SpudFiles

I'm planning on optimizing a new small air gun of mine for efficiency at a certain range. This required me to write some rudimentary computer models of the internal and external ballistics of an air gun. Those parts are done for the post part, however, what is not done is figuring out the best configuration for efficiency.

Maximizing the efficiency of a projectile is relatively easy. I basically have to make it as aerodynamic as possible and figure out the optimal mass for the least required kinetic energy to get a certain range. My external ballistics model can do this rather easily.

The efficiency of the pneumatic gun is harder to optimize in comparison. Some things like high flow valves, fast opening times, low dead volumes, etc., are obvious and after a certain saturation point improving them will make little or no difference in efficiency.

I'm focusing on what can make a difference after that. Varying pressure and air chamber volume is basically all that's left. Looping through different chamber volumes to find the minimum pressure required to get a certain muzzle velocity, I can find a maximum, but the efficiency is still rather low. For a small gun like what I'm interested in, 25% efficiency is looking excellent, and if I remember correctly I could get 33% if I had nearly no dead volume.

Is there anything else I can do to improve efficiency beyond this? I've searched a great deal and can't find much about fixing performance and maximizing efficiency for that level. Most people seem interested in maximizing performance rather than efficiency.

There's a few things I'm going to look at:
- barrel length (right now I'm fixed at 12 inches for simplicity)
- extremely high flow valves (this may be impractical)
- smoothing out the inside of the pipes and reducing bends to reduce pressure drop (this likely won't result in any substantial gain)
- projectile mass (perhaps a heavier mass would increase efficiency enough to offset the projectile's inefficiency)

For a given amount of potential energy in your chamber, this can take the form of relatively low pressure and high volume or relatively high pressure and low volume. Can your model find the optimal balance between volume and pressure if energy is kept constant?

Chamber energy can easily be calculated from the ideal gas law and work-pressure-volume relationship, as my model does. To my model, efficiency is the kinetic energy of the projectile over the energy of the air chamber plus the energy of the pilot volume. My model fixes kinetic energy and figures out the required pressure for a certain volume to get that kinetic energy. The chamber energy varies for different volumes (with the corresponding pressure to get the projectile kinetic energy). This is how efficiency varies for different volumes (and the associated pressure) to get a fixed level of performance.

If this is confusing at all I can explain in more general terms.

Well explained, I think I get it. Does your model take into account the fact that the chamber energy does not equal the projectile energy since a non-optimal barrel length will result in pressurized air being wasted after the projectile is gone? Also, like I think you mentioned in your first post, a heavier projectile will yield greater efficiencies (i.e. decreasing mass does not return as much increase in velocity as the conservation of kinetic energy model would suggest)

Yes, my model takes into account that the chamber energy does not equal the projectile energy. To say the two are equal is to assume 100% efficiency.

Here's a link to the code of my model: http://www.spudfiles.com/forums/compute ... 16861.html

There's been a few changes (all detailed in the thread) but it's essentially as described there.

I'll look at heavier projectiles too. That was on the list.

My quick look at a barrel that's 50% longer than my standard shows slightly reduced efficiency (about 1% loss). I'm now checking out a barrel that's about 33% shorter. These are rather time consuming calculations because I basically loop my model until the desired muzzle velocity is met. Brute-force methods like this are slow but work.

Have you seen GGDT? It may help you.

Yes, I have seen GGDT. It is a great program, but I will not use it for this. This is a DIY hobby, and I extend that to everything within reason. Also, as an engineer I feel a need to know what's happening. Perhaps most importantly, GGDT doesn't do what I want to do here as far as I can tell.

Another problem is that I run Linux and I don't particularly feel like futzing with Wine to get GGDT to work. I know it'll run because I've done it before, but I don't feel like doing it again.

So you are optimizing for the smallest potential energies in the chamber to obtain a specific performance with a certain sized barrel?

One way you can boost efficiency (assuming you will be shooting multiple times) would be to not use all of the air in your chamber, because after your projectile leaves the barrel any air that leaves the chamber following that is completely wasted.

A little self tooting...
I built a valve I call the HEAR valve that is made to open and allow high flow while still being able to close before the chamber is completely evacuated. The relative dimensions can be adjusted to control when it starts to close. It also helps boost efficiency by eliminating the need to exhaust pilot air. You can see my only implementation (so far) of the valve on my <a href="http://www.spudfiles.com/forums/gb-semi-t7899.html">GB Semi</a>.

Another thing to consider is that your equation for potential energy in a gas accounts for the work needed compress the gas further, so if you take a given chamber and half the volume and double the pressure it has more potential energy. While this does actually happen, it is often not representative of the actual conditions. Since most spudguns are filled from a pre-compressed reservoir, such as bottled gas or a compressor storage tank, the compression is already done. So as long as you are under the maximum pressure of your supply, reducing the chamber volume and increasing the pressure of the gas to maintain a constant PV will result in the same amount of energy taken from the storage tank regardless of which PV you choose.

Yes, I had actually started looking at the GB Semi today when I saw you post in my other thread! The idea is very sound. I'm hesitant to make my own valves because I don't have a lathe, but my university has one and then some, so I figure there's no reason to not use what's available to me.

I've actually been thinking a good deal about the air that shoots out after the projectile leaves. It's very substantial according to my model. If I can figure out how to close the valve when the pressure hits a certain level (i.e. the level the projectile leaves at), this should increase efficiency greatly. Your implementation is the only one I've seen so I intend to study it.

Are there any other implementations of this valve or valves with similar goals?

Edit: Could you explain your last paragraph further? I measure the potential energy as the work from decompressing the gas to atmospheric pressure. Is this not correct?

Edit #2: I've already thought of a small improvement to the HEAR valve (though it likely has been mentioned already). When the valve closes is controlled only by the geometry in the original design. Adding a spring and a knob to adjust the displacement will allow the valve to close at different pressure levels.

If you're determined enough, you would be surprised what you could make without a lathe. I made several guns that required o-rings before getting my lathe, but if you do have access to one it would certainly make things a lot easier.

As far as I know the GB Semi is the only gun using a HEAR valve at the moment. I have plans for other guns using it but those are very far down in my things to do list, and I don't remember seeing anybody else build one. No telling when I'll have it up, but I've been working on a writeup that outlines the design procedures and things to consider when making a HEAR valve.

There are other valves that close before the chamber is vented. If you seal the piston completely in a normal piston valve you can either put a spring behind it or use an air spring. Then by raising the chamber pressure the valve will eventually fire, let out some air from the chamber and close before all the air is exhausted. Like the HEAR it can be controlled using geometry changes. This is very similar to how commercial pressure relief valves work. There are a few implementations of this, but the only one I can think of off the top of my head is from Brian the brain, he called it a "snap valve" I believe.

A similar method has also been proposed and <i>maybe</i> used a time or two that uses a standard piston valve, but only partially exhausting the pilot air (by allowing it expand into a larger volume). Once the chamber pressure reaches the pressure that you exhaust to the valve will start to close again, you just have to make sure the geometry allows the valve to fire with whatever exhausted pilot pressure you go with. I believe Hotwired wrote up a post discussing this idea (or something similar) a while back.

You are right in your calculation of potential energy, but what I am trying to say is that the potential energy you are calculating isn't significant to most spudding situations because the work done to compress the gas is already done, so you may need to consider the performance as it relates to the volume of air used rather than the theoretical potential energy.

I'll try to give an example.
Lets say you have reservoir on your compressor at 150 psi and you want to examine the performance of:
10 in^3 chamber at 10 psi
or a
1 in^3 chamber at 100 psi

We'll just use 15 psi as atmospheric
The PE of the large chamber is 10*25*ln(25/15) = 128
Small is 1*115*ln(115/15) = 234

Or very roughly twice the PE in the small chamber. Lets say these two chambers are on a gun such that the smaller chamber launches with about twice the kinetic energy of the larger chamber, so when you run through the efficiency calculation you would get about the same efficiency for both chambers.

However, just because they have the same efficiency doesn't mean they are equally desirable. Since they use the same volume of air both chambers will drop your reservoir pressure by the same amount, but you get twice the power out of the smaller chamber. So basically what I am trying to say is that most of the time when people talk about an efficient pneumatic gun, what you really want is the maximum kinetic energy per ammount of air used. If you use a constant PV for any given ammount of air then performance will always increase as P increases, so you'll always want to use the highest pressure that your pressure supply can output (or the highest pressure you gun can safely withstand) and you'll only be left looking for the most kinetic energy per chamber volume, which would be an interesting figure to look into.

There may be some exceptions to this... I suppose if you are using a hand pump then KE/PE may actually be a relevant figure since the PE represents how hard the pumping will be.


The spring and the knob would probably work great on smaller HEAR valves, but as they get bigger the spring would have to be applying a lot of force to change pressure levels significantly. For mine a spring applying 20 lbs would change the closing pressure by about 6 psi. It is certainly something to think about, thanks for the idea.

Edit: Ugh, sorry about the long post, I was trying to keep it brief

btrettel wrote: Some things like high flow valves, fast opening times, low dead volumes, etc., are obvious and after a certain saturation point improving them will make little or no difference in efficiency.

They are obvious because they make the most difference.

If you want to make the most use of the air in the chamber, go for a burst disk or valveless design.

Edit: Ugh, sorry about the long post, I was trying to keep it brief

That's fine. If you have something to say and it can't be said in brief, say it. I read through that in about a minute, which isn't unreasonable.

I'm fixing muzzle velocity and figuring out acceptable pressures and volumes after that, so the efficiencies I'm looking at should be directly comparable. Because the goal is to reduce total air consumption, I first must choose an acceptable level of performance before looking at efficiencies. Perhaps it would be most wise to look at simple air volume rather than energy though. There might be a deviation.

They are obvious because they make the most difference.

No, actually, they don't make much of a difference in efficiency beyond the saturation point (according to my model at least). I'm already at these saturation points so I'm looking for other suggestions.

Valves that close early in comparison don't seem to have any limit beyond what is practical. Edit: I'll revise this statement. My math earlier was incorrect. Valves that close early like the HEAR valve can and do help, but to a much more limited extent than I had believed and only in certain configurations. In some configurations that type of valve would hurt efficiency (marginally) because the projectile's momentum starts pulling a vacuum. Let me investigate further before making any statements about their efficacy. I also intend to investigate valves that close before the projectile leaves the barrel because I think these might be the most efficient.

Because I'm looking at a semi-auto design, burst disks would be impractical, but higher flow valves are something I'm considering. Efficiency increases very slowly after a certain point, but it does still increase slightly, so I'm thinking an ultra-fast and extremely high flow valve could improve efficiency.

The valveless design I find very interesting, but it's not for this project because my projectiles (Nerf darts) won't seal under pressure. Maybe I'll design another gun around that design. Thanks for the link.

btrettel wrote:I'm fixing muzzle velocity and figuring out acceptable pressures and volumes after that, so the efficiencies I'm looking at should be directly comparable. Because the goal is to reduce total air consumption, I first must choose an acceptable level of performance before looking at efficiencies. Perhaps it would be most wise to look at simple air volume rather than energy though. There might be a deviation.

Well as long as you are supplying air from a pre-compressed source what I said still applies, and if you are fixing muzzle velocity then optimizing for total air consumption is very strait-forward and easy. Use the highest pressure that your supply can output or that your gun can handle, then simply find the chamber volume that gives you the desired muzzle velocity.

If you don't believe me that using the highest pressure you have available is most air efficient it should be pretty simple to check yourself. Use whatever chamber volume and pressure you are calculating as most energy efficient and calculate P*V for that chamber. Now assuming that your "optimized" pressure is less than your maximum allowable pressure, model your gun with the highest pressure you have available and decrease the chamber size until you get to your desired muzzle velocity. Then calculate P*V for your highest pressure. I can almost guarantee that P*V for the higher pressure will be less than the other P*V, if it is not then either I need to check my head or you need to check your model. Lower P*V means less air used from your reservoir.

Yep, higher pressures do result in higher air efficiency, at least assuming an isothermal process. I'm in the process of changing my model to assume an isentropic process but that shouldn't change the total much or the trend at all.

Also, I'm not sure a valve that closes when the projectile leaves is worthwhile in most cases. My modeling so far indicates that unless you make an oversized chamber at low pressure you're not going to save any air, and it'd still only be about as energy efficient as a normal valve at its optimal configuration. Something to keep in mind.

btrettel wrote:Also, I'm not sure a valve that closes when the dart leaves is worthwhile. My modeling so far indicates that unless you make an oversized chamber at low pressure you're not going to save much or any air. Something to keep in mind.

It depends what you are looking for, if you have higher pressures available it is far easier to just use raise your pressure to increase air efficiency, but if you are stuck with a compressor that goes to 100 psi then a fast closing valve is really the best option for increasing efficiency. With a self closing valve the efficiency will increase with increasing chamber sizes, but it also increases all the dimensions of the gun. Note that I am talking about air efficiency and not energy efficiency.

It's primarily for increasing performance without sacrificing efficiency given a barrel size and maximum pressure. Say you want a 3 foot barrel and only have 100 psi available. The only way to increase performance at this point is to make the chamber larger, but as you increase the chamber size you end up wasting a ton of air. A self closing valve allows you to get the performance of a large chamber with much less air usage.

Basically if your desired performance level needed a chamber to barrel ratio of 1:1 or higher at your maximum pressure and you didn't want to increase barrel length then a self closing valve would start looking like a good option.

Edit: Or if you need an automatic/very fast semi-auto valve.