Are there any aircraft where minimum-V1 is limited by Vmcg? V1, unlike all the other Vspeeds, is not rigidly determined by the laws of physics, the aircraft’s specific abilities, and the conditions of the particular takeoff being attempted,1 but is, rather, chosen by the pilots from a range of possible V1s.


The lower limit of this range is generally set by the speed past which the takeoff can safely be continued while maintaining adequate obstacle clearance, even in the event of an engine failure (henceforth known as the first-safe-go speed).
The upper limit of this range is set by the speed past which the aircraft can no longer be guaranteed to stop on the runway in the event of a maximum-effort no-reverse-thrust rejected takeoff (henceforth known as the last-safe-RTO speed).


However, if an aircraft is sufficiently light and has sufficiently-powerful engines (especially if said engines are mounted far from the aircraft’s centerline), one could potentially conceive of a situation where the lower limit of the V1 envelope is not, in fact, determined by the first-safe-go speed, but, rather, by...


...the speed below which the aircraft has insufficient rudder authority to maintain directional control at takeoff thrust in the event of an asymmetric engine failure (known as the minimum controllable speed - ground, or Vmcg).


Such a light, sporty aircraft could easily have a theoretical first-safe-go speed that is lower than Vmcg, as low total weight and high thrust-per-engine both decrease the first-safe-go speed,2 and, simultaneously, increase Vmcg.3  This would force the lower limit of the possible-V1s range to be set, not at the theoretical first-safe-go speed, but, rather, some distance above that, at Vmcg (as an asymmetric engine failure at or above the theoretical first-safe-go speed, but below Vmcg, would result in an immediate loss of directional control, necessitating a rejected takeoff).  For added complexity, some aircraft have engines at varying distances from the aircraft’s centerline (for instance, a trijet with one engine slung under each wing and one mounted in the tailcone, or a quadjet with one outboard and one inboard engine slung under each wing), resulting in different Vmcgs for different engine-out scenarios, such that, at a given speed, an aircraft might be able to safely continue a takeoff if a centerline or close-to-centerline engine fails, but would suffer a loss of directional control, and have to reject, should a far-from-centerline engine fail.

Are there actually any aircraft for which the minimum-allowable-V1 is limited by Vmcg, rather than the first-safe-go speed?



1: ...except in the special case of the aircraft being at exactly its maximum allowable weight for the takeoff being attempted, in which case there is only one possible value of V1.

2: ...as a lighter aircraft needs less speed (and, thus, less thrust) to become airborne, and an aircraft with powerful engines has more thrust to work with in the event of an engine failure.

3: ...as an aircraft with powerful engines needs more rudder authority (and, thus, more speed) to maintain directional control with an asymmetric engine failed and the other(s) at takeoff thrust (a problem which grows steadily worse the further the asymmetric engine(s) get from the aircraft’s centerline, due to the larger and larger yawing moment arm generated as they move away from the centerline), and a lighter aircraft has less weight on its landing gear (and, thus, less traction force acting to resist the yawing moment from an asymmetric engine failure).
Yes

Almost any transport category jet will reach its Vmcg V1 limit in favorable conditions.

The rationale is quite easy: When fully loaded with heavy fuel load (ie. at maximum takeoff weight) some 20% of weight is payload and about 20% is fuel. When the same jet is taking off with light passenger load for a short hop with low fuel load, there is massive surplus of thrust available so there is some acceleration available in case of engine failure on ground. This is especially true for twins.