How long is the ball in the barrel when shot?

[Webmaster]

OK - first off I have mad props to Earon Carter - hes a god. But in the following interview he makes this statement:

From: http://www.paintball.com/features/story.cfm?placementID=1439

"Selecting a larger bore size helps. This will reduce the number of paintballs that your gun cuts. During testing, we calculate that the balls are only separated by 3”- 4” inches moving down the barrel. It’s amazing. The speed is so fast that the paintballs look like a straight line of paint. "

Earlier he mentioned markers shooting at 20 bps...

The problem is - the math! And Im now a math idiot! But - if I rember right, Tom said the ball is in the barrel for 14 milliseconds. So.. that means you would have to shoot somewhere around 72 bps in order to have two ball in the barrel at the same time - much less have them 3"-4" apart.

Am I right? Do I remember right, Tom? Are my numbers about right? Is this another case of "them" guessing where as AGD knows.

[synreal]

// disclaimer: few hard facts were used to come to the following conclusions, mostly opinion, take it is you may //

quick mental math says that your feelings are most likely correct. lets assume that the balls are being fired at 300fps muzzle velocity (or a foot every 300th of a second) that means that a ball already up to speed would clear the length of a 16" barrel in 4 milliseconds.

the average speed of the ball during the course of its travel down the barrel is going to be nowhere near its exit velocity (it spends most of its time down the barrel speeding up), and i lack the equipment, time and dedication to do adiquate testing, but an average barrel speed of roughly 1/3 to 1/4 muzzle velocity sounds completely reasonable, putting its time in barrel at about 16 milliseconds.

again, this is just me trying to logically think the problem through, but something tells me that their numbers are a bit off (not to mention dealing with how you would chrono a marker that could theoretically have atleast partial energy from anywhere from 1 to 4 bursts of air propelling any given paintball down range).

[hitech]

Here is the answer from Tom's Tech Tips:


Barrel Efficiency, Tech Tip #1

...The balls acceleration rate is approx. 50,000 feet per second to get to 300 feet per second in 10 inches. The entire barrel travel time is about 6 thousandths of a second... Although this may sound incredible if someone out there would like to do the math you will see that I'm close.

[Webmaster]

so... if its 6ms - that means you would need to shoot over 166 bps to get two in the same barrel...

Does this mean I win?

[hitech]

Originally posted by Webmaster
Does this mean I win?

Yup. No way are they spaced 3 to 4 inches apart!

[shartley]

You are VERY correct. I would however LOVE to see this proved on film.

The way to do this is to make a replica barrel out of CLEAR plastic (or glass) and film a marker shooting at its highest sustained ROF. I don’t know if it would be worth the time or effort to do so however, since simple math does quite well on its own. ;) But it WOULD make for some good footage.

[Thordic]

Uhm, is he kidding? :)

Hmm.. 300 fps... average 10 BPS for our purposes...

I count 30 feet between balls.

How about you guys? :)

[AGD]

Ahhhh such a good deep blue question...... If I were you I would focus on the 30 foot idea.

AGD

[shartley]

So… Tom…. Are you saying to get a MUCH longer barrel? ;)

[ShooterJM]

Originally posted by Thordic
Uhm, is he kidding? :)

Hmm.. 300 fps... average 10 BPS for our purposes...

I count 30 feet between balls.

How about you guys? :)

Seems logical to me, I'm betting every one of us has run through a sustained firing lane without getting tagged. 3-4" spacing would be highly improbable to be able to run through.

[Miscue]

Earon: The first criteria, and most obvious, is to match the bore size with the
Larger bore size, longer barrel for the back
paint you are shooting. Players still forget that basic step. Rate-of-fire is another point to keep in mind. Back players shoot more paint, so <B>they should look for larger bore diameters to increase their rate-of-fire.</B> Front players need to shoot more precisely, like a BB, rather than more often. They should use smaller bore sizes.

Um... say whut?

[Vegeta]

I officially raise the BS flag.

[Top Secret]

Originally posted by Vegeta
I officially raise the BS flag.

No I do. ;)

[EchoX]

Take note that the ball has to accelerate down the barrel, making the ball slow at hte beginning. Now calculus would have to play a part in this math.

[athomas]

There is a thread here in deep blue from a while back where we were debating the acceleration profile of a mag. What we discovered is that the ball is only in the barrel for a few milliseconds. I can't remember the exact numbers, but I think it was around 3.5ms.

Another factor that would limit the rate at which the balls could follow each other is the rate at which they drop into the breach, even with a warp feed or a halo. The warp feed and halo claim they can feed at about 22 balls per second. Thats about 4.5ms between balls.

Edit: Oops that's supposed to be 45ms between balls.

The first 3.5ms - 5ms is only about 12 - 16" because of the acceleration of the first ball. The breach feed rate of 45 ms is while the first ball accelerates to 300fps (~5ms) plus the time the ball travels at 300bps (~40ms) which translates into about 160 - 200". So the minimum distance between balls will be around 160" - 200" (depending on barrel) without adding any other factors if you could feed balls and pull the trigger at a rate of 22bps.

Edit: Explaination was not as clear as I would have liked. I also changed the numbers to reflect distance in inches instead of feet.

[SlartyBartFast]

Alright, the BS flag has already been raised. But think about this:

How on earth could two balls be in a barrel at the same time? :confused:

that would mean you would either be opening the bolt while there is still pressure in the barrel. Imagine the blow back.:rolleyes:

**EDIT**

Had to take a dig at this ludicrous statement as well:


Originally posted by Miscue
Earon: Rate-of-fire is another point to keep in mind. Back players shoot more paint, so <B>they should look for larger bore diameters to increase their rate-of-fire.</B> Front players need to shoot more precisely, like a BB, rather than more often. They should use smaller bore sizes.

Um... say whut?

I'm with Miscue. What black magic is a larger bore barrel supposed to do to increase the ROF?

I think I know! I has to be so that the balls can not only travel one after the other in the barrel, but so that there's enough room for them to travel side by side! :D

I think we've gone from BS to absolute certifiable Moron here.

[Top Secret]

Originally posted by SlartyBartFast
Alright, the BS flag has already been raised. But think about this:

How on earth could two balls be in a barrel at the same time :confused:

that would mean you would either be opening the bolt while there is still pressure in the barrel. Imagine the blow back.:rolleyes:

Also the fact that the first ball would no longer have any air pushing it, causing the next ball to go slamming into it...

[ShooterJM]

Originally posted by Top Secret


Also the fact that the first ball would no longer have any air pushing it, causing the next ball to go slamming into it...

Granted I've seen that before, but that's a blooper shot followed up by a full strength. One of the raceframe videos on here had one I think. Even then, the first shot is out of the barrel by about a foot before the second shot hits it.

[pbjosh]

Man-0-man,

Okay, I did read the total interview. For a guy who makes a great barrel (I love the steelwind and my old school Dye 1 piece) I can't believe the numbers he doesn't know. To bad.

Okay,

For times, take a look at the charts that AGD posted for us in the "Official Data Thread" covering times and pressures behind the ball for various guns. If you look at those time you can figure that the ball takes somewhere between 5-9ms, depending on the gun and barrel length, to make it out the tip from the point that air pressure is applied to the ball.

Since I have numbers for cockers I will use those:

For a gun to cycle at 20 bps it needs to go through its total operation in 50ms

Here is a time line:

20 bps using the settings 7,7,17,10,16 (Halo B or Warp)

1ms after the trigger is pulled the grip solenoid is turned on
3ms after the hammer releases.
5ms after the hammer hits the valve
7ms after the front solenoid is turned on, causing the air to start routing for the 5-way
9-10ms after the bolt starts moving
10-11ms after the bolt has moved far enough that the breech is exposed- allowing for Suction if timed right.
22-23ms after the bolt has moved back far enough that the ball can now pe pushed in by the HALO.
24ms after the bolt has moved back far enough to allow the hammer lug to pass b the sear. At this point, the bolt is fully open.
23-34ms after the ball has been pushed in by the HALO.
34ms after the front solenoid turns off, allowing the bolt to return
50ms after the board allows a new input/shot to happen.

Now, the balls are 50ms apart to run at 20bps. So, given a final speed of 300fps (it doesn't matter how fast they are going at any other point, they all are moving at 300fps 50ms after each other) then the balls would be 15 ft from each other. Having shot paint at near 20bps several times through these cockers, I will say, shooting at close range targets (50ft or so) you can easily see 2 balls in the air, maybe 3, but no more.

unless there are some MAJOR mistakes, there should not be two paintballs in the barrel at once.

Oh, while HALOs take about 5-10ms to load, they only cycle at 45ms, not 4.5ms

on an interesting side note, the Doc9000, which was a Mag mounted on top of a Tippmann Carbine, worked by having the bolt come back and hit the sear on the Mag. The balls fired about 10ft after each other, so the time delay between the shots would be about 30ms.

As for which length barrel is best for each player on the field. Uhm.......... it really doesn't matter. They all should find the barrel that shoots the straightest for them, and that it that. Accuracy has NOTHING to do with ROF. Different issues. The barrel, unless it is horribly in-efficient or breaks paint alot, has nothing to do with ROF. The length of the barrel should depend on what the person wants feels comfortable playing with, that is it. And overall accuracy.

Josh

[the electrician]

that's it!
Tag it, Bag it, and sell it to the butcher.

that's the best explanation I've read on this topic.

I'd have to say it is another good example of how something can appear to be going faster, or look closer together. because 20 balss are passing the same point in one second, it looks like they are closer than they really are.

[Wat]

This is true at 300fps, but remember a that a paintball can quickly decelerate inflight. The upstream ball will slow before balls behind it will allowing them to catch up. Further out in range when the paintball is moving maybe only 150fps the distance between shots at 10bps is only 15 feet. Just pointing out that the timing between shots is the same, but the distance will not always be the same.

Just like if you watch racing, cars may seem to pull away when they come on to straights or appear to catch up entering corners, but its not the distance between cars that matters but the time.

When i hear of stuff like 2 balls in the barrel at one time, i think if its even mathematically possible and if it is, is it physically possible. The only way you could fire 300fps at 10bps and get two balls in the barrel at the same time is if the majority of the acceleration occured at the end of the barrel. So a ball would move real slow down the barrel, then another ball would be chambered, then the first ball would just hop up to 300fps. But thats not possible as it would imply that you were applying a lot more force to the first ball then the second, which you couldn't do as the second ball is now between the valve and first ball.

Boy, did that not make any sense at all.


Originally posted by ShooterJM


Seems logical to me, I'm betting every one of us has run through a sustained firing lane without getting tagged. 3-4" spacing would be highly improbable to be able to run through.

[SlartyBartFast]

I think you've got it right Wat.

It's impossible because you can't open the bolt to chamber another ball while one is accelerating because you'll release all the pressure in the barrel. This means the second ball in the barrel is would leave the barrel at much less than 300fps and the second ball (if left to accelerate the length of the barrel) would leave travelling at 300fps. Guarenteed that the second would run into (or overtake:D) the first.

The ONLY way more than one ball will be in the barrel at a time is if you have a 10ft + length barrel.:rolleyes:

[J_Hoyt]

How about people start putting down the math they're doing instead of just the answers they're getting. Here's what I've been able to get so far. Equations all look at the motion of the ball while it is in the barrel.

Vi = Initial velocity of ball
Vf = Final velocity of ball
s = displacement of ball (as it applies here, the length of the barrel)
a = Acceleration of ball
t = time the ball takes to reach the end of the barrel

16" barrel = 16/12 feet = 1.333 feet = S value
At the breach, ball is moving 0 FPS. Vi value is 0.
At the muzzle, ball is moving 300 FPS. Vf value is 300.
a and t are unknown values.

Equation 1:
2as = Vf^2-Vi^2
2(1.333)a = 300^2 - 0^2
2.666a = 90,000
a = 90,000/2.666
a = 33,758
Average acceleration of ball in a 16" barrel is 33,758 FPS/s.

Equation 2:
Vf = Vi + at
300 = 0 + 33758t
t = 300/33758
t = 0.009
Ball reaches end of 16" barrel in .009 sec or 9 milliseconds.

Vf = 300 FPS
Vi = 0 FPS
s = 1.333 feet
a = 33758 FPS/sec
t = 0.009 sec
Now we have a good description of the motion of the ball while it is in the barrel.

If 1 ball was to be shot every 0.009 seconds, then every 0.009 seconds there would be a ball in the breach beginning to accelerate at that instant and a ball at the muzzle. 2 balls in the barrel every 1/0.009 balls per second or 111.111 balls per second.

I welcome you to correct any mistakes you find in my math or logic.

Joel Hoyt

[Koosh]

Heh... Before anyone else says it...

Welcome to AO Joel! I was never a physics guy myself, so I don't know aboot your equations... but from me, they look good, so I guess thats all that matters!

[J_Hoyt]

Thanks. I think I'll like it here. :) I dont own a mag or anything but I heard this is a good place for some harcore tech talk. I also came up with another solution.

*ahem*

here it is....

"We can't shoot 100 balls a second so it doesn't really matter."

Pretty good, eh?
Joel Hoyt

[petefol]

i just learned about all that acceleration stuff in physics and it looks about right to me. but anyway, you would think a guy who makes some of the (claimed to be) best barrels, he would be a little more right.

[pbjosh]

Yes, welcome Joel.

Feel free to drop #s or anything else. The PBworld needs more numbers than it has.

Josh

[confedman75]

Originally posted by Top Secret


Also the fact that the first ball would no longer have any air pushing it, causing the next ball to go slamming into it...
not necesaraly once the second ball get to wear the first ball used to be it will be going as fast as the first ball when ti was right there so thus the second ball will never hit the first because the second ball slows down just as fast as the first:rolleyes:

[EchoX]

How come people say that the second ball will hit the first ball? Won't momentum and the rest of the air behind it take it the rest of the way. It's not like it's gonna slow down dramatically. People can still shoot paintballs with 8" barrels, so there'll be a sufficient amount of acceleration.

[SlartyBartFast]

Originally posted by confedman75
once the second ball get to wear the first ball used to be it will be going as fast as the first ball when ti was right there so thus the second ball will never hit the first because the second ball slows down just as fast as the first:rolleyes:

Not so. Under discussion is the impossible scenario of two balls being in the barrel simultaneously. The second ball will have air pushing it for the whole length of the barrel but the first only up to the point at which the second supposedly enters the barrel.
The second ball then experiences more accelration and would hit the first.

[SSMercury]

Originally posted by EchoX
Take note that the ball has to accelerate down the barrel, making the ball slow at hte beginning. Now calculus would have to play a part in this math.

Heh. Might make an effort...

Ok, made me a "pretty" (sarcasm) graph using Windows Paint to show ball slowing down, near the end, if it's loosed by a single puff of air, and forgot to add the graph of a slower, longer acceleration.

[athomas]

Originally posted by SlartyBartFast


Not so. Under discussion is the impossible scenario of two balls being in the barrel simultaneously. The second ball will have air pushing it for the whole length of the barrel but the first only up to the point at which the second supposedly enters the barrel.
The second ball then experiences more accelration and would hit the first.

Not quite. If the two balls were in the barrel at the same time and the first was moving on gained momentum while the following ball was accelerating, then the pressure built up between the balls as the 2nd approached the first would slow the 2nd and add additional acceleration to the 1st. Plus if the possibility that two balls could be in the barrel at the same time, then the bolt must reset itself while the ball is in the barrel. This would cause blowback and remove pressure from behind the traveling ball. This effect would be the same for each ball fired, not just the first ball in a two shot sequence.

[hitech]

Originally posted by J_Hoyt
How about people start putting down the math they're doing instead of just the answers they're getting.

Vi = Initial velocity of ball
Vf = Final velocity of ball
s = displacement of ball (as it applies here, the length of the barrel)
a = Acceleration of ball
t = time the ball takes to reach the end of the barrel

16" barrel = 16/12 feet = 1.333 feet = S value...
Ball reaches end of 16" barrel in .009 sec or 9 milliseconds.


Here is what Tom said in his tech tip:

Barrel Efficiency, Tech Tip #1

...The balls acceleration rate is approx. 50,000 feet per second to get to 300 feet per second in 10 inches. The entire barrel travel time is about 6 thousandths of a second... Although this may sound incredible if someone out there would like to do the math you will see that I'm close.

It seems that your numbers match Tom's pretty close. What to try it for a 10 inch barrel?

[petefol]

the acceleration in a 10" barrel would be about 54000fps if the velocity was 300fps, and the change in time would be .005 sec.
the calculations i did were the same as j_hoyt's but i used .8333ft for the displacement (10in/12ft). I'm guessing tom probably did his calculations with a different velocity, or just took an educated guess.

[J_Hoyt]

Yes, I think Tom either used an 11" barrel for his calculations or he used 270-280 FPS for his velocity. Either would have given him about 50 000 FPS/Second.

[Hoplon]

I've had multiple balls in my barrel lots of times.











It's called double feeding. ;)

[hitech]

Although this may sound incredible if someone out there would like to do the math you will see that I'm close.

So, it would appear that this is in fact correct. They did the math and Tom is close. :D

[athomas]

The acceleration curve of a paintball indicates that it achieves most of its velocity in the first 3 - 4 inches of the barrel. It takes about 3ms to reach about 80% of its final velocity. The remaining travel speed works out to approximately 3.5inches per millisecond. This is the ball gradually reaching final velocity and traveling near final velocity. There isn't much additional increase in velocity because the friction and air pressure pushing against the ball prevents any great amount of additional acceleration.

The findings of mag efficiency using a 10 - 11 inch barrel are true but the ball actually reaches much of its final velocity much sooner than that. A barrel that is 16" long would still reach much of its final velocity in the first 3 - 4 " as well. In the remaining length of the barrel, the ball would only gradually increase and possibly even decrease in velocity near the very end.

For 300fps the ball travels 3600 inches per second. That equates to 3.6 inches per millisecond.

The ball reaches much of its velocity in about 4 inches of the barrel and it takes about 3 millisecond. For every 3.6 inches farther, it takes about 1 millisecond of travel time.

Note: I did a lot of rounding in the numbers to make it more readable and generically understanable. The actual numbers and acceleration profile is here in deep blue from a while ago for those wishing to see the relationship.

[Ryderdude15]

hey i'm not in calc or anything but i was thinking... would it be possible for two balls to be in the barrel at the same time if like the balls had a good enough seal that the second ball going down the barrel was causing pressure to push the first ball out of the barrel. i think someone earlier said that there would be no pressure in the barrel to propel the first ball once the bolt backed up or whatever but thats like two rubber stoppers in a plastic tube... if you have the right amount of friction the stopper will get pushed down the tube from the pressure between the two stoppers. does this make any sense? i'm real tired so i dunno. jus thought i would say what jus popped into my head. lemme know if what im talkin about is possible. thanks

[athomas]

What you are saying is sort of true. The first ball would have the same momentum and velocity if a second ball was in the barrel or not if the gun was setup so that it obtained maximum velocity at the end of the barrel under those conditions. The conditions being that the bolt opens before the ball exits the gun. The second ball could never catch the first in the barrel because of the situation you mentioned.

One problem with getting two balls in the barrel at the same time would be the acceleration that would have to be placed on the second ball to get it into the breach. The first ball would have to be at or above its maximum velocity before the bolt is opened. Once the bolt is opened the barrel loses pressure behind the ball and further acceleration is gone. The first ball will actually start to decrease in velocity at this point. In order to get the second ball into the breach before the first ball exits the barrel it must be done in less than 2 ms given that the first ball takes at least 4 ms to accelerate to 300fps and is only in the barrel about 6ms total. Even then you could only start firing the second ball as the first exits the barrel.

To actually fire the second ball and have it traveling down the barrel behind the first ball it would have to be in the barrel in about 1 ms. The travel distanc is about 1" to get the ball into the breach. The average velocity is about 83fps which means the actual final velocity is probably more than 160fps. At 160fps the ball will probably break as it hits the back side of the breach in the barrel.

[Joemafia69]

joel, your numbers look right, but not for the every day scenario. your equations are for a constant accleration in a vacuum. Thus elimanting friction, air resistance, and variable acceleration over the whole 16" barrel. what you still need to look at is the "fluid" flow of the air. For the sake of simplicity assume it is a lamanar flow over the whole time of travel, BUT you can't do it over the whole 16" (unless the barrel is not ported) then your equations would work (not counting friction and air resistance) over the first 6-8 inches of the barrel (er however long it is to the porting) because of conservation of mass (assuming no losses as well) try redoing the calculations not counting the barrel porting, because after that the ball does not accelerate constantly anymore. a good setup to try is if anyone has a freak, set the velocity of the gun so it is 300 fps with the tip on, then take the tip off and then fire the ball over the cronograph. this will tell you the velocity to use as your VF and give a better model to use. i will try crunching through it with the bernouli equation tomorrow inclass to see what i get as a theoretical Vf, if anyone can try the model i described and post the velocity they get over teh chrono i would greatly appreciate it