KW your reply makes perfect sense (to me) if I change a few words based on F=MA or
acceleration = F/M where both M and F are pretty much constant after you set power.
thus
Many JAR ATPL students have a little bit of difficulty with this subject. The best way of approaching it is to start by going back to the definition of V1 then consider the implications.
If an engine failure is recognised at speeds below V1 the take-off must be aborted. To do this it must be possible to bring the aircraft to a stop within the remaining accelerate-stop distance available. The greater the V1, the greater will be the distance required to stop.
If an engine failure is recognised above V1 then the take-off must be continued. To do this it is neceassry to accelerate to V2 and reach screen height within the remaining take-off distance available. The greater the V1, the less the acceleration (time) required to reach V2 and the less the distance ***********
The above requirements mean that V1 marks the demarkation between being required to stop and being required to go in the event of an engine failure. This means that at V1 the aircraft must be equally capable of stopping or going within the remaining distances available.
Any factor (such as an upward slope) that decreases acceleration *** will increase the distance required to get from V1 to V2. If spare distance is not available then V1 MUST be increased making it closer to V2. This makes an increased V1 NECESSARY.
Any factor that increases decelertaion rate decreases the distance required to stop. So V1 may be increased and still permit the aircraft to stop. This makes an increased V1 POSSIBLE, but does NOT MAKE IT NECESSARY.
So an upward slope means that V1 MUST be increased to complete the take-off and MAY be increased without preventing an abort. The overall effect is that V1 MUST be increased.
The effects of other factors such as headwinds or tailwinds can be deduced in the same manner. After a bit of practice most students find this easier than trying to remember a long list of effects.
From JAR 25.367
.........
(b) Pilot corrective action may be assumed to be initiated at the time maximum yawing velocity is reached, but not earlier than two seconds after the engine failure. The magnitude of the corrective action may be based on the control forces specified in JAR 25.397 (b) except that lower forces may be assumed where it is shown by analysis or test that these forces can control the yaw and roll resulting from the prescribed engine failure conditions.
For V1 cuts, I don\'t see how an assumption of a quicker response time can be made and I was under the impression that the more typical assumption was 4 seconds. Obviously some automated systems, ala B777 rudder kicks may alleviate some of the control reaction times but may not affect V1 stop assessments.