The landing configuration is with full flaps extended and the aircraft at landing weight. The approach segment at landing is from a 50-ft altitude to touch down. At approach, the FAR requires that an aircraft must have a minimum speed Vapp = 1.3Vstall@land. At touchdown, aircraft speed is VTD = 1.15Vstall@land. Brakes are applied 2 s after all wheels touch down. A typical civil aircraft descent rate at touchdown is between 12 and 22 ft/s. The landing runway length should be 1.667 times the computed landing distance. Generally, this works out to be slightly less than the BFL at the MTOM (but not necessarily).

For a balked landing or missed approach at landing weight, the FAR requirements are given in Table 13.6. An aircraft is configured with full flaps, undercarriage extended, and engine in full takeoff rating. In general, this is not a problem because all engines are operational and the aircraft is lighter at the end of the mission. Military aircraft requirements are slightly different: Vapp = 1.2Vstall@land and

VTD = 1.1Vstall@land.

The approach has two segments, as follows:

a steady, straight glide path from a 50-ft height

flaring in a nearly circular arc to level out for touchdown, which incurs a higher g

The distances covered in these two segments depend on how steep is the glide path and how rapid is the flaring action. This book does not address these details of analysis; instead, a simplified approach is taken by computing the distance covered during the time from a 50-ft height to touchdown before the brakes are applied; it is assumed to be 6 s herein.

13.4.3 Climb and Descent Performance

Climb is possible when the available engine thrust is more than the aircraft drag; the excess thrust (i.e., thrust minus aircraft drag, (T − D)) is converted into the potential energy of height gain. The total energy of an aircraft is the sum of its PE and KE, expressed as follows:

Figure 13.10. Climb performance

The term for the rate of change of specific energy is specific excess power (SEP):

Equation 13.7 shows that he > h by the term V2/2g in Equation 13.6. In other words, an aircraft can continue to climb by converting KE to PE until the speed is decreased to the point where the aricraft is unable to sustain the climb.

An enroute climb is performed in an accelerated climb. The equation for an accelerated climb is derived as follows (Figure 13.10). For simplicity, the subscript ∞ to represent aircraft velocity is omitted. From Figure 13.10, the force equilibrium gives:

(T − D) = mg sin γ + (m)dV/dt

This gives the gradient:

sin γ = [T − D − (W/g)dV/dt]/ W = [(T − D)/ W] − [(1/g) × dV/dt] (13.8)

Write:

dV/dt = (dV/dh) × (dh/dt)

Combining Equations 13.7 and 13.9, the rate of climb is written as:

dhe/dt = V(T − D)/ W − (V/g)(dV/dt) + V/g(dV/dt) = V(T − D)/ W (13.11) The rate of climb is a point performance and is valid at any altitude. The term

Equation 13.10) of climb depending on how fast an aircraft is accelerating during the climb. Part of the propulsive energy is consumed for speed gain rather than altitude gain. Military aircraft make an accelerated climb in the operational arena when the

it makes an enroute climb to cruise altitude at a quasi-steady-state climb by holding

the climb speed at a constant EAS or Mach number. A constant-EAS climb causes the TAS to increase with altitude gain. A constant speed indication eases a pilot’s workload. During a quasi-steady-state climb at a constant EAS, the contribution by the Vg dVdh term is minimal. The magnitude of the acceleration term decreases with altitude gain and becomes close to zero at the ceiling (i.e., defined as when R/Caccl = 100 ft/min). (Remember that V = VEAS/√σ and VEAS = Ma√σ .)

Constant EAS Climb Below Tropopause (γ = 1.4, R = 287 J/kgK, g = 9.81 m/s2)

In SI, Equation 3.1 gives a troposphere T = (288.16 – 0.0065h), and ρ = 1.225 × (T/288.16)(g/0.0065R)−1 = 1.225 × (T/288.16)(9.81/0.0065 × 287)−1 = 1.225 × (T/288.16)4.255 derives the density ratio (up to the tropopause) by replacing T in terms of its lapse rate and h:

σ = ρ/ρ0 = (288.16 − 0.0065h/288.16)4.255 = (1 − 2.2558 × 10−5 × h)4.255

This gives (dσ /dh) = −9.6 × 10−5 × (1 – 2.2558 × 10−5 × h)3.255

These equations are summarized in Table 13.7.

From Equation 3.1, the atmospheric temperature, T, can be expressed in terms of altitude, h, as follows:

T = (288 − 0.0065h)

where h is in meters. Substituting the values of γ , R, and g, the following is

'

When evaluated for altitudes, the equation gives the value as shown in Table 13.7. In a similar manner, the relationships above tropopause can be obtained. Up

to 25 km above tropopause, the atmospheric temperature remains constant at 216.65 K; therefore, the speed of sound remains invariant.

With the loss of one engine at the second-segment climb, an accelerated climb penalizes the rate of climb. Therefore, a second-segment climb with one engine inoperative is achieved at an unaccelerated climb speed, at a speed a little above V2 due to the undercarriage retraction. The unaccelerated climb equation is obtained by omitting the acceleration term in Equation 13.10, yielding the following equa-

The climb performance parameters vary with altitude. An enroute climb performance up to cruise altitude is typically computed in discreet steps of altitude (i.e., 5,000 ft; see Figure 13.10), within which all parameters are considered invariant and taken as an average value within the altitude steps. The engineering approach is to compute the integrated distance covered, the time taken, and the fuel consumed to reach the cruise altitude in small increments and then totaled. The procedure is explained herein. The infinitesimal time to climb is expressed as dt = dh/(R/Caccl). The integrated performance within the small altitude steps is written as:

Summary

The time used to climb, timeclimb = t, is obtained by summing the values obtained in the small steps of altitude gain. The distance covered during a climb,