lectures-airplane-performance

# lectures-airplane-performance - 650:460 Aerodynamics...

This preview shows pages 1–12. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

### Page1 / 53

lectures-airplane-performance - 650:460 Aerodynamics...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online