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chap3_9_17

# chap3_9_17 - AAE 439 IDEAL ROCKET EQUATION u Assumptions...

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AAE 439 Ch3 –9 IDEAL ROCKET EQUATION Assumptions: Propellant flow rate is constant, Gravity-free, No drag. Newton’s 2 nd Law: Instantaneous Vehicle Mass: Velocity Change: Velocity History: Velocity Gain due to Burn of Propellant Mass M P during Burn Time t b : dm M u u e p e A e F = M du dt du = F M dt = u eq m M dt M t ( ) = m 0 mt = m 0 1 t t b m P m 0 du = u eq α t b 1 α t t b dt Δ v = u eq ln 1 α ( ) = u eq ln m 0 m f e Δ v u eq = m 0 m f = CG dm = + mdt = dM dt dt du = u eq dM M v ( t ) = du v i v f = u eq dM M m 0 m = u eq α t b 1 α t t b 1 0 t dt

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AAE 439 Ch3 –10 IDEAL ROCKET EQUATION Ideal Rocket Equation: Usually, mission requirements are stated in terms of velocity increment, or v (“delta V”). The rocket equation defines the velocity increment, and tells us how much propellant is needed to change the velocity of a mass while its mass is changing (rockets naturally change mass as they expel burnt propellant).
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