7 replies to this topic

[AirApache]

Is there an equation which states how FAR an object would go assuming that there was no friction, no air resistance etc, and using Cx's example that the cross section between the air chamber (assume its spring powered) and the barrel?
This is shot from, again Cx's idea, 1.5 meters.

The equation would make the size of the plunger tube/shaft as the independent variable (so the barrel would be 36x that in length). The dependent variable would be length travelled, till it hits the ground.

If you could explain the not-so-obvious parts of the equation that would rock, too.
Please help! I gotta finish this by tomorrow morning..if you get my drift...

Thanks

AA

[J cobbers]

I'm sure there is a way to calculate it, but you'd have to take a physics class or trigonometry/Calculus.
Your missing some variables there as well. You'd have to know the force applied by the spring powering the plunger, the pressure generated, the pressure needed to fire the dart (in which case your going to want friction and would need to know the mass of the dart) the rate change of acceleration of the dart in the barrel ect. (the dart will continue to accelerate down the barrel at a decreasing rate as air pressure decreases) ect. A better way to calcualte theoretical range is to base it off of a measured value of velocity.
once the dart is out of the barrel it's much more simple.
Gravity effects all objects the same. Therefore the only things you need to know in the absence of friction and air resistance are hight fired from, tragectory and inital velocity. In the absence of friction/air resistance, an object won't slow down, and will fall at a constant rate 9.8m/s^2.

In any case the math is more complex than I can handle (It's been 5 years since I had physics or Calculus) and I'd think this would be up the alley of an engineer or physics major.

[NinjZ]

If their is no friction and air resistance, an object will travel forever as their is nothing to stop it.

[cxwq]

Ninjz, He's assuming there is gravity and a 1.5 meter height. I don't think he's trying to say that the ground is frictionless.

AA, it's not impossible to create an equation which gives you a rough estimate assuming no dart friction of any kind but it would be all but worthless because a spring gun with no dart/barrel friction doesn't work so well. If you add barrel constrictions into the equation it starts becoming really hard.

I think a pump gun would be easier because you would only have to deal with gas equations.

[Crankymonky]

I did that using kinematic equations, maybe I'll add a few more factors into the equation next time. But, I believe that the majority of the work is posted on NHQ in the "some of my homemade longarms" topic. The dart falls in 1.099 seconds, If I recall correctly, due to gravity of 9.8 m/(s) squared.

http://www.glenbrook...DKin/U1L6a.html

Just something I found when searching "kinematic equation" Those should give you a partial idea, but they don't include kinetic friction and many other forces.

[VeggieBoy 3000]

WEll you can do it with any gun if you can calculate muzzle velocity. Wouldnt tat be more of a testing factor though?

You could take a very small box filled with tissue paper until it is a certain mass, then hang it from fishing wire, and attach a marker to the side of it which is against a big sheet of paper on a wall. When you fire the gun directly into the box it will draw a line on the paper to show how far it went. using the mass of teh box and its distance, you can calculate the force used to move it, and then you can use the force of teh dart to calculate its velocity. Then its just a factor of seeng the distance the dart can travel in the 1.0999 seconds before it hits the ground.

Sorry I dont know all the equations. I just started physics so I cant pull them up from memory yet. Someone may be able to help me out here, or maybe I'll be un-lazy and go look them up.

I know this works for big objects like potato cannons. For nerf darts you would just need a really small box so that it moves a big enough distance to accuratley measure.

[AirApache]

Sorry guys, I didn't really mean like a working equation that would determine how far all our guns shot. There are too many variables if I did that (air leaks, trigger release time, check valve or pump handle air remission, psi in tank, etc.). I just wanted to know if there was an equation, minusing all air resistance, friction (not gravity).

Actually, I don't know why someone would make these equations due to the fact that there are so many extra variables. Maybe someone did, though...OK thanks for replying though.

[Viper]

Those variables you mentioned are irrelevant though. A genric air resitance variable can added with minimal addtional complexity. I don't have the equations in front of me, but you can just use the position equation So = -16t^2 X -9.8 + soT I can't remember the equation off my head, but it looks something like that. You can calcualte rate of change using simple implcit derivation by taking the exponent, subtracting 1 from it, then multiplying it by the coefficient. ( 2x^2 ) y' = 4x(dy/dx). This give you rate of change. Just use a chronograph to calcualte muzzle velocity nd it should work.

Edited by Viper, 01 November 2004 - 02:08 PM.