grains/CI, and Helium would weigh 4.5 grains/CI.... At very high pressures, we need to take into account the VanDerWaals correction, of course, because pressure goes up faster than density....

Bob
« Last Edit: June 10, 2017, 09:07:07 PM by rsterne »
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rsterne

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Re: What Does the Air Weigh?
« Reply #7 on: June 08, 2017, 09:37:36 PM »
Here is another visualization I just did.... It's only approximate, and only in 2 dimensions, but it will give you an idea what happens when you compress air....



The black dots represent an air molecule (oxygen or nitrogen).... They average about 4 Angstroms across (0.0000004 mm, and yeah, they are not spheres).... In a liquid (lower left), they are pretty much touching, but vibrating and changing positions, not locked into a crystal structure like in a solid.... As a gas, at 1 bar pressure, they average about 40 Angstroms apart (upper part of the diagram).... As you increase the pressure, they get closer together.... At 125 bar (1800 psi, lower right), they are about 8 Angstroms apart, about 1/5th the spacing at 1 bar (roughly enough room for one more molecule between each pair).... Since we are working in 3 dimensions, the volume occupied by a given number of molecules is the cube of the spacing.... so we have (1/5 x 1/5 x 1/5) = 1/125th the volume.... because the pressure is 125 times as great....

You may have heard me state that at very high pressures the pressure goes up faster than Boyle's Law for ideal gasses predicts.... What is happening is that the space between the molecules gets so small that they start developing additional pressure from hitting or interfering with each other, and not just the walls of the container.... It is called the VanDerWaals effect, and this diagram shows you how that might be occurring.... Now imagine each and every one of those molecules travelling in random directions at an average speed of 1650 fps.... like a crowded pool table gone mad.... in 3 dimensions.... :o

Bob
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Alan

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Re: What Does the Air Weigh?
« Reply #8 on: June 09, 2017, 04:55:08 AM »
When things really get fun, is when the pressure gets above 80 or so GPa (depends on the gas). Above that pressure level, gases start turning into metals! Imagine the number of shots you could get if your tank was filled to 80 GPa?
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rsterne

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Re: What Does the Air Weigh?
« Reply #9 on: June 09, 2017, 07:56:11 AM »
Actually, not that many more shots than if it was filled with a liquid.... Some solids are actually less dense than the liquid state.... Water is a good example, ice floats....

Bob
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Christopher

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Re: What Does the Air Weigh?
« Reply #10 on: June 09, 2017, 01:49:23 PM »
Thanks Bob for the time you took explaining all that....

Quote
At very high pressures, we need to take into account the VanDerWaals correction, of course, because pressure goes up faster than density....

How high does the pressure have to be before VanDerWaals effect is taken into consideration? I would imagine the higher the pressure the more noticeable the effect.

Quote
Now imagine each and every one of those molecules travelling in random directions at an average speed of 1650 fps....

Would you elaborate on why or how that is derived?

Just trying to learn,
Chris


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rsterne

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Re: What Does the Air Weigh?
« Reply #11 on: June 09, 2017, 03:21:06 PM »
For air, up to about 2500 psi, there is really no correction needed, and at 3000 psi it is only about 3%.... Above that, it becomes significant, and by 4500 psi, Boyle's Law for ideal gasses is out by about 10%.... and gets worse as you go higher.... Other gasses have different VanDerWaals correction factors.... If you want to know the accurate air density at a given pressure and temperature, here is a calculator.... http://www.peacesoftware.de/einigewerte/luft_e.html

The speed of molecules in a gas depends basically on two things.... the absolute temperature (atoms stop moving at absolute zero).... and the mass of the molecules.... Helium, being MW = 4 has higher molecular speeds than Nitrogen (N2) at MW = 28, or Oxygen (O2) at MW = 32, (for air we use 29), or CO2 at MW = 44, and Argon is MW = 40.... Here is a calculator that will give you that data....  http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/kintem.html#c4

Note that not all the atoms/molecules are going the same speed, there is a distribution of speeds, called the Maxwell Speed Distribution.... The value of 1650 for air a room temp. is the RMS average....

Bob

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Christopher

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Re: What Does the Air Weigh?
« Reply #12 on: June 09, 2017, 04:07:10 PM »
Thank ya sir........you're better than Google  ;D

Chris
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