Takeoff Speed Optimization – Speed Ratios V1/Vr and V2/Vs

Takeoff optimization principal has objective of attaining highest possible performance limited takeoff weight while fulfilling airworthiness requirements. Parameters influencing takeoff performance can be Sustained Parameters (can’t be changed) and Free Parameters(variable to certain extent).

As part of free parameters takeoff speed optimization is the most important method to gain better takeoff performance and hence higher value of MTOW.

MTOW can be limited by various factors:

  • Structural weight
  • Climb gradient requirement for 1st, 2nd or final takeoff segments
  • Tire speed
  • Obstacle etc

Important links:


This study note covers V1/Vr ratio and V2/Vs ratio range and their influence with respect to different factors stated above.

V1/Vr Range
  • Since V1 must always be less than Vr maximum value of V1/Vr ratio is equal to 1
  • Value of V1 speed less than 84% of Vr increase takeoff distance too much and has no performance advantage (example w.r.t. Airbus aircrafts). So minimum value of V1/Vr ratio is 0.84
  • Available band is between 0.84 to 1.0 both inclusive
V2/Vs Range
  • Minimum V2 speed is defined by regulations as 1.2Vs or 1.13Vs1g (click to read difference between Vs and Vs1g)
  • Too high V2 speed requires long takeoff distance and hence reduce climb performance
  • Maximum beneficial value of V2 max depends on aircraft type (1.35Vs1g A320 family, 1.40Vs1g A330, 1.35Vs for A300 and A310)

V1/Vr Ratio Influence

Influence of V1/Vr ration can be explained with following points, the same point numbers may be used for future references in this study note:

1A Runway limitations

  • Increase in V1/Vr ratio decreases the take of distance required and hence increase the MTOW for engine failure case. (because for engine failure go condition aircraft will have to accelerate lesser margin on single engine between V1 and Vr)
  • With increase in V1/Vr ratio ASDR (Accelerate Stop Distance Required)  increases. Hence MTOW gets limited by ASD increase.
  • Although V1 speed has no effect on climb gradient but higher V1 value decreases TODR (Takeoff Distance Required). Therefore start of takeoff flight path is obtained at a shorter distance and require lower gradient to clear the obstacles.
  • Increase in V1/Vr increase the MTOW limited by obstacle and has no effect on MTOW limited by first segment, second segment and final segment. (click to read on Segments of Takeoff)

1B Brake Energy Limitations

V1 max is limited by Vmbe(maximum brake energy speed). As the aircraft weight increases Vmbe decreases. So reduction in MTOW is required to increase Vmbe and V1.

Intersection point between two limitation curves 1A and 1B gives the optimum V1/Vr value.


V2/Vs Ratio Influence

Influence of V2/Vs ration can be explained with following points, the same point numbers may be used for future references in this study note:

2A Runway Limitations

  • Any increase in V2/Vs ratio increase the TODR for engine out as well as all engine take off conditions. Since V2 has to be reached by 35ft aircraft will accelerated longer on  ground.
  • V2 speed has no direct impact on ASDR but higher V2 needs higher Vr to provide longer ground run. Assuming fix V1/VR ratio, higher V1 will be required and hence ASD will increase.
  • As explained in above two reason any increase in V2/Vs leads to decrease in runway limited MTOW.

2B Climb and Obstacle Limitations

  • Since aircraft climbs at V2 in 1st and 2nd segment of climb, higher V2 value results in better climb gradients. So any increase in V2/Vs increase the MTOW limited by 1st segment, 2nd segment and obstacles.

2C Brake Energy and Tire Speed Limitations

  • V2 speed has no direct impact on V1 but higher V2 needs higher Vr to provide longer ground run. Assuming fix V1/VR ratio, higher V1 will be required. High value of V1 gets limited by braking energy.
  • Any increase in V2/Vs decreases the MTOW limited by brake energy and tire speed

CONCLUSION

  • For every V2/Vs value it is possible to find out optimum MTOW and associated V1/Vr ratio
  • This procedure is followed for entire range of V2/Vs.
  • At the end highest of all optimum MTOWs and associated optimum V1/Vr is retained.

This takeoff speed optimization process indicates that at MTOW takeoff can only be done with single set of takeoff speeds V1, Vr and V2. Use of any speed other than this set of value will result in MTOW reduction.


Aircraft Performance

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