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Don't understand the physics

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Don't understand the physics

Unread postAuthor: lozz08 » Wed Aug 26, 2009 9:09 am

I'm making a spring-loaded sniper rifle. With 0.2 gram bb, I want 650 feet per second. (maybe I should use at least 0.3 gram?) I've got a chamber with a plunger pushing down it. The chamber is 4.23 cm cubed (it is 1cm steel pipe 3cm long) the space behind the bb is 1.41 cm cubed with the plunger all the way.

I wont bother you with all the calculations, but I used the formula mass X velocity squared = change in pressure X change in volume.

I got my calculation of needing 3 atmospheres of pressure to get my bb going 650 fps, which is 44 PSI.

What I don't get is this: How can the work done by gas be for the whole length of the barrel when, the volume of the barrel is way more than 3 times the volume of the little space behind the bb before it starts moving, and therefore the pressure of the gas should be only one atmosphere after only a little bit of travel down the barrel? shouldn't it stop then? Just doing my head in a bit.
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Unread postAuthor: Mr.Sandman » Wed Aug 26, 2009 9:17 am

My advice dont try to build it. I dont think you will get 650 fps and if you do it will probably cost more than just a store bought sniper. Unless you have a machine shop at your disposal then this will be near impossible to get perfected. Also why do you want 650 fps?
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Re: Don't understand the physics

Unread postAuthor: D_Hall » Wed Aug 26, 2009 9:20 am

lozz08 wrote:the volume of the barrel is way more than 3 times the volume of the little space behind the bb before it starts moving,

Ask yourself this question: Is the volume of the barrel way more than 3 times the volume of the chamber the air starts out in?
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Re: Don't understand the physics

Unread postAuthor: Ragnarok » Wed Aug 26, 2009 5:37 pm

If at any point, you're confused about the physics of how something works, that will mean you're almost certainly doing the maths wrong.
While some people on this forum are capable of correctly doing such calculations themselves, they are rather few and far between. Of our regulars, I could probably count them on one hand.

My advice, click on the link for GGDT in D_Hall's signature above, download and unpack it, then do the calculations with that.
Just make sure you don't get confused over the "Outer and Inner chamber diameter" issue.

~~~~~

As an actual note, I would note that you seem to be mixing absolute and gauge pressures, and that's going to cause errors.
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Unread postAuthor: lozz08 » Thu Aug 27, 2009 1:21 am

What I was doing, which is pretty funny, was using pi times diameter squared not pi R squared. Lol. Anyway, I couldn't possibly buy and airsoft sniper in Aus, its all illegal. With my "proper" calculations, I got 0.27 cm cubed behind the bb before it fires, and a 2.36 cm chamber. This gives me a pressure of about 9.8 atm. The force on the plunger head becomes about 17 pound, so at full extent I'll have the spring pushing with about 20 pounds for good measure. With that pressure I calculated that in a perfect world I'll get over 550 fps with an 0.3g bb. Thats about 8J of kinetic energy, the top-of the range airsoft snipers have about 6J.

Heres the hard part: How much kinetic energy should I lose due to friction and pressure loss along 35cm of tightbore barrel? Im getting a hopup kit and barrel sent to me covertly so theres no problems there.
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Unread postAuthor: btrettel » Thu Aug 27, 2009 8:46 am

GGDT won't do what lozz08 wants as it doesn't do spring-plunger guns. I plan to do that in BAGS eventually but I haven't started writing that yet.

lozz08, I'm not quite sure where you get the formula from. Both sides do return units of energy, but that doesn't mean they represent anything.

An energy based approach is great for a quick-and-dirty approximation however. Assume a low efficiency of like 5% and I don't think you'll be dissatisfied with the performance. This can be used to quickly discredit some performance claims as well (if it requires greater than 50% efficiency, it's extremely unlikely to exist in reality--greater than 100% is simply impossible as well).

You probably know that spring PE = 0.5 * k * x ^ 2 where k is the spring's stiffness and x is the displacement from equilibrium. Projectile KE = 0.5 * m * v ^ 2 (the 0.5 in both of these expressions IS important but cancels out in the final expression here). Since the total energy that ends up in projectile KE is the PE multiplied by the efficiency, you can use the expression n * PE = KE where n is the efficiency.

Solving that expression for v...

v = sqrt(n * k * x ^ 2 / m)

This would be about as good of hand calculation that could be made.

Note that the efficiency definitely varies from gun to gun and very much so within a gun depending on essentially every factor. This is a quick estimate only and I think would be most useful to make sure a gun gets a certain level of performance by assuming a low efficiency and then seeing what'll get you your desired performance) if you don't do any other calculations.
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Unread postAuthor: Ragnarok » Thu Aug 27, 2009 9:25 am

btrettel wrote:GGDT won't do what lozz08 wants as it doesn't do spring-plunger guns.

It's not that hard to get it to model such things.

If you solve the equations for the compression chamber to get a gas pressure, temperature and volume, and feed those into GGDT, the answers are more than good enough.
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Unread postAuthor: btrettel » Thu Aug 27, 2009 10:45 am

That would be one way to do it that I had not considered, but I'd be wary of the results as the plunger's movement to the end of the cylinder would take a significant fraction (if not even more time) than the projectile takes to leave the barrel. It's worth mentioning nonetheless and definitely is better than the simple energy approach.
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Unread postAuthor: Technician1002 » Thu Aug 27, 2009 11:27 am

btrettel wrote:That would be one way to do it that I had not considered, but I'd be wary of the results as the plunger's movement to the end of the cylinder would take a significant fraction (if not even more time) than the projectile takes to leave the barrel. It's worth mentioning nonetheless and definitely is better than the simple energy approach.


This factor was a strong design consideration when I built my launchers. I had a design goal of keeping the piston mass close to the projectile mass so the piston would be fully open in the same time the projectile would have moved a couple inches maximum. Size, weight, and material density were all considered in selecting a piston. Great point. Thanks for pointing it out.
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Unread postAuthor: Ragnarok » Thu Aug 27, 2009 12:11 pm

btrettel wrote:The plunger's movement to the end of the cylinder would take a significant fraction (if not even more time) than the projectile takes to leave the barrel.

Actually, given that the pressure doesn't really start to build up all that dramatically until the piston has travelled most of the distance (and it is then at some speed, covering the final distance very fast) the piston is usually near the end of its travel before the projectile has moved any significant amount.

The fact that springer air rifles record better energies with lighter pellets than heavier ones (up to a point) is decent evidence that the "projectile leaving the barrel too fast" is normally a non-issue. (As for why the heavier ones are less energetic, blowby and heat loss are both parts of it.)

If you do it as I suggest, it will slightly overestimate. However, it's normally "more than good enough".
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Unread postAuthor: btrettel » Thu Aug 27, 2009 12:43 pm

Technician, this is about springers, not piston pneumatics. They're different. Though it's rarely bad to have a low weight piston (vibration and bounce are two potential issues off the top of my head).

Rag is right; that is the case in good springers. Too little static friction is bad as the pressure never gets a chance to build. Adding a burst disk to the springer would be even better (though fairly silly).

Modeling the gun as a burst disk pneumatic (as there should be little flow restriction between the chamber and valve) and ensuring the physical gun has high static friction (for the initial part of the barrel, at least) should be reasonably adequate upon further thought.
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Unread postAuthor: lozz08 » Fri Aug 28, 2009 7:02 am

Ok guys I think I know what's going on. The volume of the barrel is 9.9cm cube. I calculated that if I want the bb to be at 650 fps at the end of it, it would need to accelerate at 57143 meters per second squared, giving it a total time in the barrel of 3.5ms. Now I know this is all theoretical, but I'm still in high school for god's sake, my brain can't handle much. So If we want the bb to get to the end of the barrel in 3.5ms, then we have to move the volume of air in the barrel behind the bb in that time. To make it easier I decided to make my chamber way bigger in diameter to give the shortest plunger stroke possible, and hence reduce friction.

So I calculated that for a chamber 3cm in diameter, I would have to move the piston/plunger 1.4cm in 3.5 ms, let's call it 1.5. So its acceleration must be 2500 meters per second squared in order to do this. I realise 50 grams is a way heavy piston and I probably will have it much lighter, but I'm just crunching numbers here. So in order to accelerate a 50 gram mass at an average 2500 meters per second squared over 1.5cm, I calculated a needed average spring force of about 125N needed, I dont have the exact number on hand. Call it 150N for efficiency.

So that sounds like it could work, but wait, there's more.
In order for the spring to give an average force of 150N over 1.5cm, we have to do some calculations, as the spring force decreases as it is released, f=Kx. I don't know how big the spring should be or anything, thats the problem, and what is worse, is the complication that, in order for my piston to accelerate so fast, the spring force must be acting on it for the whole 1.5cm, and if this is the case, then the spring must also accelerate at an average 2500 ms2, in order to make contact with the piston for the whole time, which means the spring must be sufficiently light, but also powerful enough. So to find the right spring, I'm just stuck as to how to calculate it. What would be a good mass, spring constant and deflection length?
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Unread postAuthor: lozz08 » Fri Aug 28, 2009 7:20 am

ffs double post

sorry,
so you were saying that the bb doesn't start moving until the piston is close to the end of its needed distance? in that case, maybe I wouldn't need such a high piston acceleration... And I have no idea how I'm gonna find out my efficiency, so I guess a lot of this will be trial and error. At least I'll only be rebuilding pistons and chambers, and replacing springs, so it won't be too costly.
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Unread postAuthor: Ragnarok » Fri Aug 28, 2009 11:06 am

lozz08 wrote:I calculated that if I want the bb to be at 650 fps at the end of it, it would need to accelerate at 57143 ms<sup>-2</sup>

I'm a little surprised at the mixing of metric and imperial units, but we'll move on.

We're looking at an average force in the barrel of 11.4 Newtons for a 0.2 gram projectile to reach 200 ms<sup>-1</sup> at the end of the 35cm barrel. In other words, an average pressure of pretty much exactly 400 kPa (or 4 bar, if you prefer).

It's easily possible for spring piston power-plants to reach those average pressures. For example, my air rifle works at average pressures of around 3900 kPa, around 10 times as much (with the potential for more).
However, my air rifle is built like a tank, weighing 10 pounds. And it needs to be, given the forces involved in a spring rifle of that kind of power.

The important thing is that the compression chamber should have a volume considerably larger than that of the barrel, which isn't the case here, as you seem to have a 1:1 ratio.
On my air rifle it's something like 20 times the volume of the barrel. That's not automatically necessary, but you will need a larger compression chamber.

I'd also advise caution as far as spring pistons go. My attempts to build one cost me a sizeable chunk from the side of one of my fingers when the mainspring came loose and crushed it.

so you were saying that the bb doesn't start moving until the piston is close to the end of its needed distance?

Exactly. The BB won't start accelerating very fast until the pressure has started to build up, and that doesn't happen until near the end of the piston stroke, when the piston is already moving at speed.
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Unread postAuthor: lozz08 » Fri Aug 28, 2009 9:45 pm

Hey, thanks a lot for all the tips. My air chamber is actually a diameter of 3cm and a length of 15cm, I just calculated it would need to go 1.5cm to move the needed volume of air. I'm pretty sure I'll be using a spring with total compressio of 15cm, at 11N/centimeter, which would give me 165N at displacement of piston=0, and just under 150 after the 1.5cm. After that, if the bb hasn't left the barrel, any extra volume it pushes is a bonus I suppose. As you said you can't expect very high efficiency so I might need the extra.

And yeah, the systems get confusing, but it's mostly because all the info I find on the internet is with pounds/sq inch and stuff like that.

So do you think my 15cm chamber and spring setup will get the job done? I'm aiming at at least 6J of energy for the bb leaving the barrel.

Also, for my piston I was just gonna have a bit of pvc with an o-ring around it, like a plunger. Is that viable? is there some other way of making the piston airtight that is more economical?
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