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Optimization of the stage separation and the flight path of a future launch vehicle

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System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 197))

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Abstract

The computed solutions for a realistic model of a hypersonic space vehicle demonstrate the feasibility of simultaneously optimizing the stage separation and the flight path by an indirect method. This is enabled by using state of the art optimization codes such as multiple shooting and a generalization of the necessary conditions of optimal control theory. The later is necessary in order to include in the problem formulation simultaneously such important features as piecewise defined model functions and state constraints.

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Abbreviations

v:

velocity

γ:

path inclination

χ:

azimuth inclination

h:

altitude

Λ:

geographical latitude

θ:

geographical longitude

m:

mass

x:

=(v, γ, ..., m)T

CL :

lift coefficient

μ:

bank angle

δ:

mass flow

ɛ:

thrust angle

u:

=(C L, μ, δ, ɛ)T

a:

speed of sound

D, L:

drag and lift force

C D, C L :

drag and lift coefficient

f:

right hand side of o.d.e.

F:

reference area

g:

gravitational acceleration

I sp :

specific impuls

J:

performance index

m 0 :

prescribed initial total mass

m fuel,I, m fuel,II :

fuel mass of stage I / stage II

m structure,I, m structure,II :

structure mass of stage I / stage II

m payload :

payload

M:

mach number

ψI, ψII :

structure mass model

\(\hat \psi _1 ,\hat \psi _2 ,\tilde \psi\) :

boundary and interior point conditions

\(\bar \psi\) :

staging conditions

q:

dynamic pressure

r o :

Earth's radius, R = r o + h

S:

state and control constraints

T:

thrust force

t:

time

t e :

switching time of engines (stage I)

t s :

separation time of stage I and stage II

t f :

final time

ϱ:

atmospheric density

ω:

angular velocity

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Jacques Henry Jean-Pierre Yvon

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© 1994 Springer-Verlag

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Chudej, K. (1994). Optimization of the stage separation and the flight path of a future launch vehicle. In: Henry, J., Yvon, JP. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035498

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  • DOI: https://doi.org/10.1007/BFb0035498

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19893-2

  • Online ISBN: 978-3-540-39337-5

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