11.4.2 Initial Climb

From the market requirements, an initial climb starts at an 800-ft altitude at a speed Veas = 250 knots (Mach 0.38) = 250 x 1.68781 = 422 ft/s (128.6 m/s) and the required rate of climb, RC = 2,600 ft/min (792.5 m/min) = 43.33 ft/s (13.2 m/s). From the TFE731 class engine data, TSLS/T ratio = 1.5 (factor k2 from Section 10.11.3, Figure 10.46). The undercarriage and high-lift devices are in a retracted position. Lift coefficient:

CLclimb = W/(0.5 x 0.002378 x 4222 Sw) = 0.004723 x W/Sw Using Equation 11.14:

[Tsls/ W]/1.5 = 43.33/422 + (CD x 0.5 x 0.00232 x 4222 Sw)/W)

Tsls/ W = 0.154 + 310 x Cd x (Sw/ W)

11.4.3 Cruise

Requirements: Initial cruise speed must meet the high-speed cruise (HSC) at Mach 0.74 and at 41,000 ft (flying higher than bigger jets in less congested traffic corridors) using k = 0.972 in Equation 11.14.

In FPS at 41,000 ft:

p = 0.00056 slug/ft2 and V2 = (0.74 x 968.076)2 = 716.382 = 513,195 ft2/s2 In SI at 12,192 m:

p = 0.289 kg/m3 and V2 = (0.74 x 295.07)2 = 218.352 x 47,677.5 m2/s2 Equation 11.18 gives the initial cruise:

Cl = 0.972 MTOW/(0.5 x 0.289 x 47,677.5 x Sw)

= 0.0001414(W/ Sw)

where W/Sw is in N/m2.

Equation 11.19 gives:

Tsls/ W = k x 0.5p V2 x Cd/(W/Sw)

(Use factor ki = TSLS/ Ta = 4.5 from Figure 10.47.)

In FPS:

Tsls/ W = 4.5 x 0.5 x 0.00056 x 459,208.2 x Cd/(W/Sw) = 565.73 x Cd/(W/Sw)

Computing and listing in tabular form (use Figure 9.1 for the drag polar): W/S (lb/ft2) 40 50 60 70 80 W/S (N/m2) 1,915.9 2,395.6 2,874.3 3,353.7 3,832.77 Cl (from Equation 10.14) 0.2710 0.3390 0.4064 0.4740 0.5420 CD (from drag polar) 0.0255 0.0269 0.0295 0.033 0.0368 TSlS/W at 41,000 feet 0.360 0.305 0.278 0.267 0.260

In SI:

Tsls/ W = 4.5 X 0.5 X 0.289 x 42,662.5 x Cd/(W/Sw) = 27,741.3 x Cd/(W/Sw)