lecture3b - Rocket Equation The rocket equation: How much...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Rocket Equation Konstantin Tsiolkovsky The rocket equation: How much fuel is required? Rocket equation , derived from conservation of momentum, trades off exhaust velocity with payload fraction. It was first derived by Tsiolkowsky in 1895 for straight-line rocket motion with constant exhaust velocity. It is also extended for elliptical trajectories and applied to chemical and nuclear-thermal rockets. Propellant gets used up as the vehicle produces thrust to accelerate. Also, as the propellant is blasted out the exhaust nozzle, the mass of the vehicle decreases.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Rocket Equation Konstantin Tsiolkovsky The rocket equation: How much fuel is required? The ideal rocket equation estimates the amount of propellant needed to change a vehicle’s velocity Δ v. It relates mission requirements to system requirements .
Background image of page 2
MV = Δ M[V-U ex ] + [M- Δ M] [V+ Δ V] MV = Δ MV- Δ MU ex +MV - Δ MV+M Δ V- Δ M Δ V M Δ V= Δ MU ex + Δ M Δ V dt V M d F external ] [ r = Newton’s Third Law Look at a rocket in horizontal flight
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
F = Engine mass flow Engine thrust equation We shrink time as small as possible Reaction Force on Rocket Newton’s Third Law Dividing by Δ t and evaluating limit { Δ M, Δ V, Δ t} 0 ex ex U dt dM dt dV M t V M U t M t V M = Δ Δ Δ + Δ Δ = Δ Δ as limit { Δ M, Δ V, Δ t} 0 ex U dt dM dt dV M = = m propellant C e
Background image of page 4
Compare the results F= Using Fluid Conservation laws Using Newton’s laws Effective Exhaust Velocity F = m e V e + p e A e p A e () U ex = V e + p e A e p A e m e C e ex U dt dM dt dV M =
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 19

lecture3b - Rocket Equation The rocket equation: How much...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online