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 x sin у. Steady-state force equilibrium gives T = D + W x sin у or sin у = (T – D)/ W. This gives:
RC = [(T – D) x V]/W = (T/ W – D/ W) x V (11.12)
Equation 11.12 is written as:
T/ W = RC / V + (D/ W)
or T/ W = RC/ V + [(Cd x 0.5 x p x V2 x Sw)/ W] (11.13)
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.
[Tsls/W]/кг = RC/V + [(Cd x 0.5 x p x V2)Sw/ W] (11.14)
[Tsls/ W] = k2 x RC/V + k2 x [(Cd x 0.5 x p x V2)Sw/ W] (11.15)
The drag polar is now required to compute the relationships given in Equation 11.15.