Physics and Paintball

[hostage]

Okay guys, I thought yall might want to learn some physics and how it relates to paintball. First of all do to annoying US standards I will have to convert EVERYTHING into english from metric. Also, please note that I am excluding external varibles, ie wind resitence etc.

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Gravity and Acceleration on Earth

g=32.15 feet/second/second or 32.14 ft/s^2

g=a (g is an accleration so is a, so you can substitute g for a in some cases)

This is how fast an object will accelerate.
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Velocity of an object start to finish

Vo= the intial velocity of an object in feet/second or ft/s
Vf= the final velocity of an object in feet/second or ft/s

This is basicly the speed of the object ie crono at 300ft/s
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Distance and height
note: x and y can be used in many cases

Xo= the initial distance in feet
Xf= the final distance in feet

Yo=the initial height in feet
Yf=the final height in feet

ie player shot a paintball 100ft from a height of 4ft.
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Time in seconds

T= time in seconds it takes
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Now for some equations: kenematics

Vf=Vo+aT
x=.5(Vo+Vf)t
x=VoT+.5aT^2
Vf^2=Vo^2+2aX

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Now post if you want me to help you solve some equations for yall or if yall have any questions. BTW all this is covered with in the first 3 chapters of a physics I book.
-Hostage

Disclaimer: If I did anything wrong an you notice it, plz lmk. Also I am not responsible if you kill yourself or get injured from doing any experiments.

[tribalman]

"
g=a (g is an accleration so is a, so you can substitute g for a in some cases)

This is how fast an object will accelerate."

the only time that gravity will equal accleration is if the object is falling down. which means an arc or shooting a paintball straight down. and with your caculations, i don't think you take into effect arc or the variable speeds the arc will create. the speed at the begining and end of the arc are greater than the speeds at the peak, or any point inbetween. also, according to one of the equations, a paintball with initial speed of 300 fps +32.15*20seconds equals 943fps. um..no. the problem is you need to take into account wind resitance and arc. sorry, but i don't know the equations off hand, and i don't have the book that would state it.

[Kevmaster]

good work..and you'll get an answer that is close, but at 300fps (200 miles per hour) wind resistance is quite a large force. Its the reason paintballs don't accelerate positively forever! The force of wind is directly proportional to the velocity of the ball...

[Kevmaster]

the way you would solve a problem where a ball is shot at 100fps from 4ft off the ground at 20* angle is this:

1) Break into X and Y coordinates.
Y: d = Viyt + 1/2 g t ^2
4 = 100sin(20*) + 1/2 (32) t ^ 2.
from that you can solve that t = SOMETHING (since i don't haev a calculator, i will say it equals 10s)

NOTES: 100sin(20*) is the Initial Y-Direction Velocity.

X: d = Vixt + 1/2 a t ^ 2
d = 100cos(20*) x 10 + 1/2 x 0 x 10^2
d = 100cos(20*) x 10
d = RANGE.

NOTES: you plug in the answer you got above for t (10s) into t here.
the horizontal acceleration is zero as there is no force acting in the horizontal direction
100cos(20*) is the horizontal component of the initial velocity



this is, of course, ignoring the force of air resistance...which would involve calculus... I don't feel like going there right now. Just know that the distance would be shorter

[Mr. Frodo]

Unfortunately, paintballs are so light that they can be heavily affected by wind and air resistence. For example, if you shot a paintball vertically (assuming 300fps), it should travel close to 1400 feet in the air (0 = 300^2 + 2 * (-32.2) * x and solve for x). That's twice as high as the Hoover Dam! You have to take into account air resistance. And if I remember correctly, they involved the natural log calculations.

[sig11]

this is, of course, ignoring the force of air resistance...which would involve calculus... I don't feel like going there right now. Just know that the distance would be shorter

Don't really need calculus. If I remember correctly all you need to do is treat it as an energy problem and add in wind resistance as friction. I think I've got that μ somewhere...

Lee

[Mr. Frodo]

You have to love the conservation of energy!

[hostage]

Heh, if you notice, I wrote excluding air resistence. This is more to prove myths ie cockers shoot futher wrong. This is all therory and kind of a rudemntry way of showing peeps how physics works. I was refering to g=a sometimes as when the object is excelerator downward. Lets keep this simple, so we don't loose peeps and go into to much detail.
-Hostage

[Dryden]

Am I missing something, or are you reinventing the wheel here? This has already been eloquently covered in far more detail in the Paintball Spin Physics thread in Deep Blue.

Does anyone see the irony that AGD's slogan is "Quality Always Shoots Straight," despite the fact that they have proven paintballs can't fly straight?

[Kevmaster]

Don't really need calculus. If I remember correctly all you need to do is treat it as an energy problem and add in wind resistance as friction. I think I've got that ? somewhere...

Lee

that works...when mu is constant....however, the friction of air is directly proportional to the speed of the object at the current time. because of that, as it slows down, the friction force gets smaller...

life would be much nicer if you could do it that way, but i don't think you can...

[sig11]

that works...when mu is constant....however, the friction of air is directly proportional to the speed of the object at the current time. because of that, as it slows down, the friction force gets smaller...

life would be much nicer if you could do it that way, but i don't think you can...

Hey. I'm a computer scientist, not a mechanical engineer. Gimme the data and I'll write a program to analyze it.

I do see what you're saying though. That might be a fun problem to try to solve.

[xXHavokXx]

Physics don't apply to paintball, everyone knows cockers and trix's shoot farther than anyother gun.

[Kevmaster]

Hey. I'm a computer scientist, not a mechanical engineer. Gimme the data and I'll write a program to analyze it.

I do see what you're saying though. That might be a fun problem to try to solve.

as am i. although i do remember a little from my physics courses...

[spacedtedybear]

Next fall, I should be able to calculate projectiles w/ wind resistence.
BTW,
Vf=Vo+aT
x=.5(Vo+Vf)t
x=VoT+.5aT^2
Vf^2=Vo^2+2aX

Those equations you derive from calculus. Using double integration of the acceleration of the object with respect to t' (time). That'll give you at*j + c where "c" is a constant and "j" is the vector in the direction of y-axis and "i" is the x-axis. Or in this case, the initial condition of the object (intitial velocity) so that's Vo. By trig. definitions Vx= Vo Cos@i Vy=Vo Sin@j where @ is the angle with respect to the x axis. Then the resulting equation for the velocity of projectile in both x&y components would be (Vocos@)i + (Vo sine@-at)j. You take the integral again with respect to time will give you the position of the object with repect to time. So R(t)= [(Vocos@)t]i + [(Vosine@)t-at^2] +c2. Where c2 is the initial condition of the of the object (initial position) so c2 is the height at which it is fired.

So.... the overall summary of all the B.S I wrote above is " The horizontal and vertical components of a projectile in motion is independant of one another".

If you want calculations with windresistence and all that stuff get back to me in a few months.

Also, the metric value for the acceleration due to gravity is 9.8m/s^2~10m/s^2. Would you rather use 10 or 32 when you start calculating velocity components?

[vf-xx]

Hey. I'm a computer scientist, not a mechanical engineer. Gimme the data and I'll write a program to analyze it.

I do see what you're saying though. That might be a fun problem to try to solve.

Sigh.... I'll go digging through my Fluid Mechanics and Aerodynamics books and get ya'll better equations...

Everybody current with differential equations?

FYI: The most proper term for wind resistance/air resisitance is skin friction drag.