USAF STABILITY AND CONTROL DATCOM

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USAF STABILITY AND CONTROL DATCOM

MCDONNEf...L'OQUGLAS CORPORATION

DOUGLAS AIFfCRAFT OIVI~ION .

_"'

' . ,..

.

;..·

' (

...

,,.

PRINCIPAL INVESTIGATOR: R. D. FINCK

OCTOBER 1960

Contract AF33(616)-6460

REVISED APRIL 197 8

Contract F336;S-76-C-3061

Project No. 8219

,Task No. 821901

• .!.

FLI<{HT C0:Nr,IWL DIVISION

AIR FORCE FLIGOTJ)YNAMICS LABOR'ATORY

WRIGHT-PATTERSON Ai'R FORCE BASE; OHIO

~ . ; · .. ' "

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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!5-67-C-1156,

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MCDONNELL DOUGLAS CORPORATION DOUGLAS AIRCRAFT DIVISION 1967-1977

PRINCIPAL INVESTIGATORS

R. D. FINCK (1971-

)

D. E. ELLISON ( 1962-1970)

L. V. MALTHAN (1958-1962)

PRINCIPAL COLLABORATORS

D. E. Ellison .

R. B. Harris

D. E. Drake .

M.

J. Abzug .

C. S. Thorndike

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 .

Technical Director

Technical Advisor

Technical Editor, 2.1,

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Section I Section 2 2.1 2.2 2.2.1 2.2.2 2.3 Section 3 3.1 3.1.1 3.1.2 3.1.3 3.2 3.2.1 3.2.1.1 3.2.1.2 3.2.1.3 3.2.2 3.2.3 3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.4 3.5 3.6 Section 4 4.1 4.1.1 4.1.1.1 4.1.1.2 4.1.1.3 4.1.1.4 4.1.2 4.1.2.1 4.1.2.2 4.1.3 4.1.3.1 4.1.3.2 4.1.3.3 4.1.3.4 4.1.4 4.1.4.1 4.1.4.2

*Subjects for Future Additions

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 4.3.2 4.3.2.1 4.3.2.2 4.3.2.3 4.3.2.4 4.3.3 4.3.3.1 4.3.3.2 4.4 4.4.1 4.5 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

Wing Drag at Angle of Attack Bodies at Angle of Attack Body Lift

Body Lift-Cu!Ve Slope

Body Lift in the Nonlinear Angle-of-Attack Range

*Effects of Asymmetries

Body Pitching Moment

Body Pitching-Moment-Curve Slope

Body Pitching Moment in the Nonlinear Angle-of-Attack Range

Body Drag

Body Zero-Lift Drag

Body Drag at Angle of Attack

Wing-Body, Tail-Body Combinations at Angle of Attack Wing-Body Lift

*Wing-Body Zero-Lift Angle of Attack Wing-Body Lift-CuiVe Slope

Wing-Body Lift in the Nonlinear Angle-of-Attack Range Wing-Body Maximum Lift

Wing-Body Pitching Moment

Wing-Body Zero-Lift Pitching Moment Wing-Body Pitching-Moment-Curve Slope

*Wing-Body Pitching Moment in the Nonlinear Angle-of-Attack Range

Wing-Body Drag

Wing-Body Zero-Lift Drag

Wing-Body Drag at Angle of Attack

Wing-Wing Combinations at Angle of Attack (Wing Flow Fields) Wing-Wing Combinations at Angle of Attack

Wing-Body-Tail Combinations at Angle of Attack Wing-Body-Tail Lift

Wing-Body-Tail Lift-Curve Slope

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

Wing-Body-Tail Pitching Moment

Wing-Body-Tail Pitching-Moment-Cu!Ve Slope

*Wing-Body-Tail Pitching Moment in the Nonlinear Angle-of-Attack Range

Wing-Body-Tail Drag

Wing-Body-Tail Zero-Lift Drag

Wing-Body-Tail Drag at Angle of Attack Power Effects at Angle of Attack

Power Effects on Lift Variation with Angle of Attack Power Effects on Maximum Lift

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4.7.1 4.7.2 4.7.3 4.7.4 4.8 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 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 5.2.2.1 5.2.2.2 5.2.3 5.2.3.1 5.2.3.2 5.3 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

Ground Effects on Lift Variation with Angle of Attack

*Ground Effects on Maximum Lift

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

Low-Aspect-Ratio Wings and Wing-Body Combinations at Angle of Attack Wing, Wing-Body Normal Force

Wing, Wing-Body Zero-Normal-Force Angle of Attack

Wing, Wing-Body Normal-Force Variation with Angle of Attack Wing, Wing-Body Axial Force

Wing, Wing-Body Zero-Normal-Force Axial Force

Wing, Wing-Body Axial-Force Variation with Angle of Attack Wing, Wing-Body Pitching Moment

Wing, Wing-Body Zero-Normal-Force Pitching Moment

Wing, Wing-Body Pitching-Moment Variation with Angle of Attack CHARACTERISTICS IN SIDESLIP

Wings in Sideslip

Wing Sideslip Derivative Cy ~

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

Wing Sideslip Derivative Ct~

Wing Sideslip Derivative Ct~ in the Linear Angle-of-Attack Range Wing Rolling-Moment Coefficient Ct at Angle of Attack

Wing Sideslip Derivative Cn(j

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

Wing-Body Combinations in Sideslip Wing-Body Sideslip Derivative Cy ~

Wing-Body Sideslip Derivative Cy ~in the Linear Angle-of-Attack Range Wing-Body Side-Force Coefficient Cy at Angle of Attack

Wing-Body Sideslip Derivative Ct~

Wing-Body Sideslip Qerivative Ct₀in the Linear Angle-of-Attack Range *Wing-Body Rolling-Moment Coefficient Ct at Angle of Attack

Wing-Body Sideslip Derivative C₀₀ Wing-Body Sideslip Derivative C

00 in the Linear Angle-of-Attack Range

Wing-Body Yawing-Moment Coefficient C₀ at Angle of Attack Tail-Body Combinations in Sideslip

Tail-Body Sideslip Derivative Cy

0

Tail-Body Sideslip Derivative Cy

0 in the Linear Angle-of-Attack Range Tail-Body Side-Force Coefficient Cy at Angle of Attack

Tail-Body Sideslip Derivative Cto

Tail-Body Sideslip Derivative Ct

0 in the Linear Angle-of-Attack Range *Tail-Body Rolling-Moment Coefficient Ct at Angle of Attack

Tail-Body Sideslip DcrivativeC₀₀

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

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Section 6 5.5.1 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 6.1 6.1.1 6.1.2 6.1.3 6.1.4 5.6.3.1 5.6.3.2 6.1.1.1 6.1.1.2 6.1.1.3 6.1.2.1 6.1.2.2 6.1.2.3 6.1.3.1 6.1.3.2 6.1.3.3 6.1.3.4 6.1.4.1 6.1.4.2 6.1.4.3 6.1.5 6.1.5.1 6.1.5.2 6.1.6

Wing, Wing-Body Sideslip Derivative Ky .6

Wing, Wing-Body Sideslip Derivative Kv

11 at Zero Normal Force

Wing, Wing-Body Sideslip Derivative

Kv.a

Variation with Angle of Attack Wing, Wing-Body Sideslip Derivative

K[

₁₃

Wing, Wing-Body Sideslip Derivative

Ki.a

Near Zero Normal Force Wing, Wing-Body Sideslip Derivative

Kj

₁₃

Variation with Angle of Attack Wing, Wing-Body Sideslip Derivative K~.B

Wing, Wing-Body Sideslip Derivative K~{J at Zero Normal Force

Wing, Wing·Body Sideslip Derivative K~~ Variation with Angle of Attack

Wing-Body-Tail Combinations in Sideslip Wing-Body-Tail Sideslip Derivative Cy

13 Wing·Body·Tail Sideslip Derivative Cy

13 in the Linear Angle·of·Attack Range

Wing· Body-Tail Side-Force Coefficient Cy at Angle of Attack

Wing-Body.Tail Sideslip Derivative Ct

13

Wing-Body-Tail Sideslip Derivative C1~ in the Linear Angle-of-Attack Range *Wing.Body-Tail Rolling-Moment Coefficient C1 at Angle of Attack

Wing·Body-Tail Sideslip Derivative Cn 13

Wir.g·Body-Tail Sideslip Derivative C₀~ in the Linear Angle-of·Attack Range Wing-Body. Tail Yawing-Moment Coefficient C0 at Angle of Attack

CHARACTERISTICS OF HIGH-LIFT AND CONTROL DEVICES

Symmetrically Deflected Flaps and Control Devices on Wing-Body and Tail-Body

Combinations

Section Lift with High-Lift and Control Devices

Section Lift Effectiveness of High-Lift and Control Devices

Section Lift.Curve Slope with High-Lift and Control Devices

Section Maximum Lift with High-Lift and Control Devices

Section Pitching Moment with High-Lift and Control Devices

Section Pitching-Moment Increment .6.cm Due to High-Lift and Control Devices Section Derivative Cma with High-Lift and Control Devices

Section Pitching Moment Due to High-Lift and Control Devices Near Maximum Lift

Section Hinge Moment of High-Lift and Control Devices

Section Hinge-Moment Derivative Cha of High-Lift and Control Devices Section Hinge-Moment Derivative ch

6 of High-Lift and Control Devices

Section Hinge-Moment Derivative (chf)₆t of Control Surface Due to Control Tabs Section Hinge-Moment Derivative (cht)lif of Control Tab Due to Control Surface

Wing Lift with High-Lift and Control Devices

Control Derivative CL₆of High-Lift and Control Devices

Wing Lift.Curve Slope with High-Lift and Control Devices Wing Maximum Lift with High·Lift and Control Devices Wing Pitching Moment with High·Lift and Control Devices

Pitching-Moment Increment ~Cm Due to High·Lift and Control Devices Wing Derivative Cma with High-Lift and Control Devices

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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 Section 7 6.3.1 6.3.2 6.3.3 6.3.4 7.1 7.1.1 7.1.2 7.1.3 7.1.4 7.2 7.2.1 7.2.2 7.3 7.3.1 7.3.2 7.1.1.1 7.1.1.2 7.1.1.3 7.1.2.1 7.1.2.2 7.1.2.3 7.1.3.1 7.1.3.2 7.1.3.3 7.1.4.1 7.1.4.2 7.1.4.3 7.2.1.1 7.2.1.2 7.2.2.1 7.2.2.2 7.3.1.1 7.3.1.2

Drag ofHigh·Lift and Control Devices

Asymmetrically Deflected Controls on Wing·Body and Tail·Body Combinations

Rolling Moment Due to Asymmetric Deflection of Control Devices

Rolling Moment Due to Control Deflection

Rolling Moment Due to a Differentially Deflected Horizontal Stabilizer

Yawing Moment Due to Asymmetric Deflection of Control Devices Yawing Moment Due to Control Deflection

Side Force Due to Asymmetric Deflection of Control Devices *Side Force Due to Control Deflection

Special Control Methods

Aerodynamic Control Effectiveness at Hypersonic Speeds Transverse-Jet Control Effectiveness

*Inertial Controls

Aerodynamically Boosted Control·Surface Tabs DYNAMIC DERIVATIVES

Wing Dynamic Derivatives Wing Pitching Derivatives

Wing Pitching Derivative CLq

Wing Pitching Derivative Cmq

Wing Pitching Derivative Coq

Wing Rolling Derivatives

Wing Rolling Derivative Cyp

Wing Rolling Derivative C1p Wing Rolling Derivative Cnp

Wing Yawing Derivatives

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

Wing Derivative Co

a

Body Dynamic Derivatives Body Pitching Derivatives

Body Pitching Derivative CLq Body Pitching Derivative Cmq

Body Acceleration Derivatives Body Acceleration Derivative CL& Body Acceleration Derivative Cma

Wing-Body Dynamic Derivatives

Wing-Body Pitching Derivatives Wing-Body Pitching Derivative CLq Wing·Body Pitching Derivative Cmq Wing·Body Rolling Derivatives

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7.3.3 7.3.4 7.4 7.4.1 7.4.2 7.4.3 7.4.4 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 7.3.3.1 7.3.3.2 7.3.3.3 7.3.4.1 7.3.4.2 7.4.1.1 7.4.1.2 7.4.1.3 7.4.2.1 7.4.2.2 7.4.2.3 7.4.3.1 7.4.3.2 7.4.3.3 7.4.4.1 7.4.4.2 7.4.4.3 7.4.4.4 7.4.4.5 7.4.4.6

Wing-Body Yawing Derivatives Wing-Body Yawing Derivative Cy r Wing-Body Yawing Derivative C1r Wing-Body Yawing Derivative Cnr Wing-Body Acceleration Derivatives Wing-Body Acceleration Derivative CL&: Wing-Body Acceleration Derivative Cmc, Wing-Body-Tail Dynamic Derivatives Wing-Body-Tail Pitching Derivatives Wing-Body-Tail Pitching Derivative CLq

Wing-Body-Tail Pitching Derivative Cmq Wing-Body-Tail Pitching Derivative Coq

Wing-Body-Tail Rolling Derivatives

Wing-Body-Tail Rolling Derivative Cyp

Wing-Body-Tail Rolling Derivative C/p

Wing-Body-Tail Rolling Derivative Cnp

Wing-Body-Tail Yawing Derivatives Wing-Body-Tail Yawing Derivative Cyr Wing-Body-Tail Yawing Derivative Ctr Wing-Body-Tail Yawing Derivative Cnr Wing-Body-Tail Acceleration Derivatives Wing-Body-Tail Acceleration Derivative CLa Wing-Body-Tail Acceleration Derivative Cma

Wing-Body-Tail Derivative Coa

Wing-Body-Tail Derivative Cy

p

Wing-Body-Tail Derivative Ctp

Wing-Body-Tail Derivative CniJ

*Control-Surface Angular-Velocity Derivatives

MASS AND INERTIA

Aircraft Mass and Inertia Missile Mass and Inertia

CHARACTERISTICS OF VTOL-STOL AIRCRAFT

Free Propeller Characteristics

Propeller Thrust Variation with Angle of Attack

Propeller Pitching-Moment Variation with Power and Angle of Attack

Propeller Normal-Force Variation with Power and Angle of Attack Propeller-Wing Characteristics

Propeller-Wing-Flap Lift Variation with Power and Angle of Attack

*Propeller-Wing-Flap Pitching-Moment Variation with Power and Angle of Attack

Propeller-Wing-Flap Drag Variation with Power and Angle of Attack

Ducted-Propeller Characteristics

Dueled-Propeller Lift Variation with Power and Angle of Attack

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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 self-sufficient. For any given flight condition and configuration the complete

set of derivatives can be determined without resort to outside information. The book is intended to

be used for preliminary design purposes before the acquisition of test data. The use of reliable test

data in lieu of the Datcom is always recommended. However, there are many cases where the

Datcom can be used to advantage in conjunction with test data. For instance, if the lift-curve slope

of a wing-body combination is desired, the Datcom recommends that the lift-curve slopes of the

isolated wing and body, respectively, be estimated by methods presented and that appropriate

wing-body interference factors (also presented) be applied.

If

wing-alone test data are available, it is

obvious that these test data should be substituted in place of the estimated wing-alone

characteristics in determining the lifhcurve slope of the combination. Also, if test data are available

on a configuration similar to a given configuration, the characteristics of the similar configuration

can be corrected to those for the given configuration by judiciously using the Datcom material.

The various sections of the Datcom have been numbered with a decimal system, which provides the

maximum degree of flexibility. A "section" as referred to in the Datcom contains information on a

single specific item, e.g., wing lift-curve 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:

Page:

Figures:

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

right-hand page.

The page number consists of the section number followed by a dash number.

Example: Page 4. 1.3.2-4 is the 4th page of Section 4. 1.3.2.

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. 1.3.2-50b is the second figure on

Page 4. 1.3.2-50. Where a related series of figures appears on more than one page,

the figure number is the same as the first page on which the series begins.

Example: Figure 4. 1.3.2-56d may be found on Page 4. 1.3.2-57 and is the 4th in 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. 1.3.2-A is the first table to appear in Section 4. 1.3.2.

Equations: Equation numbers consist of the section number followed by a lower case dashed

letter. Example: 4.1.3.2-b is the second equation (of importance) appearing in

Section 4.1.3.2. Repeated equations are numbered the same as for the first

appearance of the equation but are called out as follows: (Equation 4.1.3.2-b).

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Section

I.

Guide to Datcom and Methods Summary (present discussion including the

Methods Summary)

Section 2. General information

Section 3. Reserved for future use

Section 4. Characteristics at angle of attack

Section 5. Characteristics in sideslip

Section 6. Characteristics of high-lift and control devices

Section 7. Dynamic derivatives

Section 8. Mass and inertia

Section 9. Characteristics of VTOL-STOL aircraft

The information in Section 2 consists of a complete listing of notation and definitions used in the

Datcom, including the sections in which each symbol is used.

It should be noted that definitions 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, wetted-area charts, etc.

Sections 4 and 5 are for configurations with flaps and control surfaces neutral. Flap and control

characteristics are given in Section 6 for both symmetric and asymmetric deflections. Section 4

includes effects of engine power and ground plane on the angle-of-attack parameters.

The Datcom presents less information on the dynamic derivatives (Section 7) than on the static

derivatives, primarily because of the relative scarcity of data, but partly because of the 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 7-A).

If more than preliminary-design information on mass and inertia (Section 8) is needed, a

weights-and-balance engineer should be consulted.

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over six hundred sources for a great variety of VTOL-STOL configurations (Table 9-A).

It

should be noted that the characteristics predicted by this volume are for rigid airframes only. The

effects of aeroelasticity and aerothermoelasticity are considered outside the scope of the Datcom.

The basic approach taken to the estimation of the drag parameters in Section 4 has been found to

be satisfactory for preliminary-design 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, wing-body, wing-wing,

and wing-body-tail 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

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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 build-up of wing,

wing-body, and wing-body-tail components, a Methods Summary has been included at the end of

this section. In addition, the methods of Sections 6. I and 6.2 are also included in the Methods

Summary. The contents of the Methods Summary present the following:

(I)

the wing, wing-body,

and wing-body-tail equations available in each speed regime, (2) the sections where the equation

components are obtained, (3) the limitations associated with the equations and their respective

components (limitations from design charts are not included), and (4) identification of the

parameters that are based on exposed planform geometry that are not specified by the subscript e.

Sometimes the same limitations, such as "linear-lift range," may occur for more than one

component in an equation. To avoid repetition, the same limitation is not repeated for 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 stability-axis system unless otherwise noted.

Transformations of stability derivatives from one axis system to another are developed in many

standard mathematics and engineering texts. In FDL-TDR-64-70, several coordinate systems 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.

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whereas the Datcom emphasizes American information.

As stated in the introduction, the work on the Datcom will be expanded and revised over the years

to maintain an up-t<>-date and useful document. In order to help achieve

this

goal, comments

concerning this work are invited and should be directed to the USAF Procuring Agency so that the

effort may be properly oriented.

DERIVATIVE

c"ll

c,

r

c.

_r

METHODS SUMMARY OUTLINE

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c,

'

1-59 through 1-61

en

_{1-61 through 1-62}

en

(16)

DERIVATIVE

CON FIG.

w

WB

SPEED

REGIME

SUBSONIC

TRANSONIC

SUPERSONIC

21r

- - =

4.1.3.2

4.1.3.2 EQUATIONS FOR DERIVATIVE ESTIMATION

(Datcom section for components indicated)

Faired curve between

(CL )

.

and

(CN )

.

a subsomc a superso01c

Figures 4.1.3.2-56a through -60

=

_4_.1_.3.2

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

4.1.3.2

4.1.3.2 HYPERSONIC

Figures 4.1.3.2-56a through -60

SUBSONIC

1 - - - -

-(CN.), =0 -;

v

ta~2

A

LE

1--~-p2

(a)

(CL )

a WB

= [

KN

+

KW(B)

+

KB(W)

l

---

4.3.1.2 Fig. 4. I

.3.249

Eq.

4.1.3.2-b

METHOD LIMITATIONS ASSOCIATED WITH

EQUATION COMPONENTS

Method I I.

'

Method

2

I.

3.

4. 5. 6.

No curved plan forms

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

Constant-section, dell" or dipped-dell" configura lions (",.E = 0)

0.58 <;;A<;; 2.55

0.;;' .;; 0.3

63° .;; A _LE.;; 80° 0.10 <;;tic<;; 0.30

M = 0.~

I. Symmetric airfoils of conventional thid\llt's:-.

distribution 3 A~ 3 if composite wings

(){ =

0

I. Straighl-lapered wings 2. M;;. 1.4 3. Linear-lift range

----+- - - -

- - - l

Eq.

4.1.3.2-h

Eq. 4.1.3.2-£

Fig. 4.1.3.2-65

Fig. 4.3.1.2-a

I.

'

3.

Double"elta and ~:ranked wings

Breaks in LE and TE at same spanwise station

1.2 <;; M <;;

3. 0

4. Linear-lift ran~e

-I. Curved planforms 2. 1.0 <;; M <;; 3. 0 3. Linear-lifl range 1. Straighl-lapered wings

2. Conventional wings of zero thickness 3. Two-dimensional slender-airfoil theory 4. (){ = 0

-I. Straight-tapered planforms 2. Wedge airfoils

3. Two-dimensional slender-airfoil theory 4. (){ = 0

Method I (body diameter)/( wing semisp"n) <;; 0.~

(see Sketch (d), 4.3.1.2)

(a) Zero wing incidence; wing-body angle of attack

varied

KN (based on exposed wing geometry) I. Bodies of revolution

2. Slender-body theory 3. Linear-lift range

(CL.),

4. No curved plan forms

5. M <;; 0.8, t/c,;;; 0.1, if cranked wings with round LE

(17)

DERIVATIVE

CL

• (Contd.)

CON FIG.

WB

(Contd.)

SPEED

REGIME

SUBSONIC

(Contd.)

EQUATIONS FOR DERIVATIVE ESTIMATION

(Datcom section for components indicated)

s.

- - -

--

-- - -

--

-(cLJws

=

K<WBJ

(cLJw

4.3.1.2 4.1.3.2

TRANSONIC

(Same as subsonic equations)

SUPERSONIC (Same as subsonic equations)

Eq. 4.3.I.2-b

Eq. 4.3.1.2-c

METHOD LIMITATIONS ASSOCIATED WITH

EQUATION COMPONENTS

(b)

Body angle of attack fixed at zero; wing incidence

varied (same limitations as (a) above)

- - - -

-Method 2 (body diameter)/(wing span) is large with delta

wing extending entire length of body

(see Sketch (c), 4.3.1.2)

(CLa)w

I. No curved planforms

2. 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. Slender-body theory

3. Linear-lift range

KB(WJ and kw(B) (based on exposed wing geometry)

(CLa)e

4. Symmetric airfoils of conventional thickness

distribution

5. A .; 3 if composite wings

6. "

=

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. Symmetric airfoils of conventional thickness

distribution

2. A .; 3 if composite wings

3. "

=

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

2. Slender-body theory

3. Linear-lift range

kB(W)

and kw(B) (based on exposed wing geometry)

(CNa)e

4.

5.

6.

7. Breaks in LE and TE at same sranwise station

M ;;. 1.4 for straight-tapered wings

(18)

SPEED EQUATIONS FOR DERIVATIVE ESTIMATION METHOD LIMITATIONS ASSOCIATED WITH DERIVATIVE CON FIG. _REGIME

(Datcom section for components indicated) EQUATION COMPONENTS

CL WB SUPERSONIC Method 2 (body diameter)/( wing span) is large with delta

•

_(Contd.) _(Contd.) wing extending entire length of body

(Contd.) (see Sketch (c), 4.3.1.2)

(CNa)w

I. Breaks in LE and TE <:~t same spanwise station

2.

M;;, 1.4 for straight-tapered wings 3. 1.2 ~ M ~ 3 for composite wings 4. 1.0 .;;; M .;;; 3 for curved planforms 5. Linear-lift range

[KN

S'

(I-~)

q" S"

S"

Method

I

bw /bH ;;, 1.5

WBT SUBSONIC _CL

=

( cl.);

+

KW(B)

+

KB(W)l'

-

_S'

'

+

(cl.);' [KW(B)

+

KB(W) ]"

-

'

_I. _{(Body diameter)/(wing semispan)}_<;

_O.R

•

q= S' S"

~

4T3.2

(see Sketch (d), 4.3.1.2)

4.1.3.2 4.3.1.2 _4.3.1.2 _4.4.1

-2.

a "'

a:~tall if high aspect ratio and unswept wings 4.4.1

Eq. 4.5.1.1-a 3.

a:<<

a:stail if low aspect ratio or swept wings

(cL.); and (CL.);'

4. No curved planforms

5. M .;;; 0.8, t/c .;;; 0.1, if cranked plan forms with round LE

KN (based on exposed wing geometry)

6.

Bodies of revolution

7. Slender-body theory

8.

Linear-lift range

of

-

(depends upon method)

00:

9. Straight-tapered wing

of

10. Other limitations depend upon

aa:

prediction method

q"

-q=

II.

Valid only on the plane of -;yrnmctry

- - - -

-- ---- - -

r - - - -

-S' _q" _{S" S"} Method 2 bw /b"

<

1.5

CL

=

_{(CL.); [KN}

₊

Kwta)

+

Katw)]'

-f

+

(cL.);' [KW(B)

+

KB(W)]"

-

'

₊

_{(cLJw "t>J} (same limitations as Method I above omitting those

•

q= S' S"

4.TTI

4.3:1.2

4.T:TI'

4.3.1.2

4.4.T

of

a.

loa)

4.5.1.1 KN and (cL) (based on exposed wing geometry)

I

a W"(v)

(19)

DERIVATIVE CL

•

(Contd.) CON FIG. WBT (Contd.)

SPEED EQUATIONS FOR DERIVATIVE ESTIMATION REGIME j Oatcom section for components indicated)

TRANSONIC (Same as subsonic equations)

SUPERSONIC (Same as subsonic equations)

METHOD LIMIT AllONS ASSOCIATED WITH EQUATION COMPONENTS

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. Bodies of revolution

5. Slender-body theory 6. Linear-lift range - (depends upon method)

a"'

7. Straight-tapered wings 8. Proportional to

eL

• q"

q~

9. Conventional trapezoidal planforrns I 0. 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)

Method I bw /l>H ;;. 1.5

(eN.);

and

(eN.);'

I. Breaks in LE and TE at same spanwise station 2. M;;. 1.4 for straight-tapered planforms 3. 1.2.;; M.;; 3 for composite planforms 4. 1.0 .;; M .;; 3 for curved planforms 5. Linear-lift range

KN (based on exposed wing geometry) 6. Bodies of revolution

KB(W) (based on exposed wing geometry)

0<

aa

8. Straight-tapered wings

9 . 0 h t er nnitatlons depend upon- prediction I. . . 0<

(20)

DERIVATIVE

CL

a

(Contd.)

CON FIG.

WBT

(Contd.)

w

SPEED

REGIME

SUPERSONIC

(Contd.)

EQUATIONS FOR DERIVATIVE ESTIMATION

(Datcom section for components indicated)

4.1.4.2

4.1.3.2 TRANSONIC

(Same as subsonic equation)

SUPERSONIC (Same as subsonic equation)

HYPERSONIC (Same as subsonic equation)

Eq. 4.1.4.2-d

q"

q~

METHOD LIMITATIONS ASSOCIATED WITH

EQUATION COMPONENTS

10. If nonviscous flow field, limited to unswept wings

11. 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)

I. M .;; 0.6; however, for swept wings with

t/c .;; 0.04, application to higher Mach numbers

is acceptable

2. Linear-lift range

CL

a

3. No curved planforms

4. M .;; 0.8, t/c .;; 0.1, if cranked plan forms with

round LE

I. Straight-tapered wings

2. Symmetric airfoil sections

3. Linear-lift range

CL

•

4. Conventional thickness distribution

5.

IY.

=

0 -I.

Linear-lift range

eN

•

2. Breaks in LE and TE at same spanwise station

3. M ;;. 1.4 for straight-tapered wings

4. 1.2 .;; M .;; 3 for composite wings

5. 1.0.;; M .;; 3 for curved planforms

I.

IY.

=

0 eN

•

2. Straight-tapered wings

3. Conventional wings of zero thickness and wedge

airfoils

4. Two-dimensional slender-airfoil theory

(21)

SPEED

EQUATIONS FOR DERIVATIVE ESTIMATION

_{METHOD LIMITATIONS ASSOCIATE() WITH}

DERIVATIVE

CON FIG.

_REGIME

(Datcom section for components indicated)

_{EQUATION COMPONENTS}

=

( n -

~) ~

xa.c.

(calculations based on exposed wing geometry)

em

_a

WB

SUBSONIC

_em

_CL

Eq. 4.1.4.2-d

-a

c,

c

a

c,

(Contd.)

--I.

Single wing with body (i.e., no cruciform or

4.3.2.2

4.3.1.2 other multipanel arrangements)

2. M .;; 0.6; however, if swept wing with t/c .;; 0.04,

application to higher M"•·h numbers is acceptable

3. Linear-lift range

CL

a

4. (Body diameter)/(wing span) .;; 0.8

5. No curved planforms

6. Bodies of revolution

7. Slender-body

th~oiy

8. M .;; 0.8, t/c .;; 0.1, if swept wing with round LE

X _a.c.

TRANSONIC

(Same as subsonic equation)

- - (c"lculations based on exposed wing geometry)

c,

I. Straight-tapered wings

2. Single wing with body (i.e., no cruciform or

other multipanel arrangements)

3. Symmetric airfoils of conventional thickness

distribution

4. Linear-lift range

CL

•

5. Bodies of revolution

6. Slender-body theory

7. _"'

=

0

X _a.c.

SUPERSONIC

(Same as subsonic equation)

--(calculations based on exposed wing geometry)

c,

I. Single wing with body (i.e., no cruciform or

other multipanel arrangements)

2.

Linear-lift range

eN

_a

3. Breaks in LE and TE at same spanwise station

4. Bodies of revolution

5. Slender-body theory

6. M

>

1.4 for straight-tapered wings

7. 1.2 .;; M

<

3 for composite wings

8. 1.0.;; M .;; 3 for curved plan forms

'

(22)

DERIVATIVE CONFIG. WBT (Contd.) SPEED REGIME SUBSONIC xc.g.

~

x' [ - - , KN

c

4.5.2.1

EQUATIONS FOR DERIVATIVE ESTIMATION

(Oat com section for components indicated)

) II S" S" _, ae q e c

- aa

qoo

?5'

C'

---4.4.1 ---4.4.1

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

::.

~: :~

+ (

cL.}w..(,J

-4.5.2.1 4.3.1.

2

4.1.3.2 4.4.1 4.5.1.1

Eq. 4.5.2.1-d'

Eq. 4.5.2.1-(

METHOD LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS

I. (Body diameter)/( wing semispan).;; 0.8 (see Sketch (d), 4.3.1.2)

2. Linear-lift range

c'

3.

(calculations based on exposed planform geometry) 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

5. Bodies of revolution 6. Slender-body theory (CL )' and (cL )" a e o: e q" q~ 7. No curved planforms

8. M .;; 0.8, t/c.;; 0.1 if cranked planforms with round LE

9. 10.

Straight·tapered wing

a.

Other limitations depend upon- prediction

method

aa

II. Valid only on the plane of symmetry

Method 2

bw

/bH

<

1.5

(same limitations as Method I above, omitting those for

ae;aa)

x - x'

'•·

"\.

--=;,;-- (calculations uased on exposed planform geometry)

c

KN and (cL ) (based on exposed wing geometry)

o: W"(v) Method I bw /bH ;;. 1.5

x

- x'

'•·

_c' I. 2. 3.

(calculations based on exposed planform geometry) Single wing with body (i.e .. no cruciform or other multipanel arrangements)

Straight-tapered wings

Symmetric airfoils of conventional thickness distribution

4. Linear-lift range __j

(23)

DERIVATIVE (Contd.) CON FIG. WBT (Contd.) SPEED REGIME TRANSONIC (Contd.)

EQUATIONS FOR DERIVATIVE ESTIMATION ( Datcom section for components indicated)

METHOD LI~IITATIONS ASSOCIATED WITH EQUATION COMPONENTS

5. Bodies of revolution 6. Slender-body theory

(cLJ:

and

(cLJ~

ae

-a

a

" q

-q~ 7. 8. 9. 10. " = 0 Proportional to CL

"

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'

'~-c' (calculations based on exposed planform geometry)

KN, KB(W)' and

(CL )

(based on exposed wing geometry)

cr W"(v)

X _e.g. x'

c' (calculations based on exposed planform geometry)

I. Single wing with body (i.e., no cruciform or other multipanel arrangements)

(based on exposed \Ving geometry) 3. Bodies of revolution

KB!Wl (based on exposed wing geometry)

(CN"): and

(CN")~

a

5. 6. 7. 8.

Breaks in LE and TE at same span wise station M ;;. 1.4 for straight-tapered planforms 1.2 :s.;;; M :s.;;; 3 for composite planforms 1.0 :s.;;; M :s.;;; 3 for curved planforms

10 . 0 t er ImitatiOns depend upon -prediction h l. . .

ae

(24)

DERIVATIVE CON FIG. _REGIMESPEED EQUATIONS FOR DERIVATIVE ESTIMATION (Datrom section for components indicated)

~---~---~---~---~~~---

_"

-em

WBT SUPERSONIC ' '

•

(Contd.) (Contd.) (Contd.) q -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 l~~·IJil1~ !rV)

c'

KN, KB(W)' and

(C

_{1 cJw '(vl (based on exposed}wi11g

geometry)

~---+---4---~---~~--~~---

---w

SUBSONIC

=(_!_+2~)

c

2

c LQ Eq. 7.1.1.1-a

- - -

4.1.4.2 4.1.3.2

TRANSONIC (Same as subsonic equation)

SUPERSONIC

₊

₂

(~)

Eq. 7.1.1.1-c

-7.1.1.1 4.1.4.2 4.1.3.2 X

c

x

-c

CL

•

I. M

<

0.0; however, for swept wings with t/c

<

0.04,application to higher Mach numher-;

is acceptable

3. No curved p\anform~

4. M ~ 0.8, t/c.;;;:; 0.1, tf cranked wings with

round LE I. 2. 3. 4. Straigllt-tapcrcd \.\- ing:s No camber

Conventional tnickness distribution

" =

0

I. Straight-tapered wings

Subsonic LF (13 cot ALE

<

I I

2. Mach lines from TE vertex may not inta""-·d L E

3. WJng-tip Mach lint'S nHJy not intersect on wi11~s

nor intersect opposit~ wing tips

(b) Supersonic LE

(iJ

cot Au

>

I)

c

4. Valid only if Mach line:-. !'rom LE vert~'\

intersect TE

5. Foremost Mach line from t'ither wing tip m;~y

not interst'ct remote half of wing

(25)

DERIVATIVE 1-16

cl

•

(Contd.) CON FIG.

w

(Contd.) WB SPEED REGIME SUPERSONIC (Contd.) SUBSONIC 4.3.1.2

EQUATIONS FOR DERIVATIVE ESTIMATION (0atcom section for components indicated I

7.iT.i

7.2.1.1

Eq. 7.3.1.1-a

7. M ;:;, 1.4

Method I (body diameter)/(wing span) is small (see 4.3.1.2 Sketch (d))

(Clq),

I. No curved planfotms 2. Linear-lift range

3. M ~ 0.6; however, for swept wings with t/c ~ 0.04, application to higher Mach numbers is acceptable

4. M ~ 0.8, t/c ~ 0.1, if cranked wing with

round LE

(Clq)B

5. Bodies of revolution

- - - f - - - ·

-Eq. 7.3.1.1-b

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)

(CL.),

I. 2. 3. 4. (Clq)B Straight-tapered wings No camber Conventional thick1 " =

0

5. Bodies of revolution Distribution

r

-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) Method 1 (body diameter)/(wing span) is small

(see 4.3.1.2 Sketch (d))

KB(W) (based on exposed wing geometry) (Clq),

2. M;:;, 1.4

(26)

DERIVATIVE CON FIG. CL WB Q (Contd.) (Contd.) WBT SPEED REGIME SUPERSONIC (Contd.) SUBSONIC

EQUATIONS FOR DERIVATIVE ESTIMATION (Datcom section for components indicated)

Eq. 7.4.1.1-a

(a) Subsonic LE (JJ cot ALE

<

I)

4. Mach lines from TE vertex may not

intersect

LE

5. Wing tip Mach lines may not intersect

on wing nor intersect opposite w1ng tips (b) Supersonic LE

(iJ

cot ALE

>

I)

6. Va!id only if Mach lines from LE vertex

intersect

TE

7. Foremost Mach line from either wing tip may not intersect remote half of wing

(CLq1

1

-Method 2 (body diameter)/(wing span) is large, Y.ith delta wing extending entire length of body (see 4.3.1.2 Sketch (c))

(same limitations as Method I above) Method I bw/bH ;;. 1.5

I . Line~r-lift range

(c )

(based on exposed wing geometry) Lq WB q" q~

2.

3.

4. 5. 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

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

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

Method 2 bw /bH

<

1.5

Eq. 7.4.1.1-b (same limitations as Method I above)

(CL ) q WB and (CL ) a W"(v) (based on exposed wing geometry)

(Ctq)wo

I.

2.

3.

4.

(based on exposed wing geometry) Straight-tapered wings

No camber

(27)

DERIVATiVE 1-18 CL

•

(Contd.) CON FIG.

WBT

(Contd.) SPEED REGIME TRANSONIC (Contd.)

EQUATIONS FOR DERIVATIVE ESTIMATION IDatcom section for components indicated)

METHOLJ LIMITATIONS ASSOCIATED WITH EQUATION COMPONENTS

5. 0: = 0

KB(WJ (based on exposed wing geometry)

q"

q~

6. 7.

(c )"

_{Lo '}

8. Additional tail limitations are identical to Items 2, 3, and 5 immediately above Method 2 bw /bH

<

1.5

(CL ) q WB , KB(W)' and (CL ) o: W .. (v) (based on exposed

wing geometry) Method I bw /bH ;;> I .5

I. Linear-lift range

(c )

(based on exposed wing geometry) Lq WB 2. 3. 4. Straight-tapered wings Bodies of revolution M;;>l.4

KBtw) (based on exposed wing geometry) (a) Subsonic LE (13 cot ALE

<

I)

5. Mach line from TE vertex may not intersect LE 6. Wing-tip Mach lines may not intersect on wing

nor intersect opposite wing tips (b) Supersonic LE (13 cot ALE

>

I)

q"

7. Valid only if Mach lines from LE vertex intersect TE

9. 10.

II.

If nonviscous flow field, limited to unswept wings If viscous flow field, valid only on plane of symmetry

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

Method 2 bw /bH

<

1.5

(CL ) q W B , KB(W)' and (CL ) ,. a: W (v) (based on exposed wing

(28)

DERIVATIVE CON FIG.

w

SPEED REGIME SUBSONIC SUPERSONIC

c

_mq

(Oat com section for components indicated) 7.1.1.1 7.1.1.1

-.\

_t

A[~~+2(ff]+

--0.7 c., cos ~"' . c/4 _A

_{+ ,...,}

_cos_A '- · c/4 1 ( A3 tan2 /\, 14 ) 24 A

+

6 cos Ac/₄

+

4. !.I 4.1.1.2 A3 tan2 1\ _o/4 ₃

-7.1.1.2 7.1.1.1 7.1.1.1 7.1.1.2

~}

Eq. 7.1.1.2-a Eq. 7.1.1.2-b Eq. 7.1.1.2-<: Eq. 7.1.1.2-d c

I.

2.

M ~ 0.6; however, for swept wings with t/c ~ 0.04, application to higher Mach numbers is acceptable

Linear-lift range

I. Symmetric airfoils of conventional thickness distribution

2. CY. = 0

(Cmq)M

"1.2

3. Straight-tapered wings (a) Subsonic LE (~ cot ALE

<

I)

4. Mach line from TE vertex may not intersect LE 5. Wing-tip Mach Jines may not intersect on wings nor

intersect opposite wing tips (b) Supersonic LE (~ cot ALE

>

I)

6. Valid only if Mach lines from LE vertex intersect

TE

Subsonic LE (~ cot ALE

<

I)

I. Mach line from TE vertex may not intersect LE 2. Wing-tip Mach lines may not intersect on wings nor

intersect opposite wing. tips (h) Supersonic LE (~cot ALE

>

I l

3. Valid only if Mach lines from LE vertex intersect

TE

5. StraighHapered wings

A. M ;;> 14

(29)

DERIVATIVE CONFIG.

em

_q WB (Contd.) SPEED REGIME SUBSONIC

IDatcom section for components indicated I

Eq. 7.3.1.2-a

Method I (body diameter)/(wing span) is small (see 4.3.1.c Sketch (d))

(cmq),

2. M ~ 0.6; however, for swept wings with t/c ,; 0.04, application to higher Mach numbers is acceptable

(Cmq)B

t 1

-Eq. 7 .3.1.2-b

- -

4.3.1.2 7.1.1.2 7.2.1.2

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 1 above)

Method I (body diameter)/( wing span) is small (see 4.3.1.2 Sketch (d))

l. Linear-lift range

(em

q) ,

3. Symmetric airfoils of conventional thickness

distri-bution

4. C< = 0

(a) Subsonic LE

W

cot ALE

<

I)

5. Mach line from TE vertex may not intersect LE

6. Wing-tip Mach lines may not inter~ect on wings nor intersect opposite wing tips

(b) Supersomc LE (~ cot ALE

>

I)

8. Foremost Mach line from either wing tip may not interesect remote half of wing

(Cmq)s

1

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

(30)

DERIVATIVE

em

_q (Contd.) CON FIG. WB (Contd.) WBT

SPEED EQUATIONS FOR DERIVATIVE ESTIMATION REGIME (Datcom section for components indicated)

SUBSONIC Eq. 7.4.1.2-a

7.3.1.2 4.3.1.2 4.5.2.1 4.4.1 4.1.3.2

t

-=

(c )

-2 mq WB

(:~) (~J(cLJ

+{cLJw.J

Eq. 7.4.1.2-b 7.3.1 .2 4.5.2.1 4.3.12 4.4.1 4.13 2 _4.5.1.1

(em.),

2.

3.

Straight-tapered wings M;;. 1.4

(a) Subsonic LE (~ cot ALE

<

I)

4. Mach line from TE vertex may not intersect LE

5. Wing-tip Mach lines may not intersect on wings nor intersect opposite wing tips

(b) Supersonic LE

(IJ

cot ALE

>

I)

(Cmq)a

-Method 2 (body diameter)/( wing span) is large with delta wing extending entire length of body

(see Sketch (c) 4.3.1.2)

(em )

(based

on

exposed

wing

geometry) q WB

q"

1 . Bodies of revolution

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

4. Valid only on the plane of symmetry

(cL.);'

5. No curved plan forms

6. M.;; 0.8,

tic.;;

0.10, if cranked planforms with round LE

Method 2 bw /bH

<

1.5

(same limitations as ~h:·thod I above)

(31)

DERIVATIVE

em

q (Contd.) 1-22 CON FIG. WBT (Contd.) SPEED REGIME

Method I bw /bH ;> 1.5

(em )

(baserl on exposed wing geometry)

q WB

, Symmetric airfoils of conventional thickness distribution

4. " = 0

(a) Subsonic LE

W

cot ALE

<

I)

5. Mach line from TE vertex may not intersect LE 6. Wing-tip Mach lines may-not intersect on wings

nor intersect opposite wing tips (b) Supersonic LE

W

cot ALE

>

I)

KB(W) (based on exposed wing geometry) q"

q~

9. 10.

(c )"

_{L" '}

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

~-

-Method 2 bw /bH

<

1.5

(Cmq)wB' KB(W)'

and

(CLJW"(v)

Method I bw /bH ;> 1.5

(em )

(based on exposed wing geometry) q WB

I. Straight-tapered wings 2. Bodies of revolution 3. M ;> 1.4

(a) Subsonic LE

(p

cot ALE

<

I)

5. Mach line from TE vertex may not intersect LE 6. Wing-tip Mach lines may not intersect on wings nor

intersect opposite wing tips (b) Supersonic LE

(p

cot ALE

>

I)

(32)

DERIVATIVE

em

_q (Contd.) CON FIG. WBT (Contd.)

w

---.---SPEED REGIME SUPERSONIC (Contd.) SUBSONIC 4.1.4.2 4.1.3.2

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

7.1.4.1

TRANSONIC (Same as subsonic equation)

SUPERSONIC

+

2 E"(~C)

----

7.1.1.1 7.1.4.1 7.1.1 .I 7.1.4.1

- - -

7.1.1.1 7.1.4.1

Eq. 7.1.4.1-a

Eq. 7.1.4.1-b

8. Foremost Mach line from either wing tip may not intersect remote half of wing

q"

9. If nonviscous flow field, limited to unswept wing" 10. If viscous flow field, valid only on the plane of

symmetry

(c )"

La '

I I. Additional tail limitations arc identical to Items 3 and 4 immediately above

- - - -

--Method 2 bw /bH < 1.5

(C ) m q WB , KB(W)' and (CL ) .. o:, W (v) (based on exposed wing

geometry) xa.c.

-G

'

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

CL (g) c, 4. 0 <~A< 4 I. Triangular planforms 2. Mer

<

M ~ 1.0 3. Linear-lift range 4. No camber

5. Symmetric airfoils of conventional thickness distribution 6.

cl

(gJ 7.

a=O

0 <~A< 4 Method I I. 2. 3. Straight-tapered wings

1-

= 0

Subsonic LE (~ cot 1\LE

<

I)

(33)

I>ERIV A TJVE

CL·

_•

(Contd.) 1-24 OONFIG.

w

(Contd.) WB SPEED REGIME SUPERSONIC (Contd.)

5. Wing·tip Mach lines may not intersect on wings nor intersect opposite wing tips

6. Linear·lift range

r - - - -

- - - -

· -M2

I

CL.;

=

fi2

(cLJl -

fi2

(cLJ2

- -

7.1.4.1 7.1.4.1 SUBSONIC 4.3.1.2

-4.3.1.2 7.1.4.1 7.2.2.1

Method 2 Eq. 7.1.4.1-c I. Straight-tapered wings Eq. 7.3.4.1-a Eq. 7.3.4.1-b 2. Unear-li ft range

(a) Subsonic LE (~ cot

ALE <

I) 3. 0.25

<A<

1.0

4. Mach line from TE vertex may npt intersect LE 5. Wing-tip Mach lines may not intersect on wings nor

intersect opposite wing tips (b) Supersonic LE (~ cot ALE

>

I)

7. Foremost Mach line from either wing tip may not intersect the remote half-wing

Method I (body diameter)/(wing span) is small (see sketch (d) 4.3.1.2)

(CL.;),

2. Triangular planforms

3. 0 <~A< 4

4. M

<

0.6; however, if swept wing with

tic<

0.04, application to higher Mach numbers is acceptable

(cL.).

-Method 2 (body diameter)/( wing span) is large with delta wing extending entire length of body

(same limitations as Method I above) Method I (body diameter)/(wing span) is small

(see Sketch (d) 4.3.1.2) I. Linear-lift range

KB (W) (based on exrosed wing geometry)

(CL.),

3.

4.

5.

Triangular planforrns

Symmetric airfoils with conventional thickness distribution

O<M<4

(34)

DERIVATIVE CON FIG.

cL.

WB

•

(Contd.) (Contd.) WBT SPEED REGIME TRANSONIC (Contd.)

SUBSONIC

(Datcom section for components indicated)

(cl,Js

---~

Method 2 (body diameter)/(wing span) is large with delta wmg

j

extending entire length of body

I

(same limitations as Method 1 above) Method ! (body dlameter)/(wing span) is small

(see Sketch (d) 4.3.1.2) I. Straight-tapered wing 2. Linear-lift range

K

8 (W) (based on exposed wing geometry)

( cl,),

(a) Subsonic LE (~ cot ALE < I)

3. Mach line from TE vertex may not mtersect LE 4. Wing-tip Mach lines may not intersect on wings

nor intersect opposite wing tips (b) Supersonic LE

W

cot ALE

>

I)

6. Foremost Mach line from either wing tip may not intersect remote half-wing

Bodies of revolution

-Method 2 (body diameter)/(wing span) is large with delta wing extending entire length of body

(see Sketch (c) 4.3.1.2)(limitations of Method I)

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

(c )

L,; WB

q"

2. Triangular planforms

3. 0 <~A< 4

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

6. Valid only on the pl<tne of symmetry

USAF STABILITY AND CONTROL DATCOM