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 :D

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]

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

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 (http://www.automags.org/forums/showthread.php?t=64669) 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.

[phantomhitman]

i usually pull the trigger and my marker shoots paintballs :p i am glad we have people this smart on this board, that way i can brag about it to lesser boards that are not worthy :D

[FallNAngel]

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

you forgot flatter.... farther and flatter than any other gun.

[Destructo6]

Of course you will need calculus. How else can you derrive x'(t) velocity and x''(t) acceleration from the position function?

There are a bunch of programs on the net that will solve your projectile motion problems.

[Smitty2k1]

Good old physics I and its ignoring air resistance and friction and just about anything.

Physics II should be fun, and then off to college.

Here I come mechanical engineering!

[kscullin]

Unfortunately, how wind resistance affects the ball also depends on windspeed and direction. Paintballs are so lightweight compared to their cross section that a decent tailwind can affect the range, as can a decent headwind. Those also don't take into account crosswinds (tangential velocities). I think it'd take some tables to really lay it out, along with assumptions about actual realistic playing conditions (e.g. I doubt anyone would try to play with 15mph winds - or at least would expect good range/accuracy results).

[Orion33]

whats weird is no matter what..unless something generates lift...

an object will fall 9.8 metres/second

so if u shoot a gun..every second the bullet will drop that much...its just it moves so fast u have a greater range

[goddom]

I didn't see anyone ask this question: "why do we need to know this?" I have taken physics before and I don't think it will help one bit to knwo the equations to shoot someone. I won't be sitting behind the bunker with a laptop computer measuring wind speed/direction and then caluctaion teh proper trajectory of the shot. I guess I could, but it doesn't seem like as much fun to me :-).

But a computer program that can calculate the speed of a paintball at various distances from the gun and the effects of wind resistence would be cool.

[spacedtedybear]

Well, yeah the gravitational acceleration downward will always be 9.8 m/s^2 unless the mass of Earth changes. Yes, one cannot apply highschool physics to real world applications. When we do use these basic calculations, we are assuming ideal conditions ( no air resistence, no drag, no spin, CG is right at center of ball), because this is based on the initial conditions that everything is equal. IE same paint, same barrel. That and because there aren't a whole lot of people that can do or understand complex calculus, and advanced mechanics.

[sig11]

Of course you will need calculus. How else can you derrive x'(t) velocity and x''(t) acceleration from the position function?

He just gave you the first and second derivatives. :)


Physics II should be fun, and then off to college.
College Phys 2 for me is electricity and magnetism. Its kinda fun. heh I don't see what everyone complained about. Its pretty simple.


Yes, one cannot apply highschool physics to real world applications. When we do use these basic calculations, we are assuming ideal conditions
It may not be exact, but it gives a good general idea. Do you need to know that the range is about .3m shorter because of air resistance? :)

[Pacifist_Farmer]

Actually for all intents and purposes, High school physics will get you farther in paintball flight than 6 or 8 years of college level physics.

Being able to say "the ball will travel this far, at these speeds" is much more useful to us in the paintball world than accurately modeling the system with every minor detail. Assume some "efficiency", like 70 or 60 percent, multiply your ""highschool physics" results by the chosen effieciency, and youll probably get a pretty good idea of the balls path.

Now if your really getting into the mechanics of your marker where actual effeciencies do matter, and performance doesnt necessarily vary with regard to wind resistance, which is a constantly changing variable, then you'll need some higher level fluid flow, and thermodynamic thinking. This is where your college degree might come in handy.

[kscullin]

Goddom, you don't sit behind your bunker with your graphing calculator plotting trajectories and angles before you snapshoot? Doc would be disappointed. I thought we all did that by this point. :p

[Pacifist_Farmer]

you know whats great..... the TI-92 .....it has a full keyboard in addition to all the numerical and operator buttons

[sig11]

you know whats great..... the TI-92 .....it has a full keyboard in addition to all the numerical and operator buttons

Bah, get a real calculator... an HP!

[vf-xx]

Bah, get a real calculator... an HP!

I own 3. 49, 48G, 48SX.

Doesn't matter much tho. This year they re-did the rules for the FE banning all calculators with Alpha numeric storage.... :(

Poo.

[Mr. Frodo]

Bah, get a real calculator... an HP!

I get a kick out of lending mine to people who don't know RPN. :D

[Pacifist_Farmer]

yeah the ban on the EIT exam makes me mad, I have a perfectly good calculator right here and I have to go out and get a new one

[sig11]

I get a kick out of lending mine to people who don't know RPN. :D

They get this funny look on their faces... like they had an accident.

[spacedtedybear]

It may not be exact, but it gives a good general idea. Do you need to know that the range is about .3m shorter because of air resistance?
Well, it depends on your elevation. :D



College Phys 2 for me is electricity and magnetism. Its kinda fun. heh I don't see what everyone complained about. Its pretty simple.
You're smoking crack. ;) Of course, I had an instructer with a russian accent thicker than molasses on a cold winter day in Canada. Trying to understand the material and translate the lecture at the same time is very exhausting.


Being able to say "the ball will travel this far, at these speeds" is much more useful to us in the paintball world than accurately modeling the system with every minor detail. Assume some "efficiency", like 70 or 60 percent, multiply your ""highschool physics" results by the chosen effieciency, and youll probably get a pretty good idea of the balls path.
Yeah, but it's frustrating to hear some people **tch & moan about how velocity and distance calculations is totally inaccurate because we're not counting windresistence and such. I just want to actually calculate it with every minor detail so that when someone says something about it, I can just whip out the calculations, lean back, and smile while they're looking at it dumbfounded. :) ( <- Kinda like that)


Now if your really getting into the mechanics of your marker where actual effeciencies do matter, and performance doesnt necessarily vary with regard to wind resistance, which is a constantly changing variable, then you'll need some higher level fluid flow, and thermodynamic thinking. This is where your college degree might come in handy.
Which is in line with what I may want to go into someday. That or nuclear stuff.

[tony3]

Does anyone else hate physics? I know I sure do....

[Pacifist_Farmer]

I hate it with all my heart, and thats why i choose a field based on it


ugh.. Nuclear is sooooo 1990's (insert valley girl accent)

go with fluid dynamics (CFD's), whatever type of program that may be at your chosen college, its being used everywhere, and as long as people use computers youll have a job.

[spacedtedybear]

I don't know. A nuclear powered paintball marker sounds very appealing. :D

[Mr. Frodo]

I don't know. A nuclear powered paintball marker sounds very appealing. :D

Speaking of which... back in the day of Splat Masters, I remember seeing an ad for a type of paintball that had fins on it. It's shape reminded me of one of our first nukes, Fat Man.

[goddom]

I was reading something either in this forum or on the AGD site talking about a bullet shaped paintball. The army asked AGD to design a more accurate paintball and so the design they came out with was bullet shaped. It would be cool if they persued that, but the cost to manufacture it and the resulting accuracy increase may not be worth it.

I saw on TV once cops practicing hostage rescue and all that through buildings and they were shooting each other with a paintball like thing that was shot from an actual pistol and was propelled with gunpowder. It looked like it might hurt like hell, but it was it looked like it might be fun.Plus the masks they had were pretty cool too. They looked like really nice paintball masks.