Figure 11.2. Aircraft climb trajectory

aircraft, no correction is needed and the simplified equations are as follows: In the FPS system, this can be written as:

In the SI system, this becomes:

11.3.2 Sizing for the Initial Rate of Climb

The initial rate of climb is a user specification and not a FAR requirement. In general, the FAR requirement for the one-engine inoperative, second-segment climb gradient provides sufficient margin to give a satisfactory all-engine initial climb rate. However, from the operational perspective, higher rates of climb are in demand when it is sized accordingly. Military aircraft (some with a single engine) requirements stipulate faster climb rates and sizing for the initial climb rate is important. The methodology for aircraft sized to the initial climb rate is described in this section. Figure 11.2 shows a typical climb trajectory.

For a steady-state climb, the expression for rate of climb, RC = V × sin γ . Steady-state force equilibrium gives T = D + W × sin γ or sin γ = (T − D)/ W. This gives:

Equation 11.13 is based on a climb-thrust rating that is lower than the TSLS; it must be written in terms of TSLS. The TSLS/ T ratio (factor k2; see Section 10.11.3 and Figure 10.46) varies depending on the engine BPR.

The drag polar is now required to compute the relationships given in Equation 11.15.

11.3.3 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:

Dividing both sides of the equation by the initial cruise weight, Wincr = k × MTOW due to fuel burned to climb to the initial cruise altitude. The factor k 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:

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:

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 k1; see Section 10.11.3 and Figure 10.47) varies depending on the engine BPR. The factor k1 is computed from the engine data supplied. Then, Equation 11.18 can be rewritten as:

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 wingloadings (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.

11.3.4 Sizing for Landing Distance

The most critical case is when an aircraft must land at its maximum landing weight of 0.95 MTOW. In an emergency, an aircraft lands at the same airport for an aborted takeoff, assuming a 5% weight loss due to fuel burn in order to make the return