I am about to get my MEL added to my CFI, and I cannot get my head around the multiple explanations for how gross weight affects Vmc.
The accepted answer is that The higher the gross weight, the lower is the Vmc. I have been proffered two contradictory explanations, from both internet articles, manufacturer documents, and other CFIs, both of which seem to me (I have an MSME masters degree in Aero) to be flawed.
- That because the aircraft is slightly banked into the direction of the good engine, the horizontal component of Lift (HCL) opposes the yaw from the rudder, thus allowing the aircraft to slow to a lower airspeed before full rudder authority is required to counteract the yaw from the operating engine. This is wrong, because if you're in a bank, the HCL (by definition, it is HORIZONTAL!), is no longer lined up with the lateral axis of the aircraft. It is misaligned by exactly the bank angle, so, although there is a component of the HCL opposing the yaw force from the rudder, there is an exactly equal and compensating component of the Vertical Component of Lift (VCL) that will be augmenting the Yaw force. This argument is bogus.
I mean if you think about it simpler, the Lift vector is always, ALWAYS, perpendicular to the wings, so that any effect of Lift along the lateral axis (parallel with yaw forces), must necessarily be zero.
The fact that is not aligned with the earth horizon is irrelevant.
The other rationale I have been presented with is that as the gross weight increases, the resistance to motion (Engineers would call this rotational inertia) increases, and makes the aircraft more stable. This is true, but it is an argument about dynamic stability, not about static stability. In other words, this affects the aircrafts resistance to changes in yaw/sideslip angle. Vmc is about static stability, i.e., at what airspeed does the aircraft, in a static, (unchanging) zero sideslip angle, require full rudder defection to hold the aircraft (STATICALLY) at that zero sideslip angle against all the yaw forces being produced by all the factors resulting from Asymmetric thrust?
So this argument or rationale also seems to be incorrect to me.
Where is the flaw in this reasoning?
By the way, the only effect of Gross weight on Vmc that I can think of is the obvious one, The higher the gross weight, the greater the Angle of Attack required to hold 1 G (Level flight), and obviously, both P-Factor and adverse yaw increases with AOA. So the higher the Gross weight, the greater the P-Factor, and the greater the yaw-induced aerodynamic effects of the asymmetric thrust. So, if this logic is correct, Higher Gross weight means Higher Vmc, not Lower.