PARASITE DRAG

In addition to the drag caused by the de­velopment of lift (induced drag) there is the obvious drag which is not due to the develop­ment of lift. A wing surface even at zero lift will have “profile” drag due to skin friction and form. The other components of the air­plane such as the fuselage, tail, nacelles, etc., contribute to drag because of their own form and skin friction. Any loss of momentum of the airstream due to powerplant cooling, air conditioning, or leakage through construction or access gaps is, in effect, an additional drag. When the various components of the airplane are put together the total drag will be greater than the sum of the individual components because of “interference” of one surface on the other.

The most usual interference of importance occurs at the wing-body intersection where the growth of boundary layer on the fuselage re­duces the boundary layer velocities on the wing root surface. This reduction in energy allows the wing root boundary layer to be more easily separated in the presence of an adverse pressure gradient. Since the upper wing surface has the more critical pressure gradients, a low wing position on a circular fuselage would create greater interference drag than a high wing position. Adequate filleting and control of local pressure gradients is necessary to mini­mize such additional drag due to interference.

The sum of all the drags due to form, fric­tion, leakage and momentum losses, and inter­ference drag is termed “parasite” drag since it is not directly associated with the develop­ment of lift. While this parasite drag is not directly associated with the production of lift it is a variable with lift. The variation of parasite drag coefficient, CDpt with lift coef­ficient, CL, is shown for a typical airplane in figure 1.34. The minimum parasite drag co­efficient, CDn, usually occurs at or near zero

■nwn J

lift and parasite drag coefficient increases above this point in a smooth curve. The in­duced drag coefficient is shown on the same graph for purposes of comparison since the total drag of the airplane is a sum of the parasite and induced drag.

In many parts of airplane performance it is necessary to completely distinguish between drag due to lift and drag not due to lift. The total drag of an airplane is the sum of the para­site and induced drags.

С© = (jDp~h^D і

where

CD=airplane drag coefficient CDp=parasite drag coefficient CDf= induced drag coefficient

C *

=°-318s

From inspection of figure 1.34 it is seen that both CDp and CD( vary with lift coefficient. However, the usual variation of parasite drag allows a simple correlation with the induced drag term. In effect, the part of parasite drag above the minimum at zero lift can be ‘ Tumped”

1.2

0 1.0

1 °e

ё 0.6

О

I-

u.

□ 0.4

0.2

in with the induced drag coefficient by a con­stant factor which is defined as the “airplane efficiency factor", e. By this method of ac­counting the airplane drag coefficient is ex­pressed as:

C

l I

D = ‘-‘Dp. "t

C

с»=с"-.,+°-318(ж«)

where

_ minimum parasite drag Coefficient

CDi= induced drag coefficient

e = airplane efficiency factor

In this form, the airplane drag coefficient is expressed as the sum of drag not due to lift

(CDp ( ) and drag due to lift (—0- The air­plane efficiency factor is some constant (usually less than unity) which includes parasite drag due to lift with the drag induced by lift. CDts is invariant with lift and represents the

■*min t

parasite drag at zero lift. A typical value of CB„ would be 0.020, of which the wing may account for 50 percent, the fuselage and nacelles 40 percent, and the tail 10 percent. The term

(

Q 2 <

0.318 accounts for all drag due’ to

lift—the drag induced by lift and the extra parasite drag due to lift. Typical values of the airplane efficiency factor range from 0.6 to 0.9 depending on the airplane configuration and its characteristics. While the term of drag due to lift does include some parasite drag, it is still generally referred to as induced drag.

The second graph of figure 1.34 shows that C ■

the sum of Cn„ and can approximate the

гmin g L A

actual airplane CD through a large range of lift coefficients. For airplanes of moderate aspect ratio, this representation of the airplane total drag is quite accurate in the ordinary range of lift coefficients up to near 70 percent of CLmax. At high lift coefficients near CLmax, the proced­
ure is not too accurate because of the sharper variation of parasite drag at high angles of attack. In a sense, the airplane efficiency fac­tor would change from the constant value and decrease. The deviation of the actual airplane drag from the approximating curve is quite noticeable for airplanes with low aspect ratio and sweepback. Another factor to consider is the effect of compressibility. Since compressi­bility effects would destroy this relationship, the greatest application is for subsonic perform­ance analysis.

The total airplane drag is the sum of the parasite and induced drags.

D=DP+Di Di= induced drag

=(°-318lf>

Dp = parasite drag
CDp qS

^mn

When expressed in this form the induced drag, Diy includes all drags due to lift and is solely a function of lift. The parasite drag, Dp, is the parasite drag and is completely independent of lift—it could be called the “barn door” drag of the airplane.

An alternate expression for the parasite drag is:

DP=fq

where

/= equivalent parasite area, sq. ft.

f=CDp. S

mm

q= dynamic pressure, psf

<rV2

or

293 faV2 295

In this form, the equivalent parasite area, /, is the product of CD and S and relates an

1 Pmin

impression of the “bam door” size. Hence, parasite drag can be appreciated as the result of the dynamic pressure, q, acting on the equivalent parasite area, /. The “equivalent” parasite area is defined by this relationship as a hypothetical surface with a CD= 1.0 which produces the same parasite drag as the air­plane. An analogy would be a barn door in the airstream which is equivalent to the air­plane. Typical values for the equivalent para­site area range from 4 sq. ft. for a clean fighter type airplane to 40 sq. ft. for a large transport type airplane. Of course, when any airplane is changed from the clean configuration to the landing configuration, the equivalent parasite area increases.

EFFECT OF CONFIGURATION. The par­asite drag, Dp, is unaffected by lift, but is variable with dynamic pressure and equivalent parasite area. This principle furnishes the basis for illustrating the variation of parasite drag with the various conditions of flight. If all other factors are held constant, the para­site drag varies directly with the equivalent parasite area.

■^P2_ //Л

DP1 KfJ

where

DPl = parasite drag corresponding to some orig­inal parasite area, fi

DP2=parasite drag corresponding to some new parasite area, Д

(V and a are constant)

As an example, the lowering of the landing gear and flaps may increase the parasite area 80 percent. At any given speed and altitude this airplane would experience an 80 percent increase in parasite drag.

EFFECT OF ALTITUDE. In a similar man­ner the effect of altitude on parasite drag may be appreciated. The general effect of altitude is expressed by: where

DPl = parasite drag corresponding to some orig­inal altitude density ratio, oi

Dpj=parasite drag corresponding to some new altitude density ratio, c2

(and /, V are constant)

This relationship implies that parasite drag would decrease at altitude, e. g., a given air­plane in flight at a given TAS at 40,000 ft. (a=0.25) would have one-fourth the parasite drag when at sea level (<r= 1.00). This effect results when the lower air density produces less dynamic pressure. However, if the air­plane is flown at a constant EAS, the dynamic pressure and, thus, parasite drag do not vary. In this case, the TAS would be higher at altitude to provide the same EAS.

EFFECT OF SPEED. The effect of speed alone on parasite drag is the most important. If all other factors are held constant, the effect of velocity on parasite drag is expressed as:

о*, /рл2

DPl VJ

where

Dpparasite drag corresponding to some orig­inal speed, Vt

DPi=parasite drag corresponding to some new speed, Vs

(J and a are constant)

This relationship expresses a powerful effect of speed on parasite drag. As an example, a given airplane in flight at some altitude would have four times as much parasite drag at twice as great a speed or one-fourth as much parasite drag at half the original speed. This fact may­be appreciated by the relationship of dynamic pressure with speed—twice as much V, four times as much q, and four times as much Dp. This expressed variation of parasite drag with speed points out that parasite drag will be of greatest importance at high speeds and prac­tically insignificant in flight at low dynamic pressures. To illustrate this fact, an airplane in flight just above the stall speed could have a parasite drag which is only 25 percent of the total drag. However, this same airplane at maximum level flight speed at low altitude would have a parasite drag which’ is very nearly 100 percent of the total drag. The predominance of parasite drag at high flight speeds emphasizes the necessity for great aero­dynamic cleanness (low /) to obtain high speed performance.

In the subsonic regime of flight, the ordinary configuration of airplane has a very large por­tion of the equivalent parasite area determined by skin friction drag. As the wing contrib­utes nearly half of the total parasite drag, the profile drag of the wing can be minimized by the use of the airfoil sections which produce extensive laminar flow. A subtle effect on parasite drag occurs from the influence of the wing area. Since the wing area (T) appears directly in the parasite drag equation, a reduc­tion in wing area would reduce the parasite drag if all other factors were unchanged. While the exact relationship involves con­sideration of many factors, most optimum airplane configurations have a strong preference for the highest practical wing loading and minimum wing surface area.

As the flight speeds of aircraft approach the speed of sound, great care must be taken to delay and alleviate compressibility effects. In order to delay and reduce the drag rise associated with compressibility effects, the components of the airplanes must be arranged to reduce the early formation of shock waves on the airplane. This will generally require fuselage and nacelles of high fineness ratio, well faired canopies, and thin wing sections which have very smooth uniform pressure dis­tributions. Low aspect ratios and sweepback are favorable in delaying and reducing the compressibility drag rise. In addition, inter­ference effects are quite important in transonic and supersonic flight and the airplane cross section area distribution must be controlled to minimize local velocity peaks which could create premature strong shock wave formation.

The modern configuration of airplane will illustrate the features required to effect very high speed performance—’low aspect ratio, sweepback, thin low drag sections, etc. These same features produce flight characteristics at low airspeeds which necessitate proper flying technique.