Sonic Choke? Maybe not. 2162 FPS

[Buldawg76]

The average air velocity right behind the pellet is higher than the air velocity entering the barrel. The mass flow rate is the same. Think about it!

On Lloyd's last test, the air enters at 1650fps (or 1854fps) and the first molecules to reach the muzzle were going 2162fps. What's the problem?

I am not quite understanding the theory behind the statement that the air entering the barrel behind the pellet is either moving at 1650 fps or 1845 fps since it is at 4500 psi at the release of the pellet. I do not fully understand most of the math equations presented here so if that velocity is a result of the calculations done in this thread that has resulted in those being the velocities of the airs speed as it hits the pellet when released then disregard my question, but it seems to me that air at 4500 psi that is suddenly and fully released into the barrel behind the pellet would /should be moving at a much higher velocity if not close to the final velocity of the pellet at the muzzle.

I understand the acceleration of the smaller column of air in the center 1/3 to 1/2 of the diameter of the barrel as the walls of the barrel will tend to form a boundary layer of air that will slow down as it moves down the length of the barrel and thereby accelerating the center column of air faster as it nears the muzzle.

So is the 1650/1845 FPS of the initial release of the 4500 psi air part of the resulting calculations that have been worked out here or is it a fixed number from one of the laws of physics used in the calculations that states that is the maximum velocity the air can be moving. Please put it in laymen's terms as to how those numbers were derived to be stated and used as a basis for the extensive math shown through out this thread.

Thanks Mike

[lloyd-ss]

I wrote a paper on the 1640fps "myth". Object was to better explain it to others:

http://www.scotthull.us/1640-myth.htm

Any comments as to clarity of explanation would be appreciated. I did not want to get too technical.

Scott,
Well presented paper.  Enough technical information without being overly so.  I definitely see merit in your argument, but I, like Bob, do not have enough of a thermodynamics background to add additional thoughts.
Lloyd

[rsterne]

Mike, the 1640 fps is the RMS (call it an average) velocity of the air molecules, bouncing around in random directions inside the reservoir before firing.... On firing, the molecules that would hit the base of the pellet and bounce back into the reservoir, now shove the pellet down the bore, and are replaced with more from the reservoir....

My idea is that the new ones exiting the reservoir, hit the ones in the barrel, which are already moving down the bore, accelerating them further, one packet of air pushing the one in front, and the front one pushing the pellet.... Add that to Scott's point about there being a velocity profile inside the barrel, with the molecules in the center moving faster than the average, and the ones on the side moving slower (from barrel friction), I don't think we are exceeding any laws of physics at all.... I can see it entirely possible for the RMS average of the molecular velocity to be 1640, but the ones in the center of the barrel are double that.... they are the ones in right hand, high-speed part of the Maxwell speed distribution curve.... some of which are moving more than twice the average speed.... The barrel merely "focuses" them to do useful work on the pellet....

Bob

[Scotchmo]

The average air velocity right behind the pellet is higher than the air velocity entering the barrel. The mass flow rate is the same. Think about it!

On Lloyd's last test, the air enters at 1650fps (or 1854fps) and the first molecules to reach the muzzle were going 2162fps. What's the problem?

I am not quite understanding the theory behind the statement that the air entering the barrel behind the pellet is either moving at 1650 fps or 1845 fps since it is at 4500 psi at the release of the pellet. I do not fully understand most of the math equations presented here so if that velocity is a result of the calculations done in this thread that has resulted in those being the velocities of the airs speed as it hits the pellet when released then disregard my question, but it seems to me that air at 4500 psi that is suddenly and fully released into the barrel behind the pellet would /should be moving at a much higher velocity if not close to the final velocity of the pellet at the muzzle.

I understand the acceleration of the smaller column of air in the center 1/3 to 1/2 of the diameter of the barrel as the walls of the barrel will tend to form a boundary layer of air that will slow down as it moves down the length of the barrel and thereby accelerating the center column of air faster as it nears the muzzle.

So is the 1650/1845 FPS of the initial release of the 4500 psi air part of the resulting calculations that have been worked out here or is it a fixed number from one of the laws of physics used in the calculations that states that is the maximum velocity the air can be moving. Please put it in laymen's terms as to how those numbers were derived to be stated and used as a basis for the extensive math shown through out this thread.

Thanks Mike

The air behind the pellet is less dense than the air entering the barrel. For any given mass flow rate, that means that the air behind the pellet is moving faster than the air entering the barrel.

[Scotchmo]

Mike, the 1640 fps is the RMS (call it an average) velocity of the air molecules, bouncing around in random directions inside the reservoir before firing.... On firing, the molecules that would hit the base of the pellet and bounce back into the reservoir, now shove the pellet down the bore, and are replaced with more from the reservoir....

My idea is that the new ones exiting the reservoir, hit the ones in the barrel, which are already moving down the bore, accelerating them further, one packet of air pushing the one in front, and the front one pushing the pellet.... Add that to Scott's point about there being a velocity profile inside the barrel, with the molecules in the center moving faster than the average, and the ones on the side moving slower (from barrel friction), I don't think we are exceeding any laws of physics at all.... I can see it entirely possible for the RMS average of the molecular velocity to be 1640, but the ones in the center of the barrel are double that.... they are the ones in right hand, high-speed part of the Maxwell speed distribution curve.... some of which are moving more than twice the average speed.... The barrel merely "focuses" them to do useful work on the pellet....

Bob

Something to remember about that statement in red:
The center column or cone has the higher mass flow rate, but the outer skin would have the higher molecular velocity.

The average (molecular_velocity + mass_velocity) of all regions in the barrel is the same.

We are looking at it as different molecules all having different molecular velocities that result in an RMS velocity. Instead, imagine them as vibrating molecules. Very high frequency vibration. At higher temps, the molecular velocity increases. They vibrate "faster" (higher amplitude). The molecules spread apart, reducing the density.

The RMS velocity is really a vibration which can take various forms:

[rsterne]

Now you're dealing with Physical Chemistry, and although not my Forte, I do understand a tiny bit about that.... The vibration modes you are showing are WITHIN the molecule, not how one molecule interacts with another.... IMO that is NOT what the RMS velocity is referring to at all, it refers to the velocity of the complete molecule, relative to the others, and the container, not one atom vibrating relative to another within the Nitrogen and Oxygen molecules.... Your diagrams, BTW, are for a molecule such as water (in fact they probably are water), with two Hydrogen and one Oxygen.... Water is a "bent" molecule, with the spare electrons on the Oxygen occupying the positions shown on your drawings, and does, in fact, vibrate as you show.... N2 and O2, being diatomic, only have two atoms, so all they can do is stretch and compress (imagine just one blue and one yellow in the first two diagrams), there is no interatomic force to make them vibrate like a tuning fork (like in the third diagram)....

Your statement about the center of the flow having the higher mass flow rate, but the edges a higher molecular velocity total confuse me.... Mass flow is molecules per second, so the only way that could happen would be for the air density to be higher in the middle of the barrel....

Bob

[Bill G]

Just got caught up with all the posts. I'm still out of town and do't have access to all of my toys. 

Lloyd, your valve concept is about exactly the same as the one That I have been working on.  The biggest difference is that the reservoir is under the the dump chamber.  The dump chamber if fed through a reg that will be externally adjustable in the future iteration of design.  from the reg it passes through a TP and then through a floating piston. The air then travels to the rear of the piston causing it to to push forward thus closing the access to the barrel.  There is a check valve in the bulkhead that the piston slides in.  You know how the rest works as to the evacuation.  What I am designing is very similar to our current poppet valve at the rear of the piston and bulkhead. The head of the poppet  will close the passage to through the piston when the stem is hit.  this will allow the air to evacuate causing the needed imbalance that causes the dump camber to empty.  when the piston shifts rearward it will maintain the seal of the piston port until the dump chamber is evacuated(nearly).  once the dump chamber psi is low enough the rear poppet and piston will separate allowing the cycle to be restarted.  Ideally the reservoir and dump valve as described will be separated by what I call the spar, which the TP is placed.  This spar will be what the barrel mounts to and will allow the barrel to slide forward to allow access to the chamber for loading.  the gap between the piston and the rear poppet will be equal to the certain distance required for maximum flow rate into the barrel.  it looks like the "waisted" volume to rear of the piston and dump chamber will be dependant on the I.D. of the dump chamber.  AS of now that is about .005 in^3 and I think that I may be able to decrease that. 

I had been working on this as a leap of faith and on what I had been getting from modeling using my calculator.  The fudge factor is exactly what I had been trying to explain away and make "automatic". Then Lloyd starts this thread, Bob and Scot start crushing the math.  Definitely at a perfect time for me.  I am hoping to be able to start fabricating more parts this winter when my sons aren't burning all my time with baseball.  New job isn't helping much either due to traveling for training.  Thanks a million fellas for all the hard work.  It has renewed the desire to move forward with this project since our calculations are so close to Lloyd's findings.  Bob and Scot are closer than me.  If I introduce the 70% efficiency factor I'm much closer,  within just a few FPS of what Bob and Scot have been getting .  I'd just like to be able to have that factor auto correct and it is just beyond my ability I suppose. 

Bob, the graph showing a divergence at 2000+ psi is very interesting.  I think that this showed up with Lloyd's early testing on the 3500 psi testing.  They all seemed to follow a power regression.  I had previously noted that they were above .99 on the R^2  but when the model was carried out to predict outcome at lower and higher psi's, the results were unrealistic.  But when modeled as a power regression the trends were very realistic. 

Great work gentlemen. 

Bill G           

[Scotchmo]

Now you're dealing with Physical Chemistry, and although not my Forte, I do understand a tiny bit about that.... The vibration modes you are showing are WITHIN the molecule, not how one molecule interacts with another.... IMO that is NOT what the RMS velocity is referring to at all, it refers to the velocity of the complete molecule, relative to the others, and the container, not one atom vibrating relative to another within the Nitrogen and Oxygen molecules.... Your diagrams, BTW, are for a molecule such as water (in fact they probably are water), with two Hydrogen and one Oxygen.... Water is a "bent" molecule, with the spare electrons on the Oxygen occupying the positions shown on your drawings, and does, in fact, vibrate as you show.... N2 and O2, being diatomic, only have two atoms, so all they can do is stretch and compress (imagine just one blue and one yellow in the first two diagrams), there is no interatomic force to make them vibrate like a tuning fork (like in the third diagram)....

Your statement about the center of the flow having the higher mass flow rate, but the edges a higher molecular velocity total confuse me.... Mass flow is molecules per second, so the only way that could happen would be for the air density to be higher in the middle of the barrel....

Bob

You know more about chemistry than I do. Maybe I'm grasping at straws.

It still makes sense that (molecular_velocity + mass_velocity) of all regions in the barrel is the same.

Or, more precisely, (KEmolecular+KEmass) of all regions is the same.

And the motion that determines that KE can takes many forms. We have been focusing on the translation, but need to consider them all:



"...so the only way that could happen would be for the air density to be higher in the middle of the barrel.... "
Exactely!

Efficiency losses occur in the boundary layer. Raising the temperature in the boundary layer. Density goes lower on the edges. Now the density of the air in the middle of the barrel is higher than the average throughout that region of the barrel.

Edit: Calling the RMS a velocity is OK for total KE calculations, but it is not really a velocity. A translating velocity is a vector. RMS is not. RMS is a speed that has no direction. RMS is usually used to quantify the speed of something undergoing vibration.

[rsterne]

RE your second diagram.... the RMS molecular speed (you are correct, it is not a velocity, because it is random) is TRANSLATION....

Bob

[Scotchmo]

Bob,

You are saying that KEmolecular is from translation only. I'll go with that. That part is recoverable.

Gas molecules don't just translate.

The energy is divided between translation and any other degrees of freedom. (equipartition of energy?)

I think that is the same as the K=1.4 ratio for air.

The part of that is not recoverable goes to heat. The question is still whether it is enough heat.

Your original checks led you to believe that the temperature rise from the inefficiencies would be insufficient to account for the needed molecular speed.

I suspect that once it is integrated as an incremental increase along the barrel, it will be just enough.

The other possibility is that the molecular velocity has nothing to do with a speed limit. Until we exhaust all other possibilities, I'll have trouble letting that one go. In either case, a model that correctly includes temperature rise from fluid friction will give the most accurate model. Definitely better than a straight fudge factor.

Lloyd already proved that the 70F 1640fps molecular speed is not a limit. But the tests did not prove whether or not molecular velocity has any bearing on the speed limit.

A better model may help justify whether the molecular speed (at any temperature) is a limit to PCP velocity. I can't do the advanced math that is needed. I might be able to do a better numerical integration.  I'm just not sure I want to put that much work into it.

I'm slowly reworking my spreadsheet. I'm switching all inputs to SI units before doing the integration. The imperial units were getting too confusing. I'll still have the user input imperial when desired, but I'll convert any grains, inches, psi, fps, degreeF, lbf, etc. to kg, meters, kpa, m/s, degreeK, newtons, etc., before doing any integration.

I am learning (and relearning) a lot from this whole exercise.

[Buldawg76]

Ok Bob and Scott got a better grasp on the molecular FPS thing except for the fact that the 4500 psi air in the dump chamber is stagnate until the release of the pellet is it not so is it the fact that the heat contained it that 4500 psi air is causing the molecules to stay moving inside the dump chamber at a much reduced speed until the pellets release and basically then all heck breaks loose and the race is on to see who makes it to barrels end first.

Bob  I understand your packet of air theory with each one pushing harder on the one ahead of it since the ones still accelerating out of the dump chamber would still have more energy to release than the ones already ahead of the ones leaving the chamber and it acts as a continuation of momentum from the back to the front so that the more molecules compressed into the barrel the harder they push on the ones in front of them hence increasing the ones at the very fronts speed until it is all released at the barrel end.

I also know from racing and building race engines that the venturi effect inside an intake manifold from the air speed outside of the carb or throttle body to where it passes thru the restriction at the throttle plates serves to increase its velocity quite significantly and helps prevent the boundary layer of air/fuel molecules to collect along the walls of the intake manifold and lean the mixture out from lack of the full air fuel charge making it into the cylinders. That is why the inner surface of most street cars intakes work better with a slightly rough surface to prevent that accumulation of that boundary layer from forming and causing the air/fuel molecules to collect on the walls of the intake much like the dimples on a golf ball increase it flight distance due to decreased drag.. Now a full on race engine like top fuel dragsters and Nascar engines that are designed to run at peak rpm only all the time and only see low rpm situations when at the starting line or in the pits benefit much more from a highly polished intake walls since the air/fuel molecules are moving at the highest possible velocities all the time and don't have time to form a boundary layer of air/fuel on the intake walls that amount to any significant amount that would decrease power and torque output. I am talking the difference of 2000 rpm to 4500 rpm on the street and 8000 rpm to 10,000 rpm on the race track being a constant engine speed or to put it a better perspective. A Nascar engine at 8000 rpm has a piston speed of 5000 FPS and a top fuel dragster at 10,000 rpm has a piston speed of 6000 FPS with the pistons stopping and starting back to that speed at every revolution at top dead center and bottom dead center or twice for every single revolution of the engine. Where as a street driven car that will last 100,000 plus miles as they do today has a average piston speed of 2000 to 3000 FPS at interstate speed of say 2000 to 2500 rpms and 70 MPH.

Mike

[rsterne]

Scott, if you work strictly with the idea that RMS molecular speed is needed that will exceed the pellet velocity, then for Lloyd's 2162 fps shot you need over 230*C just to match the pellet velocity.... As Steve keeps pointing out, Adiabatic expansion should cause a net cooling effect on the air, so you need to not only generate enough heat to completely overcome that, but to raise the temperature to over 500*K.... It is highly unfortunate that he continues to slide in comments about how you can't get to where we are today, or why your theory is wrong, without putting any actual effort into explaining it.... Perhaps as Lloyd says, he already knows the answer but is not willing to share his insight to explain the facts which overturned his long held position.... If so, that would indeed be a great shame.... I am hoping he is as much in the dark as the rest of us, and simply doesn't want to admit it....

I'm still convinced that the original thought I had many years ago, that since the RMS value is much less than the speed of a portion of the molecules (as shown by Maxwell's speed distribution).... there are enough "fast ones" to drive the pellet well past 1650 fps.... as I first saw on the CAF way back when.... Your idea of the velocity profile, where the outer molecules are slowed by friction with the barrel, while the inner ones are moving much faster than 1650, is I think sufficient explanation of what amounts to a focusing of the high velocity molecules down the center, providing plenty of push on the pellet to explain Lloyd's results, without violating the RMS average at the ambient average temperature in the barrel, whatever that is....

You can drive a solid object to hypersonic speeds, and the molecules in it are still vibrating independent of the forward velocity.... A liquid is the same thing, but the molecules are more loosely bound, but still vibrating.... A gas is yet the same thing again, but the molecules are not bound to each other, but colliding, providing "pressure".... Why should it be possible to accelerate one to extreme velocity but not the other?.... Perhaps the whole concept of molecular speed having anything to do with it is what is flawed....

Bob

[Scotchmo]

Bob,

Looking at is as some of the RMS molecules being faster than others and allowing/causing the higher velocities - That parallels what I'm saying. The only difference is that I see those faster molecules as being concentrated behind the pellet.

I know that the temperature needed to keep the molecular speed above the projectile speed (2150fps) seems very high. But I'm not ready to say that those high temps can't happen for a millisecond right behind the pellet.

I decided that I need to start over on my spreadsheet. Integrating by barrel length increment was convenient at first, but is now messing things up. I now want to do it by air mass increment. Track each milligram of air as it enters the barrel and works it's way to the muzzle. That will let me to heat it, expand it, without also having to deal with a change in quantity.

"Why should it be possible to accelerate one to extreme velocity but not the other?.... Perhaps the whole concept of molecular speed having anything to do with it is what is flawed...."

There is a difference between accelerating a solid and accelerating a gas. The solid stays the same length. The gas shrinks in volume as you accelerate it. Is it shrinking fast enough to cancel out any added force trying to accelerate it?

I have suspicions too - the whole concept of molecular speed as a limit may be flawed.  If the spreadsheet model can't keep the molecular velocity ahead of the pellet velocity, I'll being going with my suspicions.

[rsterne]

My posting may dry up somewhat, I will be away until April 11....

Bob

[Buldawg76]

As far as a solid staying the same length that may hold true if that solid is only traveling in one direction but in the case of an engine with pistons and rods and a crankshaft that's most definitely untrue as the rods and crankshaft flex and bend and contort all over the place at the sudden stops and starts at top dead center and bottom dead center when running. The rods in a street car at 2000 rpm are being compressed and expanded by up to .050" every time the piston change directions as well as the crankshaft journals being twisted in the reverse direction of rotation every time a cylinder fires.

I was given the opportunity to see the inside of a small block Chevy motor running at 3000 rpm with a strobe light and camera inside the block and the crankshaft and rods looked like wet noodles being twisted and bent is all directions as it rotated and is why there are a harmonic balancer on the front of the crank and a balanced or unbalanced flywheel at the rear to help absorb all those vibrations and impulses from the cylinders firing and applying extreme forces to the rods and crankshaft not to mention the camshaft is doing the same thing under the valve trains loads. Without those counter measures to help absorb and balance the rotation cranks and rod would break in very short order.

Mike       

[Scotchmo]

I asked a somewhat rhetorical question in my last post:

"There is a difference between accelerating a solid and accelerating a gas. The solid stays the same length. The gas shrinks in volume as you accelerate it. Is it shrinking fast enough to cancel out any added force trying to accelerate it?"

First inclination might be to agree with an answer of "yes". But the 2000fps shots indicate "no". Because the dump gun creates a constant pressure process, or nearly so, the gas does not compress. So Bob is right in that respect. But there is even more - It actually grows in length as heat from friction raises the temperature while pressure stays the same. It undergoes a constant pressure (or nearly so) expansion.

We may be dealing with a mass of air that is significantly less than we think it is.

[rsterne]

While it is possible that you may be right, the fact that the spreadsheet works over a complete shot string, predicting the correct number of shots based on the volume (and therefore mass) of air per shot.... I rather doubt it suddenly is overpredicting the mass on a dump shot.... but there is really no way to prove that because the entire reservoir is dumping....

Bob

[Scotchmo]

While it is possible that you may be right, the fact that the spreadsheet works over a complete shot string, predicting the correct number of shots based on the volume (and therefore mass) of air per shot.... I rather doubt it suddenly is overpredicting the mass on a dump shot.... but there is really no way to prove that because the entire reservoir is dumping....

Bob

I can't prove it's happening, other than it can't NOT happen without breaking some laws of thermodynamics.

1) There are losses. Besides a litle bit of pellet friction, air friction is the only other.
2) The losses raise the temperature of the gas.
3) At a constant pressure, that higher temperature gas MUST expand.

If someone says, no friction, no heat gain, no expansion - I say not possible.

If we are below supersonic, the friction and expansion may be negligible. In which case the model is good as is, and air usage is about what we predict. - we can ignore heat gain. When the apparent efficiency drops enough, we need to account for it when looking at air use efficiency. And it may not be quite as bad as our spreadsheet shows, because we are attributing the net energy to more air than we should.

I'm postulating, so I'm willing to change when more info/ideas are are included.

[MicErs]

While it is possible that you may be right, the fact that the spreadsheet works over a complete shot string, predicting the correct number of shots based on the volume (and therefore mass) of air per shot.... I rather doubt it suddenly is overpredicting the mass on a dump shot.... but there is really no way to prove that because the entire reservoir is dumping....

Bob

Bob


One could do the statistics by taking thirty samples or so.... Yes one shot is a total dump of teh reservoir but you can still sample 30 shots.  So yeah... While I agree with you I disagree that "there is really no way to prove that".

[dan_house]

Wow, just wow.... You guys ROCK! Great Job Lloyd! Kudos to Scott and Bob for their analysis and support for Lloyd.

It amazes how much work got done when the three of you worked together, debated, argued yet always acted civilly... Quite the contrast to other places.... And this whole discussion, the objectives and the results, have made me realize a number of things. First, it is possible to gather smart folks and let them work toward a common goal, second, the current airgun setups are flawed in any number of ways (but had to be given the state of technology when they are/were designed, customer base and efforts to ensure reliability), third out of this research and experimental test will come the next/new generation of air gun mechanisms. 

While reading the entirety of this thread (and the references to the yellow and other forums) I had the thought(s) rolling around in my head about how to transliterate Lloyd's setup into something I could shoulder and take to the range. It may take some time, but I wont be surprised to see upgrades and improvements that is rooted in this research and experiments.

Again, you all deserve a huge round of applause