Vmc Question

[mhcasey]

Max gross weight: I've heard two theories. One states that Vmc is lowered at max gross weight because the heavier aircraft has more inertia, therefore requiring greater asymmetrical thrust to accomplish the same yaw rate.

The other theory is that Vmc is increased at max gross because chances are the aircraft is going to yaw at least a little bit before you input rudder control, and this heavier aircraft will therefore have greater momentum and will require more rudder to bring the nose back around.

In regards to the latter: All else equal, even if we accept theory two, it seems that the momentum shouldn't be an issue. The same asymmetrical thrust/drag (force) is acting on both aircraft, so the lighter aircraft will just yaw faster and have the same momentum.

This is a quote from my D.E.'s website: "A multiengine airplane experiences a sudden failure of the critical engine while in flight. The airplane begins to yaw to the left, regardless of its mass. The surprised pilot then applies right rudder in order to stop the yawing motion, stabilize the airplane around its vertical axis and then maintain a constant heading. A heavier airplane will require more rudder effectiveness to accomplish this. At some point, the rudder may reach full deflection and Vma will be reached. This will occur at a higher airspeed for a heavier airplane."

Anyone want to shed some light on this issue? Does the higher angle of attack required at max gross for any given airspeed have any effect on Vmc?

Here's another one regarding banking into the inoperative engine:

"Holding a bank in the direction of the operating engine may increase the performance of the multiengine in some respects, but it definitely raises Vmca...The pilot of this airplane has banked five degrees in the direction of the operating engine in an attempt to maintain coordinated flight. In order to maintain that bank, the aileron controls must be held in a bank to the right...The result is that drag is increased on the left and decreased on the right, increasing the yawing moment to the left. The asymmetrical drag increases the rotational force vector and raises Vmca."

Essentially he's saying that banking into the operative engine increases Vmc because of adverse yaw. I can't help but wonder if this is actually the case in an engine out scenario? It seems like a component of the aircraft's weight may be vectored opposite the asymmetrical thrust/drag, therefore reducing the yawing moment? If this is the case, the max gross lowering Vmc would hold more merit also. Your thoughts?

[tgrayson]

Max gross weight: I've heard two theories.

You have surely heard more than those two "theories", because I know that I, among others, have posted the correct explanation here. The two you listed are both fallacious. Let me repost what I said in another thread on crosswind capability:

1. If the increased mass were located at the CG, there would be no difference in the yawing capacity of the aircraft, since it yaws *around* the CG. What you would really be interested in is the distribution of mass, not its absolute quantity. This is addressed by the concept of moment of inertia. A large moment of inertia means that the mass is distributed toward the extremities of the object, rather than at the center. (Think of a dumbbell.)
2. Even if there were a high moment of inertia (resistance to yawing), it would merely affect the acceleration of yaw, not the maximum quantity of yaw achievable. The aircraft would respond sluggishly to the rudder, but it would respond.

Weight affects Vmc because weight affects the sideslip velocity achievable with a five degree bank. A heavier airplane can achieve a greater sideslip into the good engine and thus achieve greater directional control authority.

This is a quote from my D.E.'s website: "A multiengine airplane experiences a sudden failure of the critical engine while in flight. The airplane begins to yaw to the left, regardless of its mass.

Your DE would have somewhat of a point if he substituted "Moment of Inertia" for weight. But this is only because that Vmc testing measures static Vmc and Dynamic Vmc, the dynamic Vmc scenario being similar to what he describes. The requirement is that the control must be reestablished before the heading changes more than 20 degrees. An aircraft with a high moment of inertia would make that more difficult.

Your DE is trying to explain a phenomenon in terms of physics that he understands, rather than the actual physics that hasn't been explained to him. When I was in high school, I racked my brains for an explanation as to how phasers could work in terms of physics that I knew. All I could come up with was that the beam was electricity, because that could both stun and blow things up. I still couldn't figure out why the color changed from season to season.

Here's another one regarding banking into the inoperative engine: "Holding a bank in the direction of the operating engine may increase the performance of the multiengine in some respects, but it definitely raises Vmca...

Your DE is greatly mistaken about this. Even the Airplane Flying Handbook knows better. He should be beaten with a stick.

[mhcasey]

Thanks Tgrayson. Sorry I missed the earlier discussion in the x-wind topic...I lost it in that philosophical debate that continued in page 2.

Anyway, checkride is on Thursday, so I'll probably be back again tomorrow with more questions.

[tgrayson]

Originally Posted by mhcasey

Anyway, checkride is on Thursday, so I'll probably be back again tomorrow

Thank goodness you aren't waiting until the last minute.

[ClearedToThe]

Originally Posted by mhcasey

Thanks Tgrayson. Sorry I missed the earlier discussion in the x-wind topic...I lost it in that philosophical debate that continued in page 2.

Anyway, checkride is on Thursday, so I'll probably be back again tomorrow with more questions.

Everything that tgrayson said is 100% spot on. For any given angle of bank, a heavier airplane will have a higher horizontal component of lift generated at that bank angle. This is due to the wing generating more TOTAL lift at a higher weight (lift = weight). A high HCL of lift equals a greater sideslip force opposing the yaw due to the asymmetrical thrust.

Also remember, 5deg bank into good engine is for CONTROL (1deg bank =(approx) 3kt reduction in vmc speed).

Zero sideslip (2-3deg of bank and 1/2-1/3ball out) is for PERFORMANCE. (less drag on plane results in more excess thrust avail. to climb, turn, etc.)

Finally, if your DE gives you crap about the 5deg of bank resulting in a higher Vmc, simply do the Vmc demo with 5deg of bank and note airspeed you lose control. Then do the Vmc demo again with 0 bank and note airspeed. I do it with my students all the time to emphasize the importance of the bank.

If he still gives you a hard time about it, just whip out the FAA's flying handbook and cite that. After all thats why the "REFERENCES: " are listed under each PTS Task.

ps - what airplane are you doing your checkride in?

[mhcasey]

So the heavier airplane flies at a higher angle of attack to produce more lift, which can be slipped into the operating engine creating more stability. It seems the higher angle of attack results in two things, though:

1) Higher stall speed (lower critical altitude)
2) More P-Factor (less stability)

I'm guessing 2 is probably out-forced by the additional weight in most cases, though I guess we'd need some engineering data for that one.

Another question from my flight school's multi engine packet: "With flaps extended a lesser angle of attack is necessary to produce the same amount of lift. Therefore, P-factor is less as well as yaw. Additionally, flaps increase drag aft of the C.G., providing a stabilizing effect."

Is this necessarily true? Flaps also increase drag and therefore power required, so to maintain altitude it seems you might actually need to increase the angle of attack, even if that means the pitch attitude being slightly lower than without flaps. My understanding was with flaps extended you may take a trade off and actually increase angle of attack in order to decrease the stall speed? Your thoughts?

Another quote from the DE: "That means that Vmca is a limitation on the ability to control the airplane around its vertical axis. The only flight control that can control the airplane around its vertical axis is the rudder. Once the rudder is at full deflection toward the operating engine, Vmca has been achieved."

Is it safe to say that his theory about bank angle is bunk because the rest of the vertical stabilizer will produce weather vaning when the aircraft is slipping, so really he should be saying, "Once the rudder is at full deflection toward the operating engine with no more than 5 degrees of bank according to FAR 23, Vmca has been achieved?"

The checkride is in a Duchess.

[sundog]

the P-factor and torque are indeed higher (in level flight) when the aircraft is heavier, however Vmc is defined as at full power on the remaining engine, so the difference is not applicable to Vmc.

whenever the total drag of the aircraft is increased the additional asymmetric drag of a dead engine is a smaller percentage of total drag and therefore has a lesser influence, decreasing Vmc.

[tgrayson]

Originally Posted by mhcasey

So the heavier airplane flies at a higher angle of attack to produce more lift, which can be slipped into the operating engine creating more stability. It seems the higher angle of attack results in two things, though:

I didn't mention higher AOA, and I don't think one is required. As the wing tilts towards the side, the vertical stabilizer starts tilting upwards, replacing the lost lift. Some rough calculations suggest that the lift provided by the vertical stabilizer is actually greater than the lift lost by the wing bank angle, which would require a smaller AOA for the main wing. Very neglible though.

Another question from my flight school's multi engine packet: "With flaps extended a lesser angle of attack is necessary to produce the same amount of lift. Therefore, P-factor is less as well as yaw.

Probably true, although I've seen no data on it. Suspect the effect is smaller than:

Additionally, flaps increase drag aft of the C.G., providing a stabilizing effect."

Note that drag behind the CG isn't the most important thing, but rather having differential drag. If the upwind flap produces more drag than the downwind flap, the aircraft will have a stabilizing moment.

Is this necessarily true?

For every rule you can come up with, you can almost always find exceptions. However, there is abundant data that shows that flaps tend to increase the directional stability of airplanes.

Flaps also increase drag and therefore power required, so to maintain altitude it seems you might actually need to increase the angle of attack

Remember that Vmc has nothing to do with performance, so yes, the power required will go up and it's possible that the aircraft will not be able to maintain altitude at that airspeed. And, yes, increasing the angle of attack may reduce the power required enough to allow the altitude to be maintained, but that means that you've moved closer to a new, lower Vmc.

even if that means the pitch attitude being slightly lower than without flaps.

Lost me there. Don't you mean "higher"?

My understanding was with flaps extended you may take a trade off and actually increase angle of attack in order to decrease the stall speed?

For trailing edge flaps, no, the resulting AOA will always be lower at a given lift coefficient (airspeed) than an unflapped wing. Leading edge flaps, different story.

Once the rudder is at full deflection toward the operating engine with no more than 5 degrees of bank according to FAR 23, Vmca has been achieved?"

That's probably more accurate, although the bank is at the option of the applicant. And to be more accurate, some airplanes are aileron limited, rather than rudder limited, but probably not an issue for the vast majority of light twins.

Note too, for rudder-limited airplanes, you can reduce Vmc to whatever number you want if you're willing to increase your bank angle past 5 degrees. You'll stall in most airplanes, though.

[ClearedToThe]

Originally Posted by tgrayson

That's probably more accurate, although the bank is at the option of the applicant. And to be more accurate, some airplanes are aileron limited, rather than rudder limited, but probably not an issue for the vast majority of light twins.

While the bank is at the option of the applicant, the PTS does still require a bank towards the operation engine.


Objective.

To determine that the applicant:

1. Exhibits knowledge of the elements related to VMC by explaining
the causes of loss of directional control at airspeeds less than
VMC, the factors affecting VMC, and safe recovery procedures.
2. Configures the airplane at VSSE/VYSE, as appropriate—
a. Landing gear retracted.
b. Flaps set for takeoff.
c. Cowl flaps set for takeoff.
d. Trim set for takeoff.
e. Propellers set for high RPM.
f. Power on critical engine reduced to idle.
g. Power on operating engine set to takeoff or maximum
available power.
3. Establishes a single-engine climb attitude with the airspeed at
approximately 10 knots above VSSE or VYSE, as appropriate.
4. Establishes a bank toward the operating engine, as required for

best performance and controllability.


Also, another thing to remember is that the FARs just limit UP TO 5deg of bank for Vmc certification. Although you can almost bet that all manufacturers used all 5deg to get the speed as low as possible... Finally, make sure you understand the control vs. performance aspects of all the Vmc items. For example, extending the flaps and landing gear will give you better controllability upon losing and engine....but why don't u extend them when you lose an engine....obviously your loss of performance would far outweigh the gain in controllability.

Good luck on your checkride!

[mhcasey]

Thanks guys. The checkride was no problem, though my examiner was a little odd and I'm not sure understood what I was trying to tell him. I'll come back to this thread in a week or two when I get some time to rehash all of this...