Fluid Dynamics... Your input?

[BoReDFaST]

Overview Of Fluid Dynamics Applied To The Ballistic Characteristics

Of Paintballs and Paintball Markers





Background – Since my introduction to paintball, I have heard the same thing as everyone else, namely that a paintball fired at 300fps has the same range as any other paintball fired at 300fps. Like many others, I realized that this did not hold true in an actual paintball environment. Many times I have been in a position where I could hit my opponent and no matter what he did, his paint would drop off long before it got to me.

This paper is meant to bring to light some of the hidden factors of paintball and explain why certain markers do have more range and accuracy than others.



Topics – In this paper I will cover several aspects of fluid dynamics and dynamic phenomena associated with paintball. Among these are:

- Types of airflow

- Bernoulli effect

- The effects of drag

- Reynolds Number



1. Airflow - There are 2 basic types of airflow. Laminar flow and Turbulent flow.



Laminar flow can best be seen when you turn on a garden hose. At a certain pressure and volume, the water flows smoothly from the hose in a solid glossy column. This type of flow allows for the maximum volume of gas/liquid to pass at the fastest rate possible. Laminar flows columns are less likely to mix with the surrounding environment.



Turbulent flow can also be seen with a garden hose when you turn the pressure up. The nice Laminar flow column will gradually become distorted and disappear completely as the pressure is increased. The flow of water will become turbulent and erratic. As you can see from the resulting spray, a turbulent flow is more likely to mix with the surrounding environment.



2. The Bernoulli effect - This is a phenomenon that can best be described by that silly thing we have all seen at supermarkets. A horizontal fan is placed so that it blows through a traffic cone. When a ball is placed on the column of air that blows up through the cone, it hovers in place and even if it is moved, it re-centers itself in the air column.



3. Drag in aero/fluid dynamics is a bizarre and very nebulous concept dealing with friction and the actual dynamic properties of an object.



4. Reynolds Number – This is a theory that describes the close order effects of turbulence on an object and can best be described by looking at a golf ball. Golf balls are dimpled to take advantage of the fact that small pockets of turbulence along the surface of a wing can actually cause air to flow over it faster than a completely smooth surface.



Assumptions – In this paper, I am assuming several things for consistency. I am aware that most of these factors are not the same in a real world scenario.

- All paintballs are exactly the same size and perfectly round and do not distort when fired.

- Barrels for each marker are the same length (breech to end).

- Temperature, barometric pressure, humidity, and elevation are constant.

- I may be assuming other things but nothing that comes to mind.





Main – For simplicity sake, I will use 2 markers that I am familiar with and we will examine a scenario for each. I will be using the Bushmaster/Defiant and the Shocker as my case studies because I am familiar with both of them.



The Bushmaster is a high-pressure blowback style marker with an operating pressure or about 350psi. When a paintball is fired, this marker produces a sharp high-pressure blast of air that propels the paintball out of the marker at 300 fps. While this is occurring, the bolt travels back so that the next ball can drop into the breech to be fired. This sharp blast of air combined with a sudden backpressure in the breech causes a turbulent airflow behind the paintball.



The Shocker is a low-pressure, closed bolt style marker that runs at an operating pressure of about 180psi. When fired, this marker produces a relatively high volume of low-pressure air that propels the paintball out of the marker at 300 fps. After this occurs, the bolt travels back so that the next paintball can drop into the breech. This method of propelling a paintball produces a much less turbulent, or Laminar flow.



After the paintball has left the marker, it is natural to assume that nothing else is acting upon the flight of the paintball, but this is not entirely true. Upon exiting the barrel, we must look at the method the paintball was propelled by.



The paintball fired from the first marker is followed out of the barrel by a turbulent volume of air that begins to immediately mix with the surrounding environment and quickly dissipates. This does little to aid the flight of the paintball, and since this turbulent air acts in a highly unstable and unpredictable manner, can actually slightly skew the flight of the paintball by causing high and low pressure zones behind the paintball.



The paintball fired from the second marker is also followed by a larger volume of air that is much more orderly. This air will resist rapid mixture with the environment outside of the barrel and continue to follow the paintball until it dissipates. In effect, this produces an aerodynamic shape rather like a comet or a teardrop instead of a sphere until this effect dissipates. Additionally, due to the phenomenon of Bernoulli’s effect, slight deviations in the flight path of the paintball will actually be corrected as this ordered column of air exerts equal pressure to the spherical shape of the paintball.







Drag will have an effect on each paintball based on its aerodynamic properties. The first paintball will succumb to the effects of drag before the second one due to the temporarily elongated wing effect that the Laminar column lends to the second paintball. This should be a relatively small difference but it is worth mentioning because we are discussing a projectile that is traveling just over 200mph and at that speed, even little differences count.



Last but not least, we need to discuss the theory behind the Reynolds Number. As I stated before, the reason that golf balls are dimpled instead of smooth is to change the way that the air flows across the surface of the ball. A golf ball is in actuality a spherical wing and the dimples create small pockets of turbulence as air travels across it. This evenly created turbulence changes the properties of the wing and actually allows more air to flow across the slightly expanded surface. The surface is actually expanded by the turbulence. This allows a dimpled golf ball to travel further than a smooth golf ball given equal or nearly equal swings from an experienced golfer (which is why they haven’t been used in ages). This also has applications in paintball. If a manufacturer could make a paintball that had the same type of consistent dimpling as a golf ball, we would see a significant increase in range for paintballs as well.



Conclusion – There are many factors that come into play in the ballistic flight of a paintball. Due to the different operating methods employed by different markers, it is safe to say that not every paintball traveling at 300fps has the same aerodynamic properties. Since this is the case, it is also safe to say that some markers will have better or worse range and accuracy depending on what properties they impart to their projectiles.



I hope this helps to clear up what seems to be a longstanding myth in the sport of paintball, and helps to explain why that guy at the end of the field with a Shocker can hit an opponent while paint from the opponent’s Angel falls short of its target.

[FatMan]

So, there are lots of holes in your theory. Not sure where to start.

First off, you have assumed lots of things are constant that aren't. I understand why you've done that, but what you have NOT done is shown that the variations in these things and the resulting effects do not completely overshadow the effects you are discussing.

You make huge leaps of logic in the main text where you suggest that issues such as operating pressure and bolt operation result in particular effects. You have no data to support those conclusions.

Even if some of these effects DO exist (and I believe some of them do - though they might not be the ones you claim) you have not shown that they affect the flight of the ball enough to alter the primary characteristic (range).

It is highly unlikely that the conditions surrounding a recently fired ball are significantly different - but they may be a bit different. The thing is, you haven't really shown anything - you've just theorized that these different effects are taking place.

Personnally, I'd like to see a more rigorous treatment of these things. I'm not sure if they would change paintball, but they'd be cool none the less.

FatMan

[BoReDFaST]

I didn't actually come up with this theory, I just need your guys' input.

[bjjb99]

The theory you present is a very interesting one. I'm not sure how valid it is, but I do know of a way to test it using high speed Schlieren photography. I'm sure many of the folks reading this forum have seen the pictures of the shockwave coming off a bullet, or the air patterns around a person's sneeze? That's Schlieren photography. Basically it's a way of detecting slight variations in the air (or other medium, such as water) resulting from pressure and temperature fluctuations.

For an example of some Schlieren systems, here's a couple of URLs:

1. http://www.grc.nasa.gov/WWW/OptInstr/schl.html
2. http://www.rit.edu/~andpph/text-schlieren-focus.html

If you use the setup in URL number 2 above, use a photographic studio stobe light as your light source, and trigger the strobe when the paintball is within the field of view of the camera, you should get images somewhat similar to the one in this URL (minus the shockwaves):

http://courses.ncssm.edu/hsi/ss/schl...ges/803_19.htm

Using this imaging technique, you could determine whether a paintball has the trailing "teardrop of gas" you theorize at various distances from the muzzle of the paintgun being tested. All in all, it would be a fascinating experiment to perform.

BJJB

[BoReDFaST]

Great, thanks for your input!

[ShinyGuy]

It is an interesting theory. You seem to assume alot of things regarding how long effects last. I'm not saying you're wrong, I'd just like to see some of these things tested.

First you assume that the shocker's low pressure/high volume flow is less turbulent by the time the gas gets to the muzzel than the high pressure/low volume burst from the bushmaster. That 4.4 inch^3 room of expansion space (in a 12 inch barrel) could reduce the turbulance quite a bit (this is the same thing a muffler on an engine does; useing volume to reduce sound/turbulence). It's likely that barrel porting has as large an effect on turbulence as the initial burst of gas. (either to disipate the turbulence to introduce it as the air flows over the ports. Again testing would be needed to see what effect this really has.)

You also mention that less turbulent gas resists flow seperation better than more turbulent gas. (We all agree that turbulence at the muzzel is bad) This effect diffinately exists (if there is any difference by the time the air is at the muzzel). The question is how long does this effect last.

It sound like you have a good basis for some very interesting experiments.

[Miscue]

Confuscious say: High speed video shows that the ball leaves the barrel before the air does. The ball does not ride with the air blast.

Turbulence from the marker is a non-issue.

You also did not mention anything about barrel pressure. Operating pressure and barrel pressure are two different things. The ball sees barrel pressure, not operating pressure. But makes no difference, just making a point.

Any gun, using any barrel... with the ball leaving at 300fps... will result in same distance.

I think the answer to why different guns vary in range in the real world can be found in a psychology book.

[ShinyGuy]

Originally posted by Miscue
Confuscious say: High speed video shows that the ball leaves the barrel before the air does. The ball does not ride with the air blast.

As the ball leaves the barrel the pressurised air behind it sees the low pressure air in front of the ball and as the air is less massive than the paintball some of the air should accelerate past the ball as both are leaving the barrel. How much air stays ahead of the ball and for how long are the big questions here. If you have evidence that show that no air passes the ball I'd like to see it (and I'd like to know why the air doesn't accelerate past the ball). If what you're saying is that the air that passes the ball is too small a quantity, or gets striped away too fast, to have any measurable effect then I suspect you're probably right.

Turbulence from the marker is a non-issue.

You also did not mention anything about barrel pressure. Operating pressure and barrel pressure are two different things. The ball sees barrel pressure, not operating pressure. But makes no difference, just making a point.

Right. The pressure and turbulence as the ball leaves the barrel are what matter, not the pressure as it starts its acceleration. While it is possible that there are differences between different guns and different barrels here it is definately not as simple as low pressure=long range.

Any gun, using any barrel... with the ball leaving at 300fps... will result in same distance.

Since we measure velocity about a foot away from the end of the barrel this is true. If the effects we are talking about are measurable they are gone by the time the ball passes the chrono. Still I would like to see if there are any differences in acceleration for the first 2 or 3 inches after the ball leaves the barrel.

I think the answer to why different guns vary in range in the real world can be found in a psychology book.

I would never think my gun is better just because I paid more for it. My gun if better because it is shiny

[bjjb99]

Another means of determining whether paintguns yield different ranges would be to measure the average paintball velocity for a given paintgun as a function of distance from the barrel.

To perform this test, you would have to set up a series of chronographs at various distances from the paintgun (say, 2 feet, 5 feet, 10 feet, 20 feet, and 50 feet). You would want to arrange the chronographs so that a single shot could pass over (or through, for "light curtain" designs) all the chronographs. Fire around a hundred shots, record the paintball velocity from each chronograph for each firing, average the results from each distance, and you've got an idea how the paintball decelerates in flight. Perform this test on several paintguns which all possess the same muzzle velocity, and see whether paint fired from some guns retains its velocity more than others.

BJJB

[ShooterJM]

Originally posted by ShinyGuy
It's likely that barrel porting has as large an effect on turbulence as the initial burst of gas. (either to disipate the turbulence to introduce it as the air flows over the ports. Again testing would be needed to see what effect this really has.)

You also mention that less turbulent gas resists flow seperation better than more turbulent gas.

I suspect that the volume and pressure scavenged by barrel porting will reduce any backpressure to negligable. Barrel length is also key.

As for less turbulent gas resisting flow seperation better then more. Not sure I understand exactly how this is being applied. Using the golf ball example, laminar flow is turned into turbulent flow to help delay boundry layer seperation.

BoReDFaST: You might be interested in this thread as well

https://www.automags.org/forums/showt...threadid=28150

[BoReDFaST]

OOOohh that helps. Thanks a lot guys for your support.

[BlackVCG]

Originally posted by bjjb99
Another means of determining whether paintguns yield different ranges would be to measure the average paintball velocity for a given paintgun as a function of distance from the barrel.

To perform this test, you would have to set up a series of chronographs at various distances from the paintgun (say, 2 feet, 5 feet, 10 feet, 20 feet, and 50 feet). You would want to arrange the chronographs so that a single shot could pass over (or through, for "light curtain" designs) all the chronographs. Fire around a hundred shots, record the paintball velocity from each chronograph for each firing, average the results from each distance, and you've got an idea how the paintball decelerates in flight. Perform this test on several paintguns which all possess the same muzzle velocity, and see whether paint fired from some guns retains its velocity more than others.

BJJB

You can do this and get a general idea by averaging the results, but the main problem with this is that chronographs have a margin of error of +/- 3%

This test was conducted a long time ago and in one of the tests the second chronograph in the series was showing a higher velocity than the second chronograph. Thus leading to the myth that barrels affect range.

[ShinyGuy]

Originally posted by ShooterJM
Using the golf ball example, laminar flow is turned into turbulent flow to help delay boundry layer seperation.

The difference between a golf ball and what we are talking about is that the golf ball is traveling through still air. By generating turbulence the golf ball reduces parasite drag. All the rules that apply to golf balls apply to paintballs equally once they are clear of the initial burst of air from the barrel. If the paintball is surounded by a pocket of air traveling at near the same speed the paintball does not experience any drag for a while as it would have a relative velocity of 0 to the air in contact with it. That pocket of moving air would be striped away by drag from the still air that it is moving through and after the moving air has been striped away the paintball will start to decelerate. I would guess that that air pocket is striped away within the first inch or 2 after the paintball leaves the barrel and thus all balls are equal by the time they pass the chrono. But I would love to see some good old experimental research on this.

[ShooterJM]

Originally posted by ShinyGuy


The difference between a golf ball and what we are talking about is that the golf ball is traveling through still air. By generating turbulence the golf ball reduces parasite drag. All the rules that apply to golf balls apply to paintballs equally once they are clear of the initial burst of air from the barrel. If the paintball is surounded by a pocket of air traveling at near the same speed the paintball does not experience any drag for a while as it would have a relative velocity of 0 to the air in contact with it. That pocket of moving air would be striped away by drag from the still air that it is moving through and after the moving air has been striped away the paintball will start to decelerate. I would guess that that air pocket is striped away within the first inch or 2 after the paintball leaves the barrel and thus all balls are equal by the time they pass the chrono. But I would love to see some good old experimental research on this.

Gotcha, (note to self: read entire thread before commenting). Yeah that would be an interesting experiment. I'd even just be interested to know what the pressure is in the barrel just as the paintball exits. Ported and non-ported.

[bjjb99]

BlackVCG,

I remember reading about the test you described. If I recall, none of the chronographs used were calibrated prior to the actual test. Calibration with a known velocity (preferably a series of known velocities spanning the expected velocities to be measured) would have detected the high readings of the second chronograph.

For the experiment I described above, the experimenter cannot just go out, get a half-dozen chrony-type chronographs, set them up, and expect to get good results. Each chronograph used in testing requires a series of calibration procedures prior to use. As demonstrated in the test you described, it's difficult to get good measurements if the ruler's length is not accurately known.

The environmental conditions during calibration and the actual test would have to remain resonably constant. I'm guessing that the test would have to be performed indoors to eliminate wind, lighting variations, and significant temperature fluctuations. An indoor shooting range might do the trick, or perhaps AGD's long hallway with the dented door at the end...

BJJB

[Hamster Huey]

Shooter/Boredfast/whoever-wants-to-read,

I don't know if you've come across this in your research or have done any calculations to the effect, but I remember reading some papers in the last couple months that pointed out that the height of the surface asperities required in order to generate a turbulent boundary layer is a lot smaller than one would imagine - certainly smaller in scale than golf ball dimples. Have you run across anything like this? I think I need to go back and review when I have some time.

[ShooterJM]

Originally posted by Hamster Huey
Shooter/Boredfast/whoever-wants-to-read,

I don't know if you've come across this in your research or have done any calculations to the effect, but I remember reading some papers in the last couple months that pointed out that the height of the surface asperities required in order to generate a turbulent boundary layer is a lot smaller than one would imagine - certainly smaller in scale than golf ball dimples. Have you run across anything like this? I think I need to go back and review when I have some time.

Yeah I did read that actually. Tried to calculate it out and I have what I think are decent starting sizes. Of course theoretical and practical are two entirely different things.

I still think the toughest part is coming up with a viable manufacturing process.

[DJSOLID]

When does the Bernoulli effect become evident? Isn't it when low pressure behind the sphere matches the coefficent of drag created by high pressure in front of the sphere? Or something to that effect? Does it really apply to this at all?

Two things would be fantastic tools to use in an experiment like this.

1. A tank fill with some kind of gaseous dye, smoke or particle that can be seen or flourecses under UV so that the gases that exit the barrel can be seen with high speed photography. - maybe this has been done - I dunno.

2. A "perfect paintball" possibly made of solid plastic or some other material that could be used as a control group. As near as I can figure it - all testing results can be compromised by low paintball quality. - also may exist - dunno.

[bjjb99]

Don't know whether the first test you mentioned has been done, DJSOLID, but I do know that AGD often uses solid nylon balls during some of their paintgun tests.

Perhaps the Schlieren photography described earlier in this thread could be combined with AGD's nylon paintballs to get an idea of how the gases are behaving behind the paintball.

BJJB

[PBchopR]

So theoretically, couldn't one use a vacuum in front of a fired paintball to reduce the inevitable compression of the barrel air that is generated when a paintball is forced through it? This probably wouldn't amount to much more velocity, but it might allow for higher speeds with less ball breakage. In fact, a paintball gun could be made to fire using vacuum instead of pressure... A simple valving system could be made utilizizing a port near the muzzle, combined with a valve.

[PBchopR]

Should I patent this or what?

[ShooterJM]

Originally posted by PBchopR
Should I patent this or what?

Sure, why not? Figure out the valve timing and an efficient way to get the needed vacuum and you could be good to go.

[Redkey]

If my memory in working with RTM molding serves me correctly... the max force that can be pulled with a vacuum is about 14 psi. Not really enough to get a ball moving with much velocity.

Also... you'd have to close off the muzzle of the barrel otherwise you would just be sucking air down the barrel while the paintball just sat there. Plus the breach behind the ball would have to be open otherwise as the ball moved forward you would generate a vacuum behind it that would counter act the vacuum pulling the ball down the barrel.

A vacuum can be generated by passing high velocity air over a series of small openings... not a very efficient process though.

The idea of shooting into a vacuum is an interesting one, although not too practical.

[PBchopR]

I think you were referring to Bernoulli's principle.. But if yo took a paintball gun barrel, open at both ends. Put a paintball at the breach end, closed off the muzzle end, and pulled vacuum at the muzzle while opening the muzzle blocking valve.... It does seem impractical but possible. But perhaps utilizing the venturi effect elswhere to evacuate some air from the barrel? I could almost do that one myself, I just don't know if there would be an advantage. Really, if that were to increase the paintball velocity, you would have to turn down the gun to stay at 300 fps anyway! You might gain efficiency, however...

[BlackVCG]

From what I know about Bernoulli's Equation, it's based on the assumption of conservation of energy. I do know that it only works for incompressible fluids because you're assuming that the specific weight at point A and the SW at point B are the same.

[Butterfingers]

If the effects we are talking about are measurable they are gone by the time the ball passes the chrono. Still I would like to see if there are any differences in acceleration for the first 2 or 3 inches after the ball leaves the barrel.


I would never think my gun is better just because I paid more for it. My gun if better because it is shiny [/B][/QUOTE]

Thats impossible. There is no force accelrating the ball when it leaves the barrel. The net positive acceleration away from the barrel the second it leaves the barrel is ZERO no matter what gun you use. All a ball carries once it leaves the gun is its momentum which is its Velocity times its Mass.

There is only a net negative acceleration in the direction opposite to a paintballs plane of motion due to air resistance and of course downward due to gravity.

[JRSJKD]

Well, my first post in here...hope I don't dissapoint.
First, I have to agree with Butterfingers.
"There is only a net negative acceleration in the direction opposite to a paintballs plane of motion due to air resistance and of course downward due to gravity."

While a lot of the stuff you guys are talking about I'm not real familiar with I do have some practical knowlege of working with aerodynamics.....at the dragstrip. My single bigest enemy when racing my bike is wind resistance. Even reducing the coeficient of drag by .6% is good for a couple mph on top, not to mention getting there quicker. This includes things as small as removing the mirrors and turn signals. What we are looking for is a smooth elongated shape that lets us slice through the wind with as small of a frontal area as we can get. A pointy shape isn't necassarily better. What is important is a tear drop shape with a small frontal signature. Too big a front area and too much pressure builds up creating more drag. You also want the flow to travel along the bike to reduce dead areas. This is where spheres(like paintballs) are weak.

I think that we are looking to hard at the problem. Other than the already stated foces(gravity, wind resistance), the inate nature of the sphere is probably its worst opponent. As a sphere travels throught the air, there is the initial pressure build up in front and then the air travels over the surface. Because of its shape, it creates a dead spot imediately behind itself creating more drag. You'll notice the more and more "racing" bicycles have gone to oval fraome components to help further reduce co-efficients of drag in order to eliminate the dead spots. To illustrate how much influence drag can have on an object in the 1950's the "dustbin" shaped motorcycle racers were able to reach speeds of around a 155mph, about the top speed of my 2000 yamaha. What's really interesting about this is that they did it with around 40hp as compared to my 95hp. Superior aerodynamics( they were outlwed )

What I would be really interested in finding out is how much even a 1 mph headwind would affect a paitball, and conversley help it in a downwind. We know that aerodynamic forces(dynamic pressure)are proportional to the square of the speed. That means you quadruple the drag or lift when you double the speed. With all of that in mind, I would be really curious to see how different velocities affect paintball distances. Are there instances where a marker shooting at a slower velocity will have better range because of a lower frontal dynamic pressure? What about in a headwind? I've seen tests done where they have shown accuracy to decrease at higher velocities, why not distance?

just a couple of thoughts....

Junior

[JRSJKD]

Just another thought or two.....

In the first post it talks about the phenomena where we have all noticed one gun outshooting another. So we start looking for reasons why this DOES happen. We eventually get into long debates over really complicated physics and concepts. What if it really comes down to only one thing....the individual marker...BUT, not the way it was stated in the first post. IMHO, what makes a marker is its valve system. Accuracy is often(and rightly so), measured by its consitency over the chrono. However, just like the way most people calculate how many BPS they shoot, it's flawed. Instead of measuring one shot, wait ...read, 2nd shot....wait....read, etc, we should be measuring in more real world terms. That is consistency during rapid fire or bursts. It will always be accuracy by volume(due to the inherent in-accuracy of a round projectile), and I don't know about you but in my personal experience people usually shoot at least in short bursts. How well a particular gun's valve system can keep up with rapid fire consistency should be the real measure of it's accuracy/range. In addition to the variable nature of different valve syatems theres the individual flow rate of different air systems. I wonder if we spend to much theorizing about laminar flow rates only to end back up at shootdown All other things aside, all guns shooting at 300fps will have the same range.....as long as its still shooting at 300fps.

All guns are not created equal........I've got my ReTro.....do u????? :P

Junior

[FatMan]

JRSJKD,

Well said. I think that hits the nail on the head - if the ball exits at(in) the same velocity/trajectory/environmental conditions, it will have the same basic range. But not all guns have the same consistency. Valving and shoot down are big important factors. Paint-to-barrel match is another. Air system can be another.

The physics is complicated - and interesting - but the critical factors have been identifed, and the marketing hype is often just that - hype.

FatMan

[PBchopR]

As far as I can tell, guns that react less during the firing/reloading cycle are capable of shooting farther accurately. I think that's where the perception of better distance comes from; Angel users can shoot far accurately, because of the minimal reciprocating mass involved in their operating cycle. I believe that the "ideal" gun would have a barrel that fits the paint exactly, a propellant that is exactly consistant with every shot, and minimal reciprocating mass(just enough to offset the ball being ejected.) The Holy Grail of guns....