Periodic Optimal Trajectories with Singular Control for Aircraft with High Aerodynamic Efficiency

  • Gottfried Sachs
  • Klaus Lesch
  • Hans Georg Bock
  • Marc Steinbach
Chapter
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 111)

Abstract

Fuel minimum range cruise of aircraft with high aerodynamic efficiency is considered as an optimal periodic control problem. Optimality conditions for trajectories with singular arcs and state variable constraints are derived.

Computation of periodic optimal trajectories in the case addressed presents strong requirements on the numerical algorithm. Computational difficulties become larger when aerodynamic efficiency is increased and wing loading is decreased. The specific nature of the numerical problems encountered and the means used to overcome them are described.

Keywords

Fuel Consumption Singular Control Wing Loading Roundoff Error Aerodynamic Efficiency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

CD

drag coefficient

CL

lift coefficient

C*L

lift coefficient at maximum lift/drag ratio

c

normalized period length

D

drag

E

aerodynamic efficiency, E = (C L/C D)max

g

acceleration due to gravity

H

Hamiltonian

h

altitude

J

performance criterion

K

factor according to lift dependent drag, C D = C D0 + KC 2 L

L

lift

m

mass

mV

exponent denoting the effect of speed on fuel consumption

P

propulsive power, P = TV

S

reference area

S̄

switching function

T

thrust

V

speed

V*0

speed for best glide ratio at sea level (h = 0)

x

horizontal coordinate

y

state variable vector

γ

flight path angle

δ

throttle setting

ε

glide ratio

λ

Lagrange multiplier

ϱ

atmospheric density

σ

fuel consumption factor

ξ

independent variable

ξ

a bar denotes a normalized quantity, e.g. V

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References

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Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • Gottfried Sachs
    • 1
  • Klaus Lesch
    • 1
  • Hans Georg Bock
    • 2
  • Marc Steinbach
    • 2
  1. 1.Institute of Flight Mechanics and Flight ControlTechnische Universität MünchenMünchen 2Germany
  2. 2.Interdisciplinary Center of Scientific ComputingUniversität HeidelbergHeidelbergGermany

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