how fast to shoot to rundown a sprinter

[booyah]

situation,

a runner sprinting across the feild, you at a decent distance putting a line of paint where you KNOW he is going to run, say at a 90 degree angle to his run... i got bored and did some math for all of you!!!

lets say your shooting 10 balls a second, and your gun is running 280 fps velocity (now i am assuming this is done in a vaccum cause i wasnt that bored to try to figure air resistance) how fast does that person have to be running to run through that rain of paint to have a chance of coming out okay?

heres my math, correct me if you find mistakes!!!

i converted many of these numbers to meters and such so bear with me

280fps is about 85meters/second (Mps)
1meter is about 39.25 inches


first off
10balls a second means one ball every .1 second. that means that your paintballs are spaced at a distance from each other of .1 * 280 or 28 feet (8.5 meters)

heres where individual sizes come into affect.

i'll use my meassurements on this. we are assuming the player is running perpendicular to the stream of paint (90 degrees) so the width of their chest and thickness is very important here.

the number that actually matters is a vector since they could get hit in the chest or the side. its a simple euclidien triangle

side
------|
\_____|
_\____|chest width
__\___|
___\__|
area\_|
that \|
matters

Mind you I am a bigger than average guy so this will skew the calculations slightly

Accross my shoulders i am 24 inches (2ft) wide and at my thickest (mid chest) i am 11 inches thick.

now we thank do a good ol a^2+b^2=c^2 or 24^2(576) + 11^2(121)= c^2 (697)
so the area for impact is 26.4 inches or 26 for easy math

so we have the area that can be hit (.66 meters) the time to pass the distance (.1 seconds) so how fast would i have to be moving to keep from being hit?

good ol velocity = distance/time
v=d/t v=.66/.1 or about 6.6Meters/second or almost 15miles per hour

pretty fast run that i dont think i can do....

thought this would be fun for some of you and my friday night plans were canceled....



update:

after some extra thinking, i think i missed something here, the way i figured this out, the velocity of the paint doesnt matter.... you would still have that .1 seconds to clear the .66 meters in sicne its th delay between balls....

hmmm please correct me if i'm wrong, its been years since i've done real physics....


-Booyah

[DarkPhoenix]

Geez boo-yah. You really put alot of time and effort into this post. I took a couple of semesters in physics, and given this is done in a vacuum, as you, said, this sounds right. However, there are so many more variables that we have to take into account on a real life basis. That in mind, it is always best to lead your target, cause your target to walk into your line of fire, do not chase the target. On a practical basis, you will have to estimate the amount of lead to put in your firing. Even then, there are so many more variables for this method as well....

[booyah]

this was assuming leading your target and putting down a line of paint in the air before they got to the line....


that is the best way (imho) to catch a runner



-Booyah

[DarkPhoenix]

Agreed!

[booyah]

13 balls per second is nice to catch the skinny fast guy when 10 just doesnt seem to do!!!

just grillin ya AGD, I do like the idea of the non chopping mags, just wanted to make a point...



-Booyah

[ShinyGuy]

Air resistance doesn't effect your calcs at all. The air resistance only decreases the velocity of the balls not the time between them. If you're shooting 10bps the time between balls at any distance from the shooter is .1sec weather the balls are traveling 300fps or 100fps. Look at it this way; each ball is going to pass a given point the same amount of time after leaving the barrel as the ball before it. The balls are going to be closer together (distance wise) as they slow down further from the shooter but they're still going to come 1 every .1seconds. The only thing you have to worry about is how far you move your body in the time between balls.

For example I am about 9inches (.75 feet) front to back. If I'm running right to left in front of you, you could hit my left side. Your ball could also go just in front of me and I'd run into it (taking tha ball in the chest). However, the only velocity vector driving the ball into me in this case would be me running and I just had my girlfriend drop balls in front of me as I sprint and I can't run fast enough to break all-stars. This means we can discard the hit on my front since they will all bounce. I can run about 14.3 feet per second or 1.43 feet in .1seconds (the time between balls). This gives me roughly a 52.5 percent chance of being hit in the torso by someone shooting 10bps in a strait line at 90 degrees to my direction of movement.

Of course when you factor in my arms and marker pumping forward and back theres much more target area than the size of my torso. And the run speed I just clocked was over 100 feet. The time accelerating from a crouching position behind a bunker and deccelerating into another bunker would make my average speed much slower.

Overall there are a few olympic sprinters that might be able to make it through that wall of paint... But their chances wouldn't be good.

[Nitroduck]

simple math ... my angel shooting @ 14bps , or my mag shooting @ 10bps , + 2 team mates doing the same .......................

Lets say the guy takes 2 seconds to react to the fact he's being lit up........... thats 60 balls on him (if we hit him 100% of the time , which seems to be what my angel and mag are doing at the moment )

Just remember.......... it takes 1 ball to get a guy , but then we have wipers and bounces which gives us either room to shoot more , or use staining toothpase thick fill :)

[booyah]

Originally posted by ShinyGuy

For example I am about 9inches (.75 feet) front to back. If I'm running right to left in front of you, you could hit my left side. Your ball could also go just in front of me and I'd run into it (taking tha ball in the chest). However, the only velocity vector driving the ball into me in this case would be me running and I just had my girlfriend drop balls in front of me as I sprint and I can't run fast enough to break all-stars. This means we can discard the hit on my front since they will all bounce. I can run about 14.3 feet per second or 1.43 feet in .1seconds (the time between balls). This gives me roughly a 52.5 percent chance of being hit in the torso by someone shooting 10bps in a strait line at 90 degrees to my direction of movement....

...Overall there are a few olympic sprinters that might be able to make it through that wall of paint... But their chances wouldn't be good.

also, i had a feeling it doesnt matter velocity, but it didnt look right. thats why i was asking to correct me if i was wrong... thanks for confirming it for me....


ah but the chest still counts as hittable area. a ball can hit your clothing and break on the cloth from its own velocity. the reason i counted this is It happened to me twice this season.

-Booyah

[ShinyGuy]

I see what you're saying about the chest area, the ball breaking from friction rather than impact. But I think that that sort of break is too unpredictable to really include in our model. If you'de like to try I'd be interested to see it but considering we've already ignored any hits not on the torso I'm not going to bother. I'll just always wear silk clothing:p

[ShooterJM]

Originally posted by ShinyGuy
I can run about 14.3 feet per second or 1.43 feet in .1seconds (the time between balls). This gives me roughly a 52.5 percent chance of being hit in the torso by someone shooting 10bps in a strait line at 90 degrees to my direction of movement.


Hmmmm ok so if I clock betweena 4.5 and 4.9 second 40 yard dash that means at top speed I'm hitting 24.489 - 26.667 feet per second. Something like a 30% chance of being lit?

[spider54]

if u guys do this for fun i am gonna seriously think about how bad i want to be on AO

j/k

[Schnitzel]

i think i could do it, but it would have to be for a distance of about 15-25 feet. other wise, people start to lead you, and you're screwed. fo course, if it was me, i wouldn't run that far at once, I'd be stopping along the way.