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REPORT 11 DRAG POLAR ESTIMATION

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11. DRAG POLAR ESTIMATION

This chapter deals with the estimation of drag polar including the effects of landing gear.

11.1 Introduction

Drag Estimation: The total drag polar of an airplane is considered to consist of two different

types in the subsonic regime of flight.

(i) zero-lift drag (ii) Induced drag where The zero-lift drag has form drag, skin-friction drag, leakage and protuberance drag. The form

drag is due to the pressure field around the body and skin friction drag is due to the shear

stresses at the surface of the body. The induced drag arises as a consequence of the production

of lift and represents the cost of producing lift by pushing a body through a fluid.

11.2 Calculation of Zero-Lift Drag Coefficient ():Component Buildup Method:

The zero-lift drag of an aircraft is defined as: where - total zero-lift drag of the aircraft

q - Dynamic pressure

- Wing reference area.This equation may also be written as, where the summation signindicates the summation of the values of parasite drag coefficient for all components of the

aircraft including interference. The term (D/q) is often called the equivalent flat plate area,

because the term has the units of square feet (or square meters) and is numerically roughly

equal to the drag of a flat plate which is held normal to the flow. Aircraft components may be

broken down into three categories,

1. Components that are streamlined for which the reference area is usually the wettedarea of the component, which produces the drag known as skin friction, drag.

2 .Components that are bluff (such as landing gear) for which the reference area is usually

the frontal (or maximum cross sectional) area, which produces drag called miscellaneous

drag.


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3. Other drag effects, such as leakage and protuberances, which may be expressed as a

percentage of the total drag of the aircraft, which produces drag known as leakage and

protuberance drag.

The estimation of parasite drag coefficient (

) is done based on component build-up method.

In this method the subsonic parasite drag is estimated by considering each component of

aircraft for calculations of their skin friction drag (, form factor (FF) and interference factor(Q).

Total parasite drag (zero lift drag) co-efficient is given by[1]

,

(11.1)where, subscript c indicates those values are different for different components.

of components

11.2.1 Skin Frictional Drag Coefficient-

Skin friction drag coefficient depends upon Mach number, Reynolds number and

surface roughness. The Reynolds number is estimated and depending on the flow to be laminar

or turbulent, skin friction coefficient of all the components has been calculated.

For laminar flow

The skin friction coefficient is given by[1]

(11.2)


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The skin friction coefficient for turbulent flow is given by[1]

(11.3)The Reynolds number is given by

where

,

Fuselage

Table 11.1Fuselage details

Characteristic length(fuselage length) 1.2 m

Reynolds number 12.4138

Nature of flow Turbulent

4.25499 Wing

Table 11.2Wing details

Characteristic length(chord) 0.188 m

Reynolds number 1.94484 Nature of flow Laminar

3.011314


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Horizontal tail

Table 11.3Horizontal tail details

Characteristic Length( mean chord) 0.1426 m


3.4576

Vertical tail

Table 11.4Vertical tail details

11.2.2 Form factor for various components

Fuselage

The form factor for fuselage is given by[1]

(11.4)Since the cross section is rectangular, the equivalent diameter is found using the following

relation

FF

Characteristic length(mean chord) 0.08944 m


4.36584


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Wing

The form factor for wing is given by[1]

(11.5)

FF=0.957132

Horizontal, Vertical Tail

The same airfoil NACA 0012 is selected and the form factor is given by[1]

(11.6)

FF=0.99419

11.2.3 Interference factor

The interference factor[1]

for wing and fuselage is 1.1 and empennage is taken as 1.03.


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11.2.4 Wetted area estimation

Fuselage

The wetted area is given by[1]

(11.7)Wing

The exposed area is given by

(11.8)

The wetted area is given by [1]

( ) (11.9)Horizontal Tail

The exposed area is given by

(11.10)

The wetted area is given by[1]

( ) (11.11)


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Table11.5 Skin friction drag estimation

Component FF(Formfactor)

Q(Interference

factor)

()

Fuselage 4.25499 1.058774 1.1 2.2472 11.1372

Wing 0.957132 0.957132 1.1 2.03033 6.43705

Horizontal

tail

3.4576 0.99419 1.03 0.59865 2.1196

Vertical tail 4.3658 0.99419 1.03 0.17352 0.77575

Total CF 20.4696

11.3 Miscellaneous drag coefficient:

In addition to the basic parasite drag of the major components, the drag due to landing

gear, aft-fuselage upsweep, and control surface gaps must be consider for parasite drag .One of

the major contributions for miscellaneous drag is Landing Gear (no retracting mechanism). The

drag coefficient for landing gear is estimated by comparison of test data for a similar gear

arrangement. But if the above data is not given then the gear drag can be estimated as

summation of drags of wheels, struts and other gear components using the table below

Table 11.6Drag coefficient for landing gear components

Configuration (D/q)

Regular wheel and tire 0.25

Second wheel and tire in tandem 0.15

Streamlined wheel and tire 0.18

Wheel and tire with fairing 0.13

Streamline strut 0.05

Round strut 0.30

Flat spring gear leg 1.4

Fork,bogey,irregular fitting 1.0-1.4


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Table no 11.7 Landing Gear Dimensions

S. No Component Description Dimensions

1

Nose

landinggear

Front Wheel

Wheel Diameter 35 mm

Wheel thickness 10 mm

Frontal Area 350 mm2

= 0.003767 Ft2

2 Strut

Strut Length 115 mm

Strut Width 5 mm

Strut thickness 5 mm

Frontal Area (1 Struts) 575 mm2

= 0.006189 Ft2

S. No Component Description Dimensions

3

Rearlandinggear

Rear Wheel

Wheel Diameter 35 mm

Wheel thickness 10 mm

Frontal Area 350 mm2

= 0.003767 Ft2

4 Strut

Strut Length 200.5 mm

Strut Width 5 mm

Strut thickness 5 mm

Frontal Area (2 Struts) 2005 mm2

= 0.0215816 Ft2

Drag Coefficient of Landing gear:

By using the above table

for nose landing gear,

CDo (front wheel) = [0.25 x 0.003767] / Sref

= [0.25 x 0.003767] / 2.2907

= 0.000411


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for front wheel strut,

(strut) = [0.3 x 0.006189] / Sref= [0.3 x 0.006189] / 2.2907

= 0.000810

for rear wheels,

(rear wheel) = [0.25 x 0.003767 x 2] / Sref= [0.25 x 0.003767 x 2] / 2.2907

= 0.000822

for rear wheel strut,

(strut) = [0.3 x 0.0215816] / Sref= [0.3 x 0.0215816] / 2.2907

= 0.002826

= = 0.0048911.4 Protuberance and Leakage Drag

Drag due to leakage and protuberance is difficult to estimate. Leakage drag is due totendency of aircraft to inhale through holes and gapes in high pressure region and exhale into

low pressure zones. Protuberance drag includes drag due to manufacturing defects that is

protruding rivets, rough skin panels etc. For a normal airplane, leaks and protuberance drags

can be estimated as about 2-5% of the parasite drag of the airplane

The parasite drag coefficient is given by


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11.5 Ostwald efficiency

The Ostwald efficiency factor is given by[1]

(11.12)AR=6

The new drag polar equation is given by

11.6 Conclusion

The final drag polar equation including the contribution of landing gear is given by

11.7 References

[1] Daniel P Raymer, Aircraft Design: A Conceptual Approach, 2nd edition AIAA

Educational series, 1989.

[2] John D Anderson Jr, Aircraft Performance and Design, 4th reprint 2011, McGraw- Hill, New

York.


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List of Symbols

1. - Aspect ratio2. - Top area of fuselage3.

- Side area of fuselage

4. - span5. c - chord6. - Parasite drag coefficient7. - Induced drag coefficient8. - Miscellaneous drag coefficient9. - Leakage and protuberance drag10. - Skin friction coefficient11. Deq - Equivalent diameter of fuselage12.

- Parasite drag

13. e - Ostwalds efficiency14. - Form factor of the components15. - Length16. - Mach number17. q - Dynamic pressure18. - Interference factor19. - Reynolds number20. Sexp - Exposed area21. Sref - Reference wing area22. Swet - Wetted area of wing23. - Thickness to chord ratio24. v - velocity25. - chord wise location26. - Sweep of maximum thickness line27. - density28. - viscosity

(drag polar)

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