Optimal Aircraft Trajectories
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Foundation ::
Trajectories and Orbital Mechanics ::
Optimal Aircraft Trajectories
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Optimal Aircraft Trajectories
Optimal Aircraft Trajectories for Specified Range
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Moderators:
Adopt This Application!
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SOURCE CODE AVAILABLE
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For an aircraft operating over a fixed range, the operating costs are
basically a sum of fuel cost and time cost. While minimum fuel and minimum
time trajectories are relatively easy to calculate, the determination of
a minimum cost trajectory can be a complex undertaking. Optimal Aircraft Trajectories for Specified Range
was developed to optimize trajectories with respect to a cost function
based on a weighted sum of fuel cost and time cost.
As a research tool,
the program could be used to study various characteristics of optimum trajectories
and their comparison to standard trajectories. It might also be
used to generate a model for the development of an airborne trajectory optimization
system. The program could be incorporated into an airline flight
planning system, with optimum flight plans determined at takeoff time for
the prevailing flight conditions. The use of trajectory optimization could
significantly reduce the cost for a given aircraft mission.
The algorithm incorporated in the program assumes that a trajectory
consists of climb, cruise, and descent segments. The optimization of each
segment is not done independently, as in classical procedures, but is performed
in a manner which accounts for interaction between the segments.
This is accomplished by the application of optimal control theory. The
climb and descent profiles are generated by integrating a set of kinematic
and dynamic equations, where the total energy of the aircraft is the independent
variable. At each energy level of the climb and descent profiles,
the air speed and power setting necessary for an optimal trajectory are determined.
The variational Hamiltonian of the problem consists of the rate
of change of cost with respect to total energy and a term dependent on the
adjoint variable, which is identical to the optimum cruise cost at a specified
altitude. This variable uniquely specifies the optimal cruise energy,
cruise altitude, cruise Mach number, and, indirectly, the climb and descent
profiles. If the optimum cruise cost is specified, an optimum trajectory
can easily be generated; however, the range obtained for a particular optimum
cruise cost is not known a priori. For short range flights, the program
iteratively varies the optimum cruise cost until the computed range converges
to the specified range. For long-range flights, iteration is unnecessary
since the specified range can be divided into a cruise segment distance
and full climb and descent distances.
The user must supply the program with engine fuel flow rate coefficients
and an aircraft aerodynamic model. The program currently includes
coefficients for the Pratt-Whitney JT8D-7 engine and an aerodynamic model
for the Boeing 727. Input to the program consists of the flight range to be
covered and the prevailing flight conditions including pressure, temperature,
and wind profiles. Information output by the program includes: optimum
cruise tables at selected weights, optimal cruise quantities as a function
of cruise weight and cruise distance, climb and descent profiles, and a
summary of the complete synthesized optimal trajectory.
Optimal Aircraft Trajectories for Specified Range carries the NASA case number ARC-11282. It was originally released as part of the NASA COSMIC collection.
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