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USAF STABILITY AND CONTROL DATCOM
MCDONNEf...L'OQUGLAS CORPORATION DOUGLAS AIFfCRAFT OIVI~ION . ' . ,.. . '
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...,. PRINCIPAL INVESTIGATOR: R. D. FINCK
OCTOBER 1960 Contract AF33(616)6460
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REVISED APRIL 197 8 Contract F336;S76C3061 Project No. 8219 ,Task No. 821901
FLI<{HT C0:Nr,IWL DIVISION AIR FORCE FLIGOTJ)YNAMICS LABOR'ATORY WRIGHTPATTERSON Ai'R ' FORCE BASE; OHIO . ; ·.. ~
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FOREWORD The current volume entitled 'USAF Stability and Control Datcom' has been prepared by the Douglas Aircraft Division of the McDonnell Douglas Corporation under Contracts AF33(616)6460, AF33(615)1605, F336!567C1156, F3361568C1260, F3361570CJ 087, F3361571C1298, F3361572C1348, F3361573C3057, F3361574C3021, F3361575C3067, and F3361576C3061. (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, WrightPatterson 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 to provide timely stability and flight control data and methods for the design of manned 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
CONTRIBUTORS DOUGLAS AIRCRAFT COMPANY, INC. 19601965 MCDONNELL DOUGLAS CORPORATION DOUGLAS AIRCRAFT DIVISION 19671977
PRINCIPAL INVESTIGATORS R. D. FINCK (1971) D. E. ELLISON ( 19621970) L. V. MALTHAN (19581962) 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 & Illustrations
iv
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 WingMounted Store Installations
3.1.1 3.1.2 3.1.3
Lift Increment Due to FuselageMounted 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
NeutralPoint Shift Due to Lift Transfer from Store Installation to Clean Aircraft
3.3
Effect of External Stores on Aircraft Neutral Point NeutralPoint Shift Due to Interference Effects on Wing Flow Field NeutralPoint Shift Due to Change in Tail Effectiveness Total NeutralPoint 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 ZeroLift Angle of A !tack Section LiftCurve 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 ZeroLift Pitching Moment Section PitchingMoment Variation with Lift Wing Lift
4.1.3.1 4.1.3.2 4.1.3.3 4.1.3.4
Wing ZeroLift Angle of Attack Wing LiftCurve Slope Wing Lift in the Nonlinear AngleofAttack Range Wing Maximum Lift Wing Pitching Moment Wing ZeroLift Pitching Moment
4.1.3
4.1.4 4.1.4.1 4.1.4.2
Wing PitchingMomentCurve Slope
*Subjects for Future Additions
v
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 AngleofAttack Range Wing Drag Wing ZeroLift Drag Wing Drag at Angle of Attack Bodies at Angle of Attack Body Lift Body LiftCu!Ve Slope Body Lift in the Nonlinear AngleofAttack Range *Effects of Asymmetries
Body Pitching Moment Body PitchingMomentCurve Slope Body Pitching Moment in the Nonlinear AngleofAttack Range *Effects of Asymmetries
Body Drag Body ZeroLift Drag Body Drag at Angle of Attack WingBody, TailBody Combinations at Angle of Attack WingBody Lift *WingBody ZeroLift Angle of Attack WingBody LiftCuiVe Slope WingBody Lift in the Nonlinear AngleofAttack Range WingBody Maximum Lift WingBody Pitching Moment
4.3.2 4.3.2.1 4.3.2.2 4.3.2.3 4.3.2.4
WingBody ZeroLift Pitching Moment WingBody PitchingMomentCurve Slope *WingBody Pitching Moment in the Nonlinear AngleofAttack Range *Effects of Asymmetries
WingBody Drag
4.3.3 4.3.3.1 4.3.3.2
WingBody ZeroLift Drag WingBody Drag at Angle of Attack WingWing Combinations at Angle of Attack (Wing Flow Fields)
4.4
WingWing Combinations at Angle of Attack
4.4.1
WingBodyTail Combinations at Angle of Attack
4.5
WingBodyTail Lift
4.5.1 4.5.I.l 4.5. 1.2 4.5.1.3 4.5.2 4.5.2.1 4.5.2.2 4.5.3 4.5.3.1 4.5.3.2 4.6 4.6.1 4.6.2 4.6.3
WingBodyTail LiftCurve Slope WingBodyTail Lift in the Nonlinear AngleofAttack Range WingBodyTail Maximum Lift WingBodyTail Pitching Moment WingBodyTail PitchingMomentCu!Ve Slope *WingBodyTail Pitching Moment in the Nonlinear AngleofAttack Range WingBodyTail Drag WingBodyTail ZeroLift Drag WingBodyTail 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 Power Effects on PitchingMoment Variation with Angle of Attack
vi
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 PitchingMoment Variation with Angle of Attack Ground Effects on Drag at Angle of Attack LowAspectRatio Wings and WingBody Combinations at Angle of Attack
4.8
Wing, WingBody 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, WingBody ZeroNormalForce Angle of Attack Wing, WingBody NormalForce Variation with Angle of Attack Wing, WingBody Axial Force Wing, WingBody ZeroNormalForce Axial Force Wing, WingBody AxialForce Variation with Angle of Attack Wing, WingBody Pitching Moment Wing, WingBody ZeroNormalForce Pitching Moment Wing, WingBody PitchingMoment 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 AngleofAttack Range *Wing SideForce Coefficient Cy at Angle of Attack Wing Sideslip Derivative Ct~ Wing Sideslip Derivative Ct~ in the Linear AngleofAttack Range Wing RollingMoment Coefficient Ct at Angle of Attack
Wing Sideslip Derivative Cn(j Wing Sideslip Derivative C 0 ~ in the Linear AngleofAttack Range *Wing YawingMoment Coefficient C0 at Angle of Attack WingBody Combinations in Sideslip WingBody Sideslip Derivative Cy~ WingBody Sideslip Derivative Cy ~in the Linear AngleofAttack Range WingBody SideForce Coefficient Cy at Angle of Attack WingBody Sideslip Derivative
5.2.2.1 5.2.2.2 5.2.3 5.2.3.1 5.2.3.2 5.3
Ct~
WingBody Sideslip Qerivative Ct in the Linear AngleofAttack Range
0
*WingBody RollingMoment Coefficient Ct at Angle of Attack WingBody Sideslip Derivative C00 WingBody Sideslip Derivative C00 in the Linear AngleofAttack Range WingBody YawingMoment Coefficient C0 at Angle of Attack TailBody 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
TailBody Sideslip Derivative Cy 0 TailBody Sideslip Derivative Cy in the Linear AngleofAttack Range 0 TailBody SideForce Coefficient Cy at Angle of Attack TailBody Sideslip Derivative Cto TailBody Sideslip Derivative Ct in the Linear AngleofAttack Range 0 *TailBody RollingMoment Coefficient Ct at Angle of Attack TailBody Sideslip DcrivativeC 00 TailBody Sideslip Derivative C 0 ~ in the Linear AngleofAttack Range TailBody YawingMoment Coefficient C0 at Angle of Attack
vii
5.4
Flow Fields in Sideslip
5.4.1
WingBody Wake and Sidewash in Sideslip
5.5.1
Wing, WingBody Sideslip Derivative Ky .6
5.5
LowAspectRatio Wings and WingBody Combinations in Sideslip
5.5.1.1 5.5.1.2 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, WingBody Sideslip Derivative Kv at Zero Normal Force 11 Wing, WingBody Sideslip Derivative
Kv.a
Wing, WingBody Sideslip Derivative
K[ 13
Variation with Angle of Attack
Wing, WingBody Sideslip Derivative Ki.a Near Zero Normal Force Wing, WingBody Sideslip Derivative Kj Variation with Angle of Attack 13 Wing, WingBody Sideslip Derivative K~.B Wing, WingBody Sideslip Derivative K~{J at Zero Normal Force Wing, Wing·Body Sideslip Derivative K~~ Variation with Angle of Attack WingBodyTail Combinations in Sideslip WingBodyTail Sideslip Derivative Cy 13 Wing·Body·Tail Sideslip Derivative Cy in the Linear Angle·of·Attack Range 13 Wing· BodyTail SideForce Coefficient Cy at Angle of Attack WingBody.Tail Sideslip Derivative Ct 13 WingBodyTail Sideslip Derivative C1~ in the Linear AngleofAttack Range *Wing.BodyTail RollingMoment Coefficient C1 at Angle of Attack Wing·BodyTail Sideslip Derivative Cn 13 Wir.g·BodyTail Sideslip Derivative C 0 ~ in the Linear Angleof·Attack Range WingBody.Tail YawingMoment Coefficient C0 at Angle of Attack CHARACTERISTICS OF HIGHLIFT AND CONTROL DEVICES Symmetrically Deflected Flaps and Control Devices on WingBody and TailBody Combinations Section Lift with HighLift and Control Devices Section Lift Effectiveness of HighLift and Control Devices Section Lift.Curve Slope with HighLift and Control Devices Section Maximum Lift with HighLift and Control Devices Section Pitching Moment with HighLift and Control Devices Section PitchingMoment Increment .6.cm Due to HighLift and Control Devices Section Derivative Cma with HighLift and Control Devices Section Pitching Moment Due to HighLift and Control Devices Near Maximum Lift Section Hinge Moment of HighLift and Control Devices Section HingeMoment Derivative Cha of HighLift and Control Devices Section HingeMoment Derivative ch of HighLift and Control Devices 6 Section HingeMoment Derivative (chf)6 t of Control Surface Due to Control Tabs Section HingeMoment Derivative (cht)lif of Control Tab Due to Control Surface Wing Lift with HighLift and Control Devices Control Derivative CL6 of HighLift and Control Devices Wing Lift.Curve Slope with HighLift and Control Devices Wing Maximum Lift with High·Lift and Control Devices Wing Pitching Moment with High·Lift and Control Devices PitchingMoment Increment ~Cm Due to High·Lift and Control Devices Wing Derivative Cma with HighLift and Control Devices Hinge Moments of HighLift 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 HingeMoment Derivative Cho of HighLift 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 TransverseJet 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 WingBody Dynamic Derivatives WingBody Pitching Derivatives WingBody Pitching Derivative CLq Wing·Body Pitching Derivative Cmq Wing·Body Rolling Derivatives
ix
7.3.2.1 7.3.2.2 7.3.2.3
WingBody Rolling Derivative Cyp WingBody Rolling Derivative Ctp
7.3.3.1 7.3.3.2 7.3.3.3
7.4.4.1 7.4.4.2
WingBody Yawing Derivative Cy r WingBody Yawing Derivative C1r WingBody Yawing Derivative Cnr WingBody Acceleration Derivatives WingBody Acceleration Derivative CL&: WingBody Acceleration Derivative Cmc, WingBodyTail Dynamic Derivatives WingBodyTail Pitching Derivatives WingBodyTail Pitching Derivative CLq WingBodyTail Pitching Derivative Cmq WingBodyTail Pitching Derivative Coq WingBodyTail Rolling Derivatives WingBodyTail Rolling Derivative Cyp WingBodyTail Rolling Derivative C/p WingBodyTail Rolling Derivative Cnp WingBodyTail Yawing Derivatives WingBodyTail Yawing Derivative Cyr WingBodyTail Yawing Derivative Ctr WingBodyTail Yawing Derivative Cnr WingBodyTail Acceleration Derivatives WingBodyTail Acceleration Derivative CLa WingBodyTail Acceleration Derivative Cma
7.4.4.3
WingBodyTail Derivative Coa
7.4.4.4
WingBodyTail Derivative Cy p
7.4.4.5
WingBodyTail 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
WingBody Rolling Derivative Cnp WingBody Yawing Derivatives
WingBodyTail Derivative CniJ
*ControlSurface AngularVelocity Derivatives MASS AND INERTIA Aircraft Mass and Inertia Missile Mass and Inertia CHARACTERISTICS OF VTOLSTOL AIRCRAFT Free Propeller Characteristics Propeller Thrust Variation with Angle of Attack Propeller PitchingMoment Variation with Power and Angle of Attack Propeller NormalForce Variation with Power and Angle of Attack PropellerWing Characteristics PropellerWingFlap Lift Variation with Power and Angle of Attack *PropellerWingFlap PitchingMoment Variation with Power and Angle of Attack PropellerWingFlap Drag Variation with Power and Angle of Attack DuctedPropeller Characteristics DueledPropeller Lift Variation with Power and Angle of Attack DuctedPropeller PitchingMoment Variation with Power and Angle of Attack DuctedPropeller 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 organized in such a way that it is selfsufficient. 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 the Datcom can be used to advantage in conjunction with test data. For instance, if the liftcurve slope of a wingbody combination is desired, the Datcom recommends that the liftcurve slopes of the isolated wing and body, respectively, be estimated by methods presented and that appropriate wingbody interference factors (also presented) be applied. If wingalone test data are available, it is obvious that these test data should be substituted in place of the estimated wingalone 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 a single specific item, e.g., wing liftcurve slope. Sections can, in general, be deleted, added, or revised with a minimum disturbance to the remainder of the volume. The numbering system used throughout the Datcom follows the scheme outlined below: Section:
An orderly decimal system is used, consisting of numbers having no more than four 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 a righthand page.
Page:
The page number consists of the section number followed by a dash number. Example: Page 4. 1.3.24 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 for referencing purposes. For pages with more than one figure, a lower case letter follows the figure number. Example: Figure 4. 1.3.250b is the second figure on Page 4. 1.3.250. 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. 1.3.256d may be found on Page 4. 1.3.257 and is the 4th in a series 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. 1.3.2A 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: 4.1.3.2b 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 4.1.3.2b). 11
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 highlift and control devices
Section 7.
Dynamic derivatives
Section 8.
Mass and inertia
Section 9.
Characteristics of VTOLSTOL 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 are also 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 the engineer, such as geometric parameters, airfoil notation, wettedarea 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 angleofattack 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 complexities of 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 7A). If more than preliminarydesign information on mass and inertia (Section 8) is needed, a weightsandbalance engineer should be consulted. Section 9 is a unified section covering aerodynamic characteristics of VTOLSTOL aircraft, with the exception of groundeffect machines and helicopters. The Datcom presents less information in this area than that presented for conventional configurations because of the scarcity of data, the complexities 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 is 12
restricted to first approximations of the aerodynamic characteristics of individual components or simple component combinations. However, the Datcom does present a literature summary from over six hundred sources for a great variety of VTOLSTOL configurations (Table 9A). 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 to be satisfactory for preliminarydesign stability studies. No attempt is made to provide drag estimation 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, wingbody, wingwing, and wingbodytail sections. The latter three categories generally utilize component information as presented 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. Each section of the Datcom is organized in a specific manner such that the engineer, once familiar with the system, can easily orient himself in a given section. A typical section is diagramed below: Section Number and Title General Introductory Material A.
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 Tables Working Charts
13
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 lowspeed transitionflight ;egime. In a few sections, where applicable, material is included for the rarefiedgas regime as paragraph 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, and sample 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 give reasonably 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 the methods is afforded by comparison with the test results. To facilitate the engineer's orientation to those Datcom sections that use a buildup of wing, wingbody, and wingbodytail 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, wingbody, and wingbodytail 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 the parameters that are based on exposed planform geometry that are not specified by the subscript e. Sometimes the same limitations, such as 'linearlift range,' may occur for more than one component in an equation. To avoid repetition, the same limitation is not repeated for each component. 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 to minimize 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 stabilityaxis system unless otherwise noted. Transformations of stability derivatives from one axis system to another are developed in many standard mathematics and engineering texts. In FDLTDR6470, several coordinate systems are defined 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 results with results calculated by the methods recommended. Geometric and test variables are also tabulated 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 the user. However, with a few exceptions, the grids used are of two sizes only: centimeter and halfinch 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 14
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 upt<>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 the effort may be properly oriented. METHODS SUMMARY OUTLINE DERIVATIVE
PAGES
DERIVATIVE
17 through 111
149 throuch 1SO
1·11 through 115 ).)5 through 118
PAGES
1·50 t.c2
max
150
J.i9 through 123
c'll
123 through 127
151
1·27 through 131
1S 1
131 through 134
1·52
134 through 138
153
138 through 140
153
140 through 141
154 through 155
141 through 143
155
143 through 145
156
f45
t56 through 157
c,r
145 through 147
157 through 158
c.r
147
158
15
DERIVATIVE
CD
c,
'
en en
16
PAGES
159 159 through 161 161 through 162
'
162
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
w
SUBSONIC
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated) 21r
 =
Fig. 4. I .3.249
Method I
I.
'
Eq. 4.1.3.2b 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 4.1.3.256a through 60

Constantsection, dell' or dippeddell' configura lions (',.E = 0) 0.58 <;;A<;; 2.55
4.
5. 6.
TRANSONIC
No curved plan forms M <;; 0.8, tic<;; 0.1. if cr'nked pl'nforms wtth round·LE
Symmetric airfoils of conventional thidllt's:. distribution A~ 3 if composite wings
3
(){ = 0
I. 2. 3.
Straighllapered wings M;;. 1.4 Linearlift range
I.
3. 4.
'
Double'elta and ~:ranked wings Breaks in LE and TE at same spanwise station 1.2 <;; M <;; 3. 0 Linearlift ran~e
I. 2. 3.
Curved planforms 1.0 <;; M <;; 3. 0 Linearlifl range
1. 2. 3. 4.
Straighllapered wings Conventional wings of zero thickness Twodimensional slenderairfoil theory (){ = 0
I. 2. 3. 4.
Straighttapered planforms Wedge airfoils Twodimensional slenderairfoil theory (){ = 0
+              
=
Eq. 4.1.3.2h
_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 4.1.3.256a through 60
v ta~2
1     
(CN.), =0 ;
Fig. 4.1.3.265 LE
1~
p2
WB
SUBSONIC
(a)
(CL )WB a

  A
= [ KN + KW(B) +
KB(W)
l
4.3.1.2
Fig. 4.3.1.2a
l

Method I (body diameter)/( wing semisp'n) <;; 0.~ (see Sketch (d), 4.3.1.2) (a) Zero wing incidence; wingbody angle of attack
varied KN (based on exposed wing geometry) I. 2. 3.
Bodies of revolution Slenderbody theory Linearlift range
(CL.), 4. 5.
No curved plan forms M <;; 0.8, t/c,;;; 0.1, if cranked wings with round LE
I7
METHODS SUMMARY DERIVATIVE
CON FIG.
CL •
WB
(Contd.)
(Contd.)
SPEED REGIME
EQUATIONS 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 WITH EQUATION COMPONENTS (b)
Eq. 4.3.I.2b
Body angle of attack fixed at zero; wing incidence varied (same limitations as (a) above)
Eq. 4.3.1.2c
(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 with round 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. Slenderbody theory 3. Linearlift range KB(WJ and kw(B) (based on exposed wing geometry)
(CLa)e 4.
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)w I. 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 Slenderbody theory Linearlift range kB(W) and kw(B) (based on exposed wing geometry)
2. 3.
(CNa)e 4.
5.
6. 7.
18
Breaks in LE and TE at same sranwise station M ;;. 1.4 for straighttapered wings 1.2 .; M .; 3 for composite wings 1.0.;; M .;; 3 for curved plan forms
METHODS SUMMARY DERIVATIVE
CL
•
(Contd.)
CON FIG.
SPEED REGIME
WB (Contd.)
SUPERSONIC (Contd.)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION 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.
WBT
SUBSONIC
CL
•
=
S'
( cl.); [KN
+ KW(B) + KB(W)l'
 ' + (cl.);' S'
~
4.1.3.2
4T3.2
4.3.1.2
[KW(B)
+ KB(W) ]'
4.3.1.2
(I~) 4.4.1
q'


q=
S'
S'
S' S'
Method
I
bw /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:<<
I.
4.4.1 Eq. 4.5.1.1a
Breaks in LE and TE <:~t same spanwise station M;;, 1.4 for straighttapered wings 1.2 ~ M ~ 3 for composite wings 1.0 .;;; M .;;; 3 for curved planforms Linearlift range
a:stail if low aspect ratio or swept wings
(cL.); and (CL.);' No curved planforms M .;;; 0.8, t/c .;;; 0.1, if cranked plan forms with round LE KN (based on exposed wing geometry) 6. Bodies of revolution Slenderbody theory 7. 8. Linearlift range 4. 5.
of

00:
(depends upon method)
9. 10.
Straighttapered wing
Other limitations depend upon method
of aa:
prediction
q'

q=
II.
Valid only on the plane of ;yrnmctry
                 r    <          =  ' + + + f + + • a. S'
CL
(CL.); [KN
4.TTI
Kwta)
4.3:1.2
Katw)]'
(cL.);' [KW(B)
4.T:TI'
KB(W)]'
4.3.1.2
q'
S'
S'
q=
S'
S'
4.4.T
Method 2 bw /b'
(cLJw 't>J 4.5.1.1
I
1.5 (same limitations as Method I above omitting those of loa) KN and (cL)
(based on exposed wing geometry)
a W'(v)
Eq. 4.5.1.1b
19
METHODS SUMMARY DERIVATIVE
CL
•
(Contd.)
CON FIG.
WBT (Contd.)
SPEED REGIME TRANSONIC
METHOD LIMIT AllONS ASSOCIATED WITH EQUATION 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< = 0 KB(Wl (based on exposed wing geometry) KN (based on exposed wing geometry)
4. 5. 6. 
a'
Bodies of revolution Slenderbody theory Linearlift range
(depends upon method) 7. 8.
Straighttapered wings Proportional to
eL
q'
•
q~
9. I 0.
Conventional trapezoidal planforrns Valid· only on the plane of symmetry
r Method 2 bw /bH
<
1.5
(same limitations as Method l above omitting those of
a< I oC<) KN, KB(W)• and (CLa)W'(v) (tJ.sed on exposed wing geometry) 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 straighttapered planforms 3. 1.2.;; M.;; 3 for composite planforms 4. 1.0 .;; M .;; 3 for curved planforms 5. Linearlift range KN (based on exposed wing geometry) 6. 7.
Bodies of revolution Slenderbody theory
KB(W) (based on exposed wing geometry)
0<
aa 8.
9.
110
Straighttapered wings 0< . . . 0 t her Innitatlons depend upon prediction method OC<
METHODS SUMMARY DERIVATIVE
CL
a
(Contd.)
CON FIG.
SPEED REGIME
WBT (Contd.)
SUPERSONIC (Contd.)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION 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 of symmetry
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 wing o: W'(v)
geometry)
w
I.
Eq. 4.1.4.2d 4.1.4.2
2.
4.1.3.2 CL
TRANSONIC
a
(Same as subsonic equation) CL
SUPERSONIC
HYPERSONIC
(Same as subsonic equation)
eN
•
•
(Same as subsonic equation)
eN
M .;; 0.6; however, for swept wings with t/c .;; 0.04, application to higher Mach numbers is acceptable Linearlift range
•
3. 4.
No curved planforms M .;; 0.8, t/c .;; 0.1, if cranked plan forms with round LE
I. 2. 3.
Straighttapered wings Symmetric airfoil sections Linearlift range
4.
Conventional thickness distribution =0
5.
IY.
I.
Linearlift range
2. 3. 4.
5.
Breaks in LE and TE at same spanwise station M ;;. 1.4 for straighttapered wings 1.2 .;; M .;; 3 for composite wings 1.0.;; M .;; 3 for curved planforms
I.
IY.
2. 3.
Straighttapered wings Conventional wings of zero thickness and wedge airfoils Twodimensional slenderairfoil theory
4.

=
0
111
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
em 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() WITH EQUATION COMPONENTS xa.c.
CL
a

Eq. 4.1.4.2d
(calculations based on exposed wing geometry)
c,
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 Slenderbody 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.
Straighttapered wings Single wing with body (i.e., no cruciform or other multipanel arrangements) Symmetric airfoils of conventional thickness distribution Linearlift range
5. 6. 7.
Bodies of revolution Slenderbody theory = 0
3.
CL
X
SUPERSONIC
Single wing with body (i.e., no cruciform or other multipanel arrangements) M .;; 0.6; however, if swept wing with t/c .;; 0.04, application to higher M'•·h numbers is acceptable Linearlift range
•
'
a.c.
(calculations based on exposed wing geometry) c,
(Same as subsonic equation)
2.
Single wing with body (i.e., no cruciform or other multipanel arrangements) Linearlift range
3. 4. 5. 6. 7. 8.
Breaks in LE and TE at same spanwise station Bodies of revolution Slenderbody theory M > 1.4 for straighttapered wings 1.2 .;; M < 3 for composite wings 1.0.;; M .;; 3 for curved plan forms
I.
eN a
'
I 112
METHODS SUMMARY DERIVATIVE
CONFIG.
SPEED REGIME
WBT
SUBSONIC
(Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION (Oat com section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION 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) Linearlift range
I.
4.5.2.1
2. ae
 aa
q
II
)
qoo
S' S' _, e c
?5'
C'
(calculations based on exposed planform geometry)
c'
Eq. 4.5.2.1d'
3.
Single wing with body (i.e., no cruciform or other multipanel 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 smallangle assumptions made with respect to angle of attack; equation as given is valid for most configurations
5. 6.
Bodies of revolution Slenderbody theory
(CL )' and (cL )' a e
o: e
7. 8.
No curved planforms M .;; 0.8, t/c.;; 0.1 if cranked planforms with round LE
9.
Straight·tapered wing
a.
10.
Other limitations depend upon prediction method aa
II.
Valid only on the plane of symmetry
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 other multipanel arrangements) Straighttapered wings Symmetric airfoils of conventional thickness distribution Linearlift range __j
L________L______~~~~I13
METHODS SUMMARY DERIVATIVE
(Contd.)
CON FIG.
SPEED REGIME
WBT (Contd.)
TRANSONIC (Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION ( Datcom section for components indicated)
METHOD LI~IITATIONS ASSOCIATED WITH EQUATION COMPONENTS KB(W) (based on exposed wing geometry) KN (based on exposed wing geometry)
5.
Bodies of revolution
6.
Slenderbody 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 for
ae;aa) x
 x'
'~
(calculations based on exposed planform geometry)
c'
KN, KB(W)' and
SUPERSONIC
(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 other multipanel arrangements) 2. Linearlift range (based on exposed Ving geometry) 3.
Bodies of revolution
4.
Slenderbody theory KB!Wl (based on exposed wing geometry)
(CN')~
(CN'): and 5. Breaks in LE and TE at same span wise station 6. M ;;. 1.4 for straighttapered planforms
7. 8.
1.2 :s.;;; M :s.;;; 3 for composite planforms 1.0 :s.;;; M :s.;;; 3 for curved planforms
9.
Straighttapered wings . . . ae 0 t her l ImitatiOns depend upon prediction method aa
aa 10.
114
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
METHOD LIMITATIONS ASSOCIATED WITH EQUATION 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' ,~t symmetry
Method 2 bw /bH
<
1.5
(same limitations as Method I. omitting those of Of ;Oul X
e.g.
''(calculation hased on exposOO planfor:n c' KN, KB(W)' and geometry)
(C 1cJw '(vl (based on exposed wi11g
~+4~~~~~
w
SUBSONIC
X
=(_!_+2~) 2 c
cLQ

Eq. 7.1.1.1a
c I.
4.1.4.2 4.1.3.2
2.
TRANSONIC
7.1.1.1
(~)
4.1.4.2 4.1.3.2
M < 0.0; however, for swept wings with t/c < 0.04,application to higher Mach numher;
is acceptable Linearlift range
3. 4.
No curved panform~ M ~ 0.8, t/c.;;;:; 0.1, tf cranked wings with round LE
I.
2.
Straigllttapcrcd . ing:s No camber
3. 4.
' =
I.
Straighttapered wings
x c
CL
+ 2


(Same as subsonic equation)
SUPERSONIC
l~~·IJil1~ !rV)
• Conventional tnickness distribution
0
Eq. 7.1.1.1c Subsonic LF (13 cot
ALE
<
II
2. 3.
Mach lines from TE vertex may not inta'·d LE WJngtip 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 not interst'ct remote half of wing
m;~y
c
6.
Linearlift range
~~~L~~~~ I I 5
METHODS SUMMARY DERIVATIVE
cl
• (Contd.)
CON FIG.
w (Contd.)
WB
SPEED REGIME
EQUATIONS FOR DERIVATIVE ESTIMATION (0atcom section for components indicated I
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
SUPERSONIC (Contd.)
7.
SUBSONIC
Eq. 7.3.1.1a 4.3.1.2
7.iT.i
7.2.1.1
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 Linearlift range M ~ 0.6; however, for swept wings with t/c ~ 0.04, application to higher Mach numbers is acceptable M ~ 0.8, t/c ~ 0.1, if cranked wing with round 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 body Eq. 7.3.1.1b (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.
Straighttapered wings No camber Conventional thick1 Distribution '
=
0
Bodies of revolution
rMethod 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.
116
Straighttapered wings M;:;, 1.4 Linearlift range
METHODS SUMMARY DERIVATIVE
CL
Q
(Contd.)
CON FIG.
SPEED REGIME
WB (Contd.)
SUPERSONIC (Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS (a)
Subsonic LE (JJ cot ALE
<
I)
4.
Mach lines from TE vertex may not
5.
Wing tip Mach lines may not intersect
intersect 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
1Method 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. 7.4.1.1a
I.
(cLq )WB 2. 3. 4.
5.
Line~rlift range (based on exposed wing geometry) No curved planforms Bodies of revolution M <:; 0.6; however, for swept wings with t/c :s;;; 0.04, application to higher Mach numbers is acceptable M <:; 0.8, t/c <:; 0.1, if cranked wings with round 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 Eq. 7.4.1.1b
TRANSONIC
< 1.5
(same limitations as Method I above) CL ) and (CL ) (based on exposed wing geometry) ( q WB a W'(v)
(Same as subsonic equations)
(Ctq)wo (based on exposed wing geometry) I. 2.
3. 4.
Straighttapered wings No camber Conventional thh.:kness distribution Bodies of revolution 117
METHODS SUMMARY DERIVATiVE
CL
• (Contd.)
CON FIG.
WBT (Contd.)
SPEED REGIME
EQUATIONS FOR DERIVATIVE ESTIMATION IDatcom section for components indicated)
METHOLJ LIMITATIONS ASSOCIATED WITH EQUATION 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 WB o: W (v) wing geometry) SUPERSONIC
(Same as subsonic equations)
Method I bw /bH ;;> I .5 I.
(cLq )WB
Linearlift range (based on exposed wing geometry)
2. 3. 4.
Straighttapered 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 Wingtip 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 not intersect remote half of wing
q' 9. 10.
If nonviscous flow field, limited to unswept wings If viscous flow field, valid only on plane of symmetry
II.
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) 118
a: W (v)
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
METHOD LIMITATIONS ASSOCIATED WITH EQUATION 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]+
. c/4
A 3 tan 2 1o/4
A
+ ',. ., cos·
A c/4
1 ( A 24
A
3
tan
2 /, 14
+ 6 cos Ac/ 4
)
+
~}
c I. Eq. 7.1.1.2a
2.
M ~ 0.6; however, for swept wings with t/c ~ 0.04, application to higher Mach numbers is acceptable Linearlift range
3
Eq. 7.1.1.2b
7.1.1.2
I.
Eq. 7.1.1.2<:
2.
Symmetric airfoils of conventional thickness distribution CY. = 0
(Cmq)M '1.2 (a)
3. Straighttapered wings Subsonic LE (~ cot ALE < I) 4. 5.
(b)
Mach line from TE vertex may not intersect LE Wingtip 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
Eq. 7.1.1.2d
cmq 7.1.1.2
7.1.1.1
Foremost Mach line from either wing tip may not intersect remote half of wing
(~
cot ALE
<
I)
I.
7.1.1.1
(h)
Mach line from TE vertex may not intersect LE 2. Wingtip Mach lines may not intersect on wings nor intersect opposite wing. tips Supersonic LE (~cot ALE > I l 3.
Valid only if Mach lines from LE vertex intersect
TE 4.
Foremost Mach line from either wing tip may not intersect remote half of wing
5.
StraighHapered wings
A.
M ;;> 14
7.
Linearlift range 119
METHODS SUMMARY DERIVATIVE
em q
CONFIG.
WB
SPEED REGIME
EQUATIONS FOR DERIVATIVE ESTIMATION IDatcom section for components indicated I
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
Eq. 7.3.1.2a
SUBSONIC
Method I (body diameter)/(wing span) is small (see 4.3.1.c Sketch (d)) I. Linearlift range
(cmq),
(Contd.)
2.
M ~ 0.6; however, for swept wings with t/c ,; 0.04, application to higher Mach numbers is acceptable
(Cmq)B 3.
Bodies of revolution
t1
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 with delta wing extending entire length of body Eq. 7 .3.1.2b (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. Linearlift range KB(W) (based on exposed wing geometry)
(em q) ,
(a)
2. 3.
Straighttapered wings Symmetric airfoils of conventional thickness distribution
4.
C<
= 0
Subsonic LE
W cot
ALE
<
I)
5.
(b)
Mach line from TE vertex may not intersect LE 6. Wingtip 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)s 9.
Bodies of revolution
1          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)
120
METHODS SUMMARY DERIVATIVE
em q (Contd.)
CON FIG.
WB (Contd.)
SPEED REGIME
SUPERSONIC
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
(Same as subsonic equations)
Method I (body diameter)/(wing span) is small (see 4.3.1.2 Sketch (d)) 1. Linearlift range KB(WJ (based on exposed wing geometry)
(em.), 2. 3.
(a)
Straighttapered wings M;;. 1.4 Subsonic LE (~ cot ALE < I) 4.
(b)
Mach line from TE vertex may not intersect LE 5. Wingtip 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)a 8.
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. 7.4.1.2a
SUBSONIC 4.5.2.1
4.3.1.2
7.3.1.2
(em q)WB 1. 2.
4.4.1 4.1.3.2
(based
on
exposed
wing geometry)
3.
Bodies of revolution M ~ 0.6; however, if a swept wing with t/c .;; 0.04, application to higher Mach numbers is acceptable Linearlift range
4.
Valid only on the plane of symmetry
5. 6.
No curved plan forms M.;; 0.8, tic.;; 0.10, if cranked planforms with round LE
q'
(cL.);' t =
(c )
mq WB
7.3.1 .2
(:~) (~J(cLJ +{cLJw.J
2 4.5.2.1
4.3.12
4.4.1
4.13 2
4.5.1.1
Method 2 bw /bH Eq. 7.4.1.2b
<
1.5
(same limitations as and (C L ) (Cm ) q WB
et
~h:·thod .. W (v)
I above) (based on exposed wing geometry)
121
METHODS SUMMARY DERIVATIVE
CON 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 WITH EQUATION COMPONENTS Method I bw /bH ;> 1.5
(em q ) WB I. ,
(a)
(baserl on exposed wing geometry)
3.
Straighttapered wings Symmetric airfoils of conventional thickness distribution Bodies of revolution
4.
' = 0
Subsonic LE
W cot
ALE
<
I)
5. 6.
Mach line from TE vertex may not intersect LE Wingtip Mach lines maynot 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 not intersect 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 wing geometry) SUPERSONIC
(Same as subsonic equations)
Method I bw /bH ;> 1.5
(em q ) WB
(based on exposed wing geometry)
I. 2. 3. 4.
Straighttapered wings Bodies of revolution M ;> 1.4 Linearlift 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 Wingtip Mach lines may not intersect on wings nor intersect opposite wing tips Supersonic LE (p cot ALE > I) 7.
122
Valid only if Mach lines from LE vertex intersect TE
METHODS SUMMARY
.DERIVATIVE
CON FIG.
SPEED REGIME
em q
WBT (Contd.)
SUPERSONIC (Contd.)
(Contd.)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
EQUATIONS FOR DERIVATIVE ESTIMA o'ION (Datcom section for components indicated) 8.
Foremost Mach line from either wing tip may not intersect remote half of wing
q' 9. 10.
If nonviscous flow field, limited to unswept wing' If viscous flow field, valid only on the plane of symmetry
(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 WB
o:, W (v)
geometry)
w
Eq. 7.1.4.1a
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<
4
I.
Triangular planforms
2.
Mer
3.
Linearlift range
4.
No camber
5.
Symmetric airfoils of conventional thickness distribution
<M~
1.0
c,
6. cl (gJ 7.
SUPERSONIC
7.1.1.1 7.1.4.1
+ 2 E'(~C) 7.1.1 .I
Eq. 7.1.4.1b 7.1.4.1
7.1.1.1 7.1.4.1
Method I I. 2.
a=O 0
<~A<
4
Straighttapered wings
1 = 0
<
3.
Subsonic LE (~ cot
4.
Mach line from TE vertex may not intersect LE
1LE
I) 123
METHODS SUMMARY I>ERIV ATJVE
CL·•
(Contd.)
OONFIG.
w (Contd.)
SPEED REGIME
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
SUPERSONIC (Contd.)
5. 6.
Wing·tip Mach lines may not intersect on wings nor intersect opposite wing tips Linear·lift range
r                     ·
CL.;
M2
=
I
fi2 (cLJl  fi2 (cLJ2
7.1.4.1
7.1.4.1
Eq. 7.1.4.1c Method 2 I. Straighttapered wings 2. Unearli ft range (a) Subsonic LE (~ cot ALE < I) 0.25I) 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 not intersect the remote halfwing
Eq. 7.3.4.1a Method I (body diameter)/(wing span) is small (see sketch (d) 4.3.1.2) I. Linearlift 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. 7.3.4.1b 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. Linearlift range KB (W) (based on exrosed wing geometry)
(CL.),
124
3.
Triangular planforrns Symmetric airfoils with conventional thickness distribution
4.
O<M<4
5.
Mer~ M ~ 1.0
METHODS SUMMARY DERIVATIVE
cL.
•
(Contd.)
CON FIG.
WB (Contd.)
SPEED REGIME
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
EQUATIONS FOR DERIVATIVE ESTIMATION
(Datcom section for components indicated)
(cl,Js
TRANSONIC (Contd.)
6.
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. Straighttapered wing 2. Linearlift 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. Wingtip 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 halfwing 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)
WBT
SUBSONIC
Eq. 7 .4.4.1a Method I bw /hH ;;. I .5
I.
( cL,; )WB 2. 3. 4. 5.
Linearlift range (based on exposed wing geometry) 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
q' 6.
Valid only on the pl
7.
Limitations dercnd upon
a. ao:

prediction method
METHODS SUMMARY DERIVATIVE
CL.
• (Contd.)
CON FIG.
WBT (Contd.)
SPEED REGIME
SUBSONIC (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 WITH EQUATION COMPONENTS
Method 2 bw /bH < I .5 Eq. 7.4.4.1b
(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)
Linearlift 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 = 0
ll.
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. Straighttapered wing 2. Linearlift 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.
126
Mach line from TE vertex may not intersect LE Wingtip Mach lines may not intersect on wings nor intersect opposite wing tips
METHODS SUMMARY DERIVATIVE
cL.
•
(Contd.)
CON FIG.
SPEED REGIME
WBT (Contd.)
SUPERSONIC (Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION 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 not intersect remote halfwing 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 of symmetry
a< a<>
10.
Straighttapered wings
II.
Other limitations depend upon prediction a<> method
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
7.1.4.2
+ (;')
cL.
•
Eq. 7 .1.4.2a
CL.
•
~
7 .1.4.1
I. 2. 3. 4.
TRANSONIC
SUPERSONIC
(Same as subsonic equation)
(Same as subsonic equation i
a 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 Linearlift range
cL.
•
I. 2.
Triangular planforms Symmetric airfoils of conventional thickness distribution
O<JlA<4
3. 4.
Mer ~ M ~ l.C
5.
Linearlift range
c m '.
•
(a)
Subsonic LE (Jl cot ALE
I. 2.
< I)
Mach line from TE vertex may not intersect LE Wingtip Mach llnes may not intersect on wings nor intersect opposite wing tips
127
METHODS SUMMARY DERIVATIVE
CON FIG.
w (Contd.)
(Contd.)
WB
SPEED REGIME
EQUATIONS FOR DERIVATIVE ESTIMATION !Datcom section for components indicated!
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS (b)
SUPERSONIC (Contd.)
SUBSONIC
Eq. 7.3.4.2a
Supersonic LE (~cot ALF
> I)
3. 4.
Valid only if Mach lines from LE vertex intersect TE Foremost Mach line from either wing tip may not intersect remote halfwing
5. 6.
Straighttapered wings Linearlift range
Method I (body diameter)/(wing span) is small (see 4.3.1.2 Sketch id)) I. Linearlift range
(Cmo),



2.
Triangular planforms [ctuc to (CLJe] ~A<
3.
0<
4.
M < 0.6~ however, if swept wing with t/c ~ 0.04, application to higher Mach numbers is acceptable
4
5.
Bodies of revolution
     

Method 2 (body diameter)/(wing span) is large, with delta
Eq. 7.3.4.2b

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. Linearlift range KB(W) (based on exposed wing geometry)
(CmJ,
(CtJe]
2.
Triangular panforms [due to
3.
Symmetric airfoils of conventional thickness distribution
0<
M
< 4
Mcr,;;;;M~.0
6.
Bodies of revolution
rMethod 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
128
(Same as subsonic equations)
Method I (body diametcr)/(wmg span) is small (see 4.3.1.2 Sketch (d)) 1. Straighttapered wings 2. Linearlift range
METHODS SUMMARY DERIVATIVE
(Contd.)
CON FIG.
SPEED REGIME
WB (Contd.)
SUPERSONIC (Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS KB(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 Wingtip 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 not intersect remote halfwing
(Cmo.)o 7.
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. 7.4.4.2a
SUBSONIC
Method I bw /bH ;. 1.5
I. Linearlift range (Cm&)wa (based on exposed wing geometry) 2.
Triangular planforms [due to
3.
0
(cto,)e]
4. 5.
<~A< 4 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. aa
prediction method
               crn
(CLo)w''
a
7.3.4.2
TRANSONIC
4.5.2.1
!Same as subsonic equations)
4.5.1.1
Eq. 7.4.4.2b
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.
Linearlift range 129
METHODS SUMMARY DERIVATIVE
(Contd.)
CON FIG.
SPEED REGIME
WBT (Contd.)
TRANSONIC (Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION ( Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
(cmet'·) WB
(based on exposed wing geometry)
(CLo)el
:2.
Triangular planforms [due to
3.
Symmetric airfoils of conventional thickness
4.
0
5. 6.
Bodies of revolution Mer ~ M ~ 1.0
distribution <~A<
1.0
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)
Straighttapered wings Linearlift 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 Wingtip 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 not intersect the remote halfwing K 8 (W) (based on exposed wing geometry) 6.
q' q~
8. 9.
130
If nonviscous flow field, limited to unswept wings If viscous flow field, valid only on the plane of symmetry
METHODS SUMMARY DERIVATIVE
cm. Q
CON FIG.
SPEED REGIME
WBT (Contd.)
SUPERSONIC (Contd.)
(Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
(Datcom section for components indicated)
aa 10.
Limitations depend upon
a, 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. 5.1.1.1a
(Subcritical)
TRANSONIC
].
Constantchord swept wings
2
Linearlift range
Eq. 5.1.1.1c
(No method)
8M 2 = 
SUPERSONIC
I
0.0001 lfl
7TAf3' 57.3
Eq. 5.1.1.1d, b
a'
I.
Rectangular planforms
2.
Mach number and aspect ratio greater than that
for which the Mach line from LE of tip section intersects TE of opposite tip section
(A .jM 2

1                Cy
p
1T
4
AM 2
~
I
57.3
5.1.1.1
0.0001 lfl
Eq. 5.1.1.1e, b
a'

~·I.
Sweptback planforms
2.
A= 0
3.
Wing is contained within Mach cones springing from apex and TE at center of wing
(.fii'=J WB
SUBSONIC
(Cv~)ws
=
~ (Cv~)s 5.2.1.1 4.2.1.1
(
Body Re;:rence Area) +
I ;;. I)
cot ALE .;; l.Q))
Eq. 5.2.1.1a 5.1.1.1
Bodies of revolution
Linearlift range
TRANSONIC
(Same as subsonic equation)
(same limitations as subsonic above)
SUPERSONIC
(Same as subsonic equation)
(same limitations as suhsonic above)
131
METHODS SUMMARY DERIVATIVE
Cy
~
CON FIG.
SPEED REGIME
TB
SUBSONIC •
EQUATIONS FOR DERIVATIVE ESTIMATION
METHOD LLIITATIONS ASSOCIATED WITH EQUATION COMPONENTS
(Datcom section for components indicated)
(ac y~)V(WBH)

=  k (CL ) a
(Contd.)
(' +
V
5.3.1.1 4.1.3.2
aa~a)
qv
q~
Eq. 5.3.1.1b
',~.,
Method I (vertical panels on plane of symmetry) (Cla)v ____1_.
5.4.1
~aighttapered
planforms _ _ _ _ _ _ _
Eq. 5.3.1.1c Method 1 (twin vertical panels)
 1Method 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 verticaltail geometry) alp
1.
No curved planforms
2.
(b)
(acv ) H (8) ~
=
Eq. 5.3.1.1e 5.3.1.1
TRANSONIC
M ,;;; 0.8, t/c ,;;; 0.1, if cranked plan forms with round LE (b) Contribution of horizontal tail ( Cy~) B
4.2.1.1
3.
Bodies of revolution
4.
Linearlift range
I.
Horizontal tail mounted on b9dy, or no horizontal
(No method)
SUPERSONIC
= 
K'
(CN~
5.3.1.1
4.1.3.2

s.
'
Sw
Eq. 5.3.1.1f
tail Linearlift range 2. (a) Verticaltail contribution K' (based on exposed verticaltail geometry) (CN P (based on exposed verticaltail geometry)
a)
3.
(b)
(aCy ) H(B) ~
=
 5.3.1.1
HYPERSONIC
132
4.2.1.1
Eq. 5.3.1.1g
(b)
Breaks in LE and TE at same spanwise station
4. M ;;. 1.4 for straighttapered planforms 5. 1.2 ,;;; M ,;;; 3 for composite plan forms 6. 1.0 ,;;; M ,;;; 3 for curved planforms Horizontaltail contribution
(Cv~). 7.
Method I I. 2. 3.
Bodies of revolution
Horizontal tail mounted on a body Not substantiated above M = 7 Linearlift range
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
(a) Cy
I
(Contd.)
TB (Contd.)
Eq. 5.3.1.1f
K' (based on exposed verticaltail geometry) (CN
5.3.1.1 4.1.3.2
(~Cv I) H(B)
a)p 4.
(b) (b)
Verticaltail contribution
Eq. 5 3.1.1g

(Cv
M
>
3
HorizontaHail contribution
,)s 5.
Bodies of revolution
5.3.1.1 4.2.1.1
             Method 2 'Y + I I (r + I ) 2 Eq. 5.3.1.1h I. Sharpedged sections cp = <~ • bJ 2 (   ± y    + 2 4
!)~~ b)') ±
WBT
2.
5 << />
Eq. 5.6.1.1a Method I (single vertical stabilizer, and horizontal tail at any height or no horizontal tail) I. Linearlift 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
     
Straighttapered planforrns
  
      

Eq. 5.6.1.1a Method 2 (twin vertical panels) I. Linearlift range (Cv ~)wa
'2.
Bodies of revolution
5.2.1.1
5.3.1.1
Eq. 5.6.1.1b Method 3 (horizontal tail mounted on body or no horizontal tail) I. Linearlift range (Cv ~)wa
(~Cy
2.
1)P
3. 4.
TRANSONIC
Bodies of revolution
(based on exposed verticaltail geometry) No curved planforms M .;; 0.8, tic .;; 0.1, if cranked plan forms with round LE
(No method)
1·33
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
WBT
SUPERSONIC
EQUATIONS FOR DERIVATIVE ESTIMATION
METHOD LLIITATIONS ASSOCIATED WITH EQUATION COMPONENTS
(Datcom section for components indicated)
I.
Cy
~
(Contd.)
Horizontal tail mounted on body or no horizontal tail Linearlift range
Eq. 5.6.1.1b
(Contd.) ~
~
5.2 .1.1
5.3.1.1
(Cv~)wB 3.
Bodies of revolution
(LlCyP)P (based on exposed verticaltail geometry)
w
4. 5. 6. 7.
Breaks in LE and TE at same spanwise station M ;;, 1.4 for straighttapered plan forms 1.1 ~ M ~ 3 for composite plaQforms 1.0 ~ M ~ 3 for curved planforms
I. 2.
Straighttapered wings
8 tan Ac/ 4
3.
5.1.2.1
4.
Uniform dihedral (alternate form is available to account for dihedral) M.;; 0.6
S. 6.
Linearlift range
I.
Straighttapered wings
2. 3. 4. 5. 6.
A< />
SUBSONIC
Eq. 5.1.2.1a
5T2.T
5 .1.2.1

5 .1.2.1
W.t
5.1.2.1
1
c/~
= CL [_I .:. .:..}57.3 3 A
  f
rfA) 6
Eq. 5.1.2.1a'.
(c~.J,
5.1.2.1
:1:
=
(c~ )
a total
l(Cta),
~
5.1.2.1
5.1.2.1
4.1.3.2
s, [ Sw
5°:;;;;;
(3::;;.:;
+5°
Linearlift range
No twist No dihedral M.;; 0.6
5° .;;
~
.;; +5°
Linearlift range and
(ct 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. 5.1.2.1b'
No dihedral
5. 6.
M.;; 0.6 5° ~ (3
fcL ).
01
Dougle·delta and cranked wings Ai and A~< 1.0 No twist
4.
7. I
8. 1·34

Uniform dihedral M.;; 0.6
Doubledelta and cranked wings
8.

+5°
A, and A; ;;, 1.0
7.
4.1.3.2
~ ~:;;;;;
I.
5. 6.
~
5°
2. 3. 4.
Eq. 5.1.2.1b
A;;, 1.0
~
+5°
Linear·lift range and (cL ) ' 01
0
t/c ~ 0.1 if cranked wings with round LE
METHODS SUMMARY DERIVATIVE
c,
~
(Contd.)
CONFIG.
SPEED REGIME
w
TRANSONIC
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for componenis indicated)
5.1.2.1
S.U.l
5.1.2.1
(Contd.)
(CL~) M=06 4.1.3.2
4.1.3.2
4.1.3.2
Straighttapered wings 5° .;; iJ<; +5° Linearhft 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
Eq. 5.1.2.1c 4.1.3.2
I. 2. 3.
intersect remote half·wing
SUPERSONIC
C1 = 0.061 CN B
4.1.3.2
+
r
eN
(~·)
c,
Eq. 5.1.2.1e
'
I.
Straighttapered wings
2. 3. 4.
No twist
5.
M;.l.4
6. 7.
Wing tips parallel to free stream Foremost ~ach line from wing tip may not intersect remote halfwing
I.
2. 3. 4. 5. 6.
Doubledelta and cranked wings No twist No dihedral Straight trailing edge Low angles of sideslip Linearlift range
7. 8.
1.2<;M<;3 M > 1.4, if A 0 >A,
9.
A,
I. 2. 3.
Straighttapered wings Uniform dihedral M.;; Mrb so .;; ll.;; +So Linearlift range
~
r
5.1.2.1

= 0.061

Uniform dihedral Linearlift range

4.1.3.2 4.1.3.2
(CNJg and (cNJbw
0.061
< 80°. if A 0 > A,
Eq. 5.1.2.1f
WB
SUBSONIC
c,
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
K
t.c,c]
Mr
+f
5.1.2.1, 5.1.2.15.2.2.1
1C)w + 8 tan
+(AC
A,. 14
(
1 )
AC e tan
~c/4
~~
5.2.2.1
5.1.2.1 Eq. 5.2.2.1a
.
4. 5.
135
METHODS SUMMARY DERIVATIVE
c, p (Contd.)
CON FIG.
SPEED REGIME
WB (Contd.)
SUBSONIC (Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
(Datcom section for components indicated,
c,
p

CL
5.2.2.1
TRANSONIC
c, 
p
5.2.2.1
[(~L. (~:t
=
CL
(c ') Na
(c ')
M:l.4
La
4.1.3.2
Mfb
6.
M.;; 0.6
I.
Straighttapered wings Mfb.;; M.;; 1.4 ~so .;; ~.;; +so
5.2.2.1
k ~)· C:t ~ Mfb
1.4

4.1.3.2
4.1.3.2
(c ') La
2. 3. ( c L,2) M
Eq. 5.2.2.1d
Mfb
4.1.3.2
(:~ t=l.4 4. 5.

4.1.3.2
(:~
tfb
6. 7. (cL )
o: Mfb
eN SUPERSONIC
c, = p
~o.06I
eN
•
[
~
57.3
I +A (I + ALE)]
(
2 2
I+
43
ALE )(tan ALE)[ M cos ALE + en :LE) 1 ~ A
l
J
4.1.3.2
Uniform dihedral Linearlift range and (CL ) aM
8.
Symmetric airfoils of conventional thickness distribution
9.
'
I. 2. 3.
Straighttapered 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 not intersect remote halfwing
f c,
5.1.2.1
r
AC1 ]
P +(AC ) + __ 1P 'w r
.5.2:2.1
Eq.
5.2.2.1~
intersect remote halfwing
5.2.2.1
zP cos a  QP sin a
TB
SUBSONIC
(Ac1 P)p
=
(Acy P)P 5.3.1.1
TRANSONIC SUPERSONIC
bw
Eq. 5.3.2.1a
(ACy P)P (based on exposed verticaltail geometry for (ACy P)P Method 3) I.
Limitations depend upon ( ACy ) prediction method PP
I.
Horizontal tail mounted on body or no horizontal
(No method) (Same as subsonic equation)
tail ( ACy P)P (based on exposed verticaltail geometry) 2.
136
Breaks in LE and TE must be at same spanwise station
METHODS SUMMARY DERIVATIVE
cl
~
(Contd.)
CON FIG.
SPEED REGIME
TB (Contd.)
SUPERSONIC (Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS 3. 4. 5. 6. 7.
Bodies of revolution M ;;> 1.4 for straighttapered plan forms 1.2 .;;; M .;;; 3 for composite planforms 1.0 .;;; M .;;; 3 for curved plan forms Linearlift range
HYPERSONIC
(t.Cl~)P
zP cos
=
a  £ P sin a
(f>Cva)p
bw

Eq. 5.3.2.1a
Method I I.
2.
Horizontal tail mount~d on body or no horizontal tail M<7 (based on exposed verticalpanel geometry)
(t>Cy a)p 3. M ;;> 1.4 for straighttapered planforms 4. 1.2 .;;; M .;;; 3 for composite planforms 1.0 .;;; M .;;; 3 for curved planforms 5. 6. Linearlift range zP and QP (based on exposed verticalpanel geometry)
5.3.1.1
Method 2 I.
(t>Cv~)P
Horizontal tail mounted on body or no horizontal tail
(based on exposed verticalpane! geometry)
2. Sharpedge sections 3. 5 << I zP and QP (based on exposed verticalpanel geometry)



Method 3 I.
Horizontal tail mounted on body or no horizontal tail 2. Upper range of hypersonic Mach numbers ( f>Cy a)p (based on exposed verticalpanel geometry)
zP and QP (based on exposed verticalpanel 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. 5.6.2.1a
Linearlift range
(ct,)ws 2. 3. 4.
Straighttapered wings Uniform dihedral M.;;; Mrb 5. M.;;; 0.6 6. so .;;; ~.;;; +so ('l.Cy ) (based on exposed verticaltail geometry for 1 . P ( f>Cy ~)P Method 3)
(No method) 137
METHODS SUMMARY DERIVATIVE
cl
~
CON FIG.
WBT (Contd.)
SPEED
EQUATIONS FOR DERIVATIVE ESTIMATION
REGIME
( Datcom section for components indicated 1
SUPERSONIC
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS l.
(Same as subsonic equation)
Linearlift range
(CI~)WB
(Contd.)
2.
Straighttapered wings
3.
Wing tips parallel to free stream
4.
Foremost Mach line from wing tip may not intersect remote halfwing
5 M> 1.4 (Cv ~)P (based on exposed verticaltail geometry) 6.
Additional tail limitation is identical to Item 5 immediately above
w
SUBSONIC (Low Speed)
I
[
= 57.3
x sin 1,14 )]
A
I
+62 8 cos A, 14
c
41rA 
(Subcritical)
A
Eq. 5.1.3.1a
I.
Linearlift range
I.
Rectangular planform
2.
A
Eq. 5.1.3.1b
5.1.3.1 TRANSONIC
(No method)
SUPERSONIC
Eq. 5.1.3.1c
 1r
)

[''r' ~ 7. I. 1.1
 
F9(N) + 5_1.3.1

 
(A2 16



~C)]~7.1.1.2
5.1.1.1
57.3
)M2 
1 ;;. 1.0 (Mach number and aspec<
ratio greater than those for which Mach line from LE of tip section intersects TE of opposite tip section)
Eq. 5.1.3.1d
I.
2.
A = 0 ~ cot /LE .;; 1.0 (Mach number and aspect
ratio for which wing lies within Mach cones springing from apex and TE at center of wing)
I. WB
ALL SPEEDS
(c n/3)
WB
b
Linearlift range
Eq. 5 .2.3.1a
5.2.3.1 5.2.3.1
TB
SUBSONIC
Method I LiCy ) (based on exposed verticaltail geometry for Eq. 5.3.3.1a ( ~ P (LiCy ) Method 3) ~
l.
138
p
Limitations depend upon (LiCy ) prediction method ~ P
METHODS SUMMARY DERIVATIVE
c
·~
CON FIG.
SPEED REGIME
TB (Contd.)
SUBSONIC (CGntd.)
eQUATIONS FOR DERIVATIVE ESTIMATION ! Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
4.1.4.2
Method 2
(Contd.) = 
(t.Cy ~)P
(t>Cy ) (based on exposed verticaltail geometry for ~ P (t>Cy ~)P Method 3)
Eq. 5.3.3.1b
I.
5.3.lT
Limitations depend upon
method
(t>Cy ) ~
prediction
P
M .;;; 0.6; however, 1f swept planforms with t/c ~ 0.04, application to higher Mach numbers is acceptable
3. TRANSONIC
Linearlift range
(No method)
SUPERSONIC (Same as subsonic equations)
Method I I. (LlCy.6
)P
Horizontal tail mounted on body, or no horizontal tail (based on exposed verticaltail geometry J
2. 3.
Breaks in LE and TEat same spanwise station Bodies of revolution
4. 5. 6. 7.
M ;. 1.4 for straighttapered planforms 1.2 ~ M ~ 3 for composite planforms 1.0 .;;; M .;;; 3 for curved planforms Linearlift range
f          

Method 2 (same limitations as Method I above) (ACv~)P (based on exposed verticaltail geometry)
WBT
SUBSONIC

5.2.3.1
Eq. 5.6.3.1a Method I
(C•a)ws
5.3.1.1
(
L p [ (t>Cy a)p 5.2.3.1
5.3.1.1
cp b~')P)] +
I. t>Cy )
Linear·lift range
(based on exposed verticaltail geometry for (t>Cy ) ~ P Method 3) aP 2. Limitations depend upon (t>Cy) prediction method ~ P
1Eq. 5.6.3.1b
·
Method 2
(C•a)ws I.
Linearlift range
( t.Cy a)p (based on exposed verticaltail geometry for (LlCy Method 3)
2.
~/P
Limitations depend upon(t>Cy ) prediction method ~ P
139
METHODS SUMMARY DERIVATIVE
en
6
CON FIG.
SPEED REGIME
WBT (Contd.)
SUBSONIC (Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
METHOD LIMITATIONS ASSOCI A TED WITH EQUATION COMPONENTS (xa.c.)p
M ~ 0.6; however, if swept planforms with t/c ..o;; 0.04, application to higher Mach numbers is acceptable Linearlift 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.
Linearlift range (based on exposed verticaltail geometry)
3. 4. 5. 6. 7.
Breaks in LE and TE at same spanwise station Bodies of revolution M ~ 1.4 for straighttapered planforms 1.2 ,._; ; M ~ 3 for composite planforrns 1.0 ~ M ~ 3 for curved planforms Linearlift range
.a)p
8.
      
  
Method 2 (same limitations as Method I above) (t>.Cy ~)P (based on verticaltail geometry)
Cyp
w
SUBSONIC
Cyp =
K

[(~:
7.1.2.1
)CL•O CL
1
+ (t>.Cy p)r
M
Eq. 7.1.2.1a

7.1.2.1
7.1.2.1
< o:
I.
Q'
2.
Test data for lift and drag
stall
K
(;Lpt•O M
TRANSONIC
3.
M<;;M
I.
Thin. sweptback, tapered wings with strearnwise tips Low iift coefficients
(No method)
SUPERSONIC Figure 7.1.2.110
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. 7.1.2.1a
I. 2.
a< astall
3.
Test data for lift and drag
(Body diameter)/(wing span).;; 0.3
K
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
c, p
WB (Contd.)
WBSONIC (Contd.)
(Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION (Oatcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
C::t.o M
TRANSONIC SUPERSONIC
4.
M .;; M'
I.
Thin, sweptback, tapered wings with streamwise tips (Body diameter)/( wing span) .;; 0.3 Low lift coefficients
(No method) Figure 7.1.2.1iO
2. 3.
Wt!T
SUBSONIC
zp] +2 [z( Ll.Cy bw
c, p = ( Cy p) WB 7.3.2.1
~) V(WBHJ
Eq. 7.4.2.1a Method I (conventionally located vertical tails) (Cvp) WB I. (body diameter)/( wing span) .;; 0.3 2. ex ~ astall
5.3.1.1
3. 4.
Test data for lift and drag M .;; M'
(Ll.Cy ~) V(WBH) 5.
Additional or identical tail limitations depend
on (Ll.Cy ) ~
1     Cy p
=
(cvP)WB
+ [ 2z
b~ zP]
7.3.2.1 TRANSONIC
(No method)
SUPERSONIC
(No method)


~

V(WBH)
prediction method
                       Eq. 7.4.2.1c Method 2 (vertical tail directly above, or above and slightly behind wing) (same limitations as Method I above)
( Ll.Cy )v(WBH) 5.3.1.1
4.1.3.3
ct
p
w
SUBSONIC
ct p
=
c~p
)cl =0
7.1.2.2
(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. 7.1.2.2a
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
Straighttaoered wings
(No method) 141
METHODS SUMMARY DERIVATIVE
ct p (Contd.)
CON FIG.
SPEED REGIME
w
SUPERSONIC
(Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
ct p
~I p)~heory]
;
A
ct p 'c1 )
7.1.2.2
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
p
I. 2. 3.
Eq. 7 .1.2.2<1
theory
Straight·tapered wings Wing tips parallel to free stream Foremost Mach line from tip may not intersect remote halfwing Supersonic TE
7.1.2.2 4. 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)
I. 2.
Eq. 7 .1.2.2a
drag
~~· 7.1.2.2
(Body diameter)/(wing span) ...; 0.3 M ...; M'
(CL.) CL 3.
Symmetric airfoils
4.
I X 106
...;
R, ,.; 15 x 106 based on MAC
(CL.) C L=0
TRANSONIC
SUPERSONIC
5.
Straight·tapered wings
I.
Straighttapered wings. If (body diameter)/(wing span) > 0.3, valid only for triangular wings) Cylindrical or nearly cylindrical bodies
(No method)
(CIP) WB
=
ct p (ct.) w
..7.1.2.2
Eq. 7 .3.2.2a
(Ctp) d/b•O
,_._:2)'
2.
7.3.2.
(Ct.) w 3. 4.
Wing tips parallel to free stream Foremost Mach line from tip may not intersect remote halfwing
5.
WBT
SUBSONIC
ct p • (ct p ) WB .._.,_ 7.1.2.2
+ 0.5

(Ct•) H
7.1.2.2
C'~ C'Y Sw
bw
+ Hb:) [ z :wzP
I
J
(ACy g)
V(WS~) ...__
..~
5.3 1.1
Supersonic TE
Eq. 7 .4.2.2a 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
(ACy g)
6.
.;;
< 15
x 106 based on MAC
V(WBH)
Additional or identical tail limitations depend prediction method on (ACy )
g
I42
R0
V(WBH)
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
c/ p
WBT (Contd.)
SUBSONIC (Contd.)
(Contd.)
c. p
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
c/ p
=
(C/p)
+ 0.5 (C/P)

WB

7.1.2.2
w
TRANSONIC
(No method)
SUPERSONIC
(No method)
SUBSONIC
c. p
~ C'r C')
I:w [ b~ JI
+
bw
2z
zP

Eq. 7.4.2.2b Method 2 (vertical tail located directly above, or above and slightly behind wing) (same limitations as Method I above)
V(WBH)
5.3.1.1
tan a  (
[ CIP
c. P) CL
_ CL] CL0
+
(tJ.>)
M
 
7.1.2.2
(t!.Cy ~)
~
7.1.2.2
tan a  K
= C/P
H
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
7.1.2.3 7.1.2.2
7.1TI
7.1.2.3
0
.[(:;::,] (:;),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

Eq. 7.1.2.3e
7.1.2.2
2.
Lift coefficients up to stall (if reliable lift and drag data are available)
3. 4.
Straighttapered wings Symmetric airfoils
5.
I
'
X
10 6
.;;
R,.;; 15
X
!0 6 based on MAC
Method I 'Subsonic leading edges (~ cot ALE < />


7.1.2.1
7.1.2.3
c., )

M<;;M
c/ p
Eq. 7 .1.2.3a
TRANSONIC
I.
7. 1.3.3
I. 2. 3.
Straighttapered wings Streamwise wing tips Low lift coefficients
4.
Foremost Mach line from tip may not intersect remote half·wing Supersonic TE
cl p 5.
1
c.p a
=
a
c·p)
bo~y
I
[
2x + A(!:)
2
tan ALE
aXIS
7.1.2.3
WB
SUBSONIC
c.p
7.1.2.2
+
K
[ C1 tan a 
 
7.1.2.3
p
7.1.2.3
J
a

p
7.1.2.3
7. 1.2.3
7.1.2.2
0 + (:;)::,
c~~) CL CL•O
cl p

          1           Eq. 7.1.2.3g

Method 2 Supersonic leading edges(~ cot ALE (same limitations as Method I above)
(:~),
6,

> I)
7.1.2.2
CL]
Eq. 7.1.2.3a
M
n [' lO'P
Cy
7.1.2.1
= C1 tan a p

l
 
I. 2.
(Body diameter)/( wing span)<;;; 0.3 M<;;M
3.
Lift coefficients up to stall (if reliable lift and drag data are available)
'
cl p 4. 5.
Symmetric airfoils
6.
I x 106 <;;; Ro <;;; 15 x 106 ·based on MAC
Straighttapered wings
6.1.: .I 143
METHODS SUMMARY DERIVATIVE
CONFIG.
c. p
WB (Contd.)
(Contd.)
•
SPEED REGIME TRANSONI!=
EQUATIONS FOR DERIVATIVE ESTIMATION (Oatcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
(No method)
SUPERSONIC
a
(
c••
2xc.g.
+
= a/body
Eq. 7.1.2.3e
A(l +A)
Method l Subsonic leading I. 2. 3. 4.
axis
7.1.2.3
edges(~
with CL
5.
~(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 not intersect remote halfwing Supersonic TE
Eq. 7.4.2.3a Method 1 (conventionally located vertical tails) (Cnp) WB l. 2. 3. 4.
5.3.1.1
Straighttapered wings Symmetric airfoils (Body diameter)/(wing span).;; 0.3 M <;;; M
'
pWB
r
z zP] (
+ 2 .bw 
)
6.
Lift coefficients up to stall (if reliable lift and drag data are available)
X
Eq. 7.4.2.3b
~) V(WBH)
Additional or identical tail limitations depend on (L>Cy ) prediction method ~V(WBH) _ _    
7.3.2.3 )44
I
Test data
~.
[2zb: zP]
(aCy ~ )v(WBHJ 5.3.1.1
Eq. 7.4. 2.3c Method 2 (vertical tails located directly above, or above and slightly behind wing) (same limitations as for Eq. 7.4.2.3a above)
1                     1(same limitations as Method I above) c Eq. 7.4.2.3d (c•.)ws + 'p =
 __
(acnt3P ) I.
7.3.2.3
7 .3.2.3
X
(same limitations as for Eq. 7.4.2.3a above)
ac. t3p
1c•• =(C•.)ws _ tQ' cos a b: zP sin a]
l 0 6 based on MAC
1
I _ _ _ _ _ _ _ _ _ _    _ _ _ _ _ _ _ _    ____       ________
(c. )
l 0 6 .;; R, .;; 15
5.
7.
=
·
(same limitations as Method l above)
( f>Cy
c. p
P
Eq. 7.1.2.3g Method 2 Supersonic leading edges(~ cot ALE> l)
7.1.2.2 ( f>Cy
cot ALE< l)
Straighttapered wings Streamwise wing tips (Body diameter)/( wing span).;; 0.3 Lift coefficients where en varies linearly
·
1
METHODS SUMMARY DERIVATIVE
c., (Contd.)
Cv,
CONFIG.
WBT (Contd.)
w
WB
WBT
SPEED REGIME
EQUATIONS 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
p
cos a + z sin ') (
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
I.
Eq. 7 .4.3.1a
VtWBH)
(Cv,) 5.3.1.1
Aperiodic mode only
WB
2.
Test data
(
1Cy
'
w
c,
=
(No method)
SUPERSONIC
(No method)
'
= CL
c,
'


(
~JCL
•0
+ (
' CL
M
7.1.3. 2
7.1.3.2
(J
+
( < />
 r + r
7.1.3.2
(
[r:~l
~
~
7.1.3.2
(: ), .,
7.1.3.2
6.1.1.1
Eq. 7 1.3.2a
(cv ) r
WB
(No method)
SUPERSONIC
(No method)
and (
I.
Test data
I.
M~M
       
p
'
(
TRANSONIC
V(WBH)
    1    Eq. 7.4.3.1b
(Cv' )ws + 2(
TRANSONIC
SUBSONIC
         
50~
(3 ~+50
l45
METHODS SUMMARY DERIVATIVE
c,
CON FIG.
SPEED REGIME
WB
SUBSONIC
' (Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
c,
=
~c~t=O
+
( ~C1
1
'
)
C} + (r
CL
M
7.1.3.2
r +
(;'·) ·~~·· y::),•, 6 8
Eq. 7.1.3.2a
Sr

7.1.3.2
1.
(Body diameter)/(wing span)< 0.3
2.
M ~Mer
(~c1,k
f
7.1.3.2
7.1.3.2
7.1.3.2
METHOD LIMITATIONS ASSOCI ATED WITH EQUATION COMPONENTS
6.1.1.1
3. 4.
No curved planforms No twist or dihedral, if non·straighttapered wing
TRANSONIC
5. 6. 7.
t/c < 0.1 if cranked wing with round LE M < 0.6 Linearlift range
8.
5° < ~<+5°
(No method)
SUPERSONIC (No method)
WBT
SUBSONIC
cI,
 .2_ (£p b2 w
=
cos
a + z sin') (z p
p
cos
a  £P sin a) f~cy )
~
Eq. 7.4.3.2a V(WBH)
~~~~
No curved planforms
5.3.1.1
No twist or dihedral, if nonstraighttapered wing 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.
Linearlift range
8.
50<~< +50
'
(~Cy ~) V(WBH) 9.
ec, (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) 1Eq. 7 .4.3.2b
rWB
(
Cl,) WB
(same limitations as for Eq. 7.4.3.2a)
(~CI#)P
7.3.3.2
I.
Test data
f                        + 2
(~c·~)p
(Cl,) Eq. 7.4.3.2c
WB
(same limitations as for Eq. 7.4.3.2a)
(~Cn~)P (~Cy ~)V(WBHl' and(~C1 ~)P 1.
TRANSONIC' 146
(No method)
Test data
METHODS SUMMARY DERIVATIVE
CONFIG.
wu
C,r (Contd.)
(Contd.)
c.
w
•
SPEED REGIME SUPERSONIC (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.ONIC
c. r
=
(c•,)wB
Eq. 7.1.3.3a 0
No twist nor dihedral Liftcoefficient range for which Cn varies linearly with CL '
I.
2.
(~J
Eq. 7.1.3.3a

2.
No twist nor dihedral Lift coefficient range for which Cn varies linearly with CL r
I.
Aperiodic mode only
I.
7.1.3.3
7,1.3,3 TllANSONIC
CD
7T3:3
7.1.3.3
WB
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
+ _22 b
(£p COSCi
+Zp sin
~
)
Eq. 7.4.3.3a V(WBH)
2. 3.
w
5.3.1.1
7.3.3.3
(C•,)wa No twist nor dihedral Liftcoefficient range for which c. varieo linearly with CL '
( ACy ~) V(WBH) 4. Additional tail limitations depend upon (ACy ) prediction method ~
                        c. r
=
( Cn,) WB 7.3.3.3
TRANSONIC
(No method)
SUPERSONIC
(No metbod)
+2
(ACn~)~ ( ACy ~) V(WBH)
Eq. 7.4.3.3b
1
V(WBH)
            ·
(same limitations as for Eq. 7.4.3.3a above) ( ACn~)P I. Test data
5.3.1.1
147
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
w
SUBSONIC
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
Eq. 6.1.1.1a
(two dim)
I. 2.
Linearlift range Other limitations depend upon type of flap (see Equations c through j below)
Eq. 6.1.1.1b
I.
2.
Linearlift range Other limitations depend upon type of flap (see Equations c through j below)
(Co ) 0
K'
Eq. 6.1.1.1c
theory
6.1.1.1 6.1.1.1 f 
6.1.1.1


I. 2. 3.
Plain trailingedge flaps with sealed gaps No beveled trailing edges No compressibility effects
(a) Singleslotted   flaps 

      
Eq. 6 .1.1.1d (b) Fowler flaps I. Near fully extended position 2. Slot properly developed
test data 6.1.1.1
                 
rc'
Eq. 6.1.1.1e
lJI c '..'
(a) Singleslotted flaps (b) Fowler flaps
6.1.1.1 ~
~c
•=
c•
Eq. 6.1.1.1h
'c
~
..___,
6.1.1.1 t
6.1.1.1
c.
6cl
'cI
(:~
y:
'..'
6.1.1.1 
c.
'c ._=..,
'vJ
6f2 (I +
c  c
'
')
Eq. 6.1.1.1i
a
C
Eq. 6.1.1.1j
4.1.1.2 6.1.1.1
6.1.1.1
C~) +C~6r+[l+k,(;,)]6i(c•,. c:
.__, .__,

6.1.1.1 6.1.1.1 6.1.1.1
6.1.1.1
Doubleslotted flaps Ratio of forwardflap chord to aftflap chord ..;; 0.60
Doubleslotted flaps Ratio of forwardflap chord to aftflap chord ::::: 1.0
     
6.1.1.1 6.1.1.1
= c0 a
= {[l+k,(;.)]6r(c•,r
I.
2
r                dc 0
I.
2.
_'1_2_ '..'
6.1.1:1
t~c.

)+
C~ 6i}~
.._!.., .__,
.__,
6.1.1.1 6.1.1.1
6.1.1.1
I.
Split flaps
+    
Eq.6.1.1.1k
I. 2. 3. 4. 5.
Jet flaps (first approximation for multislotted flaps) Linearized thinairfoil theory No trailingedge separation No augmentorwing concept Not valid for low values of C ~
149
METHODS SUMMARY DERIVATIVE
c,. and
a•
CON FIG
w (two dim) (Contd.)
SPEED REGIME
SUBSONIC (Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
~c,
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
= ....._,_..... Ci6 of
Eq. 6.1.1.12
6.1.1.1

(Contd.)
~c
'
' 0~
=
f

Ci
•
· ·
I. Thinairfoil theory ·(a) Krueger flaps _ _ _ _ _ ~Leadingedge slats __
~o/
Eq. 6.1.1. 1n
s
....._,_..... ....._,_..... 4.1.1.2 6.1.1.1
w
(same as that for flapretracted section  see Section 6.1.1.2
SUBSONIC
(two dim) 4.1.1.2
I. 2.
Plug or flap spoiler Zerolift region
I. 2.
of .;; 20°
      
 
6.
No separated flow
Eq. 6.1.1.2a 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)
max
(~c 2 max1ase
=
6.1.1.3 6.1.1.3 6.1.1.3
Eq. 6.1.1.2b
Fixedhinge trailing and leadingedge flaps for plain flaps
5.
4.
1      
Translating trailingedge flaps and leadingedge slats ~
I.
2. 3. 4. 5.
       
I.
Eq. 6.1.1.3a
Jet flaps (first approximation for multislotted flaps) Linearized thinairfoil theory No trailingedge separation No augmentorwing concept Not valid for low values of C~ Spoilers 0 c, < 0
2. 3.
a>
I.
Trailingedge flaps
6.1.1.3
 ·
f~c
2
=
c,
6
11max
f'ls
....._,_..... ....._,_..... ....._,_..... max
' 0 .:_ f c
Eq. 6.1.1.3b (a)
5.1.1.3 6.1.1.3 6.1.1.3 (b)
150

Or .;;; 30° for single.;;lotted and Fowler flaps 5r .;;; 60° for double.;;lotted flaps Or .;; 45° for split flaps
3.
6.1.1.2
Leadingedge flaps Thinairfoil theory
Eq. 6.1. I. 1m
c
..____ ~c, =

I. 2.
I. Thinairfoil theory Leadingedge flaps 2. No Krueger flaps 3. llr < 30° Leadingedge slats 4. ll, < 20°
METHODS SUMMARY DERIVATIVE
CON FIG.
w (twodim)
SPEED REGIME
SUBSONIC
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
.:lcrn =
.:l~
[ x;f _ ( x:,P)(
'v'
'v'
6.1.1.1
6. 1.2.1
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
~·)]
Eq. 6.1.2.1a
r 
     

    
Figure 6.1.2.1 35b
Method I I. Plain, split, and multislotted trailingedge flaps 2. Linearlift range .:lc, (depends upon type of flap)            Plain trailingedge flaps Subcritical Mach numbers Linearlift range
Metho~
1. 2. 3.
1  1
(c')2 & +(xrefc + c' cc
c' rn,LE c
fLE
)
.:lc
+
'
'v'
'v'
6.1.2.1
6.1.1.1
+0.75 'v'
4.1.2.1
1
c,
(~)(~1)
I. Small leadingedge devices 2. Thinairioil theory .:lc, (depends upon type of flap)
'v'
4.1.1.1, 4.1.1.2

Eq. 6.1.2.1b

Eq. 6.1.2.1c
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 6.1.2.33
I.
(same as that for flapretracted sections)
     
Jet flaps (first approximation for muitislotted flaps) Linearized thinairfoil theory No trailingedge separation No augmentorwing concept Not valid for low values of c.

2.
Leading and trailingedge mechanical flaps No separated flow
Eq. 6.1.2.1k
I. 2. 3. 4. 5.
Jet flaps (first approximation for multislotted flaps) Linearized thinairfoil theory No trailingedge separation No augmentorwing concept Not valid for low values of c.
I.
Portion of Cm c, curve below the moment break
·
.:lc, (depends upon type of flap)
151
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
w
SUBSONIC
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
I.
Eq. 6.1.3.1a
(So:) theory
(two dim)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
2.
3.
6.1.3.1
+ 2
(c• )
a theory
4.
[
I 
4.1.1.2
6.1.3.1
c, a
(c2 a )theory
1
(tan
 ~E 2

.!.) c
Eq. 6.1.3.1b
I.
2. 3.
4.
('1.)a balance
=
,.
[('i.o)balance) '
c;. a
<;,

    
·
Radiusnose, sealed, trailingedge flaps Tangent of half the trailingedge angle No separated flow Low speeds
* t/c
I.
Eq. 6.1.3.1c
Control with nose balance
c;;Q
Q
6.1.3.1

c;, o
4.1.1.2
r      
Radiusnose, sealed, trailingedge flaps Tangent of half the trailingedge angle= t/c No separated flow Low speeds
6.1.3.1
2. 3.
Radiusnose, sealed, trailingedge flaps No separated flow 4. Low speeds ~444 TRANSONIC (No method) SUPERSONIC
= Cl
+ C2 TE
Eq. 6.1.3.1e
1.,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, straightsided flaps Cc/C < 0.5 Small flap deflections Small angles of attack Flow field supersonic and inviscid No separated flow

t
~<;.
c;.Q = ~ ( ;;; 6.1.3.1
152
) t
6.1.3.1
~
Eq. 6.1.3.1f
I. 2. 3.
Airfoils with sharp leading and trailing edges Symmetric, circulararc 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 SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
w
SUBSONIC
(two dim)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom oodion for components indicated)
l
~. • rk~ )~• 6
theory
6.1.3.2

Eq. 6.1.3.2a
(<1t6)theory
6.1.3.2
      26
I [ 6.1.3.2

6.1.1.1
c
(c2 ~theory
](tan
t/JiE _ 2
!) c
Eq. 6.1.3.2b
6.1.1.1


Eq. 6.1.3.2c
I. 2. 3. 4.
I.
Radiusnose, sealed, trailingedge flaps Tangent of half the trailingedge angle= t/c No separated flow Low speeds
2. 3. 4.
Radiusnose, sealed, trailingedge flaps Tangent of half the trailingedge angle* t/c No separated flow Low speeds
I.
Control with nose balance
2.
Radiusnose, sealed, trailingedge flaps No separated flow Low speeds
        
.6.1.3.2
6.1.3.2
3.
4.
~1~~ TRANSONIC
(No method)
SUPERSONIC
c. ·n6
= _________.. Cl + C2 t/JTE ..__.
Eq. 6.1.3.2d
6.1.3.2 6.1.3.2
1_________..
(~) ~
6.1.3.2
6.1.3.1
= Cl
w (two dim)
+
I. 2. 3.
4. 5. 6. 7.  I  Eq. 6.1.3.2e
SUBSONIC Eq. 6.1.3.3a
Airfoils with sharp leading and trailing edges Symmetric, straightsided flap cr/c·< 0.5 Small flap deflections Small angles of attack Flow field supersonic and inviscid No separated flow        
I. 2. 3.
Airfoils with sharp leading and trailing edges Symmetric, circulararc airfoil cr/c.;;; 0.5
4.
5. 6. 7.
Small flap deflections Small angles of attack Flow field supersonic and inviscid No separated flow
I.
18° .;;; 6 t .;;; I 8°
2.
3.
Does not account for effects of airfoil thickness, controlsurface gaps, control nose balance, and TE angle Low speeds
4.
Linear hingemoment range
153
METHODS SUMMARY DERIVATIVE
CONFIG.
w
SPEED REGIME
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
SUBSONIC
Eq. 6.1.3.4a
I.
18o.;;;sr.;;;J8o
2.
Does not account for effects of airfoil thickness, controlsurface gaps, control nose balance, and TE angle
3.
Low speeds
4.
Linear hingemoment range
(two dim)
4.1.3.2
w
SUBSONIC
[(a, (Z) 
Eq. 6.1.4.1a
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. 6.1.4.1b
c;
Sw
6. J:i .l

l

,....._,
6.1.4.1
'A,+ 2c; [ 'A• +~~./ 2.01
c;
liieff

Mechanical flaps Straighttapered wings
2. 3. 4. 5. 6.
Small angles of attack Linearized thinairfoil theory No trailingedge separation No augmentorwing 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. 6.1.4.1c
2.
Sw r
3.
57.3 Sw
4. 5.
6.1.1.!
6.
Eq.6.1.4.1e
CL
I.
c, 0 6.2.1.!
Straighttapered wings
M =0.6
2. 3. 4. 5. 6.
1 54
Jet flap EBF configuration Small angles of attack Linearized thinairfoil theory N,o trailingedge separation No augmentorwing concept Not valid for low values of C1
0 M = 0.6
TRANSONIC
6.1.4.1
         
Plain trailingedge flaps {3A ;;. 2 A~< 60° No beveled trailing edges No compressibility effects
7.
Symmetric airfoils of conventional thickness distribution
8.
a=
0
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
Eq. 6.1Alf
cL,
w
(Contd.)
(Contd.)
I.
SUPERSONIC
2. 3.
4.
5. 6.
7.
w
SUBSONIC
=
(cLJo=O
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 the plane 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 the wing tip Innermost Mach lines from deflected con trois do not cross the wing root chord Wing planform has leading edges swept ahead of Mach lines and has streamwise tips Controls are not influenced by tip conical flow from the opposite wing panel or by the interaction of the wingroot Mach cone with the wing tip Symmetric, straightsided flaps Nontranslating leading and trailingedge flaps No separated flow on wings and flaps
(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. 6.1.4.2a
Translating leading and trailingedge 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.6.1.4.2b          ·I Jet flaps I.
~
=
' (CL 0 ) K(A 1, C1 ) 0 { [
'v'
6.1.4.2
6.1.4.2
]
I
Kb + 1.0 ..__, 6. 1.4. I
}
+
CJ(COS sieff I)
57.3
2. (CL 0
A;;.s
),
3. 4. 5.
No separated flow on wings and flaps No curved planforms M '0.80, t/c '0. I, if cranked plan form with round LE
155
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
w
SUBSONIC
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
= .6c2
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
I.
Eq. 6.1.4.3a
max
Mechanical trailingedge flaps
6. 1. 1.3
.___
                        i          2 c /c) (bslat ) 1.28 (0.18 ~ cos2 Ac/4 1
.::lCLmax =

I.
Eq. 6. 1.4.3b
     · 
Figure 6.1.4.3 12
w
SUBSONIC
.::lCmr
= .::lCm
Slats (firstorder approximation)
I.
(~) 'v' .::lCL tan Ac/
+ KA
'v'
'v' 1.5
6.1.5.16.1.5.1
Eq. 6.1.5.1a
4
1. 2.
6.1.4.1
Firstorder approximation for EBF configuration
Linearlift range < 45°
Ac/4
.::lCL (depends upon type of flap) 3.
1AC
=
mr
/1.o
·
0
6.1.5.1

Eq. 6. 1.5.1k

Mechanical flaps Straighttapered 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 ,_..._
ACm
w
TRANSONIC
Cm
= em m ~
~
6.1.5.1
6.1.4.3
= CL 6
+ 1'1,
(;) 6
.'
c)
Az

c
~
6.1.5.1
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 leadingedge devices Constant flapchordtowingchord ratio Thinairfoil theory
1. 2. 3. 4. 5.
Jet flaps (first approximation for multislotted flaps) Linearized thinairfoil theory No trailingedge separation No augmentorwing concept Not valid for low values of
Eq, 6.1.5.1£
Eq. 6.1.5.1u
Eq. 6. 1.5.l·W

c,.
1.
Linear aerodynamic control characteristic region
2. 3.
Straighttapered wings Plain trailingedge flaps with sealed gap No beveled trailing edges ~A;;;. 2 A~< 60° Symmetric airfoils with conventional thickness distribution No compressibility effects
~
6.1.4.1 6.1.5.1
4. 5.
6. 7. 8. 9. 156
 ·
    
[em , (~')+C.:'  x:..E) c 6LE
Linearlift range Subcritical Mach numbers
Ol
=
0
METHODS SUMMARY DERIVATIVE
CONFIG.
c m;
w
(Contd)
(Contd.)
SPEED REGIME
SUPERSONIC
EQUATIONS FOR DERIVATIVE ESTIMATION !Datcom section for components indicated)
c m,
=
b, c'f
I

K,

3
.
f

Sw
C'm,
I


K2 2
. .
b,
sf
f Sw
'• .
x, s,

K3
.
6.2.1.1 6.1.5.1
6.1.5.1 6.1.5.1
6.1.5.1
C'

c

Sw
C' L,
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
Eq. 6.1.5.1q
I. 2.
...
3.
6.1.4.1
4. 5.
6. 7.
8.
Linear aerodynamic control characteristic region Symmetric straightsided 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 the plane of symmetry Controls are located either at the wing tip or far enough inboard so that outermost Mach lines from the 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 of Mach lines and has streamwise tips Con trois are not influenced by tip conical flow from the opposite wing_ panel or by the interaction of the wingroot Mach cone with the wing tip.
C'
15
9.
I 0.
chQ
w
A SUBSONIC
ch Q
=
COS
A+2
11., 14
COS
11., 14
( ch Q) balance
+
Ll.Ch
Q
Eq. 6.1.6.1a
3. 4.
High aspect ratios (A > 3) Ends of control surfaces parallel to plane of symmetry Neglects subcritical Machnumber effects Sealed, plain trailingedge controls
5. 6.
No separated flow Low speeds
I.
Symmetric, straightsided controls Con:rol root and tip chords are parallel to the plane of symmetry Wing planform has leading edges swept ahead of Mach lines and has streamwise tips Controls are not influenced by tip conical flow from the opposite wing panel or by interaction of the wingroot Mach cone with the wing tip.
I. 2.
~
6.1.6.1
6.1.3.1
Plain !>ailingedge flaps Thin wings
ch Q
TRANSONIC
SUPERSONIC
(No method)
(chJ,;,
= (I '
c2
cl .
6.1.6.1
qTE)
( cho)t/c
Eq. 6.1.6.1b = 0
2.
6.1.6.1
3. 4.
157
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
EQUATIONS FOR DERIVATIVE ESTIMATION !Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
6.1.6.1
ch
Q
(Contd)
w (Contd.)
. 't
. ,. . ,3C~
SUPERSONIC (Contd.)
2
I
~LE_
(,I+,k) :::
AHL)
1
2
[I + 2
ch)l~r
I
c )r!}
(chJt/c o =
6.16.1
6.1.6.1
I. 2.
Symmetric biconvex airfoil Other limitations identical to Items 2 through 4 immediately above
l.
High aspect ratios (A > 3) Ends of control surfaces parallel to plane of symmetry Neglects subcritical Machnumber effects Sealed, plain trailingedge flaps
6.1.6.1 Eq. 6.1.6.1b with different correction factor
w
2
SUBSONIC
=
COS
Ac/ 4
COS AH L
COS
Ac/4
A + 2 cos A, 14
6.1.3.2
6.1.1.1
6.1.3.1
]
+
Eq. 6.1.6.2a
~c
h,
2.
6.1.6.2
3. 4. ch
'
5. 6.
TRANSONIC
(No method)
SUPERSONIC Ch
6
=
~ (1  ~:

t/>TE)
6.1.6.2
~ C~,

Eq. 6.1.6.2b
I. 2.
6. [ .6.2 3. 4.
5.
6. 7.

Symmetric, straightsided 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 the plane of symmetry Controls are located either at the wing tip or far enough inboard so that outermost Mach lines from deflected 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 ahead of Mach lines and has streamwise tips Controls are not influenced by tip conical flow from the opposite wing panel or by interaction of the wingroot Mach cone with the wing tip

1
Eq. 6.1 .6.2b with different correction factor
158
No separated flow Low speeds
I 2.
~
Symmetric biconvex airfoil Other limitations identical to Items 2 through 7 immediately above
METHODS SUMMARY DERIVATIVE
CON FIG.
SPEED REGIME
w
SUBSONIC
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
METHOD LIMITATIONS ASSOCI ATED WITH EQUATION 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.
nl ~
~
~
~
6.1.7 6.1.7 6.1.7
~
~
6.J.7i6.1.7 6.1. 7 k
2:
v= 1
(18 vn )B vn
Eq. 6.1.7c
sin
n•l
~
6.1.7
~
~
~~
6.1. 7 6.1.7
~
6.1.7 6.1. 7 6.1.7
r6.1.4.1 .'.
AC·Dmin =
Acd f
K ... ~
....
~
(AcLrY
+ K'
I.
Eq. 6.1.7p
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
SUPERSONIC
(No method)
AC 0
Eq. 6.1.7q
wave
4.1.5.1
c,.
w
SUBSONIC
c,
C'
•
Eq. 6.2.1.1b
'•
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
I.
Plug or flaptype spoilers No separated flow
flex.' 5
Eq. 6.2.1.1c
2
6.2.1.1 6.1.1.1



( cl) s.poilerslotdeflector
      K
6.2.1.1
(CI)plain
spoiler
6.2.1.1
No separated flow
               
I 6
2
Plain trailingedge flaps
3.
c'      cI :
I.

0 ther limitations identical to Items I through 4 immediately above



Eq. 6.2.1.1f
I.
Spoilerslotdeflector
2. 3. 4.
ilA ;;;. 2 A~< 60° M.;;; 0.6
5.
No separated flow
(C,lplain spoiler 6. Plain flaptype spoiler 159
METHODS SUMMARY DERIVATIVE
CON FIG.
c,6
w
(Contd)
(Contd.)
SPEED REGIME
TRANSONIC
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated,)
c,
(C 1)M=o. 6 (depends upon type of control) Eq. 6.2.1.1g CL Q I. Symmetri~ airfoils of conventional thickness distribution 2. A ..;; 3 if composite win2
CL Q = (CI)M=0.6
(CLQ)M =06 6.2.1.1
METHOD LIMITATIONS ASSOCIATED WITH EQUATION 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 LE
7]c~6 [:~ c:~)6.2.1.1
SUPERSONIC
c, 6
=
('  c2 ~TE) c, ~
C' L6
sr
6
I
 Sw 2
Eq. 6.2.1.1h
+
6.1.4.1
6.2.1.1
I. 2.
3.
6.1.4.1
4. 5. 6.
Plain trailingedge 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 flow from opposite wing panel or by interaction of wingroot Mach cone with the wing tip
C/6 7.
Thin wings
8.
Symmetric, straightsided controls
I.
Plug or flaptype spoilers
I. 2. 3.
Differentially deflected horizontal stabilizer Horizontal tail mounted on body No separated flow on horizontal tail
4.
Straighttapered wing
5.
Other limitations depend upon  prediction method oa
C' L6
1
                        
Figure 6. 2.1.130
SUBSONIC
c, 6
=
'I{ l
I 
rrAw 57.3
/2)] ~ CH)
ae) + ivB(HJ C1Tarvr)(bHr aa e ~4.4.1 4.3.1.3 4.3.1.3

6.2.1.2
YH sHe bw Sw

(CL QH ) e 4.1.3.2
Eq. 6.2.1.2a
oe oa
ae
(CLQJe 6. 7. 160
No curved planforms M..;; 0.8, tfc..;; 0.10, if cranked planform with round LE
METHODS SUMMARY DERIVATIVE
cl, (Contd.)
CON FIG. T (Contd.)
SPEED REGIME TRANSONIC
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
(Same as subsonic equation)
I. 2. 3. 4.
Differentially deflected horizontal stabilizer M < l.O Bodymounted horizontal tail No separated flow on horizontal tail
5. 6.
Straighttapered wing Proportional to CL
•
(CL•H)e 7. 8.
9.
Symmetric airfoils of conventional thickness distribution A,; 3 if composite wing C< = 0
f         ···                                    · (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
c.
= 0.35 [ ivB(H) (21f; Vr)(bH>) ...
.._.,_....
4.3.1.3 4.3.!.3
+(
~H(B).,. kB(H)) l (CN'H)e
.
4.3.1.2
Eq. 6.2.1.2c
3.
...._,_,
4.1.3.2
K ~
6.2.2.1
CL
cl
Eq. 6.2.2.1a
2
..__.., '
6.2.1.1
·      
4. 5. 6. 7.
Breaks in LE and TE at same spanwise station M ;;;. 1.4 for straighttapered planforms 1.2 ,; M ,; 3 for doubledelta planforms 1.0 ,.;;; M ,.;;; 3 for curved plan forms
1. 2. 3.
Ailerontype controls No separated flow Neglects contributions due to profile drag
4. 5.
/3A ;;;. 2 A~ < 60°
6. 7. 8.
No beveled TE No compressibility effect M..; 0.6
l. 2. 3.
Plug and flaptype spoilers 0.02,; 6,/c,; 0.10 C< = 0
1. 2. 3.
Spoilerslotdeflector C< = 0 6,16d = 1.0
 
Figures 6.2.2.110, 6.2.2.111
(Cn) spoilerslotdeflector =
Differentially deflected horizontal stabilizer Bodymounted horizontal tail No separated flow on horizontal tail
(CN'H)e
(6L  6R) =
l. 2.
  _.,____      K
6.2.2.1
Eq. 6.2.2.1b
6.2.2.1
  ·
  

(Cn) plain spoile.
4.
Plain, flaptype spoiler 161
METHODS SUMMARY DERIVATIVE
c. (Contd.)
CON FIG.
w
SPEED REGIME
TRANSONIC
(Contd.)
EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)
C0
=
METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS
Eq. 6.2.2.k
(Cn )M =0.6 1. Ailerontype controls 2.
6.2.2.1
3.
4.1.3.2
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.
Straighttapered wings
9.
Symmetric airfoils of conventional thickness distribution 0
10.
'=
~~~~~SUPERSONIC
Figure 6.2.2.113
       F~ure
T
162
ALL SPEEDS
6.2.2.114
(No method)
 


   
I. Ailerontype controls 2. Neglects contributions due to profile drag f 1.
Plug and flaptype spoilers
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