Question about Vmc and Weight

[deadringer86]

Quick question here that has me stumped. We know that a heavier airplane has a lower Vmc since it can generate a greater horizontal component of lift at a given bank angle than a lighter aircraft. Therefore, we need less bank to counteract the sideslip. However, there is also the rule of thumb that Vmc decreases 3 knots per 1 degree of bank into the operating engine. Ignoring aircraft performance, wouldn't this contradict the weight theory as far as actual Vmc speed?

 

[tgrayson]

Quick question here that has me stumped. We know that a heavier airplane has a lower Vmc since it can generate a greater horizontal component of lift at a given bank angle than a lighter aircraft. Therefore, we need less bank to counteract the sideslip.

Almost, but not quite. The magic occurs not because you need less bank to achieve zero sideslip, but you have more sideslip when taking advantage of the full five degrees provided for in the regulation.

I regard this as a book reduction in Vmc, not a real one. As you noted, your goal is zero sideslip; if you achieve that, you don't have any change in Vmc.

 

[fish314]

Almost, but not quite. The magic occurs not because you need less bank to achieve zero sideslip, but you have more sideslip when taking advantage of the full five degrees provided for in the regulation.

I regard this as a book reduction in Vmc, not a real one. As you noted, your goal is zero sideslip; if you achieve that, you don't have any change in Vmc.

Hey T, is there some part of this that is due to momentum or increased mass? I remember that in the tanker on a TRT takeoff at max gross (~320 Klbs.) Vmc wasn't an issue, but you do that same TRT takeoff at 180 Klbs. and Vmc might be the S1 speed (decision speed).

I never really thought about it in terms of a force diagram, I just thought of it in terms of F=mA. If m gets bigger, and the force remains the same (two engines on one side, only one on the other), the airplane accelerates less. In this case, the acceleration in question is sideways, and since it's less it takes less to overcome it.

Based on your discussion above, seems like I've got the cart before the horse, though.

 

[MikeD]

Hey T, is there some part of this that is due to momentum or increased mass? I remember that in the tanker on a TRT takeoff at max gross (~320 Klbs.) Vmc wasn't an issue, but you do that same TRT takeoff at 180 Klbs. and Vmc might be the S1 speed (decision speed).

I never really thought about it in terms of a force diagram, I just thought of it in terms of F=mA. If m gets bigger, and the force remains the same (two engines on one side, only one on the other), the airplane accelerates less. In this case, the acceleration in question is sideways, and since it's less it takes less to overcome it.

Based on your discussion above, seems like I've got the cart before the horse, though.

Depends on the particular twin too. In the A-10, when single-engine, I don't have control challenges from spiraling slipstream, not that much torque to have to counteract, and am so power limited as-is (even moreso single engine) that isn't as much an issue unless I start getting real slow....almost uncomfortably slow and behind the power curve. Still, maintaining zero sidelip gives the least drag and the most performance, for what little performance remains, when single-engine.

Course there's always the option of jumping out too...

 

[tgrayson]

Hey T, is there some part of this that is due to momentum or increased mass?

In general, no, because increased mass just changes the amount of time it takes to lose control, not whether control is lost. Loss of control is a measure of the vertical rotational forces around the CG, and even one ounce of extra thrust over rudder lift force means that control is lost (ignoring moment arm length).

Moreover, increased mass wouldn't necessarily even affect that, because it would depend on how the mass is distributed. Increased mass at the CG wouldn't have any effect at all, but move the mass to the extremities of the a/c, and you have an increased moment of inertia, which will make the loss of control more sluggish, but just as assured.

That said, once control is lost, a high moment of inertia could make recovery difficult; supposedly they experiment with this (dynamic Vmc) during Vmc tests and will take the higher Vmc of the static versus dynamic Vmc tests. In the classic analysis of Vmc, this is ignored, and I think the concept is a bit of a distraction for those trying to understand the basic weight vs Vmc thing.

 

[MikeD]

That said, once control is lost, a high moment of inertia could make recovery difficult; supposedly they experiment with this (dynamic Vmc) during Vmc tests and will take the higher Vmc of the static versus dynamic Vmc tests. In the classic analysis of Vmc, this is ignored, and I think the concept is a bit of a distraction for those trying to understand the basic weight vs Vmc thing.

IIRC, that is how they test it and the result they use.

 

[deadringer86]

Almost, but not quite. The magic occurs not because you need less bank to achieve zero sideslip, but you have more sideslip when taking advantage of the full five degrees provided for in the regulation.

I regard this as a book reduction in Vmc, not a real one. As you noted, your goal is zero sideslip; if you achieve that, you don't have any change in Vmc.

Thanks! Makes sense.

 

[CoffeeIcePapers]

I always assumed it had little effect on VMC since the extra weight will require a higher AoA, which will give you more Pfactor and eliminate any benfit you get from the extra horizontal component of lift.

 

[mjg407]

In the mighty Orion, weight is not considered a factor in Vmc (3 or 2 engine) only density altitude and power.

 

[tgrayson]

since the extra weight will require a higher AoA, which will give you more Pfactor and eliminate any benfit you get from the extra horizontal component of lift.

No real data showing the relative magnitude of each for GA airplanes, but since all flight testing ensures the tests take place at light weights, I infer that the P-factor issue is negligible.

 

[tgrayson]

In the mighty Orion, weight is not considered a factor in Vmc (3 or 2 engine) only density altitude and power.

The increase in stall speed masks the reduction in Vmc in some airplanes due to weight, if the Vmc would otherwise be below stall speed.

Also, some large propeller aircraft are aileron limited, rather than rudder limited, so sideslip wouldn't provide a reduction in Vmc. This may be the case with the Orion.