Thanks for the correction Alex, you had me puzzled there for a while!!
I do not have access to an L1011-1 manual but I (and most people studying for the JAR ATPL) do have a CAP 698. The take-off speed charts in this (figs 4.8 for 5 degree flap and 4.9 for 15 degree flap) comply with your amended observations. As density altitude increases, VR increases slightly while V2 decreases.
My own explanation of these phenomena are detailed below. I appreciate that you are probably already aware of most of what I am saying, but the ATPL students among our readers might appreciate a detailed explanation.
JAR 25 criteria are as follows:
V2 Min must be not less than;
1.2 VS for 2 and 3 engine turboprops and jets.
1.15 Vs for 4 engine turboprops and jets.
1.1VMC.
As explained in a number of the earlier posts in this string, the magnitudes of the minimum control speeds are related to the thrust available. Increasing altitude causes air density, mass flow through the engines and hence thrust to decrease. This decreases the magnitude of the asymmetric thrust problem following an engine failure. This in turn reduces the control authority required to maintain control following engine failure, so the minimum control speeds decrease. Decreasing VMC permits V2 to be reduced, provided this does not violate any of the other criteria specified above.
If we look at the CAP 698 figures referred to above, we see that V2 does indeed decrease as pressure altitude increases, but only at masses of 50000 Kg and below at flap 5 and at masses of 55000 and below at flap 15. At higher masses, the 1.15 VS or 1.2 VS criteria become the lower limit for V2. So V2 increases very slightly with increasing density altitude.
JAR 25 criteria for VR are as follows:
VR must be not less than:
V1.
1.05 VMC.
That required to attain V2 by screen height.
That required to ensure VLOF is at least 1.1 VMU with all engine operating and 1.05 VMU with one engine failed.
As altitude increases, the decreasing thrust also reduces the acceleration rate during the take-off. This reduces the allowable gap between VR and V2. So although V2 is decreasing slightly, VR must also increase to ensure that V2 is attained by screen height. The CAP figures illustrate this effect for all masses and flap settings.
V1 is the decision speed. It is worth noting that this is the only speed at which a decision needs to be made to complete or abort the take-off in the event of an engine failure. For engine failure at all other speeds, the decision has already been made by the regulations. At lower speeds the take-off must be aborted and at higher speeds it must be continued.
V1 is the speed at which it is possible to complete or abort within the ASDA and TODA. This means that at V1 it must be possible to:
Decelerate to a halt within the remaining ASDA.
Accelerate to V2 by screen height.
Acceleration rates decrease with increasing mass and/or increasing density altitude, so the allowable gap between V1 and V2 also decreases. The minimum value of V1 therefore increases with mass and altitude. This means that the minimum value of V1 at any given mass decreases as density altitude decreases.
But the aircraft must remain controlable at all times, so the absolute minimum value for V1 is VMCG. But at low mass and low density altitudes the increased VMCG becomes the limiting factor. This is illustrated by the shaded areas in the lower regions of the CAP tables, where reference must be made to the VMCG tables.
Last edited by Keith.Williams.; 12th April 2002 at 06:55.