The Flight Optimization System (FLOPS) is an aircraft configuration optimization program developed for use in conceptual design of new aircraft and in the assessment of the impact of advanced technology. The modular makeup of the program is illustrated. It contains modules for preliminary weights estimation, preliminary aerodynamics, detailed mission performance, takeoff and landing, and execution control. An optimization module is used to drive the overall design and in defining optimized profiles in the mission performance. Propulsion data, usually received from engine manufacturers, are used in both the mission performance and the takeoff and landing analyses. Although executed as a single in-core program, the modules are stored separately so that the user may select the appropriate modules (e.g., fighter weights versus transport weights) or leave out modules that are not needed

Mccullers, L. A.

English

NASA Technical Reports Server

,÷.N8 -11743
AIRCRAFT CONFIGURATION OPTIMIZATION
INCLUDING
OPTIMIZED FLIGHT PROFILES
L. A. McCullers
Kentron International, Inc.
Hampton, Virginia
395
https://ntrs.nasa.gov/search.jsp?R=19870002310 2020-03-20T13:59:29+00:00Z
FLIGHT OPTIMIZATION SYSTEM
The Flight Optimization System (FLOPS) is an aircraft configuration
optimization program developed for use in conceptual design of new aircraft
and in the assessment of the impact of advanced technology. Figure I shows
the modular makeup of the program. It contains modules for preliminary
weights estimation, preliminary aerodynamics, detailed mission performance,
takeoff and landing, and execution control. An optimization module is used to
drive the overall design and in defining optimized flight profiles in the
mission performance. Propulsion data, usually received from engine
manufacturers, are used in both the mission performance and the takeoff and
landing analyses. Although executed as a single in-core program, the modules
are stored separately so that the user may select the appropriate modules
(e.g., fighter weights versus transport weights) or leave out modules that are
not needed.
Optimization Weights
Module Estimation
Mission Analysis Preliminary
Performance Control Aerodynamics
Figure 1
396
WEIGHTEQUATIONDEVELOPMENT
The weight equations in the preliminary weights estimation modules were
developed by curve fitting statistical data from existing aircraft using an
optimization program. A form which madesense physically was selected for
each equation and all constants (coefficients, exponents, factors, etc.) were
optimized using nonlinear programmingtechniques. The objective was to
minimize the sumof the squares of the percentage errors between the actual
and predicted weights. A nonlinear programmingtechnique is superior to
traditional curve fitting techniques in that the form of the equation and the
variables are arbitrary. Fighter weight equations were developed using a data
base of 22 recent fighter and attack aircraft. The transport data base
included aircraft from the T-39 Sabreliner to the Boeing 747. Figure 2 shows
the correlation for the fighter fuselage weight equation.
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Wfu s = 13.068 (GW / 1000 ).898( O / 100 ).635( FL / FD ).s02( 1 + .034 .A.VAR)
/
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I I I
Predicted Weight, Ibs
I I I I I I
10 5
Figure 2
397
WING WEIGHT EQUATION DATA
The FLOPS program was developed for the evaluation and optimization of
advanced aircraft concepts which usually have unconventional wings.
Insufficient statistical data existed to accurately predict the effects on
wing weight of composite aeroelastic tailoring, forward sweep, and strut
bracing and the relationship between sweep angle and flutter and divergence
weight penalties for very high aspect ratio wings. The Aeroelastic Tailoring
and Structural Optimization program (ATSO, ref. 1) was used to generate a
series of optimum wing designs to predict these effects. Trend data from
these studies, some of which are shown in figure 3, were used with data from
existing aircraft to generate a multi-term equation that accurately predicts
weights for existing wings and provides reasonable trend data for
unconventional wings.
6 [ Metal
\ I Composite
_ 5L Composite with
_ t / oeroelastic tailoring
"_._ "--.. _ I _
_. x I _ _ ,_,- /
-_- _- F----_-_--_-_________---__-
AR = 6.96 _
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I I I I I I I I
-40 -30 -20 -10 0 10 20 30 40
Quarter-Chord Sweep Angle, deg
Figure 3
398
AERODYNAMICS MODULE
Preliminary aerodynamics data are generated using the Empirical Drag
Estimation Technique (EDET, ref. 2). Modifications have been made to improve
the accuracy of the calculations, such as implementation of the Sommer and
Short T' Method for skin friction drag (ref. 3). In addition, modifications
have been made to extend the range of the program to forward swept wings and
higher aspect ratios, as indicated in figure 4, and to more accurately account
for taper ratio. FLOPS also has the capability to use input aerodynamic data
and scale it with changes in wing area and engine size. Typically, this op-
tion is used for supersonic cruise aircraft concepts, and EDET is used for
subsonic aircraft.
0
0
0
EDET-Empirical Drag Estimation Technique
Modifications "
Forward Swept Wings
Sommer and Short T' Method
Efficiency Variation with Aspect Ratio
and Taper Ratio
ALL or Part of Aerodynamics
Input and Scaled
Data May Be
Figure 4
399
TAKEOFFANDLANDINGANALYSIS
FLOPShas the capability to perform detailed takeoff and landing
analyses, as shownin figure 5, including evaluation of constraints on
approach speed, missed approach climb gradient, second segment climb gradient,
landing field length, and takeoff field length (or balanced field length for
multi-engine aircraft) including ground effects. FLOPSalso has a series of
handbook-type formulas which predict these quantities. These formulas have
been correlated against the detailed analyses and are normally used during
optimization with the detailed analysis used for a point design evaluation.
---0
Start
TAKEOFF
_xGear_
A_ Obstacle
Rotate "_'_- Liftoff
St_ Approach LANDING
O_ Flare
I _ l I To_ Brake
O.=--m
Stop
Figure 5
400
MAINMISSIONANALYSIS
Mission performance is calculated for all segments using a step
integration technique to provide precise values for fuel burned, elapsed time,
distance covered, and changes in speed and altitude. The primary mission can
be composedof any reasonable combination of climbs, cruises, refuelings,
payload releases, accelerations, turns, holds, and descents. A typical
military attack mission is shownin figure 6. Speedand altitude continuity
may be maintained or ignored at the analyst's option.
j /-_,,.  Turo
Star "__Takeoff _'-'t_ _- Taxi-out Cruise_- Release
Figure 6
401
RESERVE MISSION ANALYSIS
The reserves may be specified as a percentage of the total fuel or as the
fuel required to fly an alternate mission or as a combination of the two. A
typical reserve mission is shown in figure 7 consisting of fuel for a missed
approach, flight to an alternate airport, and a specified hold. Each type of
segment for the main and reserve missions is specified independently and the
segments are linked together to fly the mission.
_ Cruise
Climb Descent
Figure 7
402
CLIMBPROFILEOPTIMIZATION
The climb profiles may be specified by the user or they maybe optimized
by the program. For optimization, the climb is divided into a series of
energy steps, and the combination of speed and altitude that maximizes the
objective is determined for each energy level. The objective may be minimum
time to climb, minimumfuel to climb, minimumtime to distance (interceptor
mission), or minimumfuel to distance (the most economical). Figure 8 shows a
minimumfuel to climb profile superimposedon a contour plot of the objective
function used for this case.
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60
50
_0
30
20
10
0
2
I I
5 .8 1.1
Mach Number
1.7 2.0
Figure 8
403
MINIMUM TIME TO CLIMB PROFILE
A minimum time to climb profile is shown on figure 9 superimposed on
contours of its objective function, specific excess power. The program tracks
the maximum rate of climb until it reaches the specified cruise conditions.
These plots were for a small, high thrust-weight ratio fighter. A variety of
constraints, such as obeying FAA rules or not diving through Mach I, may be
placed on the climb segment. In addition, a suboptimization may be performed
on engine power setting for minimum fuel options. This is normally used for
engines with afterburners.
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×
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6O
5O
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3O
2O
I0
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2 5 8 11
Moch Number
17
!
20
Figure 9
404
IMPACT OF CRUISE OBJECTIVE
There are ten options for specifying each cruise segment: optimum
altitude, optimum Mach number, or both for either maximum specific range or
minimum fuel flow (endurance segment); fixed Mach number and altitude; fixed
altitude and constant lift coefficient; and maximum Mach number for either
fixed altitude or optimum altitude. In addition, a suboptimization may be
performed on feathering engines. This is particularly useful in endurance
missions. Figure I0 shows the differences in altitude and speed for a very
long range turboprop transport flown to achieve maximum range and maximum
endurance.
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x
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aximum Range
_rance
I
Start Cruise
Aircraft Weight
240 kts -_
I
End Cruise
Figure 10
405
DESCENT PROFILE
The descent segment may be flown along a specified profile, at a constant
lift coefficient, or at the maximum lift-drag ratio. An optimized profile is
shown in figure ii superimposed on a contour plot of an objective function
based on lift-drag ratio.
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5O
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0
X
3O
"0
20
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.2 .5 8 11
Moch Number
I z. I? 20
Figure 11
406
DESIGN VARIABLES AND CONSTRAINTS
The nine available design variables for parametric variation or
optimization as well as the six available constraints are shown in figure 12.
Usually the altitude and Mach number are determined during flight profile
optimization and are not used as design variables. Also, there are two modes
of operation of the program. If the gross weight is specified (or an active
design variable), the range (or endurance time) is calculated and should be a
constraint in an optimization. A more effective way to use the program is to
fix the range and iterate to find the gross weight. In this way the range
constraint is always satisfied and the gross weight is a fall out, not a
variable, leaving only six active design variables and five constraints for a
normal problem.
DESIGN VARIABLES CONSTRAINTS
o Wing Area o Range
o Wing Aspect Rotio o Takeoff Field Length
o Wing Thickness-Chord Ratio o Landing Field Length
o Wing Taper Ratio o Approach Speed
o Wing Sweep Angle o Second Segment
o Thrust (Engine Size) Climb Gradient
o Gross Weight o Missed Approach
o Maximum Altitude Climb Gradient
o Maximum Mach Number
Figure 12
407
PARAMETRIC VARIATION
A matrix of point designs may be created by parametrically varying one or
more design variables. If two variables are used, contour plots such as the
one shown in figure 13 can be obtained. Contours of supersonic cruise range
are plotted for variations in wing loading (which can be used instead of wing
area) and thrust-weight ratio (instead of thrust). Using this option,
sensitivities to the design variables can be determined.
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0
,(-
110
9O
7O
5O
3O
\
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Contours of
Range
50 .75 1.00 1.25 1.50
Thrust-Weight Ratio
Figure 13
408
OPTIMIZATION
As shown in figure 14, the objective function for the configuration
optimization is a function of gross weight, total fuel, and range. This
provides the capability to minimize the gross weight or fuel for a specified
range or to maximize the range for a given gross weight. Figure 14 also
indicates some of the optimization techniques used. Programs containing
simplex and feasible directions algorithms were also used for optimization.
The results, however, were inferior to those obtained using the DFP and BFGS
algorithms.
0
0
0
0
Objective = Fl.Weight + F2. Fuel + F3. Range
Davidon - Fletcher - Powell ( DFP ) or
Broyden - Fletcher- Goidfarb - Shano ( BFGS ) Algorithm
Quadratic Extended Interior Penalty Function
One-Dimensional Search Uses Quadratic
Interpolation to a Minimum
Figure 14
409
OPTIMIZATIONPATH
Figure 15 shows the path taken by the program for the unconstrained
optimization of range on a fixed gross weight supersonic cruise fighter. The
starting point thrust-weight ratio was 1.4 for high maneuverability, and the
wing loading was 40 psf for a low approach speed. The figure shows that if
both of these constraints are relaxed, the range maybe increased by over 35
percent. All contour plots shown in this presentation were madeusing the
FLOPScontour plot options.
Contours of
/
90
C
70
o
50
30
Range
m
50 .75 1.00 1.25 1.50
Thrust-Weight Rotio
Figure 15
410
WEIGHT VARIATION WITH OBJECTIVE FUNCTION
Figure 16 shows the variation of operating weight empty (OWE), gross
weight, and mission fuel with aspect ratio for a series of optimum designs.
Wing sweep, thickness-chord ratio, and wing area were also active design
variables. Delta weights shown are from values for the minimum gross weight
design at an aspect ratio of 9.3. The minimum OWE design at an aspect ratio
of less than six saves about 12,000 pounds in OWE but uses over 40,000 pounds
more fuel. The minimum fuel design at an aspect ratio of about 17 saves
nearly 20,000 pounds of fuel but has an OWE penalty of nearly I00,000 pounds
which is off the scale in the figure.
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-10
-20
-30
4
I
I
I Minimum
I
I OWE
I
6 8
OWE
Mission Fuel
I
I
I
I
I Minimum
I Gross WeightI
I
10 12 14
Wing Aspect Ratio
Weight
I
I Minimum
Mission Fuel
16 18 20
Figure 16
411
PROBLEM AREAS
There are several problem areas, as shown in figure 17, which can make
convergence to an optimum design more difficult. The degree of design
variable interdependence necessitates the use of at least an approximate
second order algorithm. For example, in order to increase the thickness-chord
ratio, it is usually necessary to increase the wing sweep or decrease the Mach
number. Design variable scaling, when dealing with variables several orders
of magnitude apart, is as important as the optimization algorithm. The
initial value to the two-thirds power seems to work well as a scaling factor.
In a program with multiple nested iterations, analytical convergence is
crucial to accurate gradients and smooth convergence of the optimization
process. In addition, the objective function is not always well defined.
In conclusion, optimization techniques and programs exist which can be
used routinely to help solve engineering problems. They should be used
not necessarily to define the optimum piece of hardware to be built, but
as essential tools in the design process.
0
0
0
0
Design VariabLe
Design Variable ScaJing
Analytical Convergence
What is the Objective ?
Interdependence
[ VALUE 2/3 ]
Figure 17
i.
.
o
REFERENCES
McCullers, L. A.; and Lynch, R. W.: Dynamic Characteristics of Advanced
Filamentary Composite Structures, Volume II - Aeroelastic Synthesis
Procedure Development. AFFDL-TR-73-111, 1974.
Feagin, Richard C.; and Morrison, William D., Jr.: Delta Method, An
Empirical Drag Buildup Technique. NASA CR-15171, 1978.
Sommer, Simon C.; and Short, Barbara J.: Free-FlighCMeasurements of
Turbulent-Boundary-Layer Skin Friction in the Presence of Severe Aero-
dynamic Heating at Mach Numbers From 2.8 to 7.0. NACA TN-3391, 1955.
412


Aircraft configuration optimization including optimized flight profiles

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