# Sizing for Takeoff Field Length

TOFL is the field length (i. e., runway plus clearway; Figure 11.1) required to clear a 35-ft (10-m) obstacle in the clearway while maintaining a specified minimum climb
gradient, y, with one engine inoperative and flaps and undercarriage extended. The FAR requirement for a two-engine aircraft minimum climb gradient is 1.2 (see Table 13.3 for aircraft with more than two engines).

For sizing, field-length calculations are at the sea-level standard day (no wind) and at a zero airfield gradient of paved runway. For further simplification, drag changes are ignored during the transition phase of liftoff to clear the obstacle (flar­ing after liftoff takes less than 3 s); in other words, the equations applied to Vuft-off are extended to V2 = 1.2Vstan. This gives V22 = [2 x 1.44 x (W/S)]/(pCLstaii). An aircraft stalls at CLmax. Chapter 13 addresses takeoff performance in detail.

A simplified expression for all engines is:

where dV/dt = a and V and a are instantaneous velocity and acceleration of the aircraft on the ground encountering friction (coefficient p = 0.025 for a paved, met­aled runway). Average acceleration, a, is taken at 0.7V2. By replacing V2 in terms of CLstall, Equation 11.1 reduces to:

fV2 „ 1 44W/S

TOFL = (1 /a) VdV = (V22/2a) = ——(11.2)

0 PCLstalla

(W/S) = (TOFL x p x a x CLstaii)/1.44 (11.3)

where average acceleration, a = F/m and applied force F = (T – D) – p(W-L). Until liftoff is achieved, W > L and F is the average value at 0.7 V2. Therefore:

a = [(T – D) – p(W – L)]g/ W = g(T/ W)[1 – D/ T – pW/ T + pL/ T] (11.4)

Substituting Equation 11.3, it becomes:

(W/S) = (TOFL x p x [g(T/ W)(1 – D/ T – pW/T + pL/ T)] x CLstaii)/1.44

(11.5)

In the FPS system, it can be written as p = 0.00238 slugs and g = 32.2 ft/s2. Therefore:

(W/S) = (TOFL x (T/ W)(1 – D/ T – pW/ T + pL/ T)] x CLai)/18.85 (11.6a)

In the SI system, it becomes p = 1.225 kg/m3 and g = 9.81 m/s2. Therefore,

(W/S) = 8.345 x (TOFL x (T/ W)(1 – D/ T – pW/ T + pL/ T)] x CLstaii)

(11.6b)

where W/S is in Newton/m2 to remain in alignment with the units of thrust in Newtons.

Checking of the second-segment climb gradient occurs after aircraft drag esti­mation, which is explained in Sections 13.5.1 and 13.5.3. If it falls short, then the TSLS must be increased. In general, TOFL requirements are not generous; there­fore, satisfying the TOFL is also likely to satisfy the second-segment climb gradient.