[Deviant]

Can anyone tell me the formula's that I need to calculate the output air pressure from a cylinder/piston/spring setup.

IE, If I have a cylinder that has a diameter of .5 inch, with a length of 1.5 inches. How strong will the spring need to be to output X pressure from an nozzle with a diameter of 3mm.

((The numbers can and will need to vary, but I'd like to know the formula's so that I can calculate the desired air pressure.))

Also, I'd like to know how to calculate the pressure needed to move an object at a specific weight to a specific velocity within a certain distance.

I hope someone can help out. I vagulely remember doing similar calculations long ago in school.

Thanks.

[Al_The_Man]

Here is what you might need http://www.team116.org/2003/lessons/...Pneumatics.pdf
Al.

[Deviant]

Very close to what I need.

I actually need to calculate the air pressure generated by a spring powered piston. Not the force generated by an air driven piston.

It could be that the formula's on the page will do what I need. However, it's making my head hurt thinking of how convert them for use.

[2muchstuff]

It has been a while for me too, but here goes:

.500" piston bore
area of a circle: pi(r*r)

A=3.1415(.250*.250)
A=3.1415(.0625)
A=.1963 square inches

100 pounds of applied force to this piston will give you 19.63 pounds of force. The amount of force will be the same whether it is mechanical or pneumatic. As for the amount of pressure at the nozzle, it will be the same no matter what size it is. All a nozzle does is regulate/restrict the amount of flow thru it.

In moving an object, a few other factors are involved. One is the amount of friction between the object and what it sits on. Otherwise Force = Mass times Acceleration.

Sorry, that is what comes to mind as of right now, hope this helps you out some.

[2muchstuff]

To figure the amount of force of a spring driven piston, you need to know the spring's constant. It is figure that tells you how much force to compress the spring a specified distance. Take that figure and multiply it by the distance of the spring's compression, that will give you the amount of force. Now multiply that by the square inches of the piston face to get the amount of air pressure.

[Deviant]

I don't think that the nozzle has zero impact on the the output force of the air.

Example, if you have a syringe with the needle on, and you squeeze the piston, you will spray water across the room. Again the same syringe without a cap on the end would cause the water to splash on the floor.

I'm sure it has something to do with the compression factor and the ratio of the piston diameter to the area the the energy is actually applied to.

Ah well, maybe some MIT student that breaths physics will jump in on this thread and set is all right.

There are similar products that use both spring and compressed air for their power supply. Both have similar results. The compressed air one use a supply of 80-150psi or so, while the spring gun isn't using anything close to an 80 pound spring.

[pmurray]

Deviant,

What you need is to use Bernoulli’s Equation. Do a google search on it – there will be lots of hits and info on how to use it. Here is one link:

http://www.grc.nasa.gov/WWW/K-12/airplane/bern.html

With out going through numbers in your example, if your nozzle is releasing to the atmosphere, then you will only have dynamic pressure at this point (rV*V/2, r = density of fluid, V = Velocity). This will be equal to the static pressure in your system, which was explained how to get in the above posts.

Try working through it, if you are still having trouble, give a shout and I’ll show you some more.

Hope this helps. . .

plm

[lerman]

I don't think that the nozzle has zero impact on the the output force of the air.

Example, if you have a syringe with the needle on, and you squeeze the piston, you will spray water across the room. Again the same syringe without a cap on the end would cause the water to splash on the floor.

I'm sure it has something to do with the compression factor and the ratio of the piston diameter to the area the the energy is actually applied to.

Ah well, maybe some MIT student that breaths physics will jump in on this thread and set is all right.

There are similar products that use both spring and compressed air for their power supply. Both have similar results. The compressed air one use a supply of 80-150psi or so, while the spring gun isn't using anything close to an 80 pound spring.

When you take the needle off the syringe, you cannot apply the same force because you can't push fast enough. The volume flow of a gas through an orifice is determined by the properties of the gas, the size and share of the orifice, an by the upstream pressure (assuming that it is several times the downstream pressure).

Ken

[Deviant]

Definately something close to what I need.

According to what I've read so far. Bernoulli's equation applies to a steady flow of incompressible fluid.

I'm not sure how that relates to a short burst of air, which can be and probably is compressed, at least some what.

I'll keep reading.

[2muchstuff]

If I may so bold as to ask, what are you trying to build.

[pmurray]

Deviant,

They are referring to the compressibility property of the fluid. You can assume the air is an incompressible fluid and also disregard pressure losses due to friction etc. – you will be close enough. Also, the terms in Bernoulli’s Equation are in units of pressure heads – so you will convert your psi to a head of pressure.

Keep in mind; I’m recalling some of this stuff from fluid dynamics and a thermo course from over 30+ years ago – I’m a little rusty.

plm

[trubleshtr]

Quick reference is


F
-----
P | A

Where :
F = force
P = pressure
A = Area
You will need to determine spring rates for the spring itself.

Question, Are you looking to find the force generated by the rod, or the amount of air pressure coming out the port on the cylinder when the spring is pushing on the piston?
just trying to clarify.

[Deviant]

This is going to be used in building a bolt action airsoft gun.

It fires a 6mm sphere, that weighs about .2 grams.

I need to generate enough pressure to move it at around 500-550 fps.

[OCNC]

This is going to be used in building a bolt action airsoft gun.

It fires a 6mm sphere, that weighs about .2 grams.

I need to generate enough pressure to move it at around 500-550 fps.

Just to make sure I'm understanding this correctly: We have a spring pushing a piston in a .5 inch bore of 1.5 inch length compressing air which will exit a 3mm dia. orifice at the end of the bore to drive a 6mm x .2gm spherical projectile out of a 6mm+ dia. muzzle of unknown length.
We've got the projectile size and weight and the muzzle velocity and the dimensions of the air chamber. Do you have an intended muzzle length? With the muzzle length we can calculate the force necessary to push the ball at 500 fps. Then we can calculate the spring requirement and finally determine what might be going on in the compression chamber.

Chris

[BillPSu]

You will need to know the velocity the air is moving. Which is based on the spring/piston velocity. Theoretically if the spring moves the 1.5 inches instantaeously then the pressure will be infinite. The spring/piston does not move instantaeously thus the pressure will be less. Use Bernoulli's equation disregarding compression and friction. Use the continuity equation to get the velocity of the air moving through the 3mm orifice. Assume the starting pressure is zero.

[lerman]

You will need to know the velocity the air is moving. Which is based on the spring/piston velocity. Theoretically if the spring moves the 1.5 inches instantaeously then the pressure will be infinite. The spring/piston does not move instantaeously thus the pressure will be less. Use Bernoulli's equation disregarding compression and friction. Use the continuity equation to get the velocity of the air moving through the 3mm orifice. Assume the starting pressure is zero.

If the pressure were infinite, the spring wouldn't move at all. In fact it would move backwards.

The solution to the problem requires solving a differential equation. Someone suggested that the air could be treated as incompressible. I doubt that is true. In order to get velocities in the range of half the speed of sound, significant pressure will be required. Even a pressure as little as 15psi would compress the air to half its volume.

I'm not familiar with the details of the physics involved, but my guess is that the problem requires solving a non-linear differential equation that has no analytic solution. That means there is no simple formula that can be applied.

Ken

[lerman]

Can anyone tell me the formula's that I need to calculate the output air pressure from a cylinder/piston/spring setup.

IE, If I have a cylinder that has a diameter of .5 inch, with a length of 1.5 inches. How strong will the spring need to be to output X pressure from an nozzle with a diameter of 3mm.

((The numbers can and will need to vary, but I'd like to know the formula's so that I can calculate the desired air pressure.))

Also, I'd like to know how to calculate the pressure needed to move an object at a specific weight to a specific velocity within a certain distance.

I hope someone can help out. I vagulely remember doing similar calculations long ago in school.

Thanks.

3mm is a huge diameter. This will not work unless the pellet you are shooting is a close fit in the bore.

Ken

[skippy]

As Chris said, I think we need some more details such as is this thing is completely manual? i.e. no miniature compressed air cyl? I am assuming that's the case and that you are going to have some kind of built in mechanism to recoil the spring and lock it in position ready for release by the trigger mechanism.
I would attack this in another manner. Firstly, assuming the 3mm orifice isn't actually a valve (to stop/start air pressure to ball) that you didn't tell us about, then I believe the only reason you need the step (orifice) at all is so that the ball can't roll backwards and drop down into the air cyl. Therefore make the step 5mm diameter as this will minimise the pressure drop and resulting energy loss that would otherwise be caused by a 3mm orifice.
What comes to mind for me is the following:
I assume the ball doesn't get loaded by just dropping it down the barrel but instead gets loaded by some kind of loading mechanism (i.e. from a hole in the side of the barrel and that hole gets covered up (sealed) by this loading mechanism) If that's the case, I would have a screw on barrel and just ahead of the ball I would machine a groove in the barrel and fit an O-ring. This will stop the ball from dropping out of barrel and more importantly provide initial resistance when fired.
So the spring and piston in the air cyl you described are recoiled (i.e. spring fully compressed), load ball, pull trigger, piston is released and during that microsecond, air pressure rises to overcome the resistance offered by the O-ring acting against the ball, and finally ball is fired from barrel.

Personally I wouldn’t waste my time doing any theoretical pressure calculations. Volume calcs yes, but pressure no. Work out the volume of the compression chamber from the face of the recoiled spring and piston assembly to the back of the ball. I would make the barrel volume (from the front side of loaded ball to end of barrel) which translates to length, about 2/3 of compression chamber volume. Why? Because theoretically they should be of equal displacement but in reality (A) a bit of extra volume (in the comp. chamber) is used up during the compression phase and (B) faster projectile speed will be obtained if we don’t stop air flow at the exact moment the ball leaves the barrel. A little bit of extra air behind the ball at this time helps.
Now, the reason I said not to worry about the pressure calculations is that put simply and assuming the volume calculations in relation to barrel length have been done correctly, if you go to your local industrial supplies place and buy a range of comp. springs it will cost you about $10 and take about 30 minutes to find out which spring works best. Test it firing in hard foam and see which fires deepest from a given distance. Starting from weak springs going to strong, you will find that the speed will increase quite rapidly with spring tension increase but then there’ll be a point where it won’t get faster. This point is determined by factors such as: the restriction size at the smallest point (= 5mm) cannot flow air any faster, the weight of the spring and piston assembly trying to accelerate, etc. The factors affecting the equation are so many that it’s not worth attempting.

Maybe I’ve assumed wrongly and the 3mm restriction is required because it’s actually an air valve. If this is the case then I would still use the same volume calculations to determine barrel length except that comp. chamber is measured to back of valve not ball. And determine your spring requirement by testing as per above.

[Deviant]

The barrel is 6.03mm inside diameter.

The bb's are roughly 6mm.

The barrel length will be about 650mm, no more than that.

As for the reasons on the calculation, I'd like to know that is possible to do what I want.

If the calculations show that I need a 30lb spring to reach 500 fps. It wouldn't be worth the effort.

However, if the calculations show that I can do it with a 8lb spring. I'd be more willing to give it a go.

As for the 3mm openning. The reason for this, as stated above, is for loading of the bb.

On the end of the cylinder will be a stem roughly15mmx6mm with a 3mm through hole. The stem will also be turned on the outside for a small oring to seal the barrel to keep the pressure from escaping back along the stem.

The stem is used for pushing the bb into the barrel from a magazine. As for stopping the bb from rolling out the end of the barrel. I planned on using a small detent, but an oring could serve the same purpose.

Thanks for all the help.


*edit*

Added picture of existing cylinder. I'm looking to make one smaller than this and recreate the feeding mechanism. This is identical to what I plan on making, but should give a better idea.

[pmurray]

Just a comment, your interpretation may vary. . .

There has been a lot of good information given on the static aspects of this problem – the pneumatics portion. However, there seems to be some speculation on solving the dynamic aspects of the problem. Not that speculation is bad but, in this case it is not necessary. This problem is rather easy to solve and is a “classic” problem that is covered within the first few weeks of a Fluid Dynamics Course.

With regards to the second part of Deviant’s question involving the dynamic aspects, it has been stated more than once that the key to solving this problem is the use of Bernoulli’s Equation with the use of the idea that the flow rate at any part of the system will be the same (Area1 * Velocity1 = Area2 * Velocity2). It has also been stated more than once to assume an incompressible fluid and disregard the friction. Using this method will give you a good ballpark answer quickly. To be any more anal is at your discretion.

BillPSu said it best:

“Use Bernoulli's equation disregarding compression and friction. Use the continuity equation to get the velocity of the air moving through the 3mm orifice.”

When I originally responded to Deviant’s question, my intentions were not to initially solve the problem for him but, to point him in the “correct” direction in order to show him how to do it – it’s more beneficial to show someone how to catch the fish than to catch the fish for them.

Other than a follow up question by Deviant to clarify some aspects in the use Bernoulli’s Equation, I never heard back from him that he was having problems and assumed that he was on his way with the solution.

Good luck Deviant and stay on course.

plm