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Effective Date: 15 June 98

Flight Performance

Flight performance is the general reference to climb, cruise, descent performance and resulting drag analysis. The procedures for reduction and analysis of flight performance data described below are for the most part direct and conventional. Computerized processing augmented by parallel hand calculation checks are recommended.

The overall philosophy of the flight performance analysis is to,

1) reduce the flight measured data to a parametric form which are incorporated into a faired array of curves reflecting the aircraft performance;

2) through an expansion process, compute any desired performance parameter for each exact test point condition thereby making a direct comparison of the measured to the calculated parameters.

Working plots are constructed for comparison purposes. The measured is plotted as an "O" and the computed as and "X". An computed line using average values of gross weight, etc. is used as a guide to identify single point deviations in searching for data errors. For final presentation, the difference between the measured and computed is added to a computed line using constant gross weight, constant altitude, standard day, etc. These are the data shown in the table below.

3) Once a satisfactory comparison of the calculated parameter with the measured is obtained, then through the same expansion process compute the desired performance parameters for a complete array of gross weights, speeds, altitudes, and ambient temperatures for Flight Manual, Guaranteed Report or Substantiating Data Report.

Reduction

In general, the flight performance reduction procedure is intended to analyze speed power data, sawtooth climb data, continuous climb data, and descent data by methods described below. The equation of motion is used to derive the lift and drag relationship. This relation is common to all of the above tests. From this point in the analysis, a different data presentation, depending upon the type of test, are constructed. These data presentations include basic instrument corrected test day data along with computed flight performance parameters, for only the test day conditions. Further analysis is performed through the expansion process that initially compares the measure data with the calculated data and then, computes a full array of desired parameters for performance charts.

Specifically, for the reduction analysis procedure of each type of test, there is produced a time history of the basic atmospheric parameters of airspeed, altitude, free air temperature, etc. to ascertain that a particular test run meets the requirements of a performance test. This plots is termed the "basic time history". Then, depending on the type of test, there are presented summary plots of the data presentation, which depends on the type of test, which are summarized below. Some of the information on the test plots have been removed in an attempt to keep the presentation as generic as possible.

Plot Types

Note: PS denotes Power Setting parameter such as EPR, N1, N2, etc. This data flow progresses to the expansion analysis discussed later.

FIGURES	TYPE OF TEST	PLOT TITLE	FORMAT
1	Level Flight	Specific Range	Vt/Wf vs Speed (Mach or KCAS)
2	Level Flight	Specific Range	Vt/Wf vs Speed (Mach or KCAS)
3	Level Flight	Specific Range	Vt/Wf vs Speed (Mach or KCAS)
4	Level Flight	Specific Range	Vt/Wf vs Speed (Mach or KCAS)
5	Level Flight	%SAR Error	%(Vt/Wf) vs Speed (Mach or KCAS)
6	Level Flight	Level Flight Performance	Drag vs Speed
7	Level Flight	Level Flight Performance	Drag vs Speed
8	Level Flight	Level Flight Performance	Drag vs Speed
9	Level Flight	Level Flight Performance	Drag vs Speed
10	Level Flight	%Cd Error	%Drag Coeff. Error vs Speed
11	Level Flight	Drag Comparison	Measured Cd vs Model Cd
12	Level Flight	Power Setting	EPR vs Speed
13	Level Flight	Power Setting	EPR vs Speed
14	Level Flight	%Thrust Error	%Thrust vs Speed
15	Level Flight	%Fuel Flow Error	%Fuel Flow vs Speed
16	Sawtooth Climb	Sawtooth Climb	R/C vs Speed
17	Sawtooth Climb	Sawtooth Climb	R/C vs Speed
18	Sawtooth Climb	Sawtooth Climb	R/C vs Speed
19	Sawtooth Climb	Rate of Climb Comparison	R/C measured vs R/C model
20	Climb Speed	Climb Schedule	R/C vs Speed
21	Climb Speed	Climb Schedule	R/C vs Speed
22	Climb Speed	Climb Schedule	R/C vs Speed
23	Climb Performance	Continuous Climb	R/C etc. vs Altitude
24	Climb Performance	Continuous Climb	Schedule vs Altitude
25	Climb Performance	Continuous Climb	R/C etc. vs Altitude
26	Climb Performance	Continuous Climb	Schedule vs Altitude
27	Descent Performance	Continuous Descent	R/C etc. vs Altitude
28	Climb Performance	Continuous Climb	Schedule vs Altitude

Instrumentation

The parameters necessary for analysis of flight performance data are as follows:

GW = Gross Weight, lb

CG = Center of Gravity Position, % MAC

Vc = Calibrated Airspeed, KCAS

Hp = Calibrated Pressure Altitude, ft

Tamb = Ambient Temperature, deg C

dr = Rudder Position, deg

df = Flap Position, deg

dg = Landing Gear Position, (usually Up/Dn)

ds = Stabilizer (Elevator) Trim, deg

de = Elevator Position, deg

a = True Angle of Attack, deg

b = Angle of Sideslip, deg

j = Angle of Pitch, deg

q = Aircraft Heading, deg

f = Angle of Bank, deg

N = Engine Speed, %RPM

ET = Engine Temperature, deg C

PS = Engine Power Setting, -- (EPR, N1, N2, etc.)

Wf = Engine Fuel Flow, lb/hr

Fn = Engine Net Thrust, lb

The methods of obtaining the above engine parameters are usually developed in coordination with the propulsion design group and the engine manufacture and is beyond the scope of this document. The remainder of the items are measure directly or use standard engineering procedures to derive the values from the actual measurement.

Derivation of Basic Aerodynamic Performance Equations

The derivation of the basic aerodynamic performance equations begin with the following illustration.

T it a L GW j g ______________________________________________

Summing the forces along the flight path:

F = T cos(a+it) - D - GW sing = ma = (GW/g)(dVt/dt) ........................................ (1)

where:

F = Force Along Flight Path

T = Total Engine Net Thrust, lb

it= Thrust Incidence Angle, deg

D = Aircraft Drag, lb

g = Gamma, Flight Path Angle, deg

ma = Mass times Acceleration

g = Acceleration Due To Gravity (32.1714) ft/sec sq

(dVt/dt) = Rate of Change of KTAS , kt/sec

Using:

sing = (RCt)/Vt ............................................................. (2)

NOTE: The term "RCt which is true (or tapeline) rate of climb is obtained from the slope of the measure pressure altitude, Hp versus time corrected by the temperature relation,

RCt = dHp [ Tamb(test)] / dt [ Tamb(STD) ] ....................................... (3)

Equation (1) is rewritten to solve for drag,

D = T cos(a + it) - GW (RCt)/Vt - (GW/g)(dVt/dt) ...................................... (4)

and the drag coefficient, CD is:

CD = D/qe Sw .............................................. (5)

where:

qe = Dynamic Pressure , psf

Sw = Wing Area, sq ft

Now summing forces perpendicular to the flight path:

F = - GW cosg + T sin(a+it) + L = (GW/g)(RCt/dt)cosg ..................................... (6)

However, the rate of climb change with time, (dRCt/dt) is normally small and is neglected for climb and cruise performance. Equation (6) in terms of lift becomes:

L = GW cosg + T sin(a + it) ............................................... (7)

and the lift coefficient, CL is:

CL = L/qe Sw ........................................................ (8)

CORRECTI0NS TO IMPROVE CONSISTENCY

All test lift and drag data may be referenced to a common CG and common Reynolds number to improve consistency. This may not be warranted for low speed aircraft with minimal CG travel. If the propulsion system produces flow over wings and such, slipstream accountability may be desired to aid in data consistency. Conversion to a drag polar representative of the production configuration can be obtained by analytically removing the drag of such equipment from the measured values.

CG Accountability

The analysis procedure used is to adjust the lift coefficient values for CG position but neglect the small drag accountability due to change in tail induced drag. Wind tunnel tests will usually show tail induced drag is negligible.

To adjust a test CL (CLtest) to any reference CG position, the d(CLtail) due to CG transfer must be added to the CLtest, hence:

CLref = CLtest + d(CLtail) ................................................... (9)

Since CLtest = CLtrim .......................................................... (10)

Then:

CLref = CLtest( 1 + (MAC/lt)[ (Xcgref-Xcgtest)/MAC ] )............... (11)

This is the final equation relating the trimmed CLref to the trimmed CLtest. This CLref along with the following CD adjusted for the external test instrumentation defines the production aircraft drag polar. The reference Cg position, probably 25 %MAC must be chosen for all tests.

Reynolds Number Correction

To further aid in the consistency of the measured higher speed drag data, it may be desirable to correct the measure data to a single Reynolds number.

RN/FT = 1.26602795(TambK + 110.4) Pamb KTAS/TambK2.5 ............. (12)

RN = MAC RNFT .................................................. (13)

CDSF = C0 - C1 LOG10(RN)+ C2 LOG10(RN)2 ................... (14)

Hence, (if elected) for the higher speed cruise data:

CDref = CDtest - CDSF (Reduction) ................................ (15)

where:

C0, C1, C2 are derived curve fit coefficients based upon conventional wind tunnel and theoretical methods.

NOTE: Must be same coefficients (curve) in reduction and expansion process.

CDref = CDtest + CDSF (Expansion) .................................. (16)

Pamb =D (Ambient Pressure), In Hg

TambK =D (Ambient Temperature), deg Kelvin

Slipstream Accountability

Where the propulsion system produces flow over the wings and such, it may be desirable to derive the influence of thrust on the drag polars in the various configuration. Convention jet engines usually require only the thrust vector accountability which is in the previously developed equations. For significant flow developed in the low speed, flaps down regime by a typical propeller driven configuration, a second order effect of thrust, usually related to thrust coefficient, CT can be developed from the data. This can be done by isolating the difference in the high power sawtooth climb data from the coupled idle descents. The difference can be related to power effects. This task was difficult before the advent of computerized curve fitting routines that now can isolate the influence. Correlation of the slipstream factor is fairly attainable now. Again, the factor, once incorporated into the reduction process, must be incorporated into the expansion process.

Flight Test Instrumentation Accountability

The flight test performance aircraft has certain external flight test equipment which is peculiar only to the flight test aircraft. This equipment may consist of an airspeed boom, external airfield cameras, temperature probes, tail skegs, trailing cone, various water ballast dump holes and possibly other miscellaneous items. In order to obtain a drag polar applicable to a production aircraft the estimated dCDg of these items are subtracted from each flight test CD value. This dCD is determined using acceptable estimating techniques and will provide an aircraft drag representative of the production configuration.

ANALYSIS PROCEDURE

Using the basic relations defined by Equations 4 and 11, drag characteristics data are obtained for each type of flight performance test.

The drag characteristics of the aircraft are determined for each configuration in the conventional form of

CDref versus CLref for the low speed flaps down with considerations to the thrust produced slipstream effect and

CDref versus CLref and Mach number for the clean high speed condition.

For the gear extended configuration, the difference between two drag polars with the same flap setting, one gear retracted the other extended will isolate the gear drag increment.

For the asymmetric thrust tests, it is necessary to determine the variations of windmilling drag and trim drag relative to the all engine operating (aeo) such that, for a one engine inoperative (oei), asymmetric condition:

CDoei = CDaeo + dCDwm + dCDtrim ..................................... (17)

where:

CDoei = Drag Coeff with All Engines Operating

CDaeo = Drag Coeff with One Engine Inoperative

dCDwm = Windmilling Drag Coeff

dCDtrim = Incremental Drag Due to Asymmetric Trim

The Incremental Drag Due to Asymmetric Trim, dCDtrim is a function of the yawing moment due to asymmetric thrust, the rudder position, bank angle, sideslip angle and dynamic pressure. Here, the increment will be considered as a function of the yawing moment coefficient, Cn which is:

Cn = [T1l1 + T2l2 - T3l3 - T4l4] cos(it) / [ qe Sw b ] ................................. (18)

COMPARISON

Now through an expansion process, it is necessary to compute any desired performance parameter for the exact test condition such that a direct comparison of the measured to the calculated parameters can be made. The purpose of this reproduction sequence is to provide a check and balance system to validate the fairings of the lift curves, drag curves, thrust curves, fuel flow curves, and such. It is possible to ascertain by comparison of calculated to measured data if accurate reproduction has been achieved. Once a satisfactory comparison of the calculated parameter with the measured is obtained, then through the same expansion process compute the desired performance parameters for a complete array of gross weights, speeds, altitudes, and ambient temperatures.

Climb and Descent Comparison

The method of calculating sawtooth climbs, continuous climbs, and descents have certain common computing procedures. Then due to the format of data presentation, the methods diverge to determine specific parameters not common to all types of tests.

Drag characteristics data are obtained through the reduction process are presented in the form of:

CDref = f[ CLref, Mach, CT* ] ................................. (19)

* possibly

(All symbol used in this section are previously defined)

There are, however, auxiliary data curves or constants used in the development of these data. Parameters, such as windmilling drag, directional trim drag, Reynolds number drag, and longitudinal trim lift increments are used for reduction analysis. These same increments must used in the expansion process. Windmilling drag coefficient, dCDwm, is considered here as a constant. (In reality, it may vary with speed depending upon the propulsion configuration.) The directional trim drag is in the form of:

dCDtrim = f[ Cn ] ............................................ (20)

where:

Cn = [T1l1 + T2l2 - T3l3 - T4l4] cos(it) / [ qe Sw b ].............................. (21)

The trim lift coefficient as defined by Equation (11) is in the form of:

CLref = f[ CLtest, CGref, CGtest ] ................................. (22)

The steps for computing climb and descent comparisons are:

1) compute thrust and fuel flow at the test airspeed, test altitude, test ambient temperature and test power setting.

2) Determine CLref by:

CLref = CLtest( 1 + (MAC/lt)[ (Xcgref-Xcgtest)/MAC ] )....................... (23)

where:

the test lift coefficient, CLtest is:

CLtest =L/qe Sw ............................................... (24)

and the lift is:

L = GW cosg + T sin(a + it) ......................................... (25)

The terms a and g are obtained through an iterations loop.

3) Drag coefficients is:

CDref = f [CLref, Mach, CT ] ....................................... (26)

4) However, this CD is not adjusted for trim drag, (dCDtrim) or windmilling drag, (dCDwm) for the one engine inoperative (oei) or multiple engine out operation. To determine the total drag coefficient for other than the all engine operating case, it is first necessary to determine dCDtrim by:

CDtrim = f[ Cn ] ...................................... (27)

Then, for the appropriate inoperative engine configuration, compute the total drag coefficient, for example:

CDoei = CDaeo + dCDwm + dCDtrim ....................................... (28)

5) An iteration loop is required through Step (2) to determine the value of "T sin(a+it)" using:

a = f[ dCL/da, a @l=0, M, Hp, CLref ] ..................................... (29)

6) The Climb Gradient, g is defined by:

RCt = 101.3 Vt [ T cos(a + it) - D ] / GW [ 1 + .08854 Vt (dVt/dH) ] ..... (30)

where:

(dVt/dH) = [(dVt/dt)/(dHp/dt)]test [TaSTD/TaTEST]................................... (31)

NOTE The term dVt/dt is developed from sloping a trace of KTAS with respect to time. The source of this is usually from a pneumatic air data system. Depending upon the air mass the aircraft is operating within, a review of the ground speed trace from an inertial measuring unit should provide the best source for the term.

7) Then for direct comparison to the measure rate of climb (or descent)

(dHp/dt) = [ RCt ] [ TaSTD/TaTEST ] .................................... (32)

The data presentation for the sawtooth climb (or descent) is illustrated below.

SAWTOOTH CLIMB

O Test Data

X Computed

___ Computed for the average test condition

Pressure Rate of Climb

_________________________________________________

Airspeed

Continuous Climbs and Descents Comparison

The comparison is complete for a sawtooth climb. For continuous climbs or descents, the calculation of time and fuel to clime (or descend) is accomplished using a step integration process with small time increments and computing the change in altitude and fuel used during these small time increments. Conventional plots reflecting a continuous climb profile are made for comparison to the "X"s and "O"s. It should be notes that the climb airspeed schedule should be smoothed for use in the calculations to be able to use reasonable time elements; else elements in the one second region may have to be used significantly increasing the computing procedure.

Cruise Comparison

The cruise comparison is similar to climbs. The test power setting, however, is not set. It is obtained through an iteration process as with the a terms. Conventional plots of specific range and power required are generated for comparison of the "X"s and "O"s.

EXPANSION

Now through the same expansion process compute the desired performance parameters for a complete array of gross weights, speeds, altitudes, and ambient temperatures. The same computing procedures are used as with the test comparisons except the flight conditions selected are an array of values that will provide aircraft performance data for the full flight spectrum.