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Unformatted text preview: 650:460 Aerodynamics Airplane Performance Prof. Doyle Knight Tel: 732 445 4464, Email: [email protected] Office hours: Tues and Thur, 4:30 pm  6:00 pm and by appointment Fall 2009 1 Airplane Performance • Takeoff Symbol Definition V s Stall speed V mc Minimum control speed V 1 Critical engine failure speed V R Takeoff rotation speed V mu Minimum unstick speed L LOF Liftoff speed V 2 Speed to clear 35 ft obstacle 2 Airplane Performance • Ground Roll From conservation of momentum m dV dt = T D μ ( W L ) where T thrust D drag μ coefficient of rolling friction (typically, 0 . 02 ≤ μ ≤ . 1) 3 Airplane Performance • Ground Effect The effect of the ground is equivalent to an image vortex system The image vortex system increases the lift and decreases the induced drag The effect is a function of b / h where h is the height of the wing above the ground 4 Airplane Performance • Ground Effect The effect is a function of b / h where h is the height of the wing above the ground For h >> b , the effect of the ground is negligible An approximate expression (valid for h / b > 1 / 3) is C D i  g C D i  ∞ = 16 parenleftbigg h b parenrightbigg 2 bracketleftBigg 1 + 16 parenleftbigg h b parenrightbigg 2 bracketrightBigg − 1 5 Airplane Performance • Estimate of Takeoff Roll for Boeing 767 Integrate the equations m dV dt = T D μ ( W L ) ds dt = V The thrust T is given by T = 1000 bracketleftBigg 55 . 6 4 . 6 parenleftbigg V 100 parenrightbigg + 0 . 357 parenleftbigg V 100 parenrightbigg 2 bracketrightBigg where V is in ft/s and T is in lbf 6 Airplane Performance • The following values are used: Quantity Value Max takeoff gross weight (lbf) 387,000 Flat plate area f (ft 2 ) 127.5 Wing planform area (ft 2 ) 3084 Wing span (ft) 156.1 Oswald efficiency factor 0.7 C D i  g / C D i  ∞ 0.4 C L 1.0 7 Airplane Performance • Method of Solution It is necessary to express the right side of the first equation m dV dt = T D μ ( W L ) as a function of V . The first term is T = 1000 bracketleftBigg 55 . 6 4 . 6 parenleftbigg V 100 parenrightbigg + 0 . 357 parenleftbigg V 100 parenrightbigg 2 bracketrightBigg as stated previously 8 Airplane Performance The second term is D = 1 2 ρ V 2 summationdisplay C D i S i = 1 2 ρ V 2 bracketleftbig C D wing S wing + C D fuselage S fuselage bracketrightbig The drag due to the wing is C D = C D min + C 2 L π Ae × (ground effect factor) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright . 4 where the first term is the friction drag and the second is the induced drag. 9 Airplane Performance We can approximate the friction drag for the wing assuming turbulent from the leading edge C D min = 0 . 455 (log 10 R ) − 2 . 58 where R = V ¯ c ν and ¯ c is an average chord defined by ¯ c = S b Note that at takeoff ( V = 0) we must set the drag equal to zero since the drag coefficient becomes infinite 10 Airplane Performance We estimate the friction drag on the fuselage by approximating it...
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This note was uploaded on 01/24/2012 for the course MECHE 343 taught by Professor Professor during the Spring '11 term at Carnegie Mellon.
 Spring '11
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