Document
11003
4.1 Some Comments on Fuselage Drag Jan Roskam University of Kansas 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.- v
0 )
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/'d will increase Swe t ; and body 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
• d i!: ihl'I ,_:_ 'V" ..._ i!•[,i!
...... .h, ,C! _,' ''i 'i"". ii i'i:" !
'.!'!: !i::L .' :i' _J:; i! I: I_ ./i . !i._ _ . x" :: ;I!:i I, ;,q _!.:: ....... , .r •
" _i ii,!:i
:': I; i':: .. HIIII t,..i!i! i :! _ii;;l : I. f.i' q i: :U i: !!!:_ i!i. !!i_ I_dL:l: ..I.
:i[ili!!i ;:_I Ii]l l-;cl::!_:: !. i_iii:!!i:i;! ;
i!iiiii!i _!l{!itiI{i'_il!i!,l
:!ill. ! :I;il
ii!i!i _:H:. H .... • ' i,:t;.! i! il!ll
eJ I-!7 !T_ .i :_:il_i:_i:!::ii: : ,!i!l'!:i :":_'; o :..k: i_i::.I'_i :I:I_ Ii*,ill O ..!:i : i;liii:i_ ii..!i.7/.:i:l:i _ .:,. ::::_.......
ii_ii:_:!i_!!i!
iTli :i !:ilii!:.
41, :];._;!I; iKI II'l:iPii• i ,...; !;:i:l':V .,l.t,,h :!t_?1_i!t',!, :::12;::: i_!_i!_ • i:Ii::! :i:!lh_!
!!i:_!i'_! :.!iiii!.!I:iiliil_il "::i i"?i?!!'Li' :7" .,,,;,.-_:_!_ ::i;i..ki_ i_ :i_ :_!: '!_:!:X
,,';,iiii_,[i_,{ibi
6' IO 12 o 2 /..i [_O_Y FINI:NgS_ RA'_IO _ "l_/d.
Figure 1. Body Zero-Lift Drag Factor as a Function of Body Fineness Ratio Table 1. Examples of Fuselage Fineness Ratios and Wetted Areas for General Aviation Aircraft Type gB Swing Swet Swet _°_ d S_'i ng Cessna 210 5.'02 175 319 1.82 Cessna 207 s.6g 174 425 2.44 Beech Sierra 5.22 146 332 2.27 Cessna 185 5.15 176 292 1.68 Beech Bonanza ('58) 4.98 181 323 1.78 Beech Baron 5.69 199.2 362 1.82 502 2.19 Piper NavaJo 5.97 229 Cessna 310 5.40 179 306 1.71 Piper Seneca 5.68 206.5 356 1.72 Beech Duke 5.59 212.9 586 2.28 Cessna 414 5.52 195.7 488 2.49 552 2.22 Beech King Atr 6.06 294 Gates Lear_et 24 8.8 _ 232 502 2.16 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.
222.__
-E
N Figure 2.
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 )
where F is a 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: (4)
= + ,,_, z,--, _*-
All symbols are defined in Reference 1. Fuselage base drag is neglected.
For given _'c , CDofu s can thus be computed as a function of _c" 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: _T- H.'T. (6) N.-r. .. . C. N.T.I L._. _"_w i_.,-_ where all symbols are defined in Reference 1.
Th_e vertical tail wetted area may be approximated by" (7)
%T ( ' "
.. _ 1.0/ where the geometry is defined in Figure 5.
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
(9)
where the symbols are defined in Reference 2. The geometry is defined in Figure 6.
..... i ......
'l
, i
i i
Figure 6. Fuselage Geometry for Estimating Directional Stability Body side area, SBs can Note than K N and KR9_ are functions of _,c.
be expressed as: (lO) where F is as in equation (3).
Note that: and _v. _ C,_F.,_I.,v,C,'_ as illustrated in Figure 7. (12) Figure 7. Definition of _v for Swept Vertical Tall From the sketch the following equations may be deduced: (13)
(14)
!
(15)
z. _v
(]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" C Having done that, it is possible to compute CDov.T. as a function of 1 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.
Definition of Horizontal Tall in Relation to Fuselage Figure 8.
"_ _d._ _,<,,-._
It is assumed, that _X'#c_ug j and _%¢w are known and fixed quantlties.
The followlng expressions can be shown to hold: -4- __...H (21) 2.
(22)
(23)
(24) 2 _,.,
(25)
d-R.= (_+>,.)_
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.
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 Zero Lift Drag Under Constant Stability Constraints 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 good research 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.
_IACA REPORT NO. 730 C_, O80 .k b
i _ J
,.I
U
t
J
/
O.J -4 -.3 -2 " -I 0 o-5 Fuseloge o/'_/e of offock.d F ,deg Figure 10. Drag of Fuselage with Transport-Type Windshields Mt 0.35; V, 265 mph t4ACA "T_ _nofi_ _ r'etoin,r_ _friD o ....
Ce_l_,'lot;o_ ono _ r-#rcV,.*_ strtD (/" / -Z) •
)"
I _l-J) a _ (T-__ ,-- P'/'s)c .'f_ (1 O_ • • s.
V j _3-/-3 I .
/: /.]
• p J , I _.1( / ,.c f- j/ e __ ....... --_-'_. I ,'_'-' _J '_,., t
I
at,,,, str;p e, (/-/.3)e.(I-/-J) .,,,_ -4 -3 -_ -/ 0 4r • "4 -J -_. -I .0 .
.F_/$e/og_ o,._/e of oHock, dy, de 9 Fmelog# o_.gl¢ of attack, _, ro deg Figure 11a. Effect of Retaining Strips Figure 11b. Effect of Retaining Strips, Combination 1-1-3, M, 0.34; V, 260 Combinations 1-1-3 and 3-1-3, M, mph 0.34; V, 260 mph Beech King Air AIO0 Grumman American AA-S Traveler " Piper Cherokee Warrior Gates Learjet 24D Cessna Cardinal RG Beech Duke B60 Cessna Skywagon 207 Figure 12. Typical General Aviation Windshields for 1975 NACh_ TR c_to 0/. • •_o. o,-,_, _°""w_p"_-'k-" " " , L,q/_tly sanded [ .08'6 --_--o Both 8_r'fOC#$ q/ozed tO OI2t -- --O Ulaloe? $_-foee g/ozed b#/-_d o12e _ __ __
oo7 .,,.t
Lower $_r£oce q/ozeGf fO 0/_¢
-
_--------_ U#_oe? S_(OCe p_tedto 071C-- h OG4 0/2 ' Lowc_- s_='foce oo=_t_d to 012c| -- 9 8of#_ _£oc_$ pa.;_fec/ to 0 71¢ 4-- .8 /2 _G L_O Pa _8 _./0 _ F_ey_oCts _umDef, R +.
I l--l,@, cI,--Q 2 !
&irt'oll
7-
leetlolL ¢_0.I.
,o,I t i 12] O/ 8 12 16 20 24 28 32_P0 e t I" I ' I ScJ_ VOte CO_t,O_ i;_C-c/_rO_ofe pr_ (=) Medel 1. NACA e_(21e)-=(lQ+_ (ml)lWt_.) airfoil :llecllon. ¢|=03. .01 • tc+_nt.d o_Cl 9.0zed -- -- I I II .0_ , .._r" fOCe conoShO._ .=;,0,_1 [ I ' ' ' ' ' I ' GOzed or_ _te@ .06 _ .oosi I I
.-- . o Refo, fed [ ] 7--77+111!
rel u i r"--_ + , !-- IP s6 _ 2'a . _ 3_x I0 _ (.} ]_d,' q _ACA 66('15) 116 l:.O. ¢,. _Oj} "irfoil 8 12 16 _0 24 28 32x10 c (b) Model 2 N.I+CA 66(215) 214 (=pprol) sirloil _ct/ol_ c.=0 13_ ..... o As fece, v¢_ COvere_ -- _.01_ -- <+ 5o_ed d----f----P,-- .0/£ Fo_r-_C 5_r'foce_ _e_C_e_ | S,.,-roce co_a,_ I I I ,t ; /_oee recto//4---- • o O,'+,c/no_, bo, e-_'_o/sk,n _- t-- .Ol_ + -- - • t_O_te_l 0f_ Over" - -J+--'-'P-- .+-__i'T" I i I i
l! i
I+n_ I I I 1 t I t _ I 8 l_ 16 _0 _ _8 3_xlO _ 8 12 /6 PO P_ P8 3_x tO • Reynot_$. _umbe_. R Reyrm/o_s _umber, R (O Model 6, ND.CA _(215)-118 pr_ti_l-4_rl_trlJlrllon llU.loil l_iolt, r,-_l_ _lplw (_ Model = I_.qCA _¢215)116 si_oil Ik-elioo. ¢_-O.IIk Figure 13. Effect of Surface Improvements on Drag Characteristics of Airfoil Sections lOl Refere noes • Roskam, J.; Methods for Estimating Drag Polars of Subsonic Airplanes; Publlshed by Roskam Aviation and Engineering Corporation; 519 Boulder, Lawrence, Kansas 66044.
Q Roskam, J.; Methods for Establishing Stability and Control Derivatives of Conventional Subsonlc Airplanes; Publlshed by Roskam Aviation and Engineering Corporation; 519 Boulder, Lawrence, Kansas 66044.
o Roskam, J.; Flight Dynamics of Rigid and Elastic Airplanes; Published by Roskam Aviation and Engineering Corporation; 519 Boulder, Lawrence, Kansas 66044.
o Robinson, R.(3. and Delano, J.B.; An [nvestlgation of the Drag of Windshields in the 8-foot High Speed Wind Tunnel; NACA TR 730, 1942.