Question 1.
The first point to note in addressing this question is that calculation of the maximum take-off mass assumes that a single engine failure has occurred. This means that this three engine aircraft effectively has only two engines.
So total thrust available 2 x 50000N = 100000N.
For small angles of climb, the % climb = 100% x Sin angle of climb
This can be rearranged to give: Sin angle of climb = % climb /100
And Sin angle of climb = (Thrust – drag) / Weight
Combing the two equations above gives:% climb / 100 = (Thrust – Drag) / weight
This can be rearranged to give: Max weight = 100 x (Thrust-Drag) / % climb
Inserting the data provided in the question gives:
Max take-off weight = 100 x (100000 – 72569) / 2.7 = 1015962.963N
This can be converted into Kg by dividing by g = 10 m/s2 to give 101596.2963 Kg or approximately 101596 Kg.
Question 2.
To solve this type of problem it must first be noted that winds do not affect the climb limited take-off mass. The wind correction need therefore be applied only to the runway limit (field limited take-off mass).
The next stage of the solution is to calculate and apply the corrections. the question specifies a correction factor of -360 kg/kt tailwind and an actual tailwind of 5 kts. this gives a correction of -360 Kg/kt x 5kt = - 1800 Kg.
Adding this to the figures provided in the question gives:
Flap angle: 5° 15° 25 °
Runway limitation (kg): 64 200 67 700 69 700
2nd segment slope limitation: 72 200 69 000 61 800
Finally select the flap setting for which the lower of the two limits is greatest. This is 15degree flap which gives a limit of 67 700 Kg.
Question 3.
The maximum climb gradient that an aircraft can achieve is inversely proportional to its mass. This can be stated in the form of an equation:
%climb at new mass x new mass = % climb at old mass x old mass
This can be rearranged to give:
New mass = % climb at old mass x old mass
% climb at new mass
Inserting the data provided in the question gives:
New mass = 2.8% x 110000 Kg = 118461.54 Kg
2.6%