Second Segment Climb Gradient After Engine Failure
A four-engine turboprop is departing a mountain airport at 1,500 ft pressure altitude with OAT 20 degrees C. The aircraft mass is 29,000 kg, flap setting is take-off, and the landing gear is retracted after the first segment. The AFM gives a second-segment net climb gradient of 3.1 percent at this mass, altitude, and temperature with one engine inoperative. The obstacle departure procedure requires a minimum climb gradient of 3.3 percent to 4,500 ft. The aircraft's maximum certified mass is 31,000 kg, and the runway is 1,900 m long with a 120 m clearway. The crew has already used 1,300 m of runway for the take-off roll. The forecast temperature at 4,500 ft is 12 degrees C, and the QNH is 1005 hPa.
1. Determine whether the aircraft can meet the required obstacle climb gradient in the second segment and identify the limiting factor.
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The AFM net second-segment gradient is 3.1 percent, but the procedure requires 3.3 percent. The aircraft therefore cannot meet the procedure as loaded. The limiting factor is mass: the aircraft is 2,000 kg below maximum certified mass, so a further reduction may raise the gradient. A rough rule is that the gradient improves by about 0.3 to 0.5 percent per 1,000 kg reduction at this mass, so reducing to about 27,500 kg might give 3.6 percent, which would satisfy the procedure. Alternatively, the crew could request a different departure procedure with a lower gradient requirement. Temperature is also a factor: the 20 degrees C at the airport is warmer than the 12 degrees C forecast at 4,500 ft, so the gradient will improve with altitude, but the critical segment is the second segment at low altitude. The crew must not depart unless the AFM gradient, after correction for mass, meets or exceeds 3.3 percent.
2. Explain how the 120 m clearway and the 1,300 m ground roll affect the take-off distance available and the decision to continue.
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The take-off distance available is the runway length plus the clearway, so 1,900 + 120 = 2,020 m. The take-off run available is the runway length only, 1,900 m, because the clearway cannot be used for ground roll. The crew has used 1,300 m for the ground roll, leaving 600 m of runway and 120 m of clearway. The take-off distance required must not exceed 2,020 m, and the take-off run required must not exceed 1,900 m. If the AFM take-off distance required at this mass and temperature is, say, 1,850 m, it is within the take-off distance available but the take-off run required may be close to the 1,900 m limit. The clearway only helps the airborne segment, not the ground roll. The crew should confirm both values from the AFM before continuing the take-off, and if either limit is exceeded, the take-off must be rejected or the mass reduced.
3. The crew considers departing with a tailwind of 5 kt instead of the current headwind. Assess the effect on the second-segment gradient and on the take-off distance.
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A tailwind increases the ground speed at lift-off and during the climb, so the aircraft covers more ground for the same height gain. The second-segment climb gradient in percent is the height gain divided by the horizontal distance, so a tailwind reduces the gradient. A rough approximation is that a 5 kt tailwind reduces the gradient by about 0.2 to 0.3 percent, which would take the 3.1 percent gradient down to about 2.8 to 2.9 percent, further below the 3.3 percent requirement. The take-off distance also increases, typically by about 5 to 10 percent for a 5 kt tailwind, so the 1,850 m estimate could rise to about 1,950 to 2,035 m, exceeding the 2,020 m take-off distance available. The tailwind therefore makes both the climb and the distance worse, and the departure should not be attempted with a tailwind unless the AFM figures confirm compliance.