Math Algorithms for Paintball (Recipes)

[tomcat]

Do you have an algorith (systematic method of solving a certain kind of repetitive problem) that could be useful to others in paintball?

[nerobro]

Paintball speed is not a constant. Time is a constant. the time between balls will remain the same as soon as you're INTO the string.

Given the balls are slowing down. 1/10 of a seccond later, the first ball will not have gone 30 feet.

As soon as you're sitting at say 60 feet you'll actually have 3 balls en route to you. and the balls will be physically closer togother. As the balls slow down they will come closer and closer to each other.

To create an accurate estimation of paintball distance we'd need to know how fast balls slow down. Balls are big, and have low mass, so they slow down really quickly.....

Actually calculating the gap gets pretty complex pretty quickly.

[nerobro]

it may work on constant velocity, but paintballs are never at a constant velocity.

I mention that the ball won't go 30 feet from the barrel in 1/10 of a seccond becuase that's the point that your guess would be closest to accurate. the further you go from the gun, the closer the balls get togother. ultimately they will start stacking on one another (but that would require shooting off a very tall cliff)

A more accurate algorythim would be based on time. But there's an unknown in the forumla we don't have on hand. That's the rate of acceleration of a paintball after it leaves the barrel.

IIRC the forumla for distance an object travels while accelerating is ViT+AT

now.. We know the initial veloicty, we know the time. And for any timeframe past the barrel of the gun we can easily calculate the distance between balls by taking one time value and adding .1 or whatever for the spacing between balls. Take the number from both timeframes and subtract the smaller number. and you have the distance balls are seperated at that range from the barrel.

so there's your algorythim. but you need to do the research to find out how fast a paintball will accelerate.

[Wat]

Nerobro is right. To find the gap between balls you'd find the time between balls * the ball speed where you want to know the gap. The gap between balls will be longer the closer you are to the shooter. The difference in gap length at 20 yards vs 30 yards is going to be substantial.

But the distance between shots is not that useful a number because the faster the ball, the distance is further but the balls clear it faster. If you're putting paint in a runners lane the time between shots is what counts.

However, nerobro your method isn't right. The formula ViT+AT is only useful in a frictionless or constant acceleration. The thing is we don't know how quickly the air resistance slows the ball.

[nerobro]

the rate of acceleration of the ball wont' be constant. You're right. becuase it's a Cd not a direct A... But the forumula was enough to make my point ;-) Drag is funny, it's calculated by the square of speed, and then it get's really screwed up when it stops. Stiction (static friction) has a whole other way of defining itself..

On a side note, most friction is a fairly steady number. it's that anoying fluid friction that really screws us up. and introduces innacuracy to our balls ;-)

[tomcat]

Feet per Second to Miles per Hour

fps x 3600 / 5280

Sample:

280 x 3600 / 5280 = 190.90 miles per hour

[Wat]

Tomcat,

An easier thing to remember is that

60mph = 88fps

[314159]

30 mph = 44 fps !

.... just trying to help out

[MasterYoda]

It is possible to find the acceleration of the ball after it exits the barrel. If one assumes that the flow is uniform and incompressible around the ball, then you can find the the drag force on the ball and use this to find the acceleration. Since the Reynolds number is on the order of 10^5 then you can assume that the skin friction is negligible since the aerodynamic drag will be much greater than any drag contributed due to friction. Cd for this case is approximately .4. An equation to approximate the aerodynamic drag is: Fd=1/2Cd*rho*V^2*A
Where rho is the density, which is assumed a constant for air at 1 atm and 20C. V is the velocity and A is the frontal area of the projectile. Sub this into Newton's 2nd law (sum(F)=m*(dV/dt)) and separarate the variables and integrate to get a function of change in velocity in terms of time. You can then use this equation to find a function of x in terms of t.

[whaarfrat]

Ball travel to target

This is a question from a non engineer, so be kind. I have thought that acceleration ceases when the ball goes beyond the effect of the propelling gas (i.e., just beyond the end of the barrel), and then begins deceleration as the air friction bleeds off its speed. You have been using the word "acceleration". It makes me very curious, and I'd appreciate it if you'd tell me how I have gone astray. Thanks, Peter "Wharf Rat" Simpson

[nerobro]

deceleration ins't a word ;-) Acceleration is a vector. and can occour in any direction. in the case of a paintball as soon as you reach the porting on the barrel the acceleration if negative.

[Redkey]

what about this

At 300 ft/sec how much pressure is the ball generating on it's leading edge? I have no idea... but, as long as the pressure in the barrel was higher than the resistance pressure, the ball would continue to accelerate. If the porting could not vent the air pressure fast enough then the ball will continue to accerate even after it has passed the porting. Only when the pressure behind the ball has dropped below the resistance pressure will the ball begin to decelerate... oh excuse me, have a negative acceleration vector.

So... saying that the ball stops accelerating once it passes the porting may not necessarily be true.

[MasterYoda]

Re: what about this

Originally posted by Redkey

So... saying that the ball stops accelerating once it passes the porting may not necessarily be true.

True, but any acceleration during this time is negligible compaired to the acceleration beforehand and afterward because it occurs over such a short time span. It makes it easier just to leave it out and assume that the acceleration stops at the porting.

[Natural Newbie]

Well some barrels have more porting than others. So the decrease in acceleration could be critical in some and not in others. (I know it's an obvious statement, just trying to warm up to techie threads )

[NastyPTA]

so a paintball fired at 280f/s in a true vacuum over a 24 hr period will travel roughly 4581 miles?? damn, whole new meaning to long ball...better start working on my tactics