. ·~·~. 'USAF STABILITY AND CONTROL DATCOM

MCDONNEf...L'OQUGLAS CORPORATIONDOUGLAS
AIFfCRAFT OIVI~ION.
"'. ,.. .
';..· '(...,,.
PRINCIPAL INVESTIGATOR: R. D. FINCKOCTOBER 1960
Contract AF33(616)-6460•.!.

REVISED APRIL 197 8
Contract F336;S-76-C-3061
Project No. 8219
,Task No. 821901

FLI<{HT C0:Nr,IWL DIVISION
AIR FORCE FLIGOTJ)YNAMICS LABOR'ATORYWRIGHT-PATTERSON
Ai'R " FORCE BASE; OHIO
.
; ·..
~

'

,...

FOREWORD
The current volume entitled "USAF Stability and Control Datcom" has been
prepared by the Douglas Aircraft Division of the McDonnell Douglas Corporation
underContracts
AF33(616)-6460, AF33(615)-1605,
F336!5-67-C-1156,
F33615-68-C-1260, F33615-70-C-J 087, F33615-71-C-1298, F33615-72-C-1348,
F33615-73-C-3057, F33615-74-C-3021, F33615-75-C-3067, and F33615-76-C3061. (The term Datcom is a shorthand notation for data compendium.) This effort
is sponsored by the Control Criteria Branch of the Flight Control Division, Air Force
Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio. The
Air Force project engineers for this project were J. W. Carlson and D. E. Hoak. The
present volume has been published in order to replace the original work and toprovide timely stability and flight control data and methods for the design ofmanned aircraft, missiles, and space vehicles. It is anticipated that this volume will
be continuously revised and expanded to maintain its currency and utility.
Comments concerning this effort are invited; these should be addressed to the
procuring agency.

iii

CONTRIBUTORSDOUGLAS AIRCRAFT COMPANY, INC. 1960-1965
MCDONNELL DOUGLAS CORPORATIONDOUGLAS AIRCRAFT DIVISION 1967-1977

PRINCIPAL INVESTIGATORS
R. D. FINCK (1971)
D. E. ELLISON ( 1962-1970)
L. V. MALTHAN (1958-1962)
PRINCIPAL COLLABORATORS
D. E. Ellison .
R. B. Harris
D. E. Drake .
M. J. Abzug .
C. S. Thorndike

Technical Director
Technical Advisor
Technical Advisor
Technical Advisor
Technical Editor, 2.1,
Sample Problems & Illustrations
4.6-, 4.7-, 5.2-, 5.3-, 5.6

R. A. Berg ..
G. L. Huggins
R. M. Seplak .
A. C. Blaschke .
P. J. Buce ..
M.S. Cahn . . .
J. W. Gresham .
N.H. Buckingham .
W. H. Rudderow.
C. 0. White .
J. L. Lundry . . .
D.P. Marsh . . .
J. L. Woodworth .
J. Hebert . . . .
M. G. Brislawn .
W. B. Fisher .
H. B. Dietrick
R. C. Leeds
S. L. Fallon .

64-, 37-

4.3-, 5-, 664-

4.26-

4-, 5-

48.1
8.2
496-

Sample Problems
Graphs & Illustrations
Graphs & Illustrationsiv

Revised Apri11978

TABLE OF CONTENTS
Section I

GUIDE TO DATCOM and METHODS SUMMARY

Section 2

GENERAL INFORMATION

2.1
2.2

General Notation
Wing Parameters
Section Parameters

2.2.1
2.2.2

Plan form Parameters

2.3

Body Parameters
EFFECTS OF EXTERNAL STORES

Section 3

3.1

Effect of External Stores on Aircraft Lift
Lift Increment Due to Wing-Mounted Store Installations

3.1.1
3.1.2
3.1.3

Lift Increment Due to Fuselage-Mounted Store Installations
Total Lift Increment Due to External Stores

3.2
3.2.1
3.2.1.1
3.2.1.2
3.2.1.3

Effect of External Stores on Aircraft Drag
Drag at Zero Lift
Basic Drag Due to Store Installations
Drag Due to Adjacent Store Interference
Drag Due to Fuselage Interference

3.2.2
3.2.3

Drag Due to Lift
Total Drag Increment Due to External Stores

3.3.1
3.3.2
3.3.3
3.3.4

Neutral-Point Shift Due to Lift Transfer from Store Installation to Clean Aircraft

3.3

Effect of External Stores on Aircraft Neutral Point
Neutral-Point Shift Due to Interference Effects on Wing Flow Field
Neutral-Point Shift Due to Change in Tail EffectivenessTotal Neutral-Point Shift Due to External Stores

3.4
3.5

Effect of External Stores on Aircraft Side Force
Effect of External Stores on Aircraft Yawing Moment• Effect of External Stores on Aircraft Rolling Moment

3.6
Section 4

CHARACTERISTICS AT ANGLE OF ATTACK

4.1

Wings at Angle of Attack

4.1.1

Section Lift

4.1.1.1
4.1.1.2
4.1.1.3
4.1.1.4
4.1.2

Section Zero-Lift Angle of A !tackSection Lift-Curve Slope
Section Lift Variation with Angle of Attack Near Maximum Lift
Section Maximum Lift
Section Pitching Moment

4.1.2.1
4.1.2.2

Section Zero-Lift Pitching Moment
Section Pitching-Moment Variation with Lift
Wing Lift

4.1.3.1
4.1.3.2
4.1.3.3
4.1.3.4

Wing Zero-Lift Angle of Attack
Wing Lift-Curve SlopeWing Lift in the Nonlinear Angle-of-Attack Range
Wing Maximum Lift
Wing Pitching Moment
Wing Zero-Lift Pitching Moment

4.1.3

4.1.4
4.1.4.1
4.1.4.2

Wing Pitching-Moment-Curve Slope*Subjects for Future Additionsv

4.1.4.3
4.1.5
4.1.5.1
4.1 .5.2
4.2
4.2.1
4.2.l.l
4.2.1.2
4.2.1.3
4.2.2
4.2.2.1
4.2.2.2
4.2.2.3
4.2.3
4.2.3.1
4.2.3.2
4.3
4.3.1
4.3.l.l
4.3.1.2
4.3.1.3
4.3.1.4

Wing Pitching Moment in the Nonlinear Angle-of-Attack Range
Wing Drag
Wing Zero-Lift Drag
Wing Drag at Angle of Attack
Bodies at Angle of Attack
Body Lift
Body Lift-Cu!Ve Slope
Body Lift in the Nonlinear Angle-of-Attack Range*Effects of Asymmetries

Body Pitching Moment
Body Pitching-Moment-Curve Slope
Body Pitching Moment in the Nonlinear Angle-of-Attack Range*Effects of Asymmetries

Body Drag
Body Zero-Lift Drag
Body Drag at Angle of Attack
Wing-Body, Tail-Body Combinations at Angle of Attack
Wing-Body Lift
*Wing-Body Zero-Lift Angle of Attack
Wing-Body Lift-CuiVe SlopeWing-Body Lift in the Nonlinear Angle-of-Attack Range
Wing-Body Maximum Lift
Wing-Body Pitching Moment

4.3.2
4.3.2.1
4.3.2.2
4.3.2.3
4.3.2.4

Wing-Body Zero-Lift Pitching Moment
Wing-Body Pitching-Moment-Curve Slope*Wing-Body Pitching Moment in the Nonlinear Angle-of-Attack Range*Effects of Asymmetries

Wing-Body Drag

4.3.3
4.3.3.1
4.3.3.2

Wing-Body Zero-Lift Drag
Wing-Body Drag at Angle of Attack
Wing-Wing Combinations at Angle of Attack (Wing Flow Fields)

4.4Wing-Wing Combinations at Angle of Attack

4.4.1

Wing-Body-Tail Combinations at Angle of Attack

4.5

Wing-Body-Tail Lift

4.5.1
4.5.I.l4.5. 1.2
4.5.1.3

Wing-Body-Tail Lift-Curve SlopeWing-Body-Tail Lift in the Nonlinear Angle-of-Attack Range

4.5.2.1
4.5.2.2

Wing-Body-Tail Pitching-Moment-Cu!Ve Slope*Wing-Body-Tail Pitching Moment in the Nonlinear Angle-of-Attack Range
Wing-Body-Tail Drag
Wing-Body-Tail Zero-Lift Drag
Wing-Body-Tail Drag at Angle of Attack
Power Effects at Angle of Attack
Power Effects on Lift Variation with Angle of Attack
Power Effects on Maximum Lift

4.5.2

4.5.3
4.5.3.1
4.5.3.2
4.6
4.6.1
4.6.2
4.6.3

Wing-Body-Tail Maximum Lift
Wing-Body-Tail Pitching Moment

Power Effects on Pitching-Moment Variation with Angle of AttackviPower Effects on Drag at Angle of Attack

4.6.4

Ground Effects at Angle of Attack

4.7

Ground Effects on Lift Variation with Angle of Attack

4.7.1
4.7.2
4.7.3
4.7.4

*Ground Effects on Maximum Lift

Ground Effects on Pitching-Moment Variation with Angle of Attack
Ground Effects on Drag at Angle of Attack
Low-Aspect-Ratio Wings and Wing-Body Combinations at Angle of Attack

4.8

Wing, Wing-Body Normal Force

4.8.1
4.8.!.!
4.8.!.2
4.8.2
4.8.2.1
4.8.2.2
4.8.3
4.8.3.1
4.8.3.2

Wing, Wing-Body Zero-Normal-Force Angle of Attack
Wing, Wing-Body Normal-Force Variation with Angle of Attack
Wing, Wing-Body Axial Force
Wing, Wing-Body Zero-Normal-Force Axial Force
Wing, Wing-Body Axial-Force Variation with Angle of Attack
Wing, Wing-Body Pitching Moment
Wing, Wing-Body Zero-Normal-Force Pitching Moment
Wing, Wing-Body Pitching-Moment Variation with Angle of Attack
CHARACTERISTICS IN SIDESLIP

Section 5

5.l
5.!.1
5.l.l.l
5.!.!.2
5.!.2
5.!.2.1
5.!.2.2
5.!.3
5.!.3.1
5.!.3.2
5.2
5.2.1
5.2.!.!
5.2.!.2
5.2.2

Wings in Sideslip
Wing Sideslip Derivative Cy ~Wing Sideslip Derivative Cy ~in the Linear Angle-of-Attack Range*Wing Side-Force Coefficient Cy at Angle of Attack
Wing Sideslip Derivative Ct~
Wing Sideslip Derivative Ct~ in the Linear Angle-of-Attack Range
Wing Rolling-Moment Coefficient Ct at Angle of Attack

Wing Sideslip Derivative Cn(jWing Sideslip Derivative C 0 ~ in the Linear Angle-of-Attack Range*Wing Yawing-Moment Coefficient C0 at Angle of Attack
Wing-Body Combinations in Sideslip
Wing-Body Sideslip Derivative Cy~
Wing-Body Sideslip Derivative Cy ~in the Linear Angle-of-Attack Range
Wing-Body Side-Force Coefficient Cy at Angle of Attack
Wing-Body Sideslip Derivative Ct~

5.2.2.1
5.2.2.2*Wing-Body Rolling-Moment Coefficient Ct at Angle of Attack

5.2.3.1
5.2.3.2

Wing-Body Sideslip Derivative C00
Wing-Body Sideslip Derivative C00 in the Linear Angle-of-Attack Range
Wing-Body Yawing-Moment Coefficient C0 at Angle of Attack

5.2.3

5.3

Wing-Body Sideslip Qerivative Ct in the Linear Angle-of-Attack Range0

Tail-Body Combinations in Sideslip

5.3.1
5.3.!.1
5.3.!.2
5.3.2
5.3.2.1
5.3.2.2
5.3.3
5.3.3.1
5.3.3.2

Tail-Body Sideslip Derivative Cy
0
Tail-Body Sideslip Derivative Cy in the Linear Angle-of-Attack Range0
Tail-Body Side-Force Coefficient Cy at Angle of Attack
Tail-Body Sideslip Derivative Cto
Tail-Body Sideslip Derivative Ct in the Linear Angle-of-Attack Range
0*Tail-Body Rolling-Moment Coefficient Ct at Angle of Attack
Tail-Body Sideslip DcrivativeC 00
Tail-Body Sideslip Derivative C 0 ~ in the Linear Angle-of-Attack Range
Tail-Body Yawing-Moment Coefficient C0 at Angle of Attack

vii

5.4

Flow Fields in Sideslip

5.4.1

Wing-Body Wake and Sidewash in Sideslip

5.5.1

Wing, Wing-Body Sideslip Derivative Ky .6

5.5

Low-Aspect-Ratio Wings and Wing-Body Combinations in Sideslip

5.5.1.1
5.5.1.2

Wing, Wing-Body Sideslip Derivative Kv.a Variation with Angle of Attack
Wing, Wing-Body Sideslip Derivative K[

5.5.2
5.5.2.1
5.5.2.2
5.5.3
5.5.3.1
5.5.3.2
5.6
5.6.1
5.6.1.1
5.6.1.2
5.6.2
5.6.2.1
5.6.2.2
5.6.3
5.6.3.1
5.6.3.2
Section 6

6.1
6.1.1
6.1.1.1
6.1.1.2
6.1.1.3
6.1.2
6.1.2.1
6.1.2.2
6.1.2.3
6.1.3
6.1.3.1
6.1.3.2
6.1.3.3
6.1.3.4
6.1.4
6.1.4.1
6.1.4.2
6.1.4.3
6.1.5
6.1.5.1
6.1.5.2
6.1.6

Wing, Wing-Body Sideslip Derivative Kv at Zero Normal Force
11

13

Wing, Wing-Body Sideslip Derivative Ki.a Near Zero Normal Force
Wing, Wing-Body Sideslip Derivative Kj Variation with Angle of Attack
13
Wing, Wing-Body Sideslip Derivative K~.B
Wing, Wing-Body Sideslip Derivative K~{J at Zero Normal Force
Wing, Wing·Body Sideslip Derivative K~~ Variation with Angle of Attack
Wing-Body-Tail Combinations in Sideslip
Wing-Body-Tail Sideslip Derivative Cy
13Wing·Body·Tail Sideslip Derivative Cy in the Linear Angle·of·Attack Range
13
Wing· Body-Tail Side-Force Coefficient Cy at Angle of Attack
Wing-Body.Tail Sideslip Derivative Ct
13
Wing-Body-Tail Sideslip Derivative C1~ in the Linear Angle-of-Attack Range*Wing.Body-Tail Rolling-Moment Coefficient C1 at Angle of Attack
Wing·Body-Tail Sideslip Derivative Cn
13
Wir.g·Body-Tail Sideslip Derivative C 0 ~ in the Linear Angle-of·Attack Range
Wing-Body.Tail Yawing-Moment Coefficient C0 at Angle of Attack
CHARACTERISTICS OF HIGH-LIFT AND CONTROL DEVICES
Symmetrically Deflected Flaps and Control Devices on Wing-Body and Tail-Body
Combinations
Section Lift with High-Lift and Control Devices
Section Lift Effectiveness of High-Lift and Control Devices
Section Lift.Curve Slope with High-Lift and Control Devices
Section Maximum Lift with High-Lift and Control Devices
Section Pitching Moment with High-Lift and Control Devices
Section Pitching-Moment Increment .6.cm Due to High-Lift and Control Devices
Section Derivative Cma with High-Lift and Control Devices
Section Pitching Moment Due to High-Lift and Control Devices Near Maximum Lift
Section Hinge Moment of High-Lift and Control Devices
Section Hinge-Moment Derivative Cha of High-Lift and Control Devices
Section Hinge-Moment Derivative ch of High-Lift and Control Devices
6
Section Hinge-Moment Derivative (chf)6 t of Control Surface Due to Control Tabs
Section Hinge-Moment Derivative (cht)lif of Control Tab Due to Control Surface
Wing Lift with High-Lift and Control Devices
Control Derivative CL6 of High-Lift and Control Devices
Wing Lift.Curve Slope with High-Lift and Control Devices
Wing Maximum Lift with High·Lift and Control Devices
Wing Pitching Moment with High·Lift and Control Devices
Pitching-Moment Increment ~Cm Due to High·Lift and Control Devices
Wing Derivative Cma with High-Lift and Control Devices
Hinge Moments of High-Lift and Control Devices

viii6.1.6.1
6.1.6.2
6.1.7
6.2
6.2.1
6.2.1.1
6.2.1.2
6.2.2
6.2.2.1
6.2.3
6.2.3.1

6.3
6.3.1
6.3.2
6.3.3
6.3.4

Hinge·Moment Derivative Ch• of High· Lift and Control Devices
Hinge-Moment Derivative Cho of High-Lift and Control Devices
Drag ofHigh·Lift and Control Devices
Asymmetrically Deflected Controls on Wing·Body and Tail·Body Combinations
Rolling Moment Due to Asymmetric Deflection of Control Devices
Rolling Moment Due to Control Deflection
Rolling Moment Due to a Differentially Deflected Horizontal Stabilizer
Yawing Moment Due to Asymmetric Deflection of Control Devices
Yawing Moment Due to Control Deflection
Side Force Due to Asymmetric Deflection of Control Devices*Side Force Due to Control Deflection
Special Control Methods
Aerodynamic Control Effectiveness at Hypersonic Speeds
Transverse-Jet Control Effectiveness*Inertial Controls
Aerodynamically Boosted Control·Surface Tabs
DYNAMIC DERIVATIVES

Section 7

7.1.1.2

Wing Dynamic Derivatives
Wing Pitching Derivatives
Wing Pitching Derivative CLq
Wing Pitching Derivative Cmq

7.1.1.3

Wing Pitching Derivative Coq

7.1
7.1.1
7.1.1.1

7.1.2
7.1.2.1
7.1.2.2
7.1.2.3
7.1.3
7.1.3.1
7.1.3.2
7.1.3.3
7.1.4
7.1.4.1
7.1.4.2

Wing Yawing Derivative Cyr
Wing Yawing Derivative C1r
Wing Yawing Derivative Cnr
Wing Acc~leration Derivatives
Wing Acceleration Derivative CLO:
Wing Acceleration Derivative Cma

7.1.4.3

Wing Derivative Co a

7.2.1.1

Body Dynamic Derivatives
Body Pitching Derivatives
Body Pitching Derivative CLq
Body Pitching Derivative Cmq
Body Acceleration Derivatives

7.2
7.2.1
7.2.1.2
7.2.2
7.2.2.1
7.2.2.2
7.3
7.3.1
7.3.1.1
7.3.1.2
7.3.2

Wing Rolling Derivatives
Wing Rolling Derivative Cyp
Wing Rolling Derivative C1p
Wing Rolling Derivative Cnp
Wing Yawing Derivatives

Body Acceleration Derivative CL&
Body Acceleration Derivative Cma
Wing-Body Dynamic Derivatives
Wing-Body Pitching Derivatives
Wing-Body Pitching Derivative CLq
Wing·Body Pitching Derivative Cmq
Wing·Body Rolling Derivativesix

7.3.2.1
7.3.2.2
7.3.2.3

Wing-Body Rolling Derivative Cyp
Wing-Body Rolling Derivative Ctp

7.3.3.1
7.3.3.2
7.3.3.3

7.4.4.1
7.4.4.2

Wing-Body Yawing Derivative Cy r
Wing-Body Yawing Derivative C1r
Wing-Body Yawing Derivative Cnr
Wing-Body Acceleration Derivatives
Wing-Body Acceleration Derivative CL&:
Wing-Body Acceleration Derivative Cmc,
Wing-Body-Tail Dynamic Derivatives
Wing-Body-Tail Pitching Derivatives
Wing-Body-Tail Pitching Derivative CLq
Wing-Body-Tail Pitching Derivative Cmq
Wing-Body-Tail Pitching Derivative Coq
Wing-Body-Tail Rolling Derivatives
Wing-Body-Tail Rolling Derivative Cyp
Wing-Body-Tail Rolling Derivative C/p
Wing-Body-Tail Rolling Derivative Cnp
Wing-Body-Tail Yawing Derivatives
Wing-Body-Tail Yawing Derivative Cyr
Wing-Body-Tail Yawing Derivative Ctr
Wing-Body-Tail Yawing Derivative Cnr
Wing-Body-Tail Acceleration Derivatives
Wing-Body-Tail Acceleration Derivative CLa
Wing-Body-Tail Acceleration Derivative Cma

7.4.4.3

Wing-Body-Tail Derivative Coa

7.4.4.4

Wing-Body-Tail Derivative Cy p

7.4.4.5

Wing-Body-Tail Derivative Ctp

7.3.3

7.3.4
7.3.4.1
7.3.4.2
7.4
7.4.1
7.4.1.1
7.4.1.2
7.4.1.3
7.4.2
7.4.2.1
7.4.2.2
7.4.2.3
7.4.3
7.4.3.1
7.4.3.2
7.4.3.3
7.4.4

7.4.4.6
7.5
Section 8

8.1
8.2
Section 9

9.1
9.1.1
9.1.2
9.1.3
9.2
9.2.1
9.2.2
9.2.3
9.3
9.3.1
9.3.2
9.3.3

Wing-Body Rolling Derivative Cnp
Wing-Body Yawing Derivatives

Wing-Body-Tail Derivative CniJ

*Control-Surface Angular-Velocity Derivatives
MASS AND INERTIA
Aircraft Mass and Inertia
Missile Mass and Inertia
CHARACTERISTICS OF VTOL-STOL AIRCRAFT
Free Propeller Characteristics
Propeller Thrust Variation with Angle of Attack
Propeller Pitching-Moment Variation with Power and Angle of Attack
Propeller Normal-Force Variation with Power and Angle of Attack
Propeller-Wing Characteristics
Propeller-Wing-Flap Lift Variation with Power and Angle of Attack*Propeller-Wing-Flap Pitching-Moment Variation with Power and Angle of Attack
Propeller-Wing-Flap Drag Variation with Power and Angle of Attack
Ducted-Propeller Characteristics
Dueled-Propeller Lift Variation with Power and Angle of Attack
Ducted-Propeller Pitching-Moment Variation with Power and Angle of Attack
Ducted-Propeller Drag Variation with Power and Angle of Attack

XRevised January 1975

SECTION l

GUIDE TO DATCOM
Fundamentally, the purpose of the Datcom (Data Compendium) is to provide a systematic
summary of methods for. estimating basic stability and control derivatives. The Datcom is organizedin such a way that it is self-sufficient. For any given flight condition and configuration the complete
set of derivatives can be determined without resort to outside information. The book is intended to
be used for preliminary design purposes before the acquisition of test data. The use of reliable test
data in lieu of the Datcom is always recommended. However, there are many cases where theDatcom can be used to advantage in conjunction with test data. For instance, if the lift-curve slopeof a wing-body combination is desired, the Datcom recommends that the lift-curve slopes of theisolated wing and body, respectively, be estimated by methods presented and that appropriate
wing-body interference factors (also presented) be applied. If wing-alone test data are available, it isobvious that these test data should be substituted in place of the estimated wing-alone
characteristics in determining the lifhcurve slope of the combination. Also, if test data are available
on a configuration similar to a given configuration, the characteristics of the similar configuration
can be corrected to those for the given configuration by judiciously using the Datcom material.
The various sections of the Datcom have been numbered with a decimal system, which provides the
maximum degree of flexibility. A "section" as referred to in the Datcom contains information on asingle specific item, e.g., wing lift-curve slope. Sections can, in general, be deleted, added, or revisedwith a minimum disturbance to the remainder of the volume. The numbering system usedthroughout the Datcom follows the scheme outlined below:
Section:An orderly decimal system is used, consisting of numbers having no more thanfour digits (see Table of Contents). All sections are listed in the Table of Contents
although some consist merely of titles. All sections begin at the top of aright-hand page.

Page:

The page number consists of the section number followed by a dash number.
Example: Page 4. 1.3.2-4 is the 4th page of Section 4. 1.3.2.

Figures:Figure numbers tre the -same as the page number. This is a convenient system forreferencing purposes. For pages with more than one figure, a lower case letter
follows the figure number. Example: Figure 4. 1.3.2-50b is the second figure on
Page 4. 1.3.2-50. Where a related series of figures appears on more than one page,
the figure number is the same as the first page on which the series begins.
Example: Figure 4. 1.3.2-56d may be found on Page 4. 1.3.2-57 and is the 4th in aseries of charts. Figures are frequently referred to as "charts" in the text.

Tables:Table numbers consist of the section number followed by an upper case dashed
letter. Example: Table 4. 1.3.2-A is the first table to appear in Section 4. 1.3.2.

Equations: Equation numbers consist of the section number followed by a lower case dashed
letter. Example: 4.1.3.2-b is the second equation (of importance) appearing in
Section 4.1.3.2. Repeated equations are numbered the same as for the first
appearance of the equation but are called out as follows: (Equation 4.1.3.2-b).
1-1

The major classification of sections in the Datcom is according to type of stability and control.1arameter. This classification is summarized below:
Section I.

Guide to Datcom and Methods Summary (present discussion including the
Methods Summary)

Section 2.

General information

Section 3.

Reserved for future use

Section 4.

Characteristics at angle of attack

Section 5.

Characteristics in sideslip

Section 6.

Characteristics of high-lift and control devices

Section 7.

Dynamic derivatives

Section 8.

Mass and inertia

Section 9.

Characteristics of VTOL-STOL aircraft

The information in Section 2 consists of a complete listing of notation and definitions used in the
Datcom, including the sections in which each symbol is used. It should be noted that definitions arealso frequently given in each section where they appear. Insofar as possible, NASA notation has
been used. Thus the notation from original source material has frequently been modified for
purposes of consistency. Also included in Section 2 is general information used repeatedly by theengineer, such as geometric parameters, airfoil notation, wetted-area charts, etc.
Sections 4 and 5 are for configurations with flaps and control surfaces neutral. Flap and control
characteristics are given in Section 6 for both symmetric and asymmetric deflections. Section 4
includes effects of engine power and ground plane on the angle-of-attack parameters.
The Datcom presents less information on the dynamic derivatives (Section 7) than on the static
derivatives, primarily because of the relative scarcity of data, but partly because of the complexitiesof the theories. Furthermore, the dynamic derivatives are frequently less important than the static
derivatives and need not be determined to as great a degree of accuracy. However, the Datcom does
present test data, from over a hundred sources, for a great variety of configurations (Table 7-A).
If more than preliminary-design information on mass and inertia (Section 8) is needed, aweights-and-balance engineer should be consulted.
Section 9 is a unified section covering aerodynamic characteristics of VTOL-STOL aircraft, with the
exception of ground-effect machines and helicopters. The Datcom presents less information in thisarea than that presented for conventional configurations because of the scarcity of data, thecomplexities of the theories, and the large number of variables involved. In most cases the Datcom
methods of this section are based on theory and/or experimental data such that their use is1-2

restricted to first approximations of the aerodynamic characteristics of individual components or
simple component combinations. However, the Datcom does present a literature summary fromover six hundred sources for a great variety of VTOL-STOL configurations (Table 9-A).
It should be noted that the characteristics predicted by this volume are for rigid airframes only. The
effects of aeroelasticity and aerothermoelasticity are considered outside the scope of the Datcom.

The basic approach taken to the estimation of the drag parameters in Section 4 has been found tobe satisfactory for preliminary-design stability studies. No attempt is made to provide dragestimation methods suitable for performance estimates.
Each of the m'lior divisions discussed above, notably Sections 4, 5, 6, and 7, is subdivided according
to vehicle components. That is, the information is presented as wing, body, wing-body, wing-wing,
and wing-body-tail sections. The latter three categories generally utilize component information aspresented in the first two categories and add the appropriate aerodynamic interference terms. In
some cases, however, estimation methods for combined components as a unit are presented. Eachsection of the Datcom is organized in a specific manner such that the engineer, once familiar withthe system, can easily orient himself in a given section. A typical section is diagramed below:
Section Number and Title
General Introductory MaterialA.

Subsonic Paragraph
Introductory Material
Specific Methods
Sample Problems

B.

Transonic Paragraph
Introductory Material
Specific Methods
Sample Problems

C.

Supersonic Paragraph
Introductory Material
Specific Methods
Sample Problems

D.

Hypersonic Paragraph
Introductory Material
Specific Methods
Sample Problems

References
TablesWorking Charts

1-3

fn general, eactl section is organii;ed accotding to speed regimes. However, Sections 6.3.1 and 6.3.2

are restricted to the hypersonic speed regime and Section 9 to the low-speed transition-flight;egime. In a few sections, where applicable, material is included for the rarefied-gas regime asparagraph E. The material for each speed regime is further subdivided into an introductory
discussion of the fundamentals of the problem at hand, a detailed outline of specific methods, andsample problems illustrating the use of the methods presented. In the selection of specific methods,
an attempt has been made to survey all known existing generalized methods. All methods that givereasonably accurate results and yet do not require undue labor or automatic computing
equipment have been included (at least this is the ultimate goal). Where feasible, the configurations
chosen for the sample problems are actual test configurations, and thus some substantiation of themethods is afforded by comparison with the test results.
To facilitate the engineer's orientation to those Datcom sections that use a build-up of wing,
wing-body, and wing-body-tail components, a Methods Summary has been included at the end of
this section. In addition, the methods of Sections 6. I and 6.2 are also included in the Methods
Summary. The contents of the Methods Summary present the following: (I) the wing, wing-body,and wing-body-tail equations available in each speed regime, (2) the sections where the equation
components are obtained, (3) the limitations associated with the equations and their respective
components (limitations from design charts are not included), and (4) identification of theparameters that are based on exposed planform geometry that are not specified by the subscript e.
Sometimes the same limitations, such as "linear-lift range," may occur for more than one
component in an equation. To avoid repetition, the same limitation is not repeated for eachcomponent. The list of limitations should not be construed as effectively replacing the discussion
preceding each Datcom method. It remains essential to read the discussion accompanying each
derivative to ensure an effective application of each method.

Proper use of the Methods Summary will enable the engineer to organize and plan his approach tominimize the interruptions and the time needed to locate and calculate the independent parameters
used in the equation under consideration.
The Datcom methods provide derivatives m a stability-axis system unless otherwise noted.
Transformations of stability derivatives from one axis system to another are developed in many
standard mathematics and engineering texts. In FDL-TDR-64-70, several coordinate systems aredefined and illustrated, and coordinate transformation relations are given.
All material presented in the Datcom has been referenced; plagiarizing has been specifically avoided.
In general, material that has not been referenced has been contributed by the authors.
In many of the sections, substantiation tables are presented that show a comparison of test resultswith results calculated by the methods recommended. Geometric and test variables are alsotabulated for convenience in comparing these results. Wherever possible, the limits of applicability
for a given method have been determined and are stated in the text.
The working charts are presented on open grid, which in general constitute an inconvenience to theuser. However, with a few exceptions, the grids used are of two sizes only: centimeter and half-inch
grid sizes. This enables the engineer to use transparent grid paper to read the charts accurately.
Another set of documents similar in intent to the Datcom is the "Royal Aeronautical Society Data
1-4

Sheets," available from the Royal Aeronautical Society of Great Britain. These documents are
particularly useful from the standpoint lhat foreign source material is strongly represented in them;whereas the Datcom emphasizes American information.
As stated in the introduction, the work on the Datcom will be expanded and revised over the years
to maintain an up-t<>-date and useful document. In order to help achieve this goal, comments
concerning this work are invited and should be directed to the USAF Procuring Agency so that theeffort may be properly oriented.
METHODS SUMMARY OUTLINEDERIVATIVEPAGESDERIVATIVE

PAGES

1-7 through 1-11

149 throuch 1-SO

1·11 through 1-15

1·50).)5 through 1-18

t.c2

max

1-50

J.i9 through 1-23
1-23 through 1-27

1-51

1·27 through 1-31

1-S 1

1-31 through 1-34

1·52

1-34 through 1-38

1-53

1-38 through 1-40

1-53

1-40 through 1-41

1-54 through 1-55

1-41 through 1-43

1-55

1-43 through 1-45

1-56

f-45

t-56 through 1-57

c,r

1-45 through 1-47

1-57 through 1-58

c.r

1-47

1-58

c"ll

1-5

DERIVATIVE

PAGES

CD

1-59

c,

1-59 through 1-61

'

en
en

1-6

1-61 through 1-62

'

1-62

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEw

SUBSONICMETHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)
21r

-- =

Fig. 4. I .3.249

Method I

I.

'

Eq. 4.1.3.2-b
4.1.3.2

4.1.3.2

Method 2
I.

SUPERSONIC

Faired curve between

3.

0.;;' .;; 0.3
63° .;; A LE .;; 80°
0.10 <;;tic<;; 0.30
M = 0.~(CLa )subsomc. and (CNa )superso01c.

I.

Figures 4.1.3.2-56a through -60---

Constant-section, dell" or dipped-dell"configura lions (",.E = 0)0.58 <;;A<;; 2.55

4.

5.
6.

TRANSONICNo curved plan forms
M <;; 0.8, tic<;; 0.1. if cr"nked pl"nforms wtth
round·LE

Symmetric airfoils of conventional thid\llt's:-.
distribution
A~ 3 if composite wings

3(){ = 0I.
2.
3.

Straighl-lapered wings
M;;. 1.4
Linear-lift range

I.

'

3.
4.

Double"elta and ~:ranked wings
Breaks in LE and TE at same spanwise station
1.2 <;; M <;; 3. 0
Linear-lift ran~e

I.
2.
3.

Curved planforms
1.0 <;; M <;; 3. 0
Linear-lifl range

1.
2.
3.
4.

Straighl-lapered wings
Conventional wings of zero thickness
Two-dimensional slender-airfoil theory(){ = 0

I.
2.
3.
4.

Straight-tapered planforms
Wedge airfoils
Two-dimensional slender-airfoil theory(){ = 0---+- - - - - - - - - - - - - - - ---l=

Eq. 4.1.3.2-h_4_.1_.3.2

4.1.3._2- - 4_._1._3._2

4.1.3.2

4.1.3.2

4.1.3.2
Eq. 4.1.3.2-£

HYPERSONIC

Figures 4.1.3.2-56a through -60

v ta~2

1-- - - - - -(CN.), =0 -;-- -- -A

Fig. 4.1.3.2-65
LE

1--~-

p2

WB

SUBSONIC(a)(CL )WB = [ KN + KW(B) + KB(W) la--------------------4.3.1.2

Fig. 4.3.1.2-a-------

Method I (body diameter)/( wing semisp"n) <;; 0.~(see Sketch (d), 4.3.1.2)(a) Zero wing incidence; wing-body angle of attack

variedKN (based on exposed wing geometry)
I.
2.
3.

Bodies of revolution
Slender-body theory
Linear-lift range(CL.),
4.
5.

No curved plan forms
M <;; 0.8, t/c,;;; 0.1, if cranked wings withround LE

I-7

METHODS SUMMARYDERIVATIVECON FIG.

CL •WB(Contd.)(Contd.)SPEED
REGIMEEQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)s.

SUBSONIC(Contd.)- - - -- -- - - -- -(cLJws = K<WBJ (cLJw
4.3.1.2 4.1.3.2

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS(b)

Eq. 4.3.I.2-b

Body angle of attack fixed at zero; wing incidence
varied (same limitations as (a) above)---------Eq. 4.3.1.2-c(CLa)w
I.
2.

TRANSONIC(Same as subsonic equations)-----

Method 2 (body diameter)/(wing span) is large with delta
wing extending entire length of body(see Sketch (c), 4.3.1.2)
No curved planforms
M .; 0.8, t/c .; 0.1, if cranked wings withround LE

Method I (body diameter)/(wing span) is small(see Sketch (d), 4.3.1.2)
KN (based on exposed wing geometry)
I.
Bodies of revolution
2.
Slender-body theory
3.
Linear-lift range
KB(WJ and kw(B) (based on exposed wing geometry)(CLa)e4.

5.
6.

Symmetric airfoils of conventional thickness
distribution
A .; 3 if composite wings" = 0--------- ------ -·Method 2 (body diameter)/(wing span) is large with delta
wing extending the entire length of the body(see Sketch (c), 4.3.1.2)(CLa)wI.
2.
3.
SUPERSONIC(Same as subsonic equations)Symmetric airfoils of conventional thickness
distribution
A .; 3 if composite wings" = 0

Method I (body diameter)/(wing span) is small(see Sketch (d), 4.3.1.2)
KN (based on exposed wing geometry)
I.

Bodies of revolution
Slender-body theory
Linear-lift rangekB(W) and kw(B) (based on exposed wing geometry)2.
3.

(CNa)e
4.

5.

6.
7.

1-8

Breaks in LE and TE at same sranwise station
M ;;. 1.4 for straight-tapered wings
1.2 .; M .; 3 for composite wings
1.0.;; M .;; 3 for curved plan forms

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMECLWB(Contd.)SUPERSONIC(Contd.)•(Contd.)METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

Method 2 (body diameter)/( wing span) is large with delta
wing extending entire length of body(see Sketch (c), 4.3.1.2)(CNa)w
I.

2.
3.
4.
5.
S'

WBT

SUBSONICCL=[KN + KW(B) + KB(W)l' - ' + (cl.);' [KW(B) + KB(W) ]"S'• ( cl.);~4.1.3.2

4T3.2

4.3.1.2

4.3.1.2

(I-~)
4.4.1

q"

-

-

q=

S"

S"

-S' -S"'

MethodIbw /bH ;;, 1.5

2.

(Body diameter)/(wing semispan) <; O.R(see Sketch (d), 4.3.1.2)
a "' a:~tall if high aspect ratio and unswept wings

3.

a:<< a:stail if low aspect ratio or swept wings

I.

4.4.1
Eq. 4.5.1.1-aBreaks in LE and TE <:~t same spanwise station
M;;, 1.4 for straight-tapered wings
1.2 ~ M ~ 3 for composite wings
1.0 .;;; M .;;; 3 for curved planforms
Linear-lift range(cL.); and (CL.);'No curved planforms
M .;;; 0.8, t/c .;;; 0.1, if cranked plan forms withround LEKN (based on exposed wing geometry)
6. Bodies of revolution
Slender-body theory
7.
8. Linear-lift range
4.
5.

of

-

00:

(depends upon method)

9.

Straight-tapered wing

10.

Other limitations depend upon aa: prediction
method

of

q"

-

q=

II.

Valid only on the plane of -;yrnmctry- - - - - - - - - - - - - - -- ---- - -r - - - -< - - - - - - - - - =- -' +
+
+
-f +
+
•
a.
S'

CL

(CL.); [KN

Kwta)

4.TTI

4.3:1.2

Katw)]'q"(cL.);' [KW(B)

4.T:TI'KB(W)]"

4.3.1.2

q=

4.4.T

S"
S'

Method 2 bw /b"

S"
S"

1.5

(cLJw "t>J

(same limitations as Method I above omitting thoseofloa)

4.5.1.1

KN and (cL)I(based on exposed wing geometry)a W"(v)

Eq. 4.5.1.1-b

1-9

METHODS SUMMARYDERIVATIVECON FIG.

CL

WBT(Contd.)•(Contd.)SPEED
REGIME
TRANSONICMETHOD LIMIT AllONS ASSOCIATED WITHEQUATION COMPONENTS

EQUATIONS FOR DERIVATIVE ESTIMATION
j Oatcom section for components indicated)(Same as subsonic equations)

Method I bw /bH ;;. 1.5(eL.); and (eL.);'
1.

Symmetric airfoils of conventional thickness
distribution
2.
A ~ 3 if composite planforms
3.
C< = 0KB(Wl (based on exposed wing geometry)
KN (based on exposed wing geometry)

4.
5.
6.
-

a"'

Bodies of revolution
Slender-body theory
Linear-lift range(depends upon method)
7.
8.

Straight-tapered wings
Proportional to

9.
I 0.

Conventional trapezoidal planforrns
Valid· only on the plane of symmetry

eL

q"

•

q~

r-------- ---Method 2 bw /bH < 1.5(same limitations as Method l above omitting those ofa< I oC<)
KN, KB(W)• and (CLa)W"(v) (tJ.sed on exposed winggeometry)
SUPERSONIC(Same as subsonic equations)

Method I bw /l>H ;;. 1.5(eN.); and (eN.);'I.
Breaks in LE and TE at same spanwise station
2.
M;;. 1.4 for straight-tapered planforms
3.
1.2.;; M.;; 3 for composite planforms
4.
1.0 .;; M .;; 3 for curved planforms
5.
Linear-lift range
KN (based on exposed wing geometry)
6.
7.

Bodies of revolution
Slender-body theory

KB(W) (based on exposed wing geometry)

0<

aa
8.

9.

1-10

Straight-tapered wings
0<. . .
0 t her Innitatlons depend upon- prediction
methodOC<

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMECLWBT(Contd.)SUPERSONIC(Contd.)a(Contd.)METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

q"
q~

10.
11.

If nonviscous flow field, limited to unswept wings
If viscous flow field, valid only on the plane ofsymmetry

Method 2 bw /bH < 1.5(same limitations as Method l above omitting those of
ae/aa)
KN , KB (W), and (CL )(based on exposed wingo: W"(v)geometry)w

I.

Eq. 4.1.4.2-d
4.1.4.2

2.

4.1.3.2
CL

TRANSONICa(Same as subsonic equation)
CL

SUPERSONICHYPERSONIC(Same as subsonic equation)

eN

•

•

(Same as subsonic equation)eN

M .;; 0.6; however, for swept wings witht/c .;; 0.04, application to higher Mach numbers
is acceptable
Linear-lift range

•

3.
4.

No curved planforms
M .;; 0.8, t/c .;; 0.1, if cranked plan forms withround LEI.
2.
3.

Straight-tapered wings
Symmetric airfoil sections
Linear-lift range

4.

Conventional thickness distribution
=0

5.

IY.

I.

Linear-lift range

2.
3.
4.

5.

Breaks in LE and TE at same spanwise station
M ;;. 1.4 for straight-tapered wings
1.2 .;; M .;; 3 for composite wings
1.0.;; M .;; 3 for curved planforms

I.

IY.

2.
3.

Straight-tapered wings
Conventional wings of zero thickness and wedge
airfoils
Two-dimensional slender-airfoil theory

4.

-

=0

1-11

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEem a

WB

SUBSONIC(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

em a = (n-

~)
~c
c,
4.3.2.2

METHOD LIMITATIONS ASSOCIATE() WITHEQUATION COMPONENTS
xa.c.

CL

-a

- - (calculations based on exposed wing geometry)Eq. 4.1.4.2-dc,I.

4.3.1.2

2.
3.
CL

a

4.
5.
6.

7.
8.

TRANSONIC(Body diameter)/(wing span) .;; 0.8
No curved planforms
Bodies of revolution
Slender-body th~oiy
M .;; 0.8, t/c .;; 0.1, if swept wing with round LE

Xa.c.

(Same as subsonic equation)- - (c"lculations based on exposed wing geometry)
c,

I.
2.

4.

Straight-tapered wings
Single wing with body (i.e., no cruciform orother multipanel arrangements)
Symmetric airfoils of conventional thickness
distribution
Linear-lift range

5.
6.
7.

Bodies of revolution
Slender-body theory
= 0

3.

CL

X

SUPERSONIC

Single wing with body (i.e., no cruciform orother multipanel arrangements)
M .;; 0.6; however, if swept wing with t/c .;; 0.04,
application to higher M"•·h numbers is acceptable
Linear-lift range

•

"'

a.c.

--(calculations based on exposed wing geometry)c,(Same as subsonic equation)

2.

Single wing with body (i.e., no cruciform orother multipanel arrangements)
Linear-lift range

3.
4.
5.
6.
7.
8.

Breaks in LE and TE at same spanwise station
Bodies of revolution
Slender-body theory
M > 1.4 for straight-tapered wings
1.2 .;; M < 3 for composite wings
1.0.;; M .;; 3 for curved plan forms

I.

eN a

'

I
1-12

METHODS SUMMARYDERIVATIVECONFIG.

SPEED
REGIMEWBTSUBSONIC(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION(Oat com section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

xc.g. ~ x' [
-

-

c

,

Method I bw /bH ;;. 1.5
KN(Body diameter)/( wing semispan).;; 0.8(see Sketch (d), 4.3.1.2)
Linear-lift range

I.

4.5.2.1

2.
ae

- aa

q

II

--)

qoo

S" S" _,ec

?5' C'(calculations based on exposed planform geometry)c'

Eq. 4.5.2.1-d'3.

Single wing with body (i.e., no cruciform or othermultipanel arrangements)
4.
M .;; 0.6; however, for swept wings with t/c.;; 0.04,
application to higher Mach n"umbers is acceptable
KN (based on exposed wing geometry)

4.4.1 4.4.1*Drag and z terms have been omitted, and small-angle assumptions made with respect
to angle of attack; equation as given is valid for most configurations

5.
6.

Bodies of revolution
Slender-body theory(CL )' and (cL )"
a e

o: e

7.
8.

No curved planforms
M .;; 0.8, t/c.;; 0.1 if cranked planforms withround LE

9.

Straight·tapered wing

10.

Other limitations depend upon- prediction
methodaa

II.

Valid only on the plane of symmetry

a.

q"
q~

Method 2

bw /bH < 1.5(same limitations as Method I above, omitting those for

ae;aa)
x::.
4.5.2.1
TRANSONIC(Same as subsonic equations)4.3.1. 2

4.1.3.2~: :~ + ( cL.}w..(,J

-

4.4.1

'•·c

- x'

--=;,;--

Eq. 4.5.2.1-((calculations "\.uased on exposed planform geometry)

KN and (cL )o: W"(v)(based on exposed wing geometry)

4.5.1.1
Method I bw /bH ;;. 1.5

x

- x'

'•·c'

(calculations based on exposed planform geometry)
I.

2.
3.
4.

Single wing with body (i.e .. no cruciform or othermultipanel arrangements)
Straight-tapered wings
Symmetric airfoils of conventional thickness
distribution
Linear-lift range__j

L________L______~--------~------------------------------------------------------~------------~-----------------I-13

METHODS SUMMARYDERIVATIVE(Contd.)CON FIG.

SPEED
REGIMEWBT(Contd.)TRANSONIC(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION( Datcom section for components indicated)

METHOD LI~IITATIONS ASSOCIATED WITHEQUATION COMPONENTS
KB(W) (based on exposed wing geometry)
KN (based on exposed wing geometry)

5.

Bodies of revolution

6.

Slender-body theory(cLJ: and (cLJ~
7.

"

8.

Proportional to CL

ae
aa

=

0

"

q"

-

q~

9.
10.

Conventional trapezoidal planforms
Valid only on the plane of symmetry- - - - -- -- -- --- -- -- -- - - -Method 2 bw /bH < I. 5
(same limitations as Method l above, omitting that forae;aa)
x

- x'

'~-

(calculations based on exposed planform geometry)c'

KN, KB(W)' andSUPERSONIC(CL )cr W"(v)(based on exposed wing geometry)(Same as subsonic equations)
X

x'

e.g.

(calculations based on exposed planform geometry)c'
I.

Single wing with body (i.e., no cruciform or othermultipanel arrangements)2.
Linear-lift range(based on exposed \Ving geometry)
3.

Bodies of revolution

4.

Slender-body theory
KB!Wl (based on exposed wing geometry)(CN")~(CN"): and5.
Breaks in LE and TE at same span wise station
6.
M ;;. 1.4 for straight-tapered planforms

7.
8.

1.2 :s.;;; M :s.;;; 3 for composite planforms
1.0 :s.;;; M :s.;;; 3 for curved planforms

9.

Straight-tapered wings. . .
ae
0 t her l ImitatiOns depend upon -prediction
method
aa

aa
10.

1-14

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEMETHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

EQUATIONS FOR DERIVATIVE ESTIMATION(Datrom section for components indicated)~------~------~------~--------------------------------------------------~~~------------------------q"em•(Contd.)WBT(Contd.)SUPERSONIC(Contd.)

'

--

'

q~

II.
12.

If nonviscous flow field, limitctl to unswl!pt .,... ing~
If viscous flow field, valid only on planl' ,~tsymmetry

Method 2 bw /bH < 1.5(same limitations as Method I. omitting those of Of ;OulX

e.g.

-'-"'---(calculation hased on exposOO planfor:n l~~·IJil1~ !rV)c'
KN, KB(W)' andgeometry)(C 1cJw '(vl (based on exposed wi11g~-------+-------4--------~----------------------------------------------------------~~--~~---------------------w

SUBSONIC

X=(_!_+2~)
2
c

cLQ

---

Eq. 7.1.1.1-ac
I.

4.1.4.2 4.1.3.2

2.

TRANSONIC

7.1.1.1(~)-4.1.4.2 4.1.3.2

is acceptable
Linear-lift range

3.
4.

No curved p\anform~
M ~ 0.8, t/c.;;;:; 0.1, tf cranked wings withround LEI.

2.

Straigllt-tapcrcd \.\- ing:s
No camber

3.
4.

" =0

I.

Straight-tapered wings

x
c

CL

+ 2

M < 0.0; however, for swept wings witht/c < 0.04,application to higher Mach numher-;-(Same as subsonic equation)

SUPERSONIC-------•
Conventional tnickness distribution

Eq. 7.1.1.1-cSubsonic LF (13 cot ALE < I I
2.
3.

Mach lines from TE vertex may not inta""-·d LE
WJng-tip Mach lint'S nHJy not intersect on wi11~s
nor intersect opposit~ wing tips(b) Supersonic LE (iJ cot Au > I)
4.

5.

Valid only if Mach line:-. !'rom LE vert~'\intersect TE
Foremost Mach line from t'ither wing tip m;~y
not interst'ct remote half of wingc6.

Linear-lift range~----~------~-------L-------------------------------------------------~------------~------------~~
I- I 5METHODS SUMMARYDERIVATIVE

cl•(Contd.)CON FIG.

w(Contd.)WB

SPEED
REGIMEEQUATIONS FOR DERIVATIVE ESTIMATION(0atcom section for components indicated I

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

SUPERSONIC(Contd.)7.

SUBSONIC

Eq. 7.3.1.1-a
4.3.1.2

7.iT.i7.2.1.1

M ;:;, 1.4

Method I (body diameter)/(wing span) is small(see 4.3.1.2 Sketch (d))(Clq),
I.
2.
3.

4.

No curved planfotms
Linear-lift range
M ~ 0.6; however, for swept wings witht/c ~ 0.04, application to higher Mach numbers
is acceptableM ~ 0.8, t/c ~ 0.1, if cranked wing withround LE- - -- -- -- -- -TRANSONIC(Same as subsonic equations)(Clq)B
5.
Bodies of revolution- - - - - - -f- - - -- -- -- -- --·Method 2 (body diameter)/(wing span) IS large, with delta
wing extending entire length of bodyEq. 7.3.1.1-b(see 4.3.1.2 Sketch (c))(same limitations as Method I above)

Method I (body diameter)/(wing span) is small(see 4.3.1.2 Sketch (d))KB(W) (based on exposed wing geometry)(CL.),
I.
2.
3.
4.

(Clq)B
5.

Straight-tapered wings
No camber
Conventional thick1
Distribution"=

0

Bodies of revolutionr------------Method 2 (body diameter)/( wing span) is large,
with delta wing extending entire length of body(see 4.3.1.2 Sketch (c))(same limitations as Method I above)
SUPERSONIC(Same as subsonic equations)

Method 1 (body diameter)/(wing span) is small(see 4.3.1.2 Sketch (d))KB(W) (based on exposed wing geometry)(Clq),
I.
2.
3.

1-16

Straight-tapered wings
M;:;, 1.4
Linear-lift range

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMECLWB(Contd.)SUPERSONIC(Contd.)Q(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS(a)

Subsonic LE (JJ cot ALE < I)

4.

Mach lines from TE vertex may not

5.

Wing tip Mach lines may not intersectintersect LE(b)on wing nor intersect opposite w1ng tips
Supersonic LE (iJ cot ALE > I)

6.
7.

Va!id only if Mach lines from LE vertex
intersect TE
Foremost Mach line from either wing tip
may not intersect remote half of wing

(CLq1
8.

Bodies of revolution

1----------Method 2 (body diameter)/(wing span) is large,
Y.ith delta wing extending entire length of body(see 4.3.1.2 Sketch (c))(same limitations as Method I above)
Method I bw/bH ;;. 1.5
WBT

SUBSONIC

Eq. 7.4.1.1-aI.

Line~r-lift range(cLq )WB (based on exposed wing geometry)
2.
3.
4.

5.

No curved planforms
Bodies of revolution
M <:; 0.6; however, for swept wings witht/c :s;;; 0.04, application to higher Mach numbers
is acceptable
M <:; 0.8, t/c <:; 0.1, if cranked wings withround LE

q"
q~

6.

Valid only on the plane of symmetry(Ct.):
7.

Additional tail limitations are identical to
Items 2 and 5 immediately above

Method 2 bw /bH < 1.5
Eq. 7.4.1.1-b

TRANSONIC(same limitations as Method I above)CL )and (CL )(based on exposed wing geometry)( q WBa W"(v)(Same as subsonic equations)(Ctq)wo (based on exposed wing geometry)
I.
2.

3.
4.

Straight-tapered wings
No camber
Conventional thh.:kness distribution
Bodies of revolution
1-17

METHODS SUMMARYDERIVATiVE

CL•(Contd.)CON FIG.

WBT(Contd.)SPEED
REGIMEEQUATIONS FOR DERIVATIVE ESTIMATION
IDatcom section for components indicated)

METHOLJ LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

5.

TRANSONIC(Contd.)0:= 0

KB(WJ (based on exposed wing geometry)

q"
q~

6.
7.

Conventional trapezoidal planforms
Valid only on the plane of symmetry( cLo)"'
8.

Additional tail limitations are identical to
Items 2, 3, and 5 immediately above

Method 2 bw /bH < 1.5(same limitations as Method I above)
CL ), KB(W)' and (CL ) ..
(based on exposed( q WBo: W (v)wing geometry)
SUPERSONIC(Same as subsonic equations)

Method I bw /bH ;;> I .5
I.

Linear-lift range(cLq )WB (based on exposed wing geometry)
2.
3.
4.

Straight-tapered wings
Bodies of revolution
M;;>l.4
KBtw) (based on exposed wing geometry)(a)

Subsonic LE (13 cot ALE < I)
5.
6.

(b)

Mach line from TE vertex may not intersect LE
Wing-tip Mach lines may not intersect on wing
nor intersect opposite wing tips
Supersonic LE (13 cot ALE > I)
7.
8.

Valid only if Mach lines from LE vertex
intersect TE
Foremost Mach line from either wing tip may notintersect remote half of wing

q"
9.
10.

If nonviscous flow field, limited to unswept wings
If viscous flow field, valid only on plane ofsymmetryII.

Additional tail limitations are identical to Items I
and 4 immediately above

Method 2 bw /bH < 1.5(same limitations as Method I above), KB(W)' and (CL ) ,.
(based on exposed wing
( CL )
q WB

geometry)
1-18

a: W (v)METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEMETHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

EQUATIONS FOR DERIVATIVE ESTIMATION(Oat com section for components indicated)-7.1.1.1 7.1.1.1

w

SUBSONIC--0.7 c.,

cos

~"'

4. !.I
4.1.1.2.\ t

A[~~+2(ff]+ 1 ( A tan. c/4

A 3 tan 2 1\o/4

3

A + '-,. ., cos· A c/4

242/\, 14

A + 6 cos Ac/ 4

)

+

~}

c
I.
Eq. 7.1.1.2-a2.

M ~ 0.6; however, for swept wings witht/c ~ 0.04, application to higher Mach numbers
is acceptable
Linear-lift range

3

Eq. 7.1.1.2-b

7.1.1.2I.

Eq. 7.1.1.2-<:

2.

Symmetric airfoils of conventional thickness
distribution
CY. = 0(Cmq)M "1.2(a)3.
Straight-tapered wings
Subsonic LE (~ cot ALE < I)
4.
5.

(b)

Mach line from TE vertex may not intersect LE
Wing-tip Mach Jines may not intersect on wings nor
intersect opposite wing tips
Supersonic LE (~ cot ALE > I)

6.

Valid only if Mach lines from LE vertex intersect

TE
7.

SUPERSONIC

Subsonic LE (~ cot ALE < I)

Eq. 7.1.1.2-dcmq
7.1.1.2--7.1.1.1

Foremost Mach line from either wing tip may notintersect remote half of wing

I.

Mach line from TE vertex may not intersect LE
Wing-tip Mach lines may not intersect on wings nor
intersect opposite wing. tips
Supersonic LE (~cot ALE > I l2.

7.1.1.1(h)

3.

Valid only if Mach lines from LE vertex intersect

TE
4.

Foremost Mach line from either wing tip may notintersect remote half of wing

5.

StraighHapered wingsA.

M ;;> 14

7.

Linear-lift range
1-19

METHODS SUMMARYDERIVATIVEem q

CONFIG.

WB

SPEED
REGIMEEQUATIONS FOR DERIVATIVE ESTIMATION
IDatcom section for components indicated I

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

Eq. 7.3.1.2-a

SUBSONIC

Method I (body diameter)/(wing span) is small(see 4.3.1.c Sketch (d))
I.
Linear-lift range(cmq),(Contd.)2.

M ~ 0.6; however, for swept wings witht/c ,; 0.04, application to higher Mach numbers
is acceptable(Cmq)B
3.

Bodies of revolution

t---------------------1---------------4.3.1.2 7.1.1.2

TRANSONIC(Same as subsonic equations)7.2.1.2

Method 2 (body diameter)/(wing span) is large withdelta wing extending entire length of bodyEq. 7 .3.1.2-b(see 4.3.1.2 Sketch (c))(same limitations as Method 1 above)
Method I (body diameter)/( wing span) is small(see 4.3.1.2 Sketch (d))
l.
Linear-lift range
KB(W) (based on exposed wing geometry)(em q) ,

(a)

2.
3.

Straight-tapered wings
Symmetric airfoils of conventional thickness
distri-bution

4.

C<

= 0

Subsonic LE W cot ALE < I)

5.

(b)

Mach line from TE vertex may not intersectLE
6.
Wing-tip Mach lines may not inter~ect on wings
nor intersect opposite wing tips
Supersomc LE (~ cot ALE > I)
7.
8.

Valid only if Mach lines from LE vertex
intersect TE
Foremost Mach line from either wing tip
may not interesect remote half of wing(Cmq)s9.

Bodies of revolution

1 - - - - - - - - - -Method 2 (body diameter)/( wing span) is large, withdelta wing extending entire length of body(see 4.3.1.2 Sketch (c))(same limitations as Method I above)

1-20

METHODS SUMMARYDERIVATIVECON FIG.

em q

WB(Contd.)(Contd.)SPEED
REGIMESUPERSONICEQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS(Same as subsonic equations)

Method I (body diameter)/(wing span) is small(see 4.3.1.2 Sketch (d))
1.
Linear-lift range
KB(WJ (based on exposed wing geometry)(em.),
2.
3.

(a)Straight-tapered wings
M;;. 1.4
Subsonic LE (~ cot ALE < I)4.

(b)Mach line from TE vertex may notintersect LE
5.
Wing-tip Mach lines may not intersect on wings
nor intersect opposite wing tips
Supersonic LE (IJ cot ALE > I)
6.
7.

Valid only if Mach lines from LE vertex
intersect TE
Foremost Mach line from either wing tip may
not intersect remote half of wing(Cmq)a8.

Bodies of revolution---------

Method 2 (body diameter)/( wing span) is large with delta
wing extending entire length of body(see Sketch (c) 4.3.1.2)(same limitations as Method I above)

Method I bw /bH ;;. 1.5
WBT

Eq. 7.4.1.2-a

SUBSONIC
7.3.1.2

4.5.2.1

4.3.1.2(em q)WB (based on exposed wing geometry)1.
2.

4.4.1 4.1.3.2

3.

Bodies of revolution
M ~ 0.6; however, if a swept wing witht/c .;; 0.04, application to higher Mach numbers
is acceptable
Linear-lift range

4.

Valid only on the plane of symmetry

5.
6.

No curved plan forms
M.;; 0.8, tic.;; 0.10, if cranked planforms withround LEq"(cL.);'
t--------- --------------=(:~) (~J(cLJ +{cLJw.J(c ) -2
mq WB

7.3.1 .2

4.5.2.1

4.3.12

4.4.1

4.13 24.5.1.1

Method 2 bw /bH < 1.5
Eq. 7.4.1.2-b(same limitations as ~h:·thod I above)and (C L ) .. (based on exposed wing geometry)
(Cm )
q WB

et

W (v)

1-21

METHODS SUMMARYDERIVATIVECON FIG.

em q

WBT(Contd.)(Contd.)SPEED
REGIME

TRANSONIC

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)(Same as subsonic equations)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS
Method I bw /bH ;> 1.5(em q ) WB (baserl on exposed wing geometry)
I.
,

3.

Straight-tapered wings
Symmetric airfoils of conventional thickness
distribution
Bodies of revolution

4.

" = 0

Subsonic LE W cot ALE < I)

(a)

5.
6.

Mach line from TE vertex may not intersect LE
Wing-tip Mach lines may-not intersect on wings
nor intersect opposite wing tips
Supersonic LE W cot ALE > I)

(b)

7.

Valid only if Mach lines from LE vertex
intersect TE
8.
Foremost Mach line from either wing tip may notintersect remote half of wing
KB(W) (based on exposed wing geometry)
q"
q~

9.
10.

Conventional trapezoidal planforms
Valid only on the plane of symmetry(c L" )"'
II.
~-

Additional tail limitations are identical to Items 2
and 4 immediately above--------------

Method 2 bw /bH < 1.5(same limitations as Method I above)(Cmq)wB' KB(W)' and (CLJW"(v) (based on exposed winggeometry)
SUPERSONIC(Same as subsonic equations)

Method I bw /bH ;> 1.5(em q ) WB (based on exposed wing geometry)
I.
2.
3.
4.

Straight-tapered wings
Bodies of revolution
M ;> 1.4
Linear-lift range
KB(WJ (based on exposed wing geometry)(a)

Subsonic LE (p cot ALE < I)

5.
6.

(b)

Mach line from TE vertex may not intersect LE
Wing-tip Mach lines may not intersect on wings nor
intersect opposite wing tips
Supersonic LE (p cot ALE > I)
7.

1-22

Valid only if Mach lines from LE vertex intersect
TE

METHODS SUMMARY-----------------.------------------------------DERIVATIVECON FIG.

SPEED
REGIMEem q

WBT(Contd.)SUPERSONIC(Contd.)(Contd.)METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

EQUATIONS FOR DERIVATIVE ESTIMA o"ION(Datcom section for components indicated)
8.

Foremost Mach line from either wing tip may notintersect remote half of wing

9.
10.

If nonviscous flow field, limited to unswept wing"If viscous flow field, valid only on the plane ofsymmetryq"(cLa)"'
I I.

Additional tail limitations arc identical to Items 3
and 4 immediately above- - - - - - - - - - - - - - - - - - - - - -Method 2 bw /bH < 1.5(same limitations as Method I above), KB(W)' and (CL ) ..
(based on exposed wing(C )m q WBo:, W (v)geometry)w

Eq. 7.1.4.1-a

SUBSONIC
4.1.4.2 4.1.3.2

I.
2.

Triangular pla:1forms
Linear·lift range

3.

M < 0.6; however, if swept wing with t/c < 0.04.
application to higher Mach numbers is acceptahle

xa.c.

-

7.1.4.1

G'

CL (g)

TRANSONIC(Same as subsonic equation)

4.

0 <~A< 4I.

Triangular planforms2.

Mer < M ~ 1.0

3.

Linear-lift range

4.

No camber

5.

Symmetric airfoils of conventional thickness
distributionc,

6.
cl (gJ
7.

SUPERSONIC---7.1.1.1 7.1.4.1+ 2 E"(~C)
7.1.1 .IEq. 7.1.4.1-b
7.1.4.1--7.1.1.1 7.1.4.1

Method I
I.
2.

a=O
0 <~A< 4

Straight-tapered wings

1- = 03.

Subsonic LE (~ cot 1\LE < I)

4.

Mach line from TE vertex may not intersect LE
1-23

METHODS SUMMARYI>ERIV ATJVEOONFIG.

CL·•(Contd.)(Contd.)w

SPEED
REGIMEEQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

SUPERSONIC(Contd.)5.
6.

Wing·tip Mach lines may not intersect on wings nor
intersect opposite wing tips
Linear·lift range

r - - - - - - - - - - - - - - - - - - - - -·-------------------M2

I

CL.; = fi2 (cLJl - fi2 (cLJ2-7.1.4.1

7.1.4.1

Eq. 7.1.4.1-c Method 2
I.
Straight-tapered wings
2.
Unear-li ft range(a) Subsonic LE (~ cot ALE < I)
0.25 <A< 1.0
Mach line from TE vertex may npt intersect LE
Wing-tip Mach lines may not intersect on wings nor
intersect opposite wing tips
Supersonic LE (~ cot ALE > I)
3.
4.
5.

(b)

6.
7.

WB

Valid only if Mach lines from LE vertex intersect
TE
Foremost Mach line from either wing tip may notintersect the remote half-wing

Eq. 7.3.4.1-a Method I (body diameter)/(wing span) is small(see sketch (d) 4.3.1.2)
I. Linear-lift range

SUBSONIC
4.3.1.2(CL.;),
2.

3.
4.

Triangular planforms

0 <~A< 4

M < 0.6; however, if swept wing with tic< 0.04,
application to higher Mach numbers is acceptable(cL.).

--------------4.3.1.2 7.1.4.1

TRANSONIC(Same as subsonic equations)7.2.2.1

5.

Bodies of revolution-------Eq. 7.3.4.1-b Method 2 (body diameter)/( wing span) is large with delta wing
extending entire length of body(see Sketch (c) 4.3.1.2)(same limitations as Method I above)
Method I (body diameter)/(wing span) is small(see Sketch (d) 4.3.1.2)
I.
Linear-lift range
KB (W) (based on exrosed wing geometry)(CL.),

1-24

3.

Triangular planforrns
Symmetric airfoils with conventional thickness
distribution

4.

O<M<4

5.

Mer~ M ~ 1.0

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEcL.

WB(Contd.)TRANSONIC(Contd.)•(Contd.)METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)(cl,Js6.

Bodies of revolution------------~
Method 2 (body diameter)/(wing span) is large with delta wmg
extending entire length of body(see Sketch (c) 4.3.1.2)(same limitations as Method 1 above)

SUPERSONIC(Same as subsonic equations)

Ij

Method ! (body dlameter)/(wing span) is small(see Sketch (d) 4.3.1.2)
I.
Straight-tapered wing2.
Linear-lift range
K 8 (W) (based on exposed wing geometry)(cl,),
Subsonic LE (~ cot ALE < I)
3.
Mach line from TE vertex may not mtersect LE
4.
Wing-tip Mach lines may not intersect on wings
nor intersect opposite wing tips(b) Supersonic LE W cot ALE > I)
(a)

5.
6.

Valid only if Mach lines from LE vertex
intersect TE
Foremost Mach line from either wing tip may
not intersect remote half-wing
Bodies of revolution--------------Method 2 (body diameter)/(wing span) is large with delta
wing extending entire length of body(see Sketch (c) 4.3.1.2)(limitations of Method I)

WBTSUBSONIC

Eq. 7 .4.4.1-a Method I bw /hH ;;. I .5

I.

Linear-lift range

2.
3.

Triangular planforms
0 <~A< 4
Bodies of revolution
M ~ 0.6; however, if swept wing with t/c ~ 0.04,
application to higher Mach numbers is acccptJble( cL,; )WB (based on exposed wing geometry)
4.
5.
q"
6.

Valid only on the pl<tne of symmetry

7.

Limitations dercnd upona. prediction methodao:-METHODS SUMMARYDERIVATIVE

CL.

•(Contd.)CON FIG.

WBT(Contd.)SPEED
REGIMESUBSONIC(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)cL.; =(cLJw. - 2 C'·•· ~ x'') (cLJw"t'>-7.3.4.1

TRANSONIC

4.5.2.1(Same as subsonic equations)-4.5.1.1

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

Method 2 bw /bH < I .5
Eq. 7.4.4.1-b(same limitations as Items I through 5 immediately above)
and(based on exposed wing geometry)(CL.)

c.: WB(cL o: ) "W (v)Method I bw /bH ;;, 1.5
(C

1.
)

L.; WB

Triangular planforms
Symmetric airfoils with conventional thickness
distribution
0 <~A< 4
Bodies of revolution

3.
4.
5.
6.
KB(W)

Linear-lift range(based on exposed wing geometry)

Mn :< M.::;;; 1.0
lbased on exposed wmg geometry)

q"
7.

a.

8.

Conventional trapezoidal plan forms
Valid only on the plane of symmetry

9.

Proportional to CL(cLJ;'
10.

ex = 0ll.

Additional tail limitation is identical to Item 3
immediately above

f-..----------·Method 2 bw /bH < 1.5(same limitations as Items I through 6 immediately above)
and(based on exposed wing geometry)( CL.)a WB

SUPERSONIC(Same as subsonic equations)(cL ) .

a W {v)

Method I hw /hH ;;, 1.5
1.
Straight-tapered wing2.
Linear-lift range
KB(W) (based on exposed wing geometry)(cLo)wB (based on exposed wing geometry)(a)3.
Bodies of revolution
Subsonic LE (~ cot ALE < I)

4.
5.

1-26

Mach line from TE vertex may not intersect LE
Wing-tip Mach lines may not intersect on wings
nor intersect opposite wing tips

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEcL.

WBT(Contd.)SUPERSONIC(Contd.)•(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS
Supersonic LE (Jl cot ALE > I)
6. Valid only if Mach lines from LE vertex
intersect TE
7.
Foremost Mach line from either wing tip may notintersect remote half-wing
KB(W) (based on exposed wing geometry)
(b)

q"

-q=
8.
9.

If non viscous flow field, limited to unswept wings
If viscous flow field, valid -only on the plane ofsymmetry

10.

Straight-tapered wings

II.

Other limitations depend upon predictiona<>method

a<
-a<>

a<

(cLJ
12.

M;;, 1.4------- - - - - - - - · Method 2 bw /bH < 1.5(same limitations as Items I through 7 immediately above)(CL.)
and (cL )(based on exposed wing geometry)
o: WB

c m.

•

w

SUBSONIC

em.

•

=

cm<i" + ( ; ' )

cL.

•

~

~

7.1.4.2

7 .1.4.1

Eq. 7 .1.4.2-a

CL.

•

I.
2.
3.
4.

TRANSONIC

SUPERSONIC(Same as subsonic equation)(Same as subsonic equation ia W"(v)

Triangular planforms
0 < JlA < 4
M ~ 0.6; however, if swept wing with t/c.;;;,; 0.04,
application to higher Mach numbers is acceptable
Linear-lift range

cL.

•

I.
2.

Triangular planforms
Symmetric airfoils of conventional thickness
distribution

O<JlA<4

3.
4.

Mer ~ M ~ l.C

5.

Linear-lift range

c m ".

•(a)

Subsonic LE (Jl cot ALE < I)I.
2.

Mach line from TE vertex may not intersect LE
Wing-tip Mach llnes may not intersect on wings
nor intersect opposite wing tips

1-27

METHODS SUMMARYDERIVATIVECON FIG.

w(Contd.)(Contd.)WB

SPEED
REGIMEEQUATIONS FOR DERIVATIVE ESTIMATION!Datcom section for components indicated!

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS(b)

SUPERSONIC(Contd.)SUBSONIC

Eq. 7.3.4.2-aSupersonic LE (~cot ALF > I)
3.
4.

Valid only if Mach lines from LE vertex intersect TE
Foremost Mach line from either wing tip may notintersect remote half-wing

5.
6.

Straight-tapered wings
Linear-lift range

Method I (body diameter)/(wing span) is small(see 4.3.1.2 Sketch id))I.
Linear-lift range(Cmo),
2.

Triangular planforms [ctuc to (CLJe]

3.

0 < ~A< 44.

M < 0.6~ however, if swept wing with t/c ~ 0.04,
application to higher Mach numbers is acceptable

5.

Bodies of revolution- - - - - - - - - - - - - - - - - - - - - - - - - - - ---- - - - - - - - - - - - - - - - - - - - - - - - - - - -----Method 2 (body diameter)/(wing span) is large, with delta

Eq. 7.3.4.2-b-----

4.3.1.2
TRANSONIC

7.1.4.2(Same as subsonic equations)7.2.2.2

wing extending over entire length of body(see 4.3.1.2 Sketch (c))(same limitations JS Method I above)
Method I (body dianleter)/(wing span) is small(see 4.3.1.2 Sketch id))I.
Linear-lift range
KB(W) (based on exposed wing geometry)(CmJ,(CtJe]

2.

Triangular p\anforms [due to3.

Symmetric airfoils of conventional thickness
distribution

0< M < 4
Mcr,;;;;M~\.0

6.

Bodies of revolutionr------------Method 2 (body diJmeter),i(wing span) is large, with delta
wing extending entire length of body(see 4.3.1.2 Sketch (c))(same limitations as Method I above)

SUPERSONIC

1-28(Same as subsonic equations)

Method I (body diametcr)/(wmg span) is small(see 4.3.1.2 Sketch (d))
1.
Straight-tapered wings
2.
Linear-lift range

METHODS SUMMARYDERIVATIVE(Contd.)CON FIG.

SPEED
REGIMEWB(Contd.)SUPERSONIC(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTSKB(WJ (based on exposed wing geometry)(Cmo.)e(a)

Subsonic LE (~ cot ALE < I)
3.
4.

(b)

Mach line from TE vertex may not intersect LE
Wing-tip Mach lines may not intersect on wings
nor intersect opposite wing tips
Supersonic LE (J3 cot ALE> I)
5.
6.

Valid only if Mach lines from LE vertex
intersect TE
Foremost Mach line from either wing tip may notintersect remote half-wing(Cmo.)o7.

Bodies of revolution----------------------Method 2 (body diameter)/(wing span). is large, with delta wing
extending entire length of body(see 4.3.1.2 Sketch (c))(same limitations as Method I above)

WBT

Eq. 7.4.4.2-a

SUBSONIC

Method I bw /bH ;. 1.5

I.
Linear-lift range(Cm&)wa (based on exposed wing geometry)
2.

Triangular planforms [due to(cto,)e]3.

0 <~A< 4

4.
5.

Bodies of revolution
M <;; 0.6; however, if swept wing with t/c <;; 0.04,
application to higher Mach numbers is acceptable

6.

Valid only on the plane of symmetry

7.

Limitations depend upon -

,

q
qoo

a.
aa

a. prediction methodaa- - - - - - - - - - - - -- - - crn-

(CLo)w"'''a7.3.4.2

TRANSONIC

4.5.2.1!Same as subsonic equations)4.5.1.1

Eq. 7.4.4.2-b

Method 2 bw /bH < 1.5(same limitations as Items I through 5 immediately above)and (CL )(based on exposed wing geometry)C )( m Q WB
o: W '(v)Method I bw /bH ;. 1.5

I.

Linear-lift range
1-29

METHODS SUMMARYDERIVATIVE(Contd.)CON FIG.

SPEED
REGIMEWBT(Contd.)TRANSONIC(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION( Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS(cmet"·) WB (based on exposed wing geometry)(CLo)el:2.

Triangular planforms [due to3.

Symmetric airfoils of conventional thickness

4.

0 <~A< 1.0

5.
6.

Bodies of revolution
Mer ~ M ~ 1.0

distribution

KB(WJ (based on exposed wing geometry)

L

q~

8.

7.

Conventional trapezoidal plan forms
Valid only on the plane of symmetry

9.

Proportional to CL
0(CLo)~
10.

"'; 0

II.

Additional tail limitation is identical to Item 3
immediately above-----------Method 2 bw /bH < 1.5(same limitations as Items I through 6 immediately above)and (CL )(based on exposed wing geometry)
C )(SUPERSONIC(Same as subsonic equations)rna, WB

e~ W"(v)Method I bw /bH ;;. 1.5

I.

2.

(cmO:) WB(a)

Straight-tapered wings
Linear-lift range(based on exposed wing geometry)

3.
Bodies of revolution
Subsonic LE (~ cot ALE < I)
4.
5.

(b)

Mach line from TE vertex may not intersect LE
Wing-tip Mach lines may not inters{'ct nn wings nor
intersect opposite wing tips
Supersonic LE (~ cot ALE > I)

Valid only if Mach lines from LE verte;; intersect
TE
7.
Foremost Mach line from either wing tip may notintersect the remote half-wing
K 8 (W) (based on exposed wing geometry)
6.

q"
q~

8.
9.

1-30

If nonviscous flow field, limited to unswept wings
If viscous flow field, valid only on the plane ofsymmetry

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEcm.

WBT(Contd.)SUPERSONIC(Contd.)Q(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATIONMETHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS(Datcom section for components indicated)aa
10.

Limitations depend upona,aa prediction method

M>I.4
Method 2 bw /bH .;; 1.5(same limitations as Items I through

(

Cm )

Q WB

and(CL )a W"(v)

7 immediately above)(based on exposed wing geometry)~------~------~-------+------------------------------------------------------+------w

I

SUBSONIC(Low Speed)- - 0.0001 lfl
57.3

Eq. 5.1.1.1-a(Subcritical)

TRANSONIC].

Constant-chord swept wings

2

Linear-lift range

Eq. 5.1.1.1-c(No method)

8M 2
=- --

SUPERSONIC

I

0.0001 lfl

7TAf3' 57.3

Eq. 5.1.1.1-d, -ba'I.

Rectangular planforms

2.

Mach number and aspect ratio greater than thatfor which the Mach line from LE of tip section
intersects TE of opposite tip section(A .jM 2 - I ;;. I)- - - - - ~------------·-

1---- - - - - - - - - - - - - - - - Cy

p

1T

4

AM 2

I

~ 57.35.1.1.1

0.0001 lfl

Eq. 5.1.1.1-e, -ba'I.

Sweptback planforms

2.

A= 0

3.

Wing is contained within Mach cones springing
from apex and TE at center of wing(.fii'=JWB

SUBSONIC(Cv~)ws = ~ (Cv~)s (5.2.1.1 4.2.1.1

Body Re;:rence Area) +cot ALE .;; l.Q))

Eq. 5.2.1.1-a
5.1.1.1

Bodies of revolution

Linear-lift range

TRANSONIC(Same as subsonic equation)(same limitations as subsonic above)

SUPERSONIC(Same as subsonic equation)(same limitations as suhsonic above)

1-31

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMECy

TB

SUBSONIC •~EQUATIONS FOR DERIVATIVE ESTIMATIONMETHOD LL\IITATIONS ASSOCIATED WITHEQUATION COMPONENTS(Datcom section for components indicated)(ac y~)V(WBH) = - k (CL a ) V (' + aa~a) qv
q~--(Contd.)5.3.1.1 4.1.3.2

Eq. 5.3.1.1-b'----,~.,----

Method I (vertical panels on plane of symmetry)(Cla)v____1_. ~aight-tapered planforms _ _ _ _ _ _ _5.4.1

Eq. 5.3.1.1-c Method 1 (twin vertical panels)-- -1-----------Method 3 (horizontal tail mounted on body or no horizontal
tail)Eq. 5.3.1.1-<1(a) Contribution of vertical panel( CL \ (based on exposed vertical-tail geometry)alp

1.

No curved planforms

2.

(b)

(acv ) H (8) =Eq. 5.3.1.1-e~

5.3.1.1

TRANSONIC

M ,;;; 0.8, t/c ,;;; 0.1, if cranked plan forms withround LE(b) Contribution of horizontal tail( Cy~) B

4.2.1.1

3.

Bodies of revolution

4.

Linear-lift range

I.

Horizontal tail mounted on b9dy, or no horizontal(No method)

SUPERSONIC

= -

s.

-

K'

5.3.1.1(CN~ -Sw'

Eq. 5.3.1.1-f

tailLinear-lift range
2.
(a) Vertical-tail contribution
K' (based on exposed vertical-tail geometry)(CN P (based on exposed vertical-tail geometry)a)4.1.3.2

3.

(b)(aCy ) H(B) =~- 5.3.1.1

HYPERSONIC

1-32

4.2.1.1

Eq. 5.3.1.1-g(b)

Breaks in LE and TE at same spanwise station

4. M ;;. 1.4 for straight-tapered planforms
5.
1.2 ,;;; M ,;;; 3 for composite plan forms
6.
1.0 ,;;; M ,;;; 3 for curved planforms
Horizontal-tail contribution(Cv~).
7.

Method I
I.
2.
3.

Bodies of revolution

Horizontal tail mounted on a bodyNot substantiated above M = 7
Linear-lift range

METHODS SUMMARYDERIVATIVECON FIG.

Cy

TB(Contd.)SPEED
REGIMEMETHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)(a)
I(Contd.)Eq. 5.3.1.1-f(b)(~Cv I) H(B)K' (based on exposed vertical-tail geometry)(CN

5.3.1.1 4.1.3.2

Vertical-tail contributiona)p4.

Eq. 5 3.1.1-g

--

M > 3

(b)

HorizontaHail contribution

(Cv

,)s
5.

Bodies of revolution

5.3.1.1 4.2.1.1- - - - - - - - - - ---------------------------------- - - Method 2'Y + I
I (r + I ) 2
Eq. 5.3.1.1-h
I. Sharp-edged sections
cp = <~ • bJ 2 ( - - ± y - - - +24!)~~ b)')
±

WBT

2.

5 <<I

Eq. 5.6.1.1-a Method I (single vertical stabilizer, and horizontal tail at
any height or no horizontal tail)I.
Linear-lift range

SUBSONIC(Cv ,)ws

2.

Bodies of revolution(~Cy I)V(WBH)3.

--------Cy 1 = (Cv 1)ws + ( ~Cy ,)v<WBH)
5.2.1.1

5.3.1.1-- -- - - - -Straight-tapered planforrns-- -- --- -- - - - - - -Eq. 5.6.1.1-a Method 2 (twin vertical panels)
I.
Linear-lift range(Cv ~)wa'2.

Bodies of revolution-------5.2.1.1

5.3.1.1

Eq. 5.6.1.1-b Method 3 (horizontal tail mounted on body or no
horizontal tail)I.
Linear-lift range(Cv ~)wa(~Cy

2.

Bodies of revolution

3.

No curved planforms
M .;; 0.8, tic .;; 0.1, if cranked plan forms withround LE

1)P (based on exposed vertical-tail geometry)

4.

TRANSONIC(No method)

1·33

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMECy

WBTSUPERSONICEQUATIONS FOR DERIVATIVE ESTIMATIONMETHOD LL\IITATIONS ASSOCIATED WITHEQUATION COMPONENTS(Datcom section for components indicated)

I.
~(Contd.)Eq. 5.6.1.1-b(Contd.)~~5.2 .1.1

5.3.1.1

Horizontal tail mounted on body or no horizontal
tailLinear-lift range(Cv~)wB
3.

Bodies of revolution(LlCyP)P (based on exposed vertical-tail geometry)

w

4.
5.
6.
7.

Breaks in LE and TE at same spanwise station
M ;;, 1.4 for straight-tapered plan forms
1.1 ~ M ~ 3 for composite plaQforms
1.0 ~ M ~ 3 for curved planforms

I.
2.

Straight-tapered wings

8 tan Ac/ 4

3.

5.1.2.1

4.

Uniform dihedral (alternate form is available toaccount for dihedral)
M.;; 0.6

S.
6.

Linear-lift range

I.

Straight-tapered wings

2.
3.
4.
5.
6.

A<l.O

SUBSONIC

Eq. 5.1.2.1-a

5T2.T 5 .1.2.1-

5 .1.2.1

W.t 5.1.2.1

1---------------- - -f--c/~ = CL [-_I.:. .:..}- rfA)
57.3 3 A\6

Eq. 5.1.2.1-a'.

5.1.2.1:1: = (c~ ) l(Cta), Sws, [a total-~5.1.2.1

5.1.2.1--

4.1.3.2

Linear-lift range
Double-delta and cranked wings
No twist
No dihedral
M.;; 0.6-5° .;; ~ .;; +5°
Linear-lift range(c~.J, and (ct8.

4.1.3.2-5°:;;;;; (3::;;.:; +5°A, and A; ;;, 1.0

7.

Jo'

t/c <; 0.10 if cranked wi,Jgs with round LE----------1-------------

I 2
57.3 3

4T3.2:: [(~t. ~ ·(~).Jj
5.!.2.1

5.1.2.1

l.
2.
3.

5.1.2.1
Eq. 5.1.2.1-b'

Dougle·delta and cranked wings
Ai and A~< 1.0
No twist

4.

No dihedral

5.
6.

M.;; 0.6-5° ~ (3 ~ +5°

7.

Linear·lift range

fcL ). and (cL ) '
\

01

I

8.
1·34

--

Uniform dihedral
M.;; 0.6

I.

5.
6.

~------5° ~ ~:;;;;; +5°

2.
3.
4.

Eq. 5.1.2.1-bA;;, 1.0010t/c ~ 0.1 if cranked wings with round LEMETHODS SUMMARYDERIVATIVECONFIG.

SPEED
REGIMEc,w

TRANSONIC~(Contd.)METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for componenis indicated)

5.1.2.1

S.U.l

5.1.2.1(Contd.)Eq. 5.1.2.1-c(CL~) M=06
4.1.3.2

4.1.3.2

4.1.3.2

4.1.3.2I.
2.
3.

Straight-tapered wings-5° .;; iJ<; +5°
Linear-hft range

4.
5.
6.
7.

Wing tips parallel to free stream
No twist
Uniform dihedral
Foremost Mach line from wing tip may not~~)M=I4

intersect remote half·wing

SUPERSONIC

C1 = -0.061 CN
B

4.1.3.2

+r

eN

(~·)

Eq. 5.1.2.1-ec,I.

Straight-tapered wings

2.
3.
4.

No twist" 5.

Uniform dihedral
Linear-lift range
M;.l.4~r

5.1.2.1

6.
7.

Wing tips parallel to free stream
Foremost ~ach line from wing tip may notintersect remote half-wing

I.

2.
3.
4.
5.
6.

Double-delta and cranked wings
No twist
No dihedral
Straight trailing edge
Low angles of sideslip
Linear-lift range

7.
8.

1.2<;M<;3
M > 1.4, if A 0 >A,

9.

A, < 80°. if A 0 > A,

( AC1 )
1C)w + 8 tan A,.14 e tan ~c/4 .

I.
2.
3.

5.1.2.1
Eq. 5.2.2.1-a4.
5.

Straight-tapered wings
Uniform dihedral
M.;; Mrb-so .;; ll.;; +So
Linear-lift range-----------------------------------------= -0.061- -----

4.1.3.2 4.1.3.2(CNJg and (cNJbw-0.061

Eq. 5.1.2.1-f

WB

SUBSONICc,c=

CL[(~I~)L

KM A

A c/2---..-.

K,~+G~ )J+r [~c~5.1.2.1 5.1.2.1 5.2.2.1 5.1.2.1

Kt.c,c]

Mr+-f-5.1.2.1, 5.1.2.15.2.2.1

+(AC

~~

5.2.2.1

1-35

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEc, p

WB(Contd.)SUBSONIC(Contd.)(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATIONMETHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS(Datcom section for components indicated,

c,

p

-

CL

5.2.2.1

TRANSONIC

c,
-

p

CL

=

5.2.2.1[(~L. -(~:t
(c ')
Na

(c ')

M:l.4

La

4.1.3.2

Mfb

6.

M.;; 0.6

I.

Straight-tapered wings
Mfb.;; M.;; 1.4~so .;; ~.;; +so

5.2.2.1k ~-)· C:t
1.4 ~ Mfb-

4.1.3.2

4.1.3.2

(c ')
La

2.
3.
( c L,2) M

Eq. 5.2.2.1-dMfb

4.1.3.2(:~ t=l.4
4.
5.

-

4.1.3.2

(:~

tfb

6.
7.
(cL )

o: MfbeN
SUPERSONICc, = ~o.06I eN
p

2 2

43

• [ I +A (I + ALE)] ( I + lALE )(tan~ALE)[ M cos
A ALE + en :LE) 1

-~

57.3

J

-4.1.3.2

Uniform dihedral
Linear-lift range
and (CL )aM

8.

Symmetric airfoils of conventional thickness
distribution

9.

"

I.
2.
3.

Straight-tapered wings
M;;. 1.4
Linear·lift range

4.
5.

Wing tips parallel to free stream
Foremost Mach line from wing tip may not

6.

Supersonic TE

~

0

c,

p

[
+r

Wing tips parallel to free stream
Foremost Mach line from wing tip may notintersect remote half-wing

r

AC1 ]

--f
- .5.2:2.1
c,

P +(AC )
+ __
1P 'w
r

5.1.2.1

Eq. 5.2.2.1~

intersect remote half-wing

5.2.2.1

zP cos a - QP sin a

TB

SUBSONIC(Ac1
P)p = (Acy P)P
5.3.1.1

TRANSONIC(No method)

SUPERSONIC(Same as subsonic equation)bw

Eq. 5.3.2.1-a(ACy P)P (based on exposed vertical-tail geometry for(ACy P)P Method 3)
I.

Limitations depend upon ( ACy ) prediction
methodPP

I.

Horizontal tail mounted on body or no horizontal

tail( ACy P)P (based on exposed vertical-tail geometry)
2.

1-36

Breaks in LE and TE must be at same spanwise
station

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEcl

TB(Contd.)SUPERSONIC(Contd.)~(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS
3.
4.
5.
6.
7.

Bodies of revolution
M ;;> 1.4 for straight-tapered plan forms
1.2 .;;; M .;;; 3 for composite planforms
1.0 .;;; M .;;; 3 for curved plan forms
Linear-lift range

HYPERSONIC(t.Cl~)PzP cos a -- £ P sin a= (f>Cva)pbw-

Eq. 5.3.2.1-a

Method I
I.

2.

Horizontal tail mount~d on body or no horizontal
tailM<7(based on exposed vertical-panel geometry)(t>Cy a)p3.
M ;;> 1.4 for straight-tapered planforms
4.
1.2 .;;; M .;;; 3 for composite planforms
1.0 .;;; M .;;; 3 for curved planforms
5.
6.
Linear-lift range
zP and QP (based on exposed vertical-panel geometry)

5.3.1.1------------Method 2
I.

Horizontal tail mounted on body or no horizontal
tail(t>Cv~)P (based on exposed vertical-pane! geometry)
2. Sharp-edge sections
3. 5 << IzP and QP (based on exposed vertical-panel geometry)- - - - - - - - - - - - - - - - - - - -Method 3
I.

Horizontal tail mounted on body or no horizontaltail
2. Upper range of hypersonic Mach numbers( f>Cy a)p (based on exposed vertical-panel geometry)zP and QP (based on exposed vertical-panel geometry)

WBT

SUBSONIC

TRANSONIC

cl

a

=

(c1a)ws +~P { (t.Cy ~)P ['" cos" b~ QP sin"]}-5.2.2.1

5.3.1.1

I.

Eq. 5.6.2.1-aLinear-lift range(ct,)ws2.
3.
4.

Straight-tapered wings
Uniform dihedral
M.;;; Mrb
5. M.;;; 0.6
6.
-so .;;; ~.;;; +so('l.Cy ) (based on exposed vertical-tail geometry for1. P ( f>Cy ~)P Method 3)(No method)
1-37

METHODS SUMMARYDERIVATIVECON FIG.

cl

WBT(Contd.)~SPEED

EQUATIONS FOR DERIVATIVE ESTIMATIONREGIME( Datcom section for components indicated 1

SUPERSONICMETHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS
l.

(Same as subsonic equation)

Linear-lift range(CI~)WB(Contd.)2.

Straight-tapered wings

3.

Wing tips parallel to free stream

4.

Foremost Mach line from wing tip may notintersect remote half-wing

5
M> 1.4(Cv ~)P (based on exposed vertical-tail geometry)
6.

Additional tail limitation is identical to Item 5
immediately abovew

SUBSONIC(Low Speed)I[= 57.3x sin 1\,14 )]A

I---+628 cos A, 14

c41rA -(Subcritical)

A

Eq. 5.1.3.1-aI.

Linear-lift range

I.

Rectangular planform

2.

A )M2 - 1 ;;. 1.0 (Mach number and aspec<

Eq. 5.1.3.1-b

5.1.3.1
TRANSONIC(No method)

SUPERSONIC

Eq. 5.1.3.1-c

-- 1r

)

- - -- -- - - -- -- - - -- - -[""'"r'~ F9(N) + (A216
7. I. 1.1

5_1.3.1~C)]-~7.1.1.2

5.1.1.1

57.3

ratio greater than those for which Mach linefrom LE of tip section intersects TE of opposite
tip section)---------------------Eq. 5.1.3.1-d

I.

2.

A = 0
~ cot /\LE .;; 1.0 (Mach number and aspectratio for which wing lies within Mach cones
springing from apex and TE at center of wing)

I.
WB

ALL SPEEDS(c n/3)WBbLinear-lift range

Eq. 5 .2.3.1-a

5.2.3.1 5.2.3.1

TB

SUBSONIC

Method I
LiCy ) (based on exposed vertical-tail geometry for
Eq. 5.3.3.1-a(~ P (LiCy ) Method 3)
~

l.

1-38

p

Limitations depend upon (LiCy ) prediction
method~ P

METHODS SUMMARYDERIVATIVEc·~

CON FIG.

SPEED
REGIME

TB(Contd.)SUBSONIC(CGntd.)eQUATIONS FOR DERIVATIVE ESTIMATION! Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

4.1.4.2

Method 2(Contd.)= -(t.Cy ~)P(t>Cy ) (based on exposed vertical-tail geometry for~ P (t>Cy ~)P Method 3)

Eq. 5.3.3.1-bI.

5.3.lT

Limitations depend upon (t>Cymethod)~predictionP

M .;;; 0.6; however, 1f swept planforms witht/c ~ 0.04, application to higher Mach numbers
is acceptable

3.
TRANSONIC

Linear-lift range(No method)

SUPERSONIC (Same as subsonic equations)

Method I
I.

)P

Horizontal tail mounted on body, or no horizontal
tail(based on exposed vertical-tail geometry J

2.
3.

Breaks in LE and TEat same spanwise station
Bodies of revolution

4.
5.
6.
7.

M ;. 1.4 for straight-tapered planforms
1.2 ~ M ~ 3 for composite planforms
1.0 .;;; M .;;; 3 for curved planforms(LlCy.6

Linear-lift range

f--- -- -- -- -- -- -- -- -- -- --Method 2(same limitations as Method I above)(ACv~)P (based on exposed vertical-tail geometry)

WBT

SUBSONIC-

5.2.3.1

Eq. 5.6.3.1-a Method I(C•a)ws

5.3.1.1(----------------------L p [- (t>Cy a)p5.2.3.1

5.3.1.1

cp b~")P)]+I.
t>Cy )

Linear·lift range(based on exposed vertical-tail geometry for (t>Cy )~ P Method 3)
aP
2.
Limitations depend upon (t>Cy) prediction
method~ P---------1Eq. 5.6.3.1-b------·-

Method 2(C•a)ws
I.

Linear-lift range( t.Cy a)p (based on exposed vertical-tail geometry for (LlCy \Method 3)

2.

~/P

Limitations depend upon(t>Cy ) prediction
method~ P

1-39

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEen

WBT(Contd.)SUBSONIC(Contd.)6

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

METHOD LIMITATIONS ASSOCI A TED WITHEQUATION COMPONENTS(xa.c.)p

M ~ 0.6; however, if swept planforms witht/c ..o;; 0.04, application to higher Mach numbers
is acceptable
Linear-lift range

3.

(Contd.)4.
fRANSONIC(No method)

SUPERSONIC(Same as subsonic equations)

Method I
I.

Horizontal tail mounted on body or no
horizontal tail(Cn~)ws(aCy

2.

Linear-lift range

3.
4.
5.
6.
7.

Breaks in LE and TE at same spanwise station
Bodies of revolution
M ~ 1.4 for straight-tapered planforms
1.2 ,._; ; M ~ 3 for composite planforrns
1.0 ~ M ~ 3 for curved planforms
Linear-lift range.a)p (based on exposed vertical-tail geometry)8.

- - - - - - - - - - ---- - Method 2(same limitations as Method I above)(t>.Cy ~)P (based on vertical-tail geometry)

Cypw

SUBSONIC

Cyp =

K

-

[(~:

7.1.2.1)CL•O CL1

+ (t>.Cy p)rM

Eq. 7.1.2.1-a-

7.1.2.1

7.1.2.1< o: stall

I.

Q'

2.

Test data for lift and dragK(;Lpt•O
M

TRANSONIC

3.

M<;;M

I.

Thin. sweptback, tapered wings withstrearnwise tips
Low iift coefficients(No method)

SUPERSONIC Figure 7.1.2.1-10

2.

WB

SUBSONIC

Cy

p

=

-

K [ ( : : )CL•O

7.1.2.1

)-40

"

M

7.1.2.1

CL] +(t>.Cy p)r-

7.1.2.1

Eq. 7.1.2.1-aI.
2.

a< a-stall3.

Test data for lift and drag(Body diameter)/(wing span).;; 0.3

KMETHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEc, p

WB(Contd.)WBSONIC(Contd.)(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION(Oatcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

C::t.oM

TRANSONIC(No method)

SUPERSONIC

Figure 7.1.2.1-iO

4.

M .;; M"I.

Thin, sweptback, tapered wings with streamwise
tips(Body diameter)/( wing span) .;; 0.3
Low lift coefficients

2.
3.

Wt!T

SUBSONIC

zp]-c, p = ( Cy p) WB +2 [z( Ll.Cy ~) V(WBHJ

Eq. 7.4.2.1-a Method I (conventionally located vertical tails)bw

7.3.2.1(Cvp) WB
I. (body diameter)/( wing span) .;; 0.3
2. ex ~ astall

5.3.1.1

3.
4.

Test data for lift and dragM .;; M"

(Ll.Cy ~) V(WBH)
5.

Additional or identical tail limitations dependon (Ll.Cy )~1---- -- ---- -- -- -- Cy p

= (cvP)WB+ [ 2zb~ zP] ( Ll.Cy ~ )v(WBH)

7.3.2.1
TRANSONIC(No method)

SUPERSONIC(No method)

V(WBH)

prediction method- - - - - - -- -- - - - - - - - - - - - - - - - - - - - - -- - Eq. 7.4.2.1-c Method 2 (vertical tail directly above, or above and slightly
behind wing)(same limitations as Method I above)

5.3.1.1

4.1.3.3ct

pw

SUBSONIC

ct p

=

c~p

)cl =07.1.2.2(f)-

4.1.1.2(CLa)cL( C1P) r+ ( Ll.CI )(Cla) CL =0 (CtP) r=o
4 1.3.2

7 .1.2.2

p

Eq. 7.1.2.2-a

I.

M.;;M

drag

"

(CLa) c L
7.1.2.2

2.

Symmetric airfoils

3.

I X !0 6 .;; R0 .;; 15 x I 0 6 based on MAC(Cla)cl=O
4.
TRANSONIC

Straight-taoered wings(No method)
1-41

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEct p

w

SUPERSONIC(Contd.)(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

ct p~I p)~heory] A

;

ct p
'c1 )

\

7.1.2.2p

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

I.
2.
3.

Eq. 7 .1.2.2-<1

theory4.

Straight·tapered wings
Wing tips parallel to free stream
Foremost Mach line from tip may notintersect remote half-wing
Supersonic TE

I.
2.

(Body diameter)/(wing span) ...; 0.3
M ...; M"

7.1.2.2

4.1.3.3__...,_._WB

SUBSONIC

ct p=(~~p)CL=O (;)~

7.1.2.2(CL.) C L-(ct.)r(CL.) CL =0(ct.) r=o~~4.1.3.2

7.1.2.2

4.1.1.2+ (.ac, p) dragEq. 7 .1.2.2-a~-~------·
7.1.2.2(CL.) CL
3.

Symmetric airfoils

4.

I X 106 ...; R, ,.; 15 x 106 based on MAC(CL.) C L=0

TRANSONIC(No method)

SUPERSONIC=(CIP) WBct p(ct.) w

Eq. 7 .3.2.2-a

Straight·tapered wings

I.

Straight-tapered wings. If (body diameter)/(wingspan) > 0.3, valid only for triangular wings)
Cylindrical or nearly cylindrical bodies(Ctp) d/b•O-..- ,_._:2)"7.1.2.2

5.

2.

7.3.2.

(Ct.) w
3.
4.
5.

WBT

SUBSONIC

ct p • (ct p ) WB + 0.5 (Ct•) H.._.,_
7.1.2.2--

7.1.2.2

C"~ C"YSw

bw+ Hb:) [ z :wzPI

J (ACy g) V(WS~)__
...
--..~

5.3 1.1

Wing tips parallel to free stream
Foremost Mach line from tip may notintersect remote half-wing

Supersonic TE

Eq. 7 .4.2.2-a Method I (conventionally located vertical tails)
and
1 )

(c

p

WB

(C1)
p

H

I.
2.
3.
4.

Straight·tapered planforms
Symmetric airfoils(Body diameter)/(wing span) ...; 0.3
M ...; M"5.

! x 106 .;; R 0 < 15 x 106 based on MAC(ACy g) V(WBH)

6.

Additional or identical tail limitations depend
prediction methodon (ACy )g V(WBH)

I-42

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEc/ p

WBT(Contd.)SUBSONIC(Contd.)(Contd.)c. p

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

-----

-----

7.1.2.2

w

TRANSONIC(No method)

SUPERSONIC(No method)SUBSONICC") C"r I:w [ b~ JI

c/ p = (C/p) WB + 0.5 (C/P) H ~

c. p

2z

zP

7.1.2.2

tan a - K

= -C/P+bw-(t!.Cy ~) V(WBH)

Eq. 7.4.2.2-b Method 2 (vertical tail located directly above, or above andslightly behind wing)(same limitations as Method I above)~

5.3.1.1

P) CL-0_ CL] + (tJ.>) 0

tan a - ( c.
CL

[ -CIPM- --7.1.2.2

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

7.1.2.3 7.1.2.2

7.1TI

7.1.2.3.[(:;::,] (:;),7.1.2.3

6,

6.1.1.1(No method)

SUPERSONIC

c.p
-- =
a

c~p )body+

2xc.g.
A(! + ;\.)axts

( c: p) - { c/p-7.1.2.1

7.1.2.3c., )-Eq. 7.1.2.3-e

7.1.2.2

2.

Lift coefficients up to stall (if reliable lift anddrag data are available)

3.
4.

Straight-tapered wings
Symmetric airfoils

5.

I X 10 6 .;; R,.;; 15 X !06 based on MAC"

Method I 'Subsonic leading edges (~ cot ALE <I)

-

-

M<;;M

c/ p

Eq. 7 .1.2.3-a

TRANSONICI.

7. 1.3.3

I.
2.
3.

Straight-tapered wings
Streamwise wing tips
Low lift coefficients

4.

Foremost Mach line from tip may notintersect remote half·wing
Supersonic TE

cl p
5.

1 - - - - - - - - - - - - - - - -- -- -- -- - - -- -- - - - - 1 - - - - - - - - - - -

c.p
-a

=

a

c·p)

bo~y

- - tan ALE l[

2x+ A(!:\)

I

Cy

2

a

J

aXIS

7.1.2.3

WB

SUBSONIC

7.1.2.1

c.p = -C1p tan a-

7.1.2.2+-K[ -C1 tan a -- -7.1.2.3p7.1.2.3

7.1.2.3

Eq. 7.1.2.3-g-

Method 2 Supersonic leading edges(~ cot ALE > I)(same limitations as Method I above)

7.1.2.2c~~)
CL CL•O CL]
7. 1.2.3

7.1.2.2

0 + (:;)::,

cl p

-

Eq. 7.1.2.3-aMn- [" l-O"P

-

p

(:~),

6,

----

I.
2.

(Body diameter)/( wing span)<;;; 0.3
M<;;M

3.

Lift coefficients up to stall (if reliable liftand drag data are available)

"

cl p
4.
5.

Symmetric airfoils

6.

I x 106 <;;; Ro <;;; 15 x 106 ·based on MAC

Straight-tapered wings

6.1.: .I
1-43

METHODS SUMMARYDERIVATIVECONFIG.

c. p

WB(Contd.)(Contd.)•SPEED
REGIME
TRANSONI!=EQUATIONS FOR DERIVATIVE ESTIMATION(Oatcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS(No method)

SUPERSONIC

a

(

c•• \

2xc.g.

+= -a-/body

Eq. 7.1.2.3-eA(l +A)

Method l Subsonic leading edges(~ cot ALE< l)
I.
2.
3.
4.

axis

7.1.2.3

Straight-tapered wings
Streamwise wing tips
(Body diameter)/( wing span).;; 0.3
Lift coefficients where en varies linearlywith CL5.

~-(c.)_P_

a

=

--"-

a

..

-[---;:-

6.

-1 - ]Cy- · - e.g.
- - tan A--"
C
A(! +A)
2
LE
a
IP

+

body

-

~

7.1.2.3

WBT

SUBSONIC

c. p = ( Cnp) WB -7.1.2.1

2( £P cos a + zp sina) [ ' - z]bw~

7.3.2.3~) V(WBH)

Foremost Mach line from rip may notintersect remote half-wing
Supersonic TE(same limitations as Method l above)

Eq. 7.4.2.3-a Method 1 (conventionally located vertical tails)(Cnp) WBl.
Straight-tapered wings
2.
Symmetric airfoils
3. (Body diameter)/(wing span).;; 0.34.
M <;;; M

5.3.1.1( f>Cy"5.

1 X l 0 6 .;; R, .;; 15 X l 0 6 based on MAC

6.

Lift coefficients up to stall (if reliable liftand drag data are available)~) V(WBH)
7.

Additional or identical tail limitations dependon (L>Cy )prediction method

I-- _ _ _ _ _ _ _ _ _ _ - - - _ _ _ _ _ _ _ _ - - - ____ - - - - - - ________()

rz- zP] (c. p = c. pWB + 2 .bw
--

-·--

Eq. 7.1.2.3-g Method 2 Supersonic leading edges(~ cot ALE> l)-7.1.2.2( f>CyP)--~-V(WBH) _ _ - - - --- __(same limitations as for Eq. 7.4.2.3-a above)ac. t3p

Eq. 7.4.2.3-b(acnt3P)I.

7.3.2.3

Test dataI

1 - - - - - - - - - ---------------------~.
Eq. 7.4. 2.3-c Method 2 (vertical tails located directly above, or abovec•• =(C•.)ws _ tQ" cos a b: zP sin a] [2zb: zP] (aCy ~ )v(WBHJ
1
7 .3.2.3

5.3.1.1

and slightly behind wing)(same limitations as for Eq. 7.4.2.3-a above)

1 - - - - - - - - - - - - - - - - - - - - - - 1 - - - - - - - - - - - - - - -----·(same limitations as Method I above)c
Eq. 7.4.2.3-d(c•.)ws +"p =7.3.2.3)-44

METHODS SUMMARYDERIVATIVECONFIG.

c.,

WBT(Contd.)(Contd.)

Cv,

w

WB

WBT

SPEED
REGIMEEQUATIONS FOR DERIVATIVE ESTIMATION~Datcom section for components indicated)

TRANSONIC(No method)

SUPERSONIC(No method)SUBSONIC(No method)

TRANSONIC(No method)

SUPERSONIC(No methcd)

SUBSONIC(No method)

TRANSONIC(No method)

SUPERSONIC(No method)SUBSONIC

Cy'= (cv ,) ws

2
- b

-

w

(e cos a + z sin ") ( <lC )
p

y i3

p

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

I.

Eq. 7 .4.3.1-a

VtWBH)

Aperiodic mode only(Cv,) WB
5.3.1.1

2.

Test data( <lCy • )V(WBH)
3.
Additional tail limitations depend on
prediction method( M~y )

1 - - - - - - - -Cy

'

w

c,

(No method)

SUPERSONIC(No method)

'

= CL

c,

'

(J

(

~JCL

•0

+ ( <lC, )Eq. 7.4.3.1-b

' CL

M

7.1.3. 2

7.1.3.2+( <lC,')-- r +
r-7.1.3.2( <l:'·) 0 +[r:~\l(: ), .,~~

7.1.3.2

7.1.3.2

6.1.1.1

Eq. 7 1.3.2-a

(cv )
r

WB

(No method)

SUPERSONIC(No method)and (<len )/3

I.

Test dataI.

M~M-- - - - - - - -p"( <lC, )' CL
2.
No curved planforms
3.
No twist or dihedral, if non~straight·taperedwings
4.
t/c <;; 0.1 if cranked wing with round LE
5.
M <;; 0.6
6.
Linear-lift range
7.

TRANSONIC

V(WBH)-- ----- - - - - 1 - - - ------= (Cv' )ws + 2(<lC)
n• pTRANSONICSUBSONIC- - - - --- - - ---50~ (3 ~+50

l-45

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEc,WB

SUBSONIC'(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)c,, =~c~t=O+( ~C1 )
'

1

CL

M

7.1.3.2

7.1.3.2

C-}
+ (r

r +

METHOD LIMITATIONS ASSOCI ATED WITHEQUATION COMPONENTS(;'·) ·~~·· y::),•,
6
8

Eq. 7.1.3.2-aSr-

7.1.3.2(Body diameter)/(wing span)< 0.3
M ~Mer(~c1,kf

7.1.3.2

7.1.3.2

1.
2.

6.1.1.1

3.
4.

No curved planforms
No twist or dihedral, if non·straight-taperedwing

TRANSONIC

5.
6.
7.

t/c < 0.1 if cranked wing with round LE
M < 0.6
Linear-lift range

8.

-5° < ~<+5°(No method)

SUPERSONIC (No method)WBT

SUBSONIC- .2_(£p cos a + zp sin") (zp cos a - £P sin a) f~cy)b2\
~ V(WBH)w~~~--~cI, =Eq. 7.4.3.2-a
No curved planforms

5.3.1.1

No twist or dihedral, if non-straight-taperedwing
3.

tic < 0.1 if cranked wiog with round LE

4.
5.
6.

(Body diameter)/(wing span)< 0.3
M < 0.6
M<M

7.

Linear-lift range

8.

-50<~< +50"(~Cy ~) V(WBH)
9.

e-----------c, (c1) - 2bw (£P cos a+ zP si~ a)1~c
1
\t3P
r

=

)

Additional or identical tail limitations depend on~Cy )prediction method(ll V(WBH)---1---------Eq. 7 .4.3.2-brWB(Cl,) WB(same limitations as for Eq. 7.4.3.2-a)(~CI#)P

7.3.3.2

I.

Test dataf - - - - - - - - - - - - - - - - - - - - - -- ---- -+ 2(~c·~)p(Cl,)
Eq. 7.4.3.2-c

WB(same limitations as for Eq. 7.4.3.2-a)(~Cn~)P (~Cy ~)V(WBHl' and(~C1 ~)P
1.

TRANSONIC'
1-46(No method)

Test data

METHODS SUMMARYDERIVATIVECONFIG.

C,r(Contd.)(Contd.)

c.

w

•

wu

SPEED
REGIMESUPERSONIC (No method)

SUIISONIC

c.

r

= (

:~·)

c2

____,..

L+( ;~J

TRANSONIC(No method)

SUPERSONIC(No method)SUBSONIC

c.

=
r

(:;·)

c2L

+

~

WBT

(NCJ method)

SUPERSONIC(No method)

SU.ONICEq. 7.1.3.3-a
0

I.

2.

(~J

Eq. 7.1.3.3-a----

No twist nor dihedral
Lift-coefficient range for which Cn varies
linearly with CL'

2.

No twist nor dihedral
Lift coefficient range for which Cn varies
linearly with CLr

I.

Aperiodic mode onlyI.

7.1.3.3

7,1.3,3
TllANSONIC

CD

7T3:3

7.1.3.3

WB

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)c. r = (c•,)wB + _22 (£p COSCi +Zp sin<i) 2 (ACy ) V(WBH)b

Eq. 7.4.3.3-a

~

2.
3.

w

5.3.1.1

7.3.3.3(C•,)wa
No twist nor dihedral
Lift-coefficient range for which c. varieo
linearly with CL'( ACy ~) V(WBH)
4. Additional tail limitations depend upon
(ACy )
prediction method~

V(WBH)------ - - - - - - - - - - - - - - - - - - - - - - - - 1 - - - - - - - - - - - - - - - ---·c. r = ( Cn,) WB + 2
7.3.3.3
TRANSONIC(No method)

SUPERSONIC(No metbod)(ACn~)~( ACy ~) V(WBH)

Eq. 7.4.3.3-b(same limitations as for Eq. 7.4.3.3-a above)( ACn~)P
I. Test data

5.3.1.1

1-47

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEw

SUBSONIC

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

Eq. 6.1.1.1-a(two dim)I.
2.

Linear-lift range
Other limitations depend upon type of flap
(see Equations -c through -j below)----------------------Eq. 6.1.1.1-b

I.

2.

Linear-lift range
Other limitations depend upon type of flap
(see Equations -c through -j below)---------------(Co )0

K'

Eq. 6.1.1.1-ctheory6.1.1.1
6.1.1.1
f--- -----------

6.1.1.1

-

I.
2.
3.

Plain trailing-edge flaps with sealed gaps
No beveled trailing edges
No compressibility effects-- -- - -- - - (a) Single-slotted flaps-- -- - - -- - -Eq. 6 .1.1.1-d (b) Fowler flaps
I. Near fully extended position
2. Slot properly developed

test data 6.1.1.1---- - - - - - - - - - - - - - - - - -r-c'

Eq. 6.1.1.1-elJIc'--..---'(a) Single-slotted flaps(b) Fowler flaps

6.1.1.1~-----------------

~c

•=

c•

Eq. 6.1.1.1-h'c~..___,

6.1.1.1
t------

6.1.1.1

c.

6cl

'cI

(:~

y:-

'--..---'

I.

2.

c - c

_'1_2_'--..---'

6.1.1:1t--~c.

--------------------------------c.

'c._=..,'-v---J

6f2 (I + '')Eq. 6.1.1.1-i

a

C

I.

2

Double-slotted flaps
Ratio of forward-flap chord to aft-flap chord ..;; 0.60

Double-slotted flaps
Ratio of forward-flap chord to aft-flap chord ::::: 1.0-- -- -- -- -- -6.1.1.1 6.1.1.1 6.1.1.1----

Eq. 6.1.1.1-j= -c0 aI.

Split flaps

4.1.1.2 6.1.1.1

r - - - - - - - - - - - - - - - - - - - -+--- -- ---- ---- ------dc 0 = {[l+k,(;.)]6r(c•,r-C~) +C~6r+[l+k,(;,)]6i(c•,.- c:-.__, .__,

6.1.1.1

6.1.1.1 6.1.1.1 6.1.1.1-)+

C~ 6i}~-.._!.., .__,.__,

6.1.1.1

6.1.1.1 6.1.1.1

6.1.1.1

Eq.6.1.1.1-k

I.
2.
3.
4.
5.

Jet flaps (first approximation for multislotted flaps)
Linearized thin-airfoil theory
No trailing-edge separation
No augmentor-wing concept
Not valid for low values of C~

1-49

METHODS SUMMARYDERIVATIVE

c,.
and

a•

CON FIGw(two dim)(Contd.)SPEED
REGIMESUBSONIC(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)~c,

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS= ....._,_.....
Ci6
ofEq. 6.1.1.1-2

6.1.1.1---------------------- --- -(Contd.)

~c

'

'
0~

=

f

-Ci

•

-·--------------- -·-I.
Thin-airfoil theory·(a) Krueger flaps_ _ _ _ _ ~Leading-edge slats __~o/Eq. 6.1.1. 1-ns....._,_..... ....._,_.....
4.1.1.2 6.1.1.1

w(same as that for flap-retracted section - see Section 6.1.1.2\

SUBSONIC(two dim)
4.1.1.2

Plug or flap spoiler
Zero-lift regionI.
2.

of .;; 20° for plain flaps-- -- -- -- -- --- -- -

--

5.
6.

No separated flow

Eq. 6.1.1.2-a
4.1.1.2
i---- ------------------c'( c'12a: - C'll ) + C'JJ.c}'--r-'
6.1.1.1

1------------- (c•.), = fc•.). =o !same as basic airfoil)w

SUBSONIC~c,(two dim)(~c 2 max1ase

max =
6.1.1.3 6.1.1.3 6.1.1.3--Eq. 6.1.1.2-b

Fixed-hinge trailing- and leading-edge flaps

Or .;;; 30° for single.;;lotted and Fowler flaps
5r .;;; 60° for double.;;lotted flaps
Or .;; 45° for split flaps

4.

1--- -- - - - - -Translating trailing-edge flaps and leading-edge
slats
~--

I.

2.
3.
4.
5.

-- -- -- -- -- --- -- --Eq. 6.1.1.3-a----------Jet flaps (first approximation for multislotted flaps)
Linearized thin-airfoil theory
No trailing-edge separation
No augmentor-wing concept
Not valid for low values of C~I.

Spoilers

2.
3.

a> 0

I.

Trailing-edge flapsc, < 06.1.1.3----- --·-

f--~c

2

=

c,

6

11max

f'ls

....._,_..... ....._,_..... ....._,_.....
max

'
0 .:_
f c

Eq. 6.1.1.3-b(a)

5.1.1.3 6.1.1.3 6.1.1.3
(b)

1-50

------

I.
2.

3.

6.1.1.2

Leading-edge flaps
Thin-airfoil theory

Eq. 6.1. I. 1-mc..____
~c, =

I.
2.

I.
Thin-airfoil theory
Leading-edge flaps
2.
No Krueger flaps
3. llr < 30°
Leading-edge slats
4. ll, < 20°

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEw

SUBSONIC(two-dim)

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated).:lcrn =METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS.:l~ [ x;f _ ( x:,P)( ~·)]'--v--''--v--'

6.1.1.1

6. 1.2.1

Eq. 6.1.2.1-a

Method I
I. Plain, split, and multislotted trailing-edge flaps
2. Linear-lift range.:lc, (depends upon type of flap)r - - - - - - - - - - - -- --- -- - - -- --- --- - - - - Metho~ - - - - - - - - - - - - - - - Figure 6.1.2.1 -35b

1.
2.
3.

Plain trailing-edge flaps
Subcritical Mach numbers
Linear-lift range

1----------- -- -----------------1------------------)(c')2 & +(xref-c + c-' -c-c .:lc' +c'rn,LE cfLE'--v--''-v-'

6.1.2.1

6.1.1.1

+0.75
'-v-'

4.1.2.1c,(~)(~-1)

I.
Small leading-edge devices
2. Thin-airioil theory.:lc, (depends upon type of flap)'-v-'

4.1.1.1,
4.1.1.2

1 - - - - - - - - - - - - - - - - --------

Eq. 6.1.2.1-b----------------

Eq. 6.1.2.1-c

I.

2.
3.
4.
5.

w

SUBSONIC(two dim)(crna ) 6 = (r._·rna )6=0

1--- - - - - - - - - - - - -6.1.2.1 6.1.2.1

w(two dim)

SUBSONIC

Figure 6.1.2.3-3

I.

(same as that for flap-retracted sections)-- -- -- -- -- --Jet flaps (first approximation for muitislotted
flaps)
Linearized thin-airfoil theory
No trailing-edge separation
No augmentor-wing concept
Not valid for low values of c.

-----

2.

Leading- and trailing-edge mechanical flaps
No separated flow

Eq. 6.1.2.1-k

I.
2.
3.
4.
5.

Jet flaps (first approximation for multislotted flaps)
Linearized thin-airfoil theory
No trailing-edge separation
No augmentor-wing concept
Not valid for low values of c.

I.

Portion of Cm c, curve below the moment break--·-.:lc, (depends upon type of flap)

1-51

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEw

SUBSONIC

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)I.

Eq. 6.1.3.1-a(So:) theory(two dim)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

2.

3.

6.1.3.1

+ 2

(c• )

a theory

4.

[

I -

4.1.1.2

6.1.3.1c, a(c2 a )theory

1

(tan

---- --- </>~E - .!.)
2c

Eq. 6.1.3.1-bI.

2.

4.1.1.2

4.

r------- ------- -- -- - - -

,.

c;. a

[('i.o)balance)"<;,----·-

Radius-nose, sealed, trailing-edge flaps
Tangent of half the trailing-edge angle
No separated flow
Low speeds* t/c------------I.

Eq. 6.1.3.1-cControl with nose balance

c;;Q

Q

6.1.3.1- - -- - - -- --

c;, o
3.

('1.)a balance =Radius-nose, sealed, trailing-edge flaps
Tangent of half the trailing-edge angle= t/c
No separated flow
Low speeds

6.1.3.1

2.
3.

Radius-nose, sealed, trailing-edge flaps
No separated flow
4. Low speeds~-----4-------------------------------------------------------4--------------------------------4
TRANSONIC (No method)
SUPERSONIC= -Cl + C2 </>TE

Eq. 6.1.3.1-e1.--,--1 1.--,--1

I.

2.

6.1.3.1 6.1.3.1

3.

4.
5.
6.

7.

Airfoils with sharp leading and trailing edges
Symmetric, straight-sided flaps
Cc/C < 0.5
Small flap deflections
Small angles of attack
Flow field supersonic and inviscid
No separated flow---t-------~<;. ) tc;.Q = ~ ( ---;;;
6.1.3.1

1-52

6.1.3.1~

Eq. 6.1.3.1-f

I.
2.
3.

Airfoils with sharp leading and trailing edges
Symmetric, circular-arc airfoils
cc/c < 0.5

4.
5.
6.
7.

Small flap deflections
Small angles of attack
Flow field supersonic and inviscid
No separated flow

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEw

SUBSONIC(two dim)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom oodion for components indicated)l--~. • rk~ )~•6

Eq. 6.1.3.2-a(<1t6)theory

theory6.1.3.2

6.1.3.2- - -------------- --------- --- -- --- -- 26

I [6.1.3.2---

6.1.1.1c(c2 ~theory](tant/JiE _!)

2c

Eq. 6.1.3.2-b6.1.1.1-------

Eq. 6.1.3.2-c

I.
2.
3.
4.

I.

Radius-nose, sealed, trailing-edge flaps
Tangent of half the trailing-edge angle= t/c
No separated flow
Low speeds

2.
3.
4.

Radius-nose, sealed, trailing-edge flaps
Tangent of half the trailing-edge angle* t/c
No separated flow
Low speeds

I.

Control with nose balance

2.

Radius-nose, sealed, trailing-edge flaps
No separated flow
Low speeds- - - - -- -- - - --.6.1.3.2

6.1.3.2

3.

4.

~-------1-------------------------------------------------------------~--------------------------------~
TRANSONIC(No method)

SUPERSONICc.
·n6= _________..
-Cl + C2 t/JTE..__.

Eq. 6.1.3.2-d6.1.3.2 6.1.3.2

1------_________..

(~) ~6.1.3.2

6.1.3.1= -Cl +w
(two dim)

I.
2.
3.

Airfoils with sharp leading and trailing edges
Symmetric, straight-sided flap
cr/c·< 0.5

4. Small flap deflections
5. Small angles of attack
6. Flow field supersonic and inviscid
7. No separated flow
- - - - -I- - - - - --- - - -- -- ------Eq. 6.1.3.2-e

SUBSONIC
Eq. 6.1.3.3-a

I.
2.
3.

Airfoils with sharp leading and trailing edges
Symmetric, circular-arc airfoil
cr/c.;;; 0.5

4.

5.
6.
7.

Small flap deflections
Small angles of attack
Flow field supersonic and inviscid
No separated flowI.

-18° .;;; 6 t .;;; I 8°

2.

3.

Does not account for effects of airfoil thickness,
control-surface gaps, control nose balance, andTE angle
Low speeds

4.

Linear hinge-moment range

1-53

METHODS SUMMARYDERIVATIVECONFIG.

w

SPEED
REGIMEEQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTSSUBSONIC

Eq. 6.1.3.4-aI.

-18o.;;;sr.;;;J8o2.

Does not account for effects of airfoil thickness,
control-surface gaps, control nose balance, andTE angle

3.

Low speeds

4.

Linear hinge-moment range(two dim)

4.1.3.2

w

SUBSONIC

[(a,
(Z)
--

Eq. 6.1.4.1-a

Kb

lcL]

-r----[---2c;- -] c2

6.1.1.1(a 6 >c

•

Q

~

A
+n t

.:lCL =

~

CL

•
I.

~ 6.1.4.1
6.1.4.1

4.1.!.2.:lc2 (depends upon type of flap)

Eq. 6.1.4.1-bc;Sw

6. J:i .l

---

l

-

,....._,

6.1.4.1"A,+ 2c;[ "A• +~~./ 2.01c;liieff-Mechanical flaps
Straight-tapered wings

2.
3.
4.
5.
6.

Small angles of attack
Linearized thin-airfoil theory
No trailing-edge separation
No augmentor-wing concept
Not valid for low values of C 1--I. ---- -- --- --Jet flap IBF configuration

SWf

A1 + 2 + 0.604(C;) 1 i 2 + 0.876

2.

- - -+-- - - I.

Eq. 6.1.4.1-c

2.

Sw r

3.

57.3 Sw

4.
5.

6.1.1.!

6.

Eq.6.1.4.1-e

CL

I.

c, 0
6.2.1.!

Straight-tapered wings

M =0.6

2.
3.
4.
5.
6.

1- 54

Jet flap EBF configuration
Small angles of attack
Linearized thin-airfoil theory
N,o trailing-edge separation
No augmentor-wing concept
Not valid for low values of C1

0 M = 0.6

TRANSONIC

6.1.4.1- - -- - - - - -- -- --Plain trailing-edge flaps{3A ;;. 2
A~< 60°No beveled trailing edges
No compressibility effects

7.

Symmetric airfoils of conventional thickness
distribution

8.

a= 0

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEEQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

Eq. 6.1Al-f

cL,w(Contd.)(Contd.)I.

SUPERSONIC

2.
3.

4.

5.
6.

7.

w

SUBSONIC=

Leading and trailing edges of the control surface
are swept ahead of Mach lines from the deflected
controls
Control root and tip chords are parallel to theplane of symmetry
Controls are located either at the wing tip or far
enough inboard so that the outermost Mach lines
from the deflected controls do not cross thewing tip
Innermost Mach lines from deflected con trois do
not cross the wing root chord
Wing planform has leading edges swept ahead ofMach lines and has streamwise tips
Controls are not influenced by tip conical flow fromthe opposite wing panel or by the interaction of
the wing-root Mach cone with the wing tip
Symmetric, straight-sided flaps
Nontranslating leading- and trailing-edge flaps
No separated flow on wings and flaps(cLJo=O (same as for unflapped wings)
4.1.3.2
3.
4.

No curved planforms
M "'0.80, t/c "'O.l,.if cranked planform with round LE----------------- ----------------- - - - - - - - - - - - - - - - - ----Eq. 6.1.4.2-aTranslating leading- and trailing-edge flaps
No separated flow on wings and flaps+(cL.) •=o'---v-'

4.1.3.2
3.
4.

No curved planforms
M "'0.80, t/c"' O.l,if cranked planform with round LE- - - - - - - - - - - 6.1.4.
-- - - - - · -Eq.-6.1.4.2-b----- - - - - - - - - --·I
Jet flaps
I.

~

=

'
]
}
(CL 0 )
K(A 1, C1 ) - I Kb + 1.0
0 { [
..__,

'---v-'

6.1.4.2

6.1.4.2

6. 1.4. I+

CJ(COS sieff- I)

57.3

2.

A;;.s

(CL 0 ),

3.
4.
5.

No separated flow on wings and flaps
No curved planforms
M "'0.80, t/c "'0. I, if cranked plan form withround LE

1-55

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEw

SUBSONIC

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)= .6c2METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

I.

Eq. 6.1.4.3-amax

Mechanical trailing-edge flaps

6. 1. 1.3.___ - - - - - -2 - - - - - - - - - - - - - - ---- - - - i - - - - - - - - - -c/c) (bslat)~ cos2 Ac/4
(0.18
1.::lCLmax = 1.28

---

I.

Eq. 6. 1.4.3-b------------------------------ - - - - · -Figure 6.1.4.3- 12w

SUBSONIC

I.

(~) '-v-'.::lCL tan Ac/.::lCmr = .::lCm + KA'-v-'

Slats (first-order approximation)'-v-' 1.5

6.1.5.16.1.5.1

Eq. 6.1.5.1-a4

6.1.4.1

First-order approximation for EBF configuration1.

Linear-lift range

2.

Ac/4 < 45°.::lCL (depends upon type of flap)
3.

1----------------------------AC

=

mr

/1.o

-·-

0

6.1.5.1-

Eq. 6. 1.5.1-k--Mechanical flaps
Straight-tapered wings- - - - - - - - - - - - - - - - - ---1
I. Linear aerodynamic control characteristic region(depends upon type of flap)

4.
C2

A

x/c

6.1.5.1

3.
L-- - - -=- - ------

---

C

I.

C

test

6. 1.2.1- - - - --- -- --6.1.4.1,_..._ACmw

TRANSONICCm= em m

c)

Az

-

c

~

~

~

6.1.5.1

6.1.4.3

6.1.5.1= -CL
6+ 1'1,

(;)
6

-.-'

p

+

E
k=i

{[c.
~

6. 1.5 .I

data

6.__.._,
1.5 .I 6.__.._,
1.5 .I

SK

"L
-57.3

sw

-

c,J A;k }
-.-'

-.-

6.1.5.1

6. 1.5 .I

2.
3.

Mechanical leading-edge devices
Constant flap-chord-to-wing-chord ratio
Thin-airfoil theory

1.
2.
3.
4.
5.

Jet flaps (first approximation for multislotted flaps)
Linearized thin-airfoil theory
No trailing-edge separation
No augmentor-wing concept
Not valid for low values of1.

Linear aerodynamic control characteristic region

2.
3.

Straight-tapered wings
Plain trailing-edge flaps with sealed gap
No beveled trailing edges~A;;;. 2
A~< 60°Symmetric airfoils with conventional thickness
distribution
No compressibility effects

Eq, 6.1.5.1-£

Eq. 6.1.5.1-u

Eq. 6. 1.5.l·W---------

c,.

~

6.1.4.1 6.1.5.1

4.
5.

6.
7.
8.
9.
1-56

-------- ----·---- - - --- ---[em , (~')+C.:' - x:..E)c
6LE

Linear-lift range
Subcritical Mach numbers

Ol

= 0

METHODS SUMMARYDERIVATIVECONFIG.

c m;w(Contd)(Contd.)SPEED
REGIMESUPERSONICEQUATIONS FOR DERIVATIVE ESTIMATION!Datcom section for components indicated)

c m,

I

-

= K,

-.-

3

b, c'f

-

f

I

b,

sf

- -Sw C'
2 f
Sw'•-.- -.-.-

-

C'm,

-

K2 -

K3

-.-

6.2.1.1 6.1.5.1

6.1.5.1 6.1.5.1

6.1.5.1

x, s,

-

-

c

-

Sw

C'
L,

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

Eq. 6.1.5.1-qI.
2.

--...--

3.

6.1.4.1

4.
5.

6.
7.

8.

Linear aerodynamic control characteristic region
Symmetric straight-sided controls
Leading and trailing edges of the control surface areswept ahead of Mach lines from the deflected
controls.
Control root and tip chords are parallel to theplane of symmetry
Controls are located either at the wing tip or far
enough inboard so that outermost Mach lines fromthe deflected controls do not cross the wing tip
Innermost Mach lines from deflected controls do
not cross the wing root chord
Wing planform has leading edges swept ahead ofMach lines and has streamwise tips
Con trois are not influenced by tip conical flowfrom the opposite wing_ panel or by the interactionof the wing-root Mach cone with the wing tip.

C'

15

9.

I 0.

chQ

w

SUBSONICch Q =A COS 11., 14
A + 2 COS 11., 14( ch Q) balance

+

Ll.Ch

Q

Eq. 6.1.6.1-a

3.
4.

High aspect ratios (A > 3)
Ends of control surfaces parallel to plane ofsymmetry
Neglects subcritical Mach-number effects
Sealed, plain trailing-edge controls

5.
6.

No separated flow
Low speeds

I.

Symmetric, straight-sided controls
Con:rol root and tip chords are parallel to theplane of symmetry
Wing planform has leading edges swept ahead ofMach lines and has streamwise tips
Controls are not influenced by tip conical flowfrom the opposite wing panel or by interaction of
the wing-root Mach cone with the wing tip.

I.
2.

~

6.1.6.1

6.1.3.1

Plain !>ailing-edge flaps
Thin wingsch Q

TRANSONIC(No method)

SUPERSONIC(chJ,;, = (I

'

c2

cl
-.-

6.1.6.1q\TE) ( cho)t/c

Eq. 6.1.6.1-b= 02.

6.1.6.1

3.
4.

1-57

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEEQUATIONS FOR DERIVATIVE ESTIMATION!Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

6.1.6.1

ch

Q(Contd)w(Contd.). ,. . ,3C-~

SUPERSONIC(Contd.)--. 't2

I--~L-E-_(-,-I+--,-k-):-::-AH-L)

1

2[I + 26.1.6.1ch)l~r -c )r!} (chJt/c oI=

6.16.16.1.6.1

I.
2.

Symmetric biconvex airfoil
Other limitations identical to Items 2 through 4
immediately abovel.

High aspect ratios (A > 3)
Ends of control surfaces parallel to plane ofsymmetry
Neglects subcritical Mach-number effects
Sealed, plain trailing-edge flaps

Eq. 6.1.6.1-bwith different
correction factorw

2 COS Ac/4

SUBSONIC=COS Ac/ 4 COS AH L

A + 2 cos A, 14

6.1.3.2

6.1.1.1

6.1.3.1]+ ~c

Eq. 6.1.6.2-ah,2.

6.1.6.2

3.
4.
ch

' 5.
6.

TRANSONIC(No method)

SUPERSONIC Ch

6=~ (1 - ~: t/>TE) ~ C~,-6.1.6.2-

Eq. 6.1.6.2-bI.
2.

6. [ .6.2
3.
4.

5.

6.
7.

--

Symmetric, straight-sided controls
Leading and trailing edges of the control surface
are swept ahead of Mach lines from the deflected
controls
Control root and tip chords are parallel to theplane of symmetry
Controls are located either at the wing tip or far
enough inboard so that outermost Mach lines fromdeflected controls do not cross the wing tip
Innermost Mach lines from deflected controls do
not cross the wing root chord
The wing planform has leading edges swept aheadof Mach lines and has streamwise tips
Controls are not influenced by tip conical flowfrom the opposite wing panel or by interaction of
the wing-root Mach cone with the wing tip---------1-

Eq. 6.1 .6.2-bwith different
correction factor

1-58

No separated flow
Low speedsI2.

--------~-

Symmetric biconvex airfoil
Other limitations identical to Items 2 through 7
immediately above

METHODS SUMMARYDERIVATIVECON FIG.

SPEED
REGIMEw

SUBSONIC

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

METHOD LIMITATIONS ASSOCI ATED WITHEQUATION COMPONENTS

k-2(I - 8vn) Bkn

I.

No separated flow over control surface
Induced drag due to control deflection
G.,
G
,
G
(depends upon type of flap)
•
n
v

Gn}

2.

n==l
~

~

~

~

6.1.7 6.1.7 6.1.7~~

6.J.7i6.1.7 6.1. 7
k

-2:

v= 1

(1--8 vn )B vn

sin </Jv]

Eq. 6.1.7-c

n•l

~

6.1.7

~

~

~~

6.1. 7 6.1.7~

6.1.7 6.1. 7 6.1.7

r--6.1.4.1.-"-.

AC·Dmin =

Acd f

K
... ~

-....-~(AcLrY+ K'

I.

Eq. 6.1.7-p

1rA

2.

~

6.1.7 6.1.4.1 6.1.7

ACL

No separated flow over control surface
Profile drag due to control deflection(depends upon type of flap)f

TRANSONIC(No method)

SUPERSONIC

AC 0

Eq. 6.1.7-q

wave

4.1.5.1c,.

w

SUBSONIC

c,

-C'

•

Eq. 6.2.1.1-b'•6.1.1.1 6.2.1.1

2.

ilA;;;. 2
A~< 60°M.;;; 0.6

4.
5.

--·
----- --

6.
7.

No beveled trailing edges
No compressibility effects

flex.' 5

Eq. 6.2.1.1-c

I.

Plug or flap-type spoilers
No separated flow2

6.2.1.1 6.1.1.1----( cl) s.poiler-slot-deflector

0 ther limitations identical to Items I through 4
immediately above--- --- --- --- --- --- --- ---K(CI)plain spoiler

6.2.1.1

6.2.1.1

No separated flow

- - --- --- --- -- -- -- - - - - -- --- -- - - - - -- -- --I 6

2

Plain trailing-edge flaps

3.

----c' -- -- -- --- --- --- cI :I.

------------Eq. 6.2.1.1-f

I.

Spoiler-slot-deflector

2.
3.
4.

ilA ;;;. 2
A~< 60°M.;;; 0.6

5.

No separated flow

(C,lplain spoiler
6. Plain flap-type spoiler
1-59

METHODS SUMMARYDERIVATIVECON FIG.

c,6w(Contd)(Contd.)SPEED
REGIME

TRANSONIC

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated,)(C 1)M=o. 6 (depends upon type of control)
Eq. 6.2.1.1-g CL
Q
I. Symmetri~ airfoils of conventional thickness
distribution
2. A ..;; 3 if composite win2

CL Q

c, = (CI)M=0.6(CLQ)M =06
6.2.1.1

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

4.1.3.2

3.

01=0(CLQ)M =0.6
4. No curved planform
5. t/c..;; 0.10, if cranked planform with round LEc~ 6[:~ c:~) 7]
6.2.1.1

SUPERSONIC

c, ~TE)c, 6 = (' - c2

~

C'
L6

--

sr

I

- Sw 2

6+

Eq. 6.2.1.1-h-----

6.1.4.1

6.2.1.1

I.
2.

3.

6.1.4.1

4.
5.
6.

Plain trailing-edge flaps
Leading (hinge line) and trailing edges of control
surfaces are supersonic (swept ahead of Mach lines)
Control surfaces are located at wing tip or far
enough inboard to prevent outermost Mach lines
from control surfaces from crossing wing tip
Innermost Mach lines from deflected control
surfaces do not cross root chord
Root and tip chords of control surfaces are
stream wise
Controls are not influenced by tip conical flowfrom opposite wing panel or by interaction of
wing-root Mach cone with the wing tip

C/6
7.

Thin wings

8.

Symmetric, straight-sided controls

I.

Plug or flap-type spoilers

I.
2.
3.

Differentially deflected horizontal stabilizer
Horizontal tail mounted on bodyNo separated flow on horizontal tail4.

Straight-tapered wing

5.

Other limitations depend upon - prediction
methodoaC'L61--------- -- -- -- -- -- -- -- -- -- -- -- - - - -- -- --- -- -- -- ---- - - -Figure 6. 2.1.1-30

SUBSONIC

c, 6

=

'I{
l

I -

rrAw
57.3

--

-YH sHe/2)] ~ CH) bw Sw (CL QH ) e-ae) + ivB(HJ C1Tarvr)(bHraae~-4.4.1
4.3.1.3 4.3.1.3-6.2.1.2-4.1.3.2

Eq. 6.2.1.2-a

oe
-oa

ae

(CLQJe6.
7.
1-60

No curved planforms
M..;; 0.8, tfc..;; 0.10, if cranked planform withround LEMETHODS SUMMARYDERIVATIVECON FIG.

cl,

T(Contd.)(Contd.)SPEED
REGIME
TRANSONIC

EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS(Same as subsonic equation)

I.
2.
3.
4.

Differentially deflected horizontal stabilizer
M < l.O
Body-mounted horizontal tailNo separated flow on horizontal tail5.
6.

Straight-tapered wing
Proportional to CL•(CL•H)e7.
8.

9.

Symmetric airfoils of conventional thickness
distributionA,; 3 if composite wingC< = 0f - - - - - - - - ···-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - · (Same as supersonic equation)
I. M > 1.0(Same limitations as for M < 1.0 above except
those of ae;aa)SUPERSONIC

C1

'

c.

w

SUBSONIC= 0.35 [ ivB(H) (21f; Vr)(bH>) + (--...--c. =.._.,_....

4.3.1.3 4.3.!.3~H(B).,. kB(H)) l (CN"H)e.

4.3.1.2

Eq. 6.2.1.2-c...._,_,

3.

4.1.3.2(CN"H)e(6L - 6R)K~

6.2.2.1

CL

cl

Eq. 6.2.2.1-a2..__..,'

6.2.1.1---· - - --- - - ----

Differentially deflected horizontal stabilizer
Body-mounted horizontal tailNo separated flow on horizontal tail

4.
5.
6.
7.

Breaks in LE and TE at same spanwise station
M ;;;. 1.4 for straight-tapered planforms
1.2 ,; M ,; 3 for double-delta planforms
1.0 ,.;;; M ,.;;; 3 for curved plan forms

1.
2.
3.

Aileron-type controls
No separated flow
Neglects contributions due to profile drag4.
5.

/3A ;;;. 2
A~ < 60°

6.
7.
8.

No beveled TE
No compressibility effectM..; 0.6l.
2.
3.

Plug and flap-type spoilers
0.02,; 6,/c,; 0.10
C< = 0

1.
2.
3.

C< = 0----- ---------

Figures 6.2.2.1-10, 6.2.2.1-11-----(Cn) spoiler-slot-deflector =l.
2.

- - ----·-- - _.,____ -- -- - - -- -- -- -- --- K

6.2.2.1

Eq. 6.2.2.1-b6.2.2.1

Spoiler-slot-deflector
6,16d

= 1.0

(Cn) plain spoile.

4.

Plain, flap-type spoiler
1-61

METHODS SUMMARYDERIVATIVECON FIG.

c.

w(Contd.)SPEED
REGIME

TRANSONIC(Contd.)EQUATIONS FOR DERIVATIVE ESTIMATION(Datcom section for components indicated)

C0=

METHOD LIMITATIONS ASSOCIATED WITHEQUATION COMPONENTS

Eq. 6.2.2.k(Cn )M =0.6
1. Aileron-type controls2.

6.2.2.1

4.1.3.2

3.
4.

5.
6.
7.

{JA ;;. 2
A~ < 60"

No beveled TE
No separated flow
No compressibility effects
Neglects contributions due to profile drag(CLn)M =06
8.

Straight-tapered wings

9.

Symmetric airfoils of conventional thickness
distribution
0

10.

"'=

~------~~--------------------------------------------------~----------~-----------------------------------SUPERSONIC

Figure 6.2.2.1-13---- -- -- --- --- --- -- --- --- --- - - --- -- -- --- -F~ure 6.2.2.1-14

T

1-62

ALL SPEEDS(No method)

I. Aileron-type controls
2. Neglects contributions due to profile dragf---- ------------1.

Plug and flap-type spoilers