Calculating range with controlled air gun

[Benigna]

1. The problem statement, all variables and given/known data
Ultimately, I need to calculate the range of projectile fired from my controlled air gun. My meter gives me pressure in psi which i keep at constant 40 psi, allows me measure (theta) 45 degrees, volume 2.48 in^3


2. Relevant equations
R=(v^2/g)*sin(2(theta)); x(t)=v cos(theta)t and factored equations that follow


3. The attempt at a solution
Well as you know, most equations solving for range require initial velocity among other things. I can solve for initial velocity easily enough, given mass, time, distance, final velocity, kinetic energy, or any mixture of those. My problem is my meter measures psi. Is there a way to convert psi into energy, use it to solve for initial velocity, or some method that will lead to my range? Please assist if you're online, I have class soon.

[tiny-tim]

Hi Benigna! Welcome to PF! :smile:

(have a theta: θ and try using the X2 icon just above the Reply box :wink:)

I'm not sure exactly how a controlled air gun works, but pressure (http://www.physicsforums.com/library.php?do=view_item&itemid=80) is force per area, and force times distance is work done (http://www.physicsforums.com/library.php?do=view_item&itemid=75) , which is the kinetic energy (http://www.physicsforums.com/library.php?do=view_item&itemid=132) imparted to the projectile,

so if the pressure P stays the same the full length L of the barrel (does it?), then the initial KE would be PL/A. :smile:

[Benigna]

Ah i see. You are correct, I did not think to relate my pressure to force and solve for work. Once initial kinetic energy is found in (joules?), i use v1 = sqrt ((2 * e) / m); where e is energy in joules. Then solve for range. Does this seem right?

[tiny-tim]

Yup! :biggrin: