- #1
Alcubierre
- 80
- 0
I am building a water rocket for my physics class and I want to make my calculations as precise as possible. I want to calculate throttle, velocity, acceleration, momentum, and max height.
With that said, what should I take into account? Gravity, wind velocity, shape of cone of the rocket, density, anything else? And would temperature be a factor?
The rocket will be made out of a coke bottle (2 L) and it will start with about 300-800 mL of water (I'm not so sure on the amount) so I will have to take into account the change of momentum over time, and we will use 45-60 psi.
This is what I have so far:
For thrust, T = [itex]\frac{\pi}{2}[/itex]PD2
Height, h = ([itex]\frac{Mi}{Mr}[/itex])2([itex]\frac{Pi}{\rho g}[/itex]) where Mi is the mass of the water only, Mr is the mass of the rocket when empty, Pi is the initial gauge pressure inside the rocket, and ρ is the air density.
External forces, M[itex]\frac{dv}{dt}[/itex] = [itex]\alpha[/itex]Ve + Fext = [itex]\alpha[/itex]Ve + Fg + Fdrag, where [itex]\alpha[/itex] is -([itex]\frac{dM}{dt}[/itex]), Ve is the velocity of the water leaving nozzle, and is it safe to suggest that Fd is Stokes' drag at small velocities (Fd [itex]\propto[/itex] -b[itex]\upsilon[/itex])?
And I don't know how to account the shape of wings and all that. Any suggestion?
And what else should I add?
In essence, I want to be able to calculate a model that would fly the highest and fastest.
With that said, what should I take into account? Gravity, wind velocity, shape of cone of the rocket, density, anything else? And would temperature be a factor?
The rocket will be made out of a coke bottle (2 L) and it will start with about 300-800 mL of water (I'm not so sure on the amount) so I will have to take into account the change of momentum over time, and we will use 45-60 psi.
This is what I have so far:
For thrust, T = [itex]\frac{\pi}{2}[/itex]PD2
Height, h = ([itex]\frac{Mi}{Mr}[/itex])2([itex]\frac{Pi}{\rho g}[/itex]) where Mi is the mass of the water only, Mr is the mass of the rocket when empty, Pi is the initial gauge pressure inside the rocket, and ρ is the air density.
External forces, M[itex]\frac{dv}{dt}[/itex] = [itex]\alpha[/itex]Ve + Fext = [itex]\alpha[/itex]Ve + Fg + Fdrag, where [itex]\alpha[/itex] is -([itex]\frac{dM}{dt}[/itex]), Ve is the velocity of the water leaving nozzle, and is it safe to suggest that Fd is Stokes' drag at small velocities (Fd [itex]\propto[/itex] -b[itex]\upsilon[/itex])?
And I don't know how to account the shape of wings and all that. Any suggestion?
And what else should I add?
In essence, I want to be able to calculate a model that would fly the highest and fastest.