THRUST TO WEIGHT RATIOAND ASPECT RATIO

Nguyễn Anh TuấnNaval Architecture and

Marine Engineering tuanshipland@gmail.com

(+84) (0) 944 113 787

TSL_Oct2010

T/W Ratio

T/W ratio estimates:• Part of the takeoff distance• Rate of climb• Maximum velocity

http://www.centennialofflight.gov/essay/Theories_of_Flight/Performance_Class2/TH25G1.htm

Takeoff distance = sg + sa = 2500 ftAccording eq. [6.95] (see [1]), Ground Roll sg

For FlapPlain Flap deflection 20o for takeoff (see table 5.3 [1])Section maximum lift coeffient (cl)max of 45o flap deflection is 0.9 (see Fig.5.28, [1])(cl)max = 0.9 (20/45) ~ 0.5 (For linear changes)

For the whole of wing, average (cl)max = 1.7 + 0.5 = 2.2

3D- effect of the finite aspect ratio

Raymer, Ref [25] of [1]

The liftoff velocity

Flight path radius

Velocity of airplane

Flight path angle == 50 ft : obstacle height

Airborn distance

Takeoff distance = sg + sa = 2500 ft

Requirement powerPA =

Note: 550ft.lb/s = 1hp

Power of the takeoff constraint ≥ 119 hp

Shaft brake power

Gross takeoff weight = 5,158lb

(cl)max

T/W W/S(Cl)max

sg

Vstall

R

sa

𝜃𝑂𝐵

T/W

VLO

V

PR = PA

P

Wo

T/W ratio and Aspect ratio

Effects

Maximum Rate of climb (R/C)max = 1000ft/min = 16.67 ft/s at sea levelSingle-engine general aviation airplanesThe ratio of wetted area to the wing referenece area Swet/Sref = 4 (See fig. 2.54, [1])The skin –friction coefficent (for early jet fighters) Cfe = 0.0043 corressponds to Reynolds number Re = 107 (See fig 2.55, [1])

The zero-lift drag coefficient (the zero-lift parasite drag coefficient)

The drag polar for airplane

The drag due to lift (downwash and so on)

The span efficiency factor to account for a nonelliptical lift distribution

along the span of the wing e

The coefficient

Based on data from famous existing airplanes, estimating a reasonable first approximation for maximum of Lift to Drag ratio for 4-6 peoples aircraft (See p.403 [1])

= = 0.075

A reasonable estimate The Oswald efficiency eo for a low-wing general aircrafts is 0.6 (See p.415 [1]) =7.07

Maximum rate of climb for a propeller-driven airplane

Shaft Brake Power for the constraint of rate of climb

W/SK Wo

Aspect Ratio

Themaximum velocity V = Vmax = 250 mi/h = 366.7 ft/h at midcruise weight and level flight 20,000ftIn level flight T=D

The weight at maximum velocity is less than the weight at takeoff stage

The midcruise weight WMC

Estimating the weight fraction

Gross takeoff weight = 5,158lb

For a propeller-driven aircraft, we use power to weight ratioFor a jet aircraft, we use thrust to weight ratioT/W and P/W are same mean

Thank you!

References

[1] John D. Anderson, Jr. 1999. Aircraft Performance and Design. McGraw-Hill[2] E. L. Houghton and N. B. Carruthers. 1986. Aerodynamics for Engineering Students. 3rd edition. Thomson Press