Modelling air rifle internal ballistics

[mman]

I made a 'quickload type' internal ballistics calculator for air rifle. The idea for this calculator first started from a question "Is it possible to launch air rifle projectile with supersonic muzzle velocity". Model helps to understand which internal ballistics effects are important and which are the ones can be ignored. The model as simple as this appears to be pretty good fit with measured results.

Following physical effects are included:

Compressibility of fluid (air)
Stagnation pressure (aka chamber pressure) as a function of air cylinder pressure and regulation setting
Impact pressure (pressure affecting to the base of bullet) as a function of flow velocity
Barrel friction

Ignored effects:

Pressure loss due to pipe flow friction
Acceleration of projectile after muzzle end (few caliber long transitional ballistics area)
And maybe something that didn't pop up into my mind.

And the answer to the initial question: "Easily, at least according to my model"

Any comments, ideas or corrections to this model?

Link to the calcultator:
http://dl.dropbox.com/u/12618884/Air%20rifle%20internal%20ballistics%20calculator.xlsm

References:
http://www.nd.edu/~pdunn/www.ame538/Chapt09.pdf
http://www.pipeflowcalculations.com/pipe-valve-fitting-flow/flow-in-pipes.php

[admin]

Impressive. I once read the "Airgun from trigger to target" from Cardew & Cardew. I just flipped some pages again, serious stuff. Although mostly oriented on spring guns it still quite informative. For spring guns they have tables of in-barrel velocities. A spring gun is more complex as  a pneumatic one, as the book shows that all of them quite heavily rely on combustion of oil.... Furthermore the book reports on the effect of pellet seating, hardness and shape.

[mman]

Yeah this is just for PCP guns. I once measured velocities (Air arms S410) from many different pellets with same regulation setting and cylinder pressure. Interestingly enough they all gave almost exactly the same muzzle energy. I used this information when testing the model. I'm just saying that this result shows that effect of pellet seating, hardness and shape are insignificant. When modelling something that happens in the real world there is lots of physics involved. Still often there is no need to take everything  into account to get reasonable accurate results. However I can't be absolutely sure that those effect you mentioned can always be ignored but it is very hard to know right input values for them even though I wanted to take them account.

[mman]

One thing I would like to add to the model is correlation with regulation length and cylinder pressure. The correlation is different for every gun but I think it could be solved from the measurements of muzzle velocity and cylinder pressure. I think the valve's equation of motion is something like this:

striker rod impact force(t) - firing valve spring force(t) -  cylinder pressure force(t) = firing valve acceleration(t) * firing valve mass

[admin]

Yeah this is just for PCP guns. I once measured velocities (Air arms S410) from many different pellets with same regulation setting and cylinder pressure. Interestingly enough they all gave almost exactly the same muzzle energy. I used this information when testing the model. I'm just saying that this result shows that effect of pellet seating, hardness and shape are insignificant.

However, the Cardews showed that for spring air rifles, this is crucial for accuracy. From the book I learned that one should take hard pellets (H&N FTT) for (my .22 HW97K) spring rifle, and softer ones for pneumatic rifles.

Half a year ago we did a test with pneumatic rifles and tin (Sn) pellets. Here we noticed an enournous effect on velocity spread and accuracy of pellet seating and the way the pellet was pressed in.  Only those rifles that mechanically pressed the pellet in where accurate.

[admin]

One thing I would like to add to the model is correlation with regulation length and cylinder pressure. The correlation is different for every gun but I think it could be solved from the measurements of muzzle velocity and cylinder pressure. I think the valve's equation of motion is something like this:

striker rod impact force(t) - firing valve spring force(t) -  cylinder pressure force(t) = firing valve acceleration(t) * firing valve mass

It is here that the Cardews did some work.

[admin]

However I can't be absolutely sure that those effect you mentioned can always be ignored but it is very hard to know right input values for them even though I wanted to take them account.

This is closely related to one of the interesting things in life. If one looks at many finite element calculations, microscopic particle simulations, etc one has to notice that most of the effects cancel each other and where they do not, simple phenomena arise together with phenomenological laws. Laws that do not depend much on details of the underlying interactions.

I am leader of the www.urbanflood.eu consortium that creates an early warning system for dike failures. In the Netherlands we have about 2400km of realy crucial dikes and some 16000km dikes that are a bit less important. However as the composition of dikes are only partly known, if any, as the measurement of this composition is neither technical possible and feasible, we realy can not rely on fundamental theory to understand sensor readings. Instead, I stimulate  the uptake of data driven modelling techniques. As dikes are "exited" by passing ships, tides, cars, rains we model their response.

The more scientific side of me is drilling down on "emergence" and the control of complex systems. Appart from dikes, "swarms" of spacecraft, telecommunication networks, wafer steppers are application cases.
 

[mman]

That indeed sounds interesting. For us closely involved with physics and modelling it's unfortunate that world is not deterministic. Newton and Einstein didn't believe it but after the the rise of quantum mechanics we have to admit that we can't predict everything.

By the way, maybe I should read that book or something else about internal ballistics. There is nothing about that subject on my bookshelf.

[gvp]

mman can you please re-upload the file .. thanks

[mman]

Done..

[mman]

Does it match with your measured results?