Requirement 3: Second Segment Climb

 Background

Climb Gradient

JAR 25.121 Climb: One-engine-inoperative.
(b) Take-off; landing gear retracted. In the take-off configuration existing at the point of the flight path at which the landing gear is fully retracted, and in the configuration used in JAR 25.111 but without ground effect, the steady gradient of climb may not be less than
      2·4 percent for two-engined aeroplanes,
      2·7 percent for three-engined aeroplanes, and
      3·0 percent for four-engined aeroplanes,
at V2 and with -
(1) The critical engine inoperative, the remaining engines at the take-off power or thrust available at the time the landing gear is fully retracted, determined under JAR 25.111, unless there is a more critical power operating condition existing later along the flight path but before the point where the aeroplane reaches a height of 400 ft above the take-off surface(...); and
(2) The weight equal to the weight existing when the aeroplane's landing gear is fully retracted, determined under JAR 25.111.

In figure 1 the second segment while the takeoff is presented according to JAR.

next: equations for calculation

 Equations

The second segment is based on the situation with one engine of the aircraft inoperative.
Therefore, the thrust of the remaining engine(s) has to be enough to climb as required. From the equilibrium condition can be got two equations:

Since these equilibrium conditions have to be achieved with one engine inoperative, the required thrust at takeoff with all engines operating has to be higher by a factor N/(N-1). N is the number of engines. The thrust to weight ratio following from the requirement is:

The climb gradient in the equation above is small. Therefore it can be simplified:

 Data

Lift to Drag Ratio

• Oswald's airplane efficiency factor e is 0.7,
• wing aspect ratio A is given or taken from statistics,
• drag coefficient at zero lift c_{D, 0} is assumed to be 0.02,
• landing gear drag coefficient c_{D, gear} is 0.015,
• slat drag coefficient c_{D, slat} is neglected and set to zero,
• flap drag coefficient c_{D, flap}:
  for c_L = 1.3 : flap deflection 15° => c_{D, flap} = 0.01
  for c_L = 1.5 : flap deflection 25° => c_{D, flap} = 0.02
  for c_L = 1.7 : flap deflection 35° => c_{D, flap} = 0.03 .

statistics of aspect ratio   equation characters - explanation page   next: calculation of takeoff thrust to weight

 Calculation

The takeoff thrust to weight ratio of the aircraft must be above the green line to fulfil the requirement for the second segment condition. (Bear in mind: Thrust means climb rate.)

 Results compared

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