getting to grips with aircraft performance 如何掌握飞机性能 2(38)

The result of this optimization process is, for a given V2/VS ratio, an optimumMTOW and an associated optimum V1/VR ratio.
2.3.3. V2/VS Ratio Influence
The purpose of this paragraph is to study the influence of V2/VS ratio variations on takeoff performance, for a given V1/VR ratio.
2.3.3.1. Runway Limitations
As a general rule, for a given V1/VR ratio, any increase in the V2/VS ratio  leads to an increase in the one-engine-out and the all-engine takeoff distances. Indeed, it is necessary to acquire more energy on the runway, in order to achieve a higher V2 speed at 35 feet. As a result, the acceleration phase is longer.
On the contrary, V2 speed has no direct impact on the ASD. But a higher V2 speed results in a higher VR speed and, therefore, for a given V1/VR ratio, in a higher V1 speed. Hence, the effect on ASD.

2.3.3.2.  Climb and Obstacle Limitations
As shown in Figure J4, any V2/VS increase results in better climb gradients (1st and 2nd segment) and, therefore, in better climb limited MTOWs (1st segment, 2nd segment, obstacle).
On the other hand, as the final takeoff segment is flown at green dot speed, it is not influenced by V2 speed variations.

Any V2/VS increase leads to (Figure J10):
.  
An increase in MTOW limited by the:

. 
 First segment

. 
 Second segment

. 
 Obstacles

.  
Not influencing the MTOW limited by the:

.  Final takeoff segment
2.3.3.3. Brake Energy and Tire Speed Limitations
V2 speed does not directly impact brake energy limitation. Nevertheless, any V2 increase results in a VR increase and, therefore, in a V1 increase, at a fixed V1/VR ratio. Hence, the effect on brake energy limited weight.

The lift-off speed, VLOF, is limited by the tire speed (Vtire). As a result, V2 is limited to a maximum value. Any V2/VS increase is then equivalent to a VS reduction, since V2 is assumed to be fixed, and thus the tire speed limited takeoff weight is reduced.

Any V2/VS increase leads to (Figure J11):
.  A decrease in MTOW limited by the:
. 
 Brake energy

. 
 Tire speed

2.4. Result of the Optimization Process
2.4.1. Maximum Takeoff Weight
The previous section shows how, for a given V2/VS ratio, it is possible to find an optimum MTOW and its associated optimum V1/VR ratio.
For each V2/VS ratio comprised between V2/Vsmin and V2/Vsmax, such a determination is carried out. In the end, the highest of all the optimum MTOWs and associated optimum V1/VR is retained. It therefore corresponds to an optimum V2/VS ratio. The result of the optimization process is, for a given runway and given takeoff conditions:

2.4.2. Takeoff Speeds
The optimization process indicates that MTOW can only be taken off with a single set of takeoff speeds (V1, VR and V2). The use of different speeds would result in an MTOW reduction.
　
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