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 th...
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)
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