火箭设计-火箭数学

The Rocket Equation • Defines the change in velocity of a rocket as it expels a propellant • Derived from Newton’s Second and Third Laws • Can be derived from Conservation of Momentum and Energy vf – vi = vrel ln (mi/mf) vf final velocity of the rocket in m/s vi initial velocity of the rocket in m/s vrel relative velocity between the exhaust and the rocket in m/s ln natural logarithm mi initial mass of the rocket in kg mf final mass of the rocket in kg Deriving the Rocket EquationDeriving the Rocket Equation Begin with F = dp/dt (Newton’s Second Law) Recall, p = m v (momentum) Do not assume m nor v are constant, so F = d(m v)/dt = v dm/dt + m dv/dt If we let the force go to zero (equilibrium), -v dm/dt = m dv/dt Reworking, dv = -v dm/m Integrating, we find the rocket equation vf – vi = vrel ln (mi/mf)