I’ve been thinking about how the rockets work and which forces are involved in making the fly. After some help from Will, Matt, Ben, and Blake, I was finally able to come to the equation that governs the flight of the paper rockets.
h = (P.rocket – P.atm)*A*x/(m*g) eq. 1
h = height of the rocket
P.rocket = Pressure of the rocket inside or the pressure of the rocket launcher compressed air tank
P.atm = Pressure of the atmosphere
A = Cross-section of the rocket body (not the fins)
x = the length of the rocket body that is in contact with the launch tube
m = mass of the rocket
g = gravity
- Note 1 – m*g = Weight, So for those working in English units you just way your rocket and subsitute it for the m*g term.
- Note 2 – make sure that your units are consistant. NASA has made catastrophic errors and lost millions of dollars due to conversion errors don’t let this happen to you! =)
Using the equation
In order to keep things simple I added in a conversion factor so that the answer will be in feet after you plug in the values. The equation then becomes
h = (P.rocket – 14.7)*A*x/(12*W) eq.2
where
h =(ft) height of the rocket
P.rocket = (Psi) Pressure of the rocket inside or the pressure of the rocket launcher compressed air tank
14.7 psi = (Psi) Pressure of the atmosphere (@sea level)
A = (in^2) Cross-section of the rocket body (not the fins) = (π*d^2)/4
x = (in) the length of the rocket body that is in contact with the launch tube
W = (lbs) weight of the rocket
Examples
I’d run through some calculations but I need a digital scale that is small enough to measure the rocket. I’d suggest buying one that has the capability to measure in grams because you will be a better resolution. Then you can convert it over to pounds.
Mad Laboratory 