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Yes, this is indeed true, however, there are 2 things that are different here:
1. The volume change is actually much smaller because the change in volume is only the wall thickness of the dummy piston (Dummy piston is hollow). As it is cocked, the steel tube is protruding further into the piston, and this is the only volume change. In my setup, lets say the stroke pull was i between 10 and 20 cm. That gives a ratio of around 1.1:1, intitail volume to cocked volume.
2. This may be a very small volume change, however, this is kind of the point of the theoben system. The small ratio of change gives a much more constant force. The trick is, the gas in the piston and dummy piston area is quite highly pressurized, The max my system can take is 260 PSI. What I will do is attach a schrader to the end of the dummy piston, and fill the entire hollow area, thats the piston volume, and the dummy piston volume, to around 230 PSI to be safe.
The force that the piston is pushed forward with is equal to the force exerted by the gas pressure on the area of the dummy piston's ID. This is where I am getting my force calculations from. With a radius of 0.48 cm of the dummy piston's ID, and a pressure of 230 PSI, I get 117 newtons of force, that is, when uncocked, the piston is pushing on the end of the cylinder with that force. With the current compression ratio that should increase to about 130 N when the gun is cocked. Hence, the force X displacement graph of the force acting on the piston would be
x=displacement in cm
If we find the area under the curve we get the kinetic energy of the piston after a certain displacement. We will use x=0.1cm.
Area under curve=kinetic energy=12.285 Joules
So that is the ideal world, no friction amount of energy the piston has if been given over that distance. If I can get the piston to hit the end of the cylinder as the bb exits the barrel, that is obviously ideal, and would give the best energy into the bb. That brings me back to why I was going to port the cylinder. If I wave hales in the cylinder allowing air to escape for the first few centimeters then the volume ratio cylinder to barrel wont be so high that the bb will be outta there before the piston hits the cylinder wall. I don't know what efficiency to expect here, that is my only problem. Or maybe its only one of my many problems lol. I want 4 Joules out of this for a 6mm bb.
Thats asking for 32.6% efficiency. possible?
OK, the air spring is used for constant force over longer distance much like a compound bow instead of a long bow for example. It has higher average power. Understood. As a bonus on the plus side the pressure drop from expansion cooling of the gas is less. On the flip side the disadvantge is higher pressure on the o rings for higher friction and faster leak down rate for any leaks. This is a trade off.
Whether the force is constant or high impulse next comes into play. With lower peak force for longer constant force the piston acceleration becomes an issue. We are already conserned on projectile motion while the pressure is building.
This design has high piston mass. Releasing the same energy into a much smaller piston would require higher peak velocity and shorter travel time. It is simply quicker. The above design eliminates the ineffeciency of a high speed air valve and small port by simply allowing the high pressure container (piston chamber assy) to move without using a valve and associated port. This is again a trade for porting for mass.
This leave us with the problem of the relatively slow mass compressing the space in the air cyliner to the projectile. It takes time to build speed and will need a relatively short stopping distance to make high compression to launch the projectile. The need for the ports and such become very real. The need for a large diameter piston becomes real compounding the mass problem. This also creates a porting problem to effeciently move this mass of air into the barrel with that transition zone.
I'm not sure that design will support the 30% or greater effeciency due to the impulse energy transferred to the frame as this high mass component accelerates and comes to a stop.
I think the newer design of the airowgun is more the line I was thinking of using an air cannon to shoot a piston into a smaller diameter cylinder at high speed producing compression heating and energy transfer to the lower mass projectile with low energy loss.
The lower mass piston in the newer design doesn't need the vents and can operate directly with the accelerated piston.
Thanks for the info. Insightful as always.
For my current setup, If I changed nothing except for the piston mass, What do you think would be a piston mass that could support 30%?
The 50 gram weight I gave was for the much longer stroke pull, 25cm, I have given up on that, and now, with current materials, I think I can achieve 30 grams. If I changed the PVC to aluminium, maybe I could get it lighter.
I think it comes down to: you want to compress as much air as possible, as quickly as possible, down the barrel, and how fast the air is compressed is a function of the piston's speed and the chamber's diameter.
Could I put it in these kind of terms?:
The desired muzzle velocity will tell us how much time it should take for the bb to go from displacement=0 to the very end of the barrel. Can I simply design a piston that moves an amount of air equal to the volume of the barrel, in that same amount of time? So figure out, how fast the piston must travel for my cylinder's 3.02cm bore. If I take friction into account, that kind of calculation should work shouldn't it?
Oh, but because of the bb's inertia it will not start moving straight away, some pressure will have to build up... God, if only there was some magical formula for this... Maybe once I figure this out I can make a fairly easy formula for others to use...
Thinking of it now, if I calculated the time of inertia, or the time it takes for the bb to start moving, and come up with a figure for its friction as well, then I could calculate how much compression has occurred in that time, as the piston has been moving, and therefore find the force on the bb due to change in pressure. Then I would have initial force. Because I know what the average force has to be on the bb to make it go my desired speed, I can also figure the final force, and therefore, make a force vs time graph, a velocity vs time graph, and because I know the force needed at any one time, I also know the pressure needed at any one time, so I can calculate how far the piston has to have moved in order to get that pressure.
Sorry, I was just thinking aloud and writing it out. Helps me figure stuff out.
ok, just ignore most of what I say, but this is important: When air pressure force acts on a bb, is the area the force acts on half of a sphere with radius 3mm, or is it just a flat circle with radius 3mm?
Also, if my air nozzle (exit of cylinder) has an internal diameter of less than 6mm, is that going to decrease the force exerted on the bb for a given air pressure?
I haven't read most of this thread so disregard my post if I'm ignorant to anything discussed in particular. I'll read the remainder later today.
Based on the limited data I've seen for Nerf guns I'd estimate that a low efficiency for a standard spring gun is 20%. A modified Nerf Crossbow is about 35% efficient from what I remember. I'm completely confident that by adjusting the parameters of a normal spring gun, efficiencies in excess of 60% are possible.
As a general rule, ignore most suggestions about efficiency unless they have cold hard numbers to back them up in some way or another (through testing or simulation). Even if they use some logic that seems valid, I still wouldn't trust it as there really are too many things going on. And if the numbers are from simulation, remember to take them with a grain of salt, especially if they are above about Mach 0.5 (the high speed limit applies primarily to simpler simulations--simulations designed to be accurate in the transonic range still are suspect due to the complexity of the problem, but much much less so than simpler simulations).
Also, in terms of efficiency, slight reductions in flow won't effect the final efficiency at all or significantly. It is easy to run simulations to note that often increasing the flow coefficient of a valve by an order of magnitude doesn't do anything. Get 90% of the way there--the last 10% shouldn't make a significant difference and it'll be annoying or hard to get.
As for trying to adjust the parameters to get maximum efficiency... this is where simulation comes in. This motivated the writing of my simulation as adjusting each parameter to see how it affects performance isn't practical in reality.
Last edited by btrettel on Tue Sep 15, 2009 1:18 pm, edited 2 times in total.
All spud gun related projects are currently on hold.
Thanks for the input man. This gives me hope
Those NASA links are just what I was looking for, I need to learn about flow dynamics and couldnt find anything on the web. Is there a better thing to type into google to get results on this kinda stuff?
Im reading your WIP book by the way, looks like it could be amazing.
(Getting the internal ballistics of spring guns bit in there would be nice for me
Here are a couple very quick sketches and some theory to chew on.
In this I didn't bother to give dimensions as things can be scaled. For some background in physics, in an elastic (springy) collision of two masses of equal weight, the acceleration of one object takes the velocity of the other mass and leaves it at rest. See Newton's cradle for more info. In an inelastic collision of two equal masses, the center of mass conserves the motion and energy is lost in the collision so the total center if mass still travels at the same speed, but the combined mass travels at the same average momentum which is 1/2 the speed of the first mass. (translation, they stick together and the average speed of fast and stopped is the final speed or 1/2 the initial speed at 1/2 the mass.)
Umm if its twice the mass and half the speed, isn't it the same energy???? Um no. 1/2 the energy was dissipated in the impact and converted to heat. Doubling the velocity increases the energy 4X.. Energy is related to the square of the velocity.
Now on to the sketch. Examine the first sketch. Springer cheezy sketch 1.
Back to the Newton's Cradle toy.. one ball stops and the energy bounces down the row of balls and the last one takes off with all the energy. Too bad we can't stick a lever in there and have a slow ball lever up speed and kick a low mass ball with lots of energy and bring the big one to a stop. Hmm maybe we can.
In the drawing I have a flying piston launched from an air cannon about to slide nicely into a chamber. At the other end of the chamber is a small piston at rest, but the same thickness as the flying piston. Let's see what happens.
1/2 way into the cylinder the air pressure rises from atmospheric to 2 atm. 3/4 the way in the pressure is rising to 4 atm. 7/8ths the way in the pressure is 8 atm and at this point the little piston is getting the idea that it should get serious about picking up some speed and getting outa there. At low pressure it wasn't too excited about getting up much speed so it hasn't moved far yet.
Let's see what our peak pressure may possibly be. If the decelleration zone is 1/4 the length of the air cannon that launched it (assuming a perfect world.. boy am I in for a lesson.) the piston should come to a nice halt at 4X the air cannon pressure because it stopped in 1/4 the time. Ouch sudden stop. Then the air spring would reverse the process and launch the piston back with the same energy except, the little piston moved.. Remember the little piston at the same thickness as the big piston? As the pressure was building it was getting more and more acceleration and it's outta here. Because of the large diameter of the large piston, it has a lot more force on it than is on the little one, but it has 4X the mass. For energy, the compression on the little piston is not like Newton's cradle with a like mass hitting a like mass. It's like a big mass hitting a lever.
See second drawing, Springer napkin engineering sketch 2.
The gas that is compressed provides an elastic collision between two dissimilar masses. The two masses have different areas, so the force from the pressure is different by 4X for a 2:1 diameter difference. This is our gas lever. Both pistons are the same length. I simply shaped one to fit the end of the chamber better to reduce flow problems into the smaller diameter (told you it wasn't a perfect world).
Due to laws of conservation of energy.. the energy through this lever action is transferred to the little projectile. Does it go 4X as fast?.. It can't. Remember the energy needed to double velocity? like energy related to velocity squared? OK 4X the energy will give you only 2X the velocity.. 600 FPS to 1200?? I'll take it.
What about supersonic?? Something about speed of sound, compressed air.. darn that again. So much for a perfect world. sigh.
Wait a minute.. Doesn't compressing air heat it and raise the speed of sound? Um yes..
Can air that goes through the transition under pressure then re-expand as the pressure drops.. and the heat drop due to cooling from expansion.. Yes again. You get the energy back if you haven't lost it along the way.
OK you've heard me ramble.. Now go build something.
I'm open for discussion.
A complex shape round, square, star, sphere, etc. Only the cross section area counts. For a sphere, it's the diameter area. In simple terms a quarter and a ball the diameter of a quarter has the same cross section for pressure.
More reading material
The teeter/totter sketch is what I thought of to speed up a sling shot.
Instead of a heavy slow mass, use a powerful sling shot at 200 fps.
Top end commercially available gas ram, max ft/lbs circa 27
Top end commercially available pneumatic, completely different league, no recoil and no mechanical effort.
This post will be long and rambling, so I apologize in advance. I did cut out a lot, but it's still a mess. There are some good bits if you read all the way through though.
lozz08, I'm not sure if I can help you much about understanding interior ballistics. What do you know?
To understand how to write a simple simulation (like BAGS is right now) you need a background in calculus, basic knowledge of thermodynamics, an ability to work with conservation laws, and an ability to numerically solve systems of ODEs (generally not hard, but some people get queasy when they see any DEs or programming). For a more complicated simulation that is accurate in the transonic range, you basically need graduate level engineering knowledge. Writing a simulation that can handle this is a research level project, hence the research papers I've linked to.
I can give you some great book suggestions if you want to learn the basics. PM me if you're interested.
As a general note, there are VERY few recent books about interior ballistics (most I've seen were written in the 50s or 60s). I have never seen a book detail the simple approach I take in BAGS. They all jump directly into a more advanced approach, generally using the method of characteristics. (Okay, I'll take this back as I do recall one linked off my website that finds a relatively simple analytical solution to the problem, but as I recall it uses restrictive simplifications, linearizations and/or small perturbations of the equations, which would basically make it good only for a rough guesstimate. There is no way to make an analytical solution to this problem without what I've mentioned. There are far too many non-linear equations. This is why fluid dynamics is a very active research area.)
The lack of recent books on interior ballistics was part of what motivated me to start the book on my website. I'm glad you like it. I didn't even know anyone took a look at it. This weekend I'll write a chunk, though, I've intentionally been avoiding the interior ballistics parts until I fill in some of the gaps in my knowledge about it. I don't know everything; if I did my simulations would be extremely significantly more advanced. Don't worry--I'll write them eventually.
To expand on what Technician said about the direction of the force on the BB, pressure always acts normal (i.e. perpendicular to) the surface. So at the center of the BB, the pressure force acts down the barrel. But, on the side it might act down, up, right, left, or a combination of those. Why doesn't that increase the force? You must look at the components of the force; here there are components down the path of the barrel and perpendicular to the path of the barrel. The force in a direction perpendicular to the path won't accelerate the projectile down the barrel, rather, it'd push the projectile against the barrel wall. So the only component of the force that matters is that which is directed down the barrel.
I wouldn't worry much about making the force constant. Pre-stressed springs can be problematic. I think one of the reasons a gas spring is desirable is that it can be stored unstressed (i.e. unpressurized). Pre-stressed coil springs put stress on the frame even when it's not in use. Not to mention that you have to design a way for the spring to be compressed into where it's held. As these springs are very powerful and not to be messed around with, I can not suggest a prestressed spring for that reason alone.
Constant force springs do exist, but again, I wouldn't worry much about it. They'd be a serious pain to work with. I'd suggest normal coil springs.
All spud gun related projects are currently on hold.
Yeah, THAT will get into Australia, no problems. I'll just buy one and see what happens. That's why I'm building one, to avoid having to get a gun license, seperate safes to store the gun and ammo, having to join a gun club, police visits, it goes on.
So can this lever system work when my fore behind the piston is constant? Or fairly constant, at the beginning, it has about 120 N force behind it, and at the end of the chamber, it has about 130 N behind it.
I think I've already decided upon my mechanism. The main piston, weighing in at 35g, is propelled for 6cm down the air cylinder, at an average force of about 125N. During this time, there will be negligable force acting on it in the opposite direction, because the port holes in the cylinder stop any compression before the 6cm mark. Once it has gone 6cm, it starts compressing. It will compress air for another 6cm. The end of the cylinder is shaped like the diagrams you have up there for good flow. The cylinder has a 3cm inner diameter. The diameter of the seat or the step to the air nozzle is only 4.5mm. If my barrel length is 50cm, do you think you should crunch some numbers and give me a rough estimate for how much energy the bb should get? (0.25g bb) Its too complicated for me with changing pressure and such.
If you have enough money
I was looking at one of these for the bb/whatever competition if it goes down. If not I'll just use a QDV with compression heating.
Yeah, I have some fairly basic physics knowledge, Im still in my last year of hi school, I'm pretty good at calculus though.
The spring I'm using isn't a coil spring, it actually is a constant force gas spring, the design for which I'm stealing from Theoben. So I can just de-pressurize it whenever I want.
Thanks for the link. This is what I tried to draw on my cheezy sketches.
This is exactly what I was looking for. At lower pressures from an air cannon, the compression cone would be much less aggressive and would resemble a straight pipe more than an obvious cone due to lower compression.
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