# 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.