ANNEX

Appendix BFlight performance calculations

B8ACCELERATING CLIMB AND FLAP RETRACTION

This usually follows the initial climb. As for all flight segments, the start-point altitude h1, true airspeed VT1, and thrust (Fn/δ)1 are those from the end of the preceding segment. The end-point calibrated airspeed VC2 and the average climb rate ROC are user inputs (bank angle ε is a function of speed and radius of turn). As they are interdependent, the end altitude h2, end true airspeed VT2, end thrust (Fn/δ)2 and segment track length Δs have to be calculated by iteration; the end altitude h2 is guessed initially and then recalculated repeatedly using equations B-16 and B-17 until the difference between successive estimates is less than a specified tolerance, e.g. one foot. A practical initial estimate is h2 = h1 + 250 feet.

The segment track length (horizontal distance covered) is estimated as:

Sseg=0,95×k2×V2T2−V2T1∕2 αmax−G×gmath

(B-17)

where

0,95

is a factor to account for effect of 8 kt headwind when climbing at 160 kt

k

is a constant to convert knots to ft/sec = 1,688 ft/s per kt

VT2
= true airspeed at segment end, kt: VT2=VC2∕σ2math

where σ2 = air density ratio at end altitude h2

αmax

= maximum acceleration in level flight (ft/s2)

= Image_r00067

G

= climb gradient Image_r00068

where ROC = climb rate, ft/min

Using this estimate of Δs, the end altitude h2′ is then re-estimated using:

h2′ = h1 + s · G/0,95

(B-18)

As long as the error h′2−h2math is outside the specified tolerance, the steps B-17 and B-18 are repeated using the current iteration segment-end values of altitude h2, true airspeed VT2, corrected net thrust per engine (Fn/δ)2. When the error is within the tolerance, the iterative cycle is terminated and the acceleration segment is defined by the final segment-end values.

Note:

If during the iteration process (amax – G·g) < 0,02 g, the acceleration may be too small to achieve the desired VC2 in a reasonable distance. In this case, the climb gradient can be limited to G = amax/g – 0,02, in effect reducing the desired climb rate in order to maintain acceptable acceleration. If G < 0,01 it should be concluded there is not enough thrust to achieve the acceleration and climb rate specified; the calculation should be terminated and the procedure steps revised42.

The acceleration segment length is corrected for headwind w by using:

ΔSw=ΔS×VT−wVT−8math

(B-19)

Accelerating segment with cutback

Thrust cutback is inserted into an acceleration segments in the same way as for a constant speed segment; by turning its first part into a transition segment. The cutback thrust level is calculated as for the constant-speed cutback thrust procedure, using equation B-1 only. Note it is not generally possible to accelerate and climb whilst maintaining the minimum engine-out thrust setting. The thrust transition is assigned a 1 000 ft (305 m) ground distance, and the corrected net thrust per engine at the end of 1 000 ft is set equal to the cutback value. The speed at the end of the segment is determined by iteration for a segment length of 1 000 ft. (If the original horizontal distance is less than 2 000 ft, one half of the segment is used for thrust change.) The final thrust on the second sub-segment is also set equal to the cutback thrust. Thus, the second sub-segment is flown at constant thrust.