Class II Methodology for Drag Estimation

PRJ-22 Aerospace Design Prof. Bento S. de Mattos

V20 – June 2009

Weight Estimation Using Class II Drag Calculation Method

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.



















Content • Fundamental principles

eroo-lilifft dr drag ag • Zer nduc uce ed drag • Ind • Wave drag

Clas ass s ex exer erci cise se • Cl





















Total drag of the airplane Ref.: TORENBEEK, E. – E. – “Synthesis of Subsonic Airplane Design”, Airplane Design”, Kluwer, 1982 (pg. 368).





















Total drag of the airplane





















Total drag of the airplane





















Total drag of the airplane • Zero-lift, or parasite, drag

C D,0 = C D,0,form + C D,0,friction • Induced drag, or drag due to lift C D,i = kC L2 =C L2 / p e peA A • Drag due to compressibility, compressibility, or wave drag C = C (M)























Drag and Required Power

Power (P) = Thrust (T) x Speed (V) Induced Drag Di ~ W2( b V)-2

“Parasite” (viscous) Drag Dp ~ Swet V2

Power ( P)required =





















C D0

CD0

C





















Drag Drag Br Brea eakd kdow own n of a Compl Complet etee Air Airpl plan anee Conf Config igur urat atio ion n





















Aerodynamic drag components acting on aircraft

Horizontal

Vertical tail drag





















Class I Method

C D 0  C fe

S wet S ref























Theoretical Background – Class II Method





















Theoretical Background – Class II Method





















Skin friction drag





















Laminar, Laminar, transitional, & turbulent Flow





















Skin friction drag in turbulent flow







































































































































































































































































Interference Factor





















Interference Factor





















Interference Factor





















Interference Factor





















Interference Factor Roskam suggests that the value for the wing-fuselage interference factor should be taken from the graph below























Interference Factor Estimated values of interference drag originating in the corners of various tail configurations





















Miscellaneous Parasite Drag





















Miscellaneous Parasite Drag The drag of some items does not quite fit the form must be computed in an alternative manner. Table below gives values of f /Afrontal , the equivalent flat plate drag area normalized by the projected frontal area, of landing gear components. Deployed flaps have a drag area given roughly by





















Drag Caused by Flap Deflection Definition of flap drag @ 0.70 CL max





















Alternative Formulation for the Calculation of Drag Coefficients for Flaps























Miscellaneous Parasite Drag





















Windm Windmill illing ing Engin Engine e and Prope Propelle llerr Drag Drag





















Landing gear Drag









































What is?







































































































































































































































































ERJ 145 CD0 Calculation for the Wing We consider the interference factor Q W=1.01 (from the Roskam’s Graph) The form factor of the wing can be calculated using the following expression FF W

FF W

 0.6   1  t / c   100  t / c 4   1.34  M 0.18 cos m 0.28   xt 

 1  0.12  100  0.124   1.34  0.780.18 cos15.5o   1.015  0.6



With X t = 0,35xCMA = 0,35 x 2,90 m = 1.1015 m The wetted area is given by

0.28

 1.384





















ERJ 145 CD0 Calculation for the Fuselage The Reynolds number for the fuselage is

Re 

  V cruise  l fus 



0.343 kg m3  230 m s  27.93m 18.27 10

6

kg

 1.206x108

ms

Considering that the fuselage presents a rough surface, the cut-off Reynolds number must also be calculated to taken this characteristic into account 1.05 3

 27930mm  Recutoff  44.62(l/k l/k )1.05 3 M 1.16  44.62     0.00635mm 

0.781.16  3.31x108

(Raymer)

Re is lower that the cut-off Reynolds number. Thus, the usual Reynolds number Re is must be taken into the equations for the calculation of Cf,lam and C f,turb . C f ,lam



1.328 Re



1.328 1.206 x 108

 1.209 x 10  4





















ERJ 145 CD0 Calculation for the Fuselage The form factor of the fuselage can be calculated by

(DATCOM 78) We consider the interference factor QF=1. The wetted area can be obtained by using a Torenbeek’s formulation





















Preliminary Weight Estimation





















2. Preliminary Weight Estimate W TO = W E + W TFO + W PLC + W F,USED + W F,RES = Take-off Take-off Weight W E

= Empty Empty Weight

W F

= W F,USED + W F,RES = Weight = Weight of Fuel Used+ Weight of Fuel Reserve = Total Fuel Weight =W PL+W CREW = Weight = Weight of Payload +Weight of Crew

W PLC























Empty weight vs take-off weight relation

WE

(1-MTFO-MFUEL) increasing

Fuel fraction needed for





















Mission Profile W F = W TO – W FINAL=W TO – ( Weight Weight at End of Mission ) W F /W TO = M FUEL= 1 – W FINAL /W TO = 1 – M FINAL Normal

Fuel Needed for Mission





















Mission Profile Segment weight fractions Wi / Wi -1 Cruise

exp[-RC j

/V(L/D)]

exp[-C /(L/D)] j Loiter

exp[-R alt.C j /V(L/D)]





















M FINAL =(W11/W10)(W10/W9)(W9/W8)….(W2/W1)(W1/W0)

M FINAL



WFINAL WTO



W 11 W0

n

 i 1

W i W i 1

Final Weight Fraction





















L/D Calculation

Cruise!























L/D Calculation





















Normal Mission Fuel Fraction vs Range





















Total Fuel Fraction vs Range





















Weight Fraction of Trapped Fuel & Oil





















Correlation of empty weight vs take-off











































































Class II Methodology for Drag Estimation

Recommend Documents