# Why does the airplane manual state S1 is equal to or greater than the higher of ground minimum control speed or critical engine failure speed

I don't understand why S1 is equal to or greater than the higher of Ground Minimum Control Speed or Critical Engine Failure Speed (Vcef). I do understand that S1 has to be the lowest of Refusal Speed, Rotation Speed, and Max Braking Speed. Take a situation where Vcef is 100 knots, and the upper bound for S1 is 120 knots. It would seem that the only factors that should matter in determining S1 would be the three speeds that determine the upper bound. Why does the manual even talk about the lower bound if you are always taking the upper bound as S1.

What is so special about Vcef that we have to be above it? I would think that being below it is not a bad thing since it would take less room to stop than it would to lift off if you lost an engine.

• Would you clarify the S1 speed you are referring to (FAA V1 [decision speed])? Also, what airplane/manual are you referring to? Thanks
– user22445
Commented May 14, 2023 at 3:08
• @757toga Manual for the T-1A. S1 is the go/no go speed also known as V1
– Name
Commented May 14, 2023 at 3:21

Having passed V1, you're committed to continuing the takeoff. If an engine fails after V1 but below VMCG, you have no viable option: you can't stop (you've already committed to continuing the takeoff), but you can't control the aircraft laterally.

The only thing that could be accomplished in that case -- and you're a test pilot doing so -- is to reduce the power on the operating symmetric engine and hope that you can find some power setting that gives both enough directional control and enough thrust to continue to takeoff and accelerate. The conventional wisdom is that this situation is unacceptable, and therefore V1 should not be lower than VMCG so that a crew isn't in that situation with no definite solution.

There is an unusual case where that risk is accepted; in C-130 "Max Effort Takeoff" procedures, it was allowed (when approved by the chain of command) to take off without that restriction; the idea being that in wartime operations, you accept the risk of an engine failure in the few seconds between V1 (calculated without considering VMCG) and VMCG in order to conduct the military mission on the short runway. The crew would be aware of VMCG and there was training that if you did in fact lose one in that window, pull power on the opposite outboard engine slightly, put in full rudder and maybe a bit more than the standard 5 degrees of bank into the operating engines, and hope real hard that you can get fast enough quickly enough to keep it all together. But there definitely was an element of additional risk in that operation.

• This has an interesting effect that sometimes (when the aircraft is light) a derated take-off requires less runway. When Vmcg is close to Vr, the point where V1 is achieved if pushed further down the runway and thus the accelerate-stop distance is longer than take-off distance. Reducing engine power reduces Vmcg and that allows using a more balanced field length that will end up being a bit shorter. Commented May 16, 2023 at 18:41

Admittedly this answer is for civil operations, military trainers might be somewhat different. But Vef is actually entirely dependent on the V1 that you select. Vef is the point at which the engine is presumed to fail, for the manufacturer to do the calculations (the acceleration is immediately reduced at Vef). It must be at least 1 second earlier than V1, allowing time for the pilots to recognise the failure and react. Remember, V1 is the speed at which you must have commenced the actions of rejecting the takeoff, not just making the decision.

V1 isn't only the last point you can abort the takeoff though. It's also the point at which you know it is safe to continue the takeoff, and that's where Vmcg plays a major role.

Vmcg is the minimum control speed on the ground. With one engine producing full thrust and one engine windmilling, you have a significant yaw in the direction of the failed engine. This has to be overcome by rudder, but if you don't have enough speed/airflow over the rudder, it won't have enough authority to overcome the yaw. Vmcg is the lowest speed at which the rudder is powerful enough to combat the yaw.

So in summary: if the engine fails before Vmcg and you attempt to continue the take-off as you've already passed V1, you will run off the side of the runway. V1 must be equal to or above Vmcg. V1 is also at least one second above Vef by definition.