User:Laura Rose P/sandbox

Fins: Physics of Stabilization
The fins on a rocket are important for stability during flight. They should be placed near the rear of the rocket.

Aerodynamic drag acts on the fins as well as on the rocket body. Fins add to the frontal surface area on which the drag force acts (and therefore should be designed not to add too much drag). The drag forces on all frontal surfaces of the rocket can be resolved into one force acting at the center of pressure. This acts to oppose the forward motion, but if the rocket nose is not pointed in the direction of its motion at a given time (perhaps due to wobbling or instability), then there will be a torque, due to the resolved drag force, acting around the center of gravity. This torque will stabilize the rocket by returning its nose to the direction of travel.

Since the torque is the cross-product of the drag force magnitude and the moment arm, torque can be maximized without increasing drag force by increasing the moment arm. The larger the distance between the center of gravity and the center of pressure, the greater the moment arm on the restoring torque. Therefore, it is desirable to have the center of pressure, and therefore the fins, as far back as possible on the rocket body.

The lift force acts to push the back end of the rocket so that the nose will face the flight direction, and the drag force does the same, even though it is pointing orthogonally to the lift force.



Predicting Peak Height
If aerodynamic drag and transient changes in pressure are neglected, a closed-form approximation for the peak height of a rocket fired vertically can be expressed as follows: h=〖(M_i/M_R )〗^2 P_i/ρg [citation needed] (h = peak height reached, M_i = Initial mass of water only, M_R = Rocket mass when empty, P_i = Initial gauge pressure inside rocket, ρ = air density, g = acceleration due to gravity) Assumptions for the above equation: (1) water is incompressible, (2) flow through the nozzle is uniform, (3) velocities are rectilinear, (4) density of water is much greater than density of air, (5) no viscosity effects, (6) steady flow, (7) velocity of the free surface of water is very small compared to the velocity of the nozzle, (8) air pressure remains constant until water runs out, (9) nozzle velocity remains constant until water runs out, and (10) there are no viscous-friction effects from the nozzle (see Wikipedia article on “Moody chart”).