4.1 Some Comments on Fuselage Drag

Jan Roskam

University of Kansas

11003

lntroduct ion

This paper focuses on the following areas relating to fuselage drag:

1. Fuselage fineness - ratio and why and how this can be selected during

prei iminary design;

2. Windshield drag;

3. Skin roughness; and

4. Research needs in the area of fuselage drag.

Fuselage Fineness Ratio and How It Can Be Selected

Table 1 presents some data on fuselage fineness ratios for several current

general aviation airplanes. It is interesting to note, that with one exception, all

have values of around _B,/d = 5 to 6. In Reference 1, the fuselage (or body) drag

is estimated from.-

0v )wi_ 5

This equation assumes zero base drag. Figure 1 shows how the C J-term in

equation (|) is related to 9_Jd. Note that the r _-terrn no longer decreases significantly

significantly after _ B/d = 6.0 is exceeded. This would indeed suggest that values of

5 to 6 for _ B/d are about optimum. However, there are three other factors to

contend with:

1. increasing _B/d will decrease CfB ;

2. increasing 9_B/'dwill increase Swet ; andbody

3. increasing _,B/'d will decrease tall wetted area requirements, for constant

stabll ity levels.

It appears that a more detailed examination of fuselage fineness ratio is there-

fore in order. The next section presents a method for minimizing the sum of fuselage and

empennage friction drag, under a constant directional and Iongffudlnal stabillty

constraint.

Preceding Page Blank

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Figure 1. Body Zero-Lift Drag Factor as a Functionof Body Fineness Ratio

Table 1. Examples of Fuselage Fineness Ratios and Wetted Areasfor General Aviation Aircraft

Type gB Swingd

Cessna 210 5.'02 175

Cessna 207 s.6g 174

Beech Sierra 5.22 146

Cessna 185 5.15 176

Beech Bonanza ('58) 4.98 181

Beech Baron 5.69 199.2

Piper NavaJo 5.97 229

Cessna 310 5.40 179

Piper Seneca 5.68 206.5

Beech Duke 5.59 212.9

Cessna 414 5.52 195.7

Beech King Atr 6.06 294

Gates Lear_et 24 8.8 _ 232

Swet Swet_°_

S_'i ng

319

425

332

292

323

362

502

306

356

586

488

552

502

1.82

2.44

2.27

1.68

1.78

1.82

2.19

1.71

1.72

2.28

2.49

2.22

2.16

88

A Method for Minimizing General Aviation Airplane Fuselage and Empennage

Friction Drag

Fuselage Drag - The objective is to show how fuselage drag and

empennage friction drag can be estimated under constant static stabillty constralnts.

It is assumed that the fuselage from nose to passenger compartment is defined

roughly as in Figure 2.

-EN

Figure 2.

222.__

Definition of Fuselage in Two Parts

It is also assumed that the tall cone can be represented by a skewed cone as

in Figure 3.

Y/

Figure 3. Modeling Aft Fuselage as a Skewed Cone

The equivalent fuselage diameter is defined such that:

(2)

The wetted area of the fuselage can now be written as:

1_¢rj_. _ 0._ r__...__ r (3 )

89

whereF isa correction factor accounting for the fact that the rear fuselage is not

a cone. F can be found by comparison to existing aircraft.

The Fuselage Drag coefficient (zero-llft) can be expressed as:

= + ,,_, z,--, _*-

Allsymbols are defined in Reference 1. Fuselage base drag is neglected.

For given _'c , CDofu s can thus be computed as a function of _c"

(4)

Empennage Drag - The horizontal tail wetted area may be approximated by.

(5)

where the geometry is defined in Figure 4.

_" I ...... _'--_

Figure 4. Horizontal Tail in Relation to Fuselage Cone

fhe horizontal tail drag coefficient can be written as:

N.-r. .. . C. N.T.I

where all symbols are defined in Reference 1.

Th_evertical tail wetted area may be approximated by"

%T ( ' ".. _ 1.0/

where the geometry is defined in Figure 5.

_T-H.'T.

L._. _"_w i_.,-_(6)

(7)

9O

I I---- I I

ic fl

Figure 5. Vertical Tail in Relation to Fuselage Cone

The vertical tail drag coefficient can be written as:

(8)

where all symbols are defined in Reference 1. Horizontal and vertical tall sizes

are here assumed to be determined by minimum stabillty requirements, i.e., :

CI"II_M,_. and _ w,_ MI'_.

Directional Stability - Neglecting the wing contribution, the directional

stability of an airplane can be written as:

C_(__ C.(_, ÷ c._ v r,, ._ \ _v

where the symbols are defined in Reference 2. The geometry is defined in

Figure 6.

(9)

91

..... i ......

'l

, ii i

Figure 6. Fuselage Geometry for Estimating Directional Stability

Note than K N and KR9_ are functions of _,c.

be expressed as:

where F is as in equation (3).

Note that:

and

Body side area, SBs can

(lO)

_v. _ C,_F.,_I.,v,C,'_ as illustrated in Figure 7. (12)

92

Figure 7. Definition of _v for Swept Vertical Tall

From the sketch the following equations may be deduced:

!

z. _v

(13)

(14)

(15)

(]6)

(17)

Now, substitute equation (13) into (9) while using equations (14), (15), and (16):

* 7,_/_,,C i+-TjC_J _-_v

For preselected values of _,,, , _ , C_,O,,_, _ j _ 'J

_wa _ and ._.t._v ._

it is now possible to solve for Sv for any given value of _'c"

Having done that, it is possible to compute CDov.T. as a function of 1C

93

Longitudinal Stability - Longitudinal stability can be expressed by."

(19a)

(19b)

where all symbols are defined in Reference 3 and where:

(20)

as shown in Figure 8.

and

Figure 8.

It is assumed, that _X'#c_ug j

Definition of Horizontal Tall in Relation to Fuselage

"_ _d._ _,<,,-._

_%¢w are known and fixed quantlties.The followlng expressions can be shown to hold:

-4- __...H2.

2 _,.,d-R.= (_+>,.)_

(21)

(22)

(23)

(24)

(25)

94

Plugging equation (21) into equation (20) and using equations (22) through (25) it is

found that:

26)I ' I

Now, setting dCm/dC L = some constant value and preselectlng: AH, _H and

ALE H , it is possible to solve for SH (using equation (19) for any given value of _'c"

Having done this, it is possible to compute CDoHT as a function of _c ).Parametric Study -The methods of of the previous sections allow the

and for given values of ALE(H,V )computation of CDofus, CDoh.t. CDov.t.

and for given values of _c"

These contributions can be plotted against _ c/d as shown in F igure 9.

Figure 9. Plotted Results of Parametric Study

If need be this process can be repeated for a variety of empennage sweep

angles. The rear fuselage length _'c for minimum fuselage plus empennage drag can

be readily found from Figure 9.

It would be of interest to include the effect of weight in this parametric

study.

95

F|gure 9a shows some results obtained from calculations using a Beech King

Air as example. It is seen that the airplane fuselage plus empennage drag is indeed

not optimum from this point of view. It would be of interest to extend this analysis

to other airplanes.

.......... -J ...... : .'.=..; ...........

10 • 0 JO *tO .fO _0 I'0

Figure 9A. Effect of Tailcone Length on Fuselage Plus Empennage ZeroLift Drag Under Constant Stability Constraints

96

Windsh|eld Drag

Reference 4 presents a series of systematic data for windshield drag of small

and transport type airplanes. It summarizes by stating that windshield drag can

range from 20 to 1 percent of airplane drag depending on how well they are faired.

This is a wide drag rangel

Figures 10 and 11 illustrate the types of windshields investigated in

reference 2.

Figure 12 illustrates a range of windshields found on current general aviation

airplanes. It is seen that windshields of 1975 are quite different from those that

prevailed in 1942. It would seem that some systematic research into this area would

pay off for certain airplanes.

Surface Finish

The subject of skin waivlness and surface finish has not been brought up,

because of the strong interplay with production and tooling costs. However, as

shown in Figure 13 there is probably considerable room for improvement. This could

be attained by a more wide spread use of metal bonding in aircraft _:abrlcatlon. This

way, it is feasible to maintain large areas of laminar flow over the forward part

of the fuselage and capitalize on the resulting lower friction drag.

Research Needs

The fuselage typically accounts for 30 to 50 percent of total airplane drag.

it seems that improvements of at least 10-20 percent could be made by taking a goodresearch look at:

1. fuselage fineness ratio;

2. windshield drag; and

3. low cost application of metal bonding to reduce skin frlct ion drag.

It would seem that research in the area of windshield drag should be in the

form of a series of systematic wind tunnel tests.

Optimization of fuseiage fineness ratio could be achieved through the

development of an appropriate computer program which would also account for the

effect of weight.

97

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Figure 10. Drag of Fuselage with Transport-Type WindshieldsMt 0.35; V, 265 mph

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Figure 11b. Effect of Retaining Strips,Combinations 1-1-3 and 3-1-3, M,0.34; V, 260 mph

99

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Cessna Skywagon 207Beech Duke B60

Figure 12. Typical General Aviation Windshields for 1975

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Refere noes

•

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o

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Roskam, J.; Methods for Estimating Drag Polars of Subsonic Airplanes;Publlshed by Roskam Aviation and Engineering Corporation; 519 Boulder,Lawrence, Kansas 66044.

Roskam, J.; Methods for Establishing Stability and Control Derivatives ofConventional Subsonlc Airplanes; Publlshed by Roskam Aviation andEngineering Corporation; 519 Boulder, Lawrence, Kansas 66044.

Roskam, J.; Flight Dynamics of Rigid and Elastic Airplanes; Publishedby Roskam Aviation and Engineering Corporation; 519 Boulder, Lawrence,Kansas 66044.

Robinson, R.(3. and Delano, J.B.; An [nvestlgation of the Drag ofWindshields in the 8-foot High Speed Wind Tunnel; NACA TR 730, 1942.

102