Requirement 4: Missed Approach Climb

Background

Climb Gradient

The climb gradient for missed approach is determined from the aviation regulations:

JAR 25.121 Climb: One-engine-inoperative.
(d) Discontinued Approach. In a configuration in which VS does not exceed 110% of the VS for the related all-engines-operating landing configuration, the steady gradient may not be less than
2·1 % for two-engined aeroplanes,
2·4 % for three-engined aeroplanes, and
2·7 % for four- engined aeroplanes, with -
(1) The critical engine inoperative, the remaining engines at the available take-off power or thrust;
(2) The maximum landing weight; and
(3) A climb speed established in connection with normal landing procedures, but not exceeding 1·5 VS.
(4) Landing gear retracted.*

* Number (4) of § 25.121 (d) exists only in JAR 25 but not in FAR Part 25.

Equation

The missed approach is similar to the second segment situation where one engine of the aircraft is inoperative. The thrust of the remaining engine(s) has to be enough to climb again as required. The second segment climb equation is expanded by the mass ratio determined already in the landing field calculation:

The climb gradient can simplified similar to the second segment:

Data

Lift to Drag Ratio

The lift to drag ratio is calculated from the following equation:

The lift coefficient is the landing lift coefficient divided by 1.69, because the climb speed is 1.3 times the stall speed.
The drag coefficient consists of five parts:

where the

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 .

background of mass relation
statistics of aspect ratio
next: calculation of takeoff thrust to weight

Calculation

With given values of takeoff lift-coefficient, wing aspect ratio, mass ratio and the number of engines it is now possible to calculate the ratio between takeoff trust and takeoff weight. The landing gear is retracted according to JAR 25 and extended in the FAR 25.

In the table are typical start values already entered. The graph is presented in Figure 2.

maximum landing lift coefficient
c_L,max,L : [ - ]

landing gear:
retracted (JAR 25)
extended (FAR 25)

number of
engines (N) :
2
3
4

landing to takeoff mass (range):
0.91 (short)
0.82 (middle)
0.73 (long)
custom:

wing aspect ratio
A : [ - ]

result :

takeoff thrust
takeoff weight

[ - ]

Figure 2: chart for calculated results

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

Results compared

Takeoff thrust to weight ratio of selected aircraft JANE'S 1995-98

Aircraft	Airbus A 300-600B	Airbus A 310-300	Airbus A 340-300	Antonov AN 124	Boeing B 737-600	Boeing B 777	McDonnell Douglas MD11	Tupolev TU 204
Takeoff thrust Takeoff weight [ - ]	0.308 - 0.324	0.290 - 0.356	0.220 - 0.240	0.231	0.307	0.292 - 0.304	0.299 - 0.309	0.341 - 0.413

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Thomas Perthel, thomas.perthel@gmx.de