Sizing to Meet Initial Cruise
There are no FAR or MILSPECS regulations to meet the initial cruise speed; initial cruise capability is a user requirement. Therefore, both civil and military aircraft sizing for initial cruise use the same equations. At a steady-state level flight, thrust required (airplane drag, D) = thrust available (Ta); that is:
D = Ta = 0.5pV2Cd x Sw (11.16)
Dividing both sides of the equation by the initial cruise weight, Wincr = к x MTOW due to fuel burned to climb to the initial cruise altitude. The factor к lies between 0.95 and 0.98, depending on the operating altitude for the class of aircraft, and it can be fine-tuned through iteration – in the coursework exercise, one round of iterations is sufficient. The factor cancels out in the following equation but is required later. Henceforth, in this part of cruise sizing, W represents the MTOW, in line with the takeoff sizing:
0.5p V2Cd x Sw/ W = Ta/ W (11.17)
The drag polar is now required to compute the relationships given in Equation 11.17. Use the Cd value to correspond to the initial cruise Cl (because they are nondimensional, both the FPS and SI systems provide the same values). Initial cruise:
Cl = к x MTOW/(0.5 x p x V2 x Sw) (11.18)
The thrust-to-weight ratio sizing for initial cruise capability is expressed in terms of TSlS. Equation 11.18 is based on the maximum-cruise thrust rating, which is lower than the TSlS. Equation 11.18 must be written in terms of TSlS. The TSLS/Ta ratio (factor кй see Section 10.11.3 and Figure 10.47) varies depending on the engine BPR. The factor ki is computed from the engine data supplied. Then, Equation 11.18 can be rewritten as:
Tsls/ W = к x 0.5pV2 x Cd/(W/Sw) (11.19)
Variation in wing size affects aircraft weight and drag. The question now is: How does the Cd change with changes in W and Sw? (Ta changes do not affect the drag because it is assumed that the physical size of an engine is not affected by small changes in thrust.) The solution method is to work with the wing only – first by scaling the wing for each case and then by estimating the changes in weight and drag and iterating – which is an involved process.
This book simplifies the method by using the same drag polar for all wing – loadings (W/S) with little loss of accuracy. As the wing size is scaled up or down (the AR invariant), it changes the parasite drag. The induced drag changes as the aircraft weight increases or decreases. However, to obtain the Cd value, the drag is divided by a larger wing, which keeps the Cd change minimal.