Influence of the weight and balance on speeds
 

Somebody ask me about the influence of the weight and balance on Vmcg, and Vmca...
I am not sure of the answer, for me:
there is an influence only in case of aircraft control loss....
thank you for your help

Vmca

CG

In general, the further aft the location of the CG, the shorter the arm of the vertical stabilizer and rudder from the location of the axis around which the the aircraft yaws. With a shorter arm, any yaw force generated at the vertical stabilizer and rudder will have less effect. Or put another way, fewer lb/ft of torque are applied about the vertical axis of the aircraft. So Vmca will be higher when the CG is at the Aft limit than when it is at the forward limit.

Weight (Mass)

In a twin engined airplane, the total loss of thrust from one engine will induce a given yaw force at Vmca. The yaw rate generated by the asymetric thrust will vary somewhat according to the present mass of the aircraft. The lighter weight aircraft will generally experience a somewhat higher yaw rate when experiencing a loss of thrust from one engine than the heavier aircraft will. A given amount of force applied to an object will cause the object to accelerate at a rate according to it's mass. The lighter the aircraft, the more quickly it will yaw and yaw-induced roll into the failed engine. This can be important since a the aircraft must be controllable within 20 degrees of heading during testing.

Determination of Vmca during certification

As a part of the certification of a multi-engine aircraft, Vmca is determined according to the certification criteria of the regulating authority. This speed is generally determined for the aircraft in the weight and balance condition and configuration which will result in the highest Vmca. Detailed testing criteria is available HERE for FAA part 25 aircraft. PDF file

Lighter and a further aft CG will normally result in the highest tested Vmca. I'll leave it for someone else to have a go at Vmcg or to make any corrections or additions to my simplified response to your question.

Best regards,

Westhawk

Thank you very much for this excellent answer!!!:)

Aft cg makes both worse as it reduces control power while not affecting the engine moment (for Vmcg it reduces nosewheel steering effectiveness as well as rudder power, even though the former isnt counted for cert anyway)

Weight classically makes Vmca worse as it reduces, not due to the dynamics effect mentioned but because of the 5 degree bank limit. The lighter the aircraft, the less sideslip is a result of a 5 deg bank and hence the less restoring yawing mom,ent can be generated to help the rudder.

Weight is nominally neutral for Vmcg.

(Note that Ive seen items from Airbus arguing for weight neutrality or for heavy weight critical for Vmca, based on the assumption of a fixed lower speed limit for Vmca and hence arguing that the higher AoA at heavier weights reduces control effectiveness more than the sideslip helps. An interesting idea, and obviously type dependent. We always test at min weight for Vmca, though)

Vmca, is based on the following:
1)MTOW
2)Rear C of G
3)Max 5` of bank
4)METO power
5)full rudder

That being said, I understand all but #1. Does weight affect Vmca (or Vmcg) I would think it does but I have read otherwise.

MTOW - No.

Vmca is most critical; at MINIMUM weight. This is because the amount of bank into the live engine is limited - by regulation - at 5 degrees.

For a given weight, the sideslip to balance 5 deg bank can be determined; the heavier the aircraft, the more sideslip you need to balance 5 deg bank. Since that sideslip HELPS control the asymettric engine, it follows that the critical case is where the sideslip is minimize, i.e. the lowest weight. Therefore Vmca is highest at the minimum weight.

Vmcg is less clear-cut and one can argue that its pretty much independent of weight. the regs/AC require testing at the weight where Vmcg is critical, but dont specify the weight, so its up to the OEM to convince the NAA that they have the right test conditions.