INITIAL ESTIMATION OF AIRPLANE DRAG

Chapter 5. Design for performance

5.3. INITIAL ESTIMATION OF AIRPLANE DRAG

At this stage, the fuselage dimensions tf, bf and hf will generally be known from a layout drawing, or may be estimated from statistical data (e.g. from Figs. 3-12 and 3-13). The fuel weight fraction can be es-timated from comparable aircraft types or from Fig. 5-1 for turbopropeller aircraft

1.5

1.0

and Fig. 5-2 for turbojet aircraft. The en- .5 gine weight will be known once the engine

is chosen. Otherwise 5 to 6% of the takeoff weight may be assumed as a typical value.

component. For wings with thickness/chord ratios of up to 20% and slender fuselages (length/diameter ratio greater than about 4), skin friction drag is predominant and it is customary to deduce the drag coeffi-cient of the components from their wetted area. Table 5-1 shows typical low-speeddrag figures for various classes of airplanes in the cruise configuration.

CD e

high-subsonic jet 0

aircraft .014 - .020 .75

-

^.85*

large

turbopropel-ler aircraft . 018

-

^.024 .80 - .85 twin-engine

pis-ton aircraft .022

-

^{.028 .75 - .80}

small single en-gine aircraft

retractable gear .020

-

^{.030 .75}

-

^.80

fixed gear .025

-

^{.040 .65}

-

^.75

agricultural air-craft:

-spray system

re-moved .060 .65

-

^.75

-spray system

in-stalled .070 - .080 .65

-

^.75

*The higher the sweep angle, the lower the e-factor

Table 5-1. Drag figures for various air-craft types

5.3.2. Low-speed drag estimation method

The example of a drag prediction method presented in this section, is a very ele-mentary approach, which can be refined if desired. A more detailed drag prediction method is given in Appendix F.

The drag of an aircraft component may be estimated by comparing it to the friction drag of an equivalent flat plate having the same wetted area and length. For this com-parison to be valid, the boundary layer must develop in a similar manner for both cases and therefore the Reynolds number, with respect to the length, must be equal, while the transition from laminar to

,tur-bulent flow is assumed to occur at the same distance from the nose or leading edge.

A second condition which must be fulfilled for the flat plate. analogy to be valid is that there should be no appreciable regions of separation, and the aircraft components should therefore be well-streamlined, mod-erately cambered and smooth in shape. With regard to sharp corners, rear fuselage up-sweep or short stubby fuselage tails, for example, the flat plate analogy yields no realistic answers. In such cases reference should be made to experimental data, a val-uable collection of which is to be found in Ref. :S-12 .

To account for distributed surface irreg-ularities and roughness drag, the boundary layer is sometimes assumed to be fully tur-bulent. In this case the friction coeffi-cient according to Prandtl-Schlichting, based on the wetted area, is given by:

c = .455

F (log Re)2.58 (5-12)

This equation is depicted in Fig. 5-5 in a normalized form, i.e. the value of CF for Re = 10 8 is taken equal to 1. To account for the thickness of the body, shape fac-tors representing the ratio of actual drag to flat plate drag are given in literature for wing sections and circular streamline bodies (e.g. in Ref. 5-12). For each air-craft the exposed (wetted) area must be calculated, interference effects estimated and extras added to account for protuber-ances, flap and control surface slots, cockpit windows and the like (Appendix F).

A detailed drag estimation is usually a very elaborate exercise, for which most airplane manufacturers have developed their own procedures. For the purpose of sizing the airplane and the engine, a somewhat simplified approach based on statistical data is suggested here. In the presentmeth-od, the zero-lift drag will be calcuJ.ated according to the following basic equation:

The various contributions will be explained

1.8

1 cessna 112 10 L-104~

2 Ct\erokee

,

F-28

'

^{cessna 414} 12 BAC·l-11 4 Seneca

,

Trident

rAe

• •

^Duke Potez 840 ¹⁴ 1S DC·9 ^Britahnia

Viscount 16 Caravella

F-27 17 KC 135

•

^OC-68

, ^,.

^707/320 DC-8 20 c-sA

.a

o·' deduced from performance data

Re= ~

f 'Vcr

below. Base* drag is not included but may be accounted for, if present, by assuming 6(C0S) = .13 times the projection of the base area on a plane normal to the flow.

a. Wing.

Uncorrected drag area for smooth wings:

where rw

t/c A .25

s

(5-14)

1.0 for cantilever and 1.1 for braced wings

mean thickness/chord ratio sweep angle at the quarter-chord line

gross planform area (Appendix A-2)

Eq. 5-14 is derived from the flat plate analogy and a typical thickness correction for t/c up to .20. The "uncorrected" drag figure applies to a smooth wing with the transition region at approximately 10% of the chord, for a Reynolds number of 12.5 million, based on the geometric mean chord length.

*

Base: a surface, usually at the rear end of the fuselage, more or less normal to the flow.

150

b. Fuselage.

Fig. 5-5. Correction factor on c₀ for scale effects, roughness, etc 0

Uncorrected parasite drag for streamline shapes:

(5-15)

fuselage length, including propeller spinner or jet engine outlet, if present,

bf,hf= max. width and height of the major cross section, including canopy, shape factor, i.e. the ratio of ac-tual wetted area to that of a fuse-lage with elliptical or circular cross-section and cylindrical mid-section, for which rf = 1.0, 1.30 - rectangular cross-section, 1.15 - one side of cross-section rectangular, other side rounded off,

diameter

.65 + 1.5 length - fully stream-lined fuselages without cylindrical mid-section.

The "uncorrected" drag figure applies to a fuselage with fully turbulent boundary layer, for a Reynolds number equal to 100 million, based on if. Calculations have shown that the thickness correction, multi-plied by the ratio of gross wetted area to the cylinder area .5 ~ if (bf+hf), yields an almost constant value of approximately .93 for most practical length/diameter

ra-tios. Great care should be taken when applyinq eq. 5-15 to aircraft with rear fuselaqe upsweep, bluff canopies, etc. , .for which considerably hiqher draq fiqures must be expected {cf. Section 3.5.1. and Fig.

3-27).

c. Tailplane.

By analyzing tailplane drag in the same way as the wing drag, it was found that in practical cases the tailplane contribution amounts to roughly 24% of fuselage plus wing drag; hence rt = 1.24 is a good aver-age. On STOL-type aircraft rt may be as high as 1.30 due to the relatively large tailplane area.

d. Engine installation and nacelles.

The parasite areas will be related to the installed thrust or power, in order to ac-count for variations of nacelle or intake scoop size and shape with engine thrust or power.

TURBOJET ENGINES

The isolated engine pod is taken as the reference case; its wetted area can be re-lated to the engine mass flow, taking due account of differences in pod design for variation in bypass ratio. On the basis of actual pod shapes and wetted areas, an un-corrected friction coefficient of .003 and typical scr~bing and supervelocity drag values for cruising flight, the following expression was found:

{C S) (5+A) Tto

D n= 1 · 72 rn rthr 1+A ~t p

0 0

{5-16) where Tto and Wto refer to standard SLS conditions and

rthr = 1.0 - thrust reversers installed,

= .82 - no thrust reversers.

The factor rn is an installation factor to account for pylon and interference drag in the case of podded engines. For buried en-gines rn represents drag due to intake scoops, exhaust pipes, etc.

The following figures are suggested as typ-ical:

1.50 - all engines podded

1.65 - two engines podded, one buried in fuselage tail {this figure includes internal drag of the central inlet) 1.25 - engines buried in nacelles, attached on the side of the fuselage 1.00 - engiRes fully buried, intake scoops on fuselage

. 30 - engines fully buried, wing root intakes

It should be noted that the factor {5+A)/

(1+A) in eq. 5-16 has no physical meaning;

it has been derived on a statistical basis from the ratio of wetted area to frontal area for actual engines with varying by-pass ratios.

TURBOPROP ENGINES

The uncorrected nacelle drag is:

(5-17)

where Pto and ~to refer to standard SLS conditions and

1.0 - ring-type inlets

1.6 - scoop-type inlets, increasing the frontal area

Eq. 5-17 is based on a typical drag coef-ficient .065 based on the nacelle frontal area, while for ring-type inlets the en-gine frontal area is approximately 65% of the nacelle frontal area.

PISTON ENGINES Wing-mounted:

(5-18) where Pto and wto refer to SLS-ISA condi-tions and

c

= nacelle frontal area n cylinder volume

Typical values for wto may be obtained from Section 4.2 or from engine manufacturers' data. A favorable effect of size is re-flected in the factor 'n' which is of the order of .012 to .015 sq.ft per cu.in.

(.07-.09 m2/liter) for engine powers up to

500 hp, but may go down to .OS to .07 sq.ft per cu.in. (.03 to .04 m2/liter) for the 2,000-4,000 hp class.

Fuselage-mounted tractor engines:

(5-19)

e. Undercarriage.

For undercarriages which are fully retract-ed within the airplane external lines* a drag penalty is not necessary (rue= 1.0).

Other values can be derived by retracing differences in measured performance of air-craft with fixed and retractable gear ver-sions and from published data on drag:

rue 1.35- fixed gear, no streamlined wheel fairings

1.25 - fixed gear, streamlined wheel fairings and struts

1.08 - main gear retracted in stream-lined fairings on the fuselage (like C-130 and C-5A)

1.03 -.main gear retracted in na-celles of turbopropeller engines

f. Wing tip tanks.

A typical figure, such as ~(c0^s) = .055 times the tank's frontal area, should be added to eq. 5-13. To compute the effective aspect ratio, the effective wing span and area should be taken as the distance and area between the tank centerlines (Ref.

5-12).

g. Corrections for Reynolds number and mis-cellaneous drag.

It can be argued that interference effects, surface irregularities, excrescences, air scoops, aerials, slots, etc. generally af-fect the boundary layer more on small low-speed aircraft than they do on large high-speed aircraft, due to differences in rel-ative size and emphasis on pure aerodynamic design. In evaluating the present method, the ratio of actual measured to basic zero lift drag was therefore plotted versus the Reynolds number, based on fuselage length

(Fig. 5-5).

*i.e. no wheel fairings are required

The following approximation accounts for the effect of the Reynolds number on tur-bulent skin friction drag and miscellane-o.us drag items:

actual zero-lift drag coefficient*=

rRe~ uncorrected drag coefficient

where

47 Re -· 2 f

vcr 1 f

"cr

(5-20)

(5-21)

The subscript "cr" refers to the design cruising altitude and speed. Figure 5-5 shows that the miscellaneous drag contri-butions amount to 25-30% for light aircraft and 10-15% or less on large transport air-craft. The rms error of the method is 4%, but this figure also allows for inaccuracy in the available data on drag polars.

5.3.3. Compressibility drag

Compressibility effects on drag are gener-ally ignored at Mach numbers below .5. The drag polars of a high-subsonic transport aircraft in Fig. 5-6 illustrate that for

.8

CL .75

.6 .80

.4

Fig. 5-6. Effect of compressibility on the drag polar

*including excrescences, protuberances, roughness, etc.

low CL values and Mach numbers up to .70 the effects of compressibility on drag are of secondary nature. Between M

=

.70 and .80 a steady increase in the drag is ob-served ("drag creep") and at a critical Mach number of approximately .85 a rapid rise is experienced in both the zero-lift drag and the induced drag. This drag rise is caused by shock waves and boundary layer separation induced by these shock waves.

The endeavor to achieve low compressibility drag, or rather a high drag-critical Mach number, is one of the most comprehensive tasks in aerodynamic design. This subject is dealt with more fully in Section 7.2.

For the purpose of initial design calcula-tions, it is fair to assume that the aero-dynamicists will achieve acceptable drag figures at the design cruising speed, pro-vided that wing sweep and thickness ratio are chosen appropriately. We may therefore assume that:

/\CD ^.0005

-

long-range cruise

condi-camp _tions

/\CD ^.0020

-

high-speed cruise

condi-camp tions

5.3.4. Retracing a drag polar from perfornr ance figures

In ord<;>r to compare an estimated drag polar with the drag figures of existing air-planes, drag coefficients may be deduced from performance data as supplied by the airplane manufacturer. To do this for a given type of aircraft, the lift coeffi-cient in cruising flight is calculated first,

C = W/S ]

L cr ~pV 2 cr (5-22)

Cruising altitude and speed are obtained from the manufacturer's brochure or other appropriate publications. The drag due to lift,

(5-23)

is estimated by assuming a typical value for e (cf. Table 5-l) and taking a condi-tion with a fairly low CL. As thrust equals drag in cruising flight, we may write:

or

cr

(jet airplanes)

(propeller airplanes)

(5-24)

(5-25)

For jet-propelled aircraft, T is the in-stalled thrust, which is lower than the un-installed thrust due to bleed air, power offtakes and inlet pressure loss. A typical figure may be 4% reduction, but for high bypass engines it may well be as high as 8%.

For propeller aircraft np represents the combined effect of installed propeller ef-ficiency, extra drag of aircraft components in the slipstream, intake losses, power and bleed air offtakes and cooling drag. Typi-cal figures are:

np = .85 - turbopropeller engines (includ-ing jet thrust)

.80 -wing-mounted piston engines .78- tractor piston engine in fuse-lage nose.

Cruise power or thrust may be obtained from the engine brochure for the appropriate rating, altitude and flight speed. In the case of piston engines, ratings are usual-ly 75% or 65% rated power for performance and economic cruising respective!y. Final-ly, the zero-lift drag is calculated:

(5-26)

A more accurate determination can be made by analyzing several flight conditions in a similar way. By plotting the values of CD vs CL , CD and e can be found by a 2 straight-line⁰approximation, in the manner indicated in Fig. 5-4.

5.3.5. Drag in takeoff and landing

Drag in the en route configuration deter-mines the cruise thrust and hourly fuel

2.5 CL 2.0 1.5 1.0 0.5

Fig. 5-7. Low-speed polars for a light transport

20

15

5

envelope specific flap system

--takeoff flaps---1

!---landing flaps-

o+---~--~---T--~----~--0 0.5 1.0 1.5

Fig. 5-B. Typical locus of lift/drag ratios for the takeoff safety speed

4.5

4.0

3.5

3.0

2.5

.3 .4 .5

o--<>

OC-!V30 BAC-1-11

727-100 737-100 747

!Jo••-Q F-28 Mk 1000 (t F-27

• L-1049

.6

Fig. 5-9. Generalized takeoff lift/drag ratios

consumption. Alternatively, drag in the low-speed configuration (flaps deflected) determines the permissible takeoff weight for a part·icular flight of a passenger air-liner and hence the maximum use;uJ

load~

On a hot and high airfield, a limitation on takeoff weight may result in a reduced pay-load or a restricted fuel weight and range.

In such a case a drag deterioration of 10%

may result in 30% less payload to be carried.

Typical polars for several flap deflections for takeoff and landing are shown in Fig.

5-7. As the available climb ^grad~ent,

y =

w

T ^(5-27·)

depends on the lift/drag ratio, the aero-dynamic characteristics are sometimes plotted accordingly (Fig. 5-Bl~* For each flap angle, the L/D ratio at the takeoff safety speed

v

₂ are indicated on the curves.

A line connecting these points forms an envelope or locus, which is useful in corn-paring one flap system with another.

Since accurate prediction of the results of a flap design program is obviously impos-sible, it is useful to compare the v₂ locus on a basis of generalized parameters, by writing the drag polar as follows:

c /C (CD /A

~ = ___ o___ +

lA

CL (5-28)

The values of CD and e refer to the con-figurations with⁰flaps deflected. Fig. 5-9 presents a collection of some published

v

₂

loci. The following approximation is sug-gested for preliminary design purposes:

(5-29)

.018, E .005, E

.70 slats extended .61 no slats or slats

retracted.

*Definition in Section B. 2 .1.

**A more complete figure is shown on Fig.

11-4

Note that this equation does not represent an actual aircraft polar; it refers to the initial climb-out after takeoff. To include drag due to engine failure at low thrust/

weight ratios, E may be reduced by approx-imately 4% for wing-mounted engines and 2%

for engines mounted on either side of the fuselage tail.

Although the accuracy of eq. 5-29 for the approach and landing configurations is probably not so good, due to the higher ra-tio of flight speed to stalling speed, it still remains. a useful first-order approx-imation.