Another Vmc question

[durind]

I have searching the forums and while I have found quite a bit of interesting discussions, I didn't quite find the answer to my question so I am going to post it in here.

So I was sitting my office debating whether or not I should do some more 141 paperwork catchup when our DPE and extremely experienced pilot with other 20,000 flight hours walks by my office and says what have you been teaching people is Vmc in the Apache!? (in a slightly accusatory tone) I respond "72 mph", exactly what the POH says, he agrees and says one of my students was saying it was 59 mph and wasn't sure where he was coming up with this number.

Anyway this leads in to a discussion of Vmc and me basically trying to prove that I'm not an incompetent multi-engine instructor. I mention aircraft weight should be lightest due to the decrease horizontal component of lift when you are banking towards the working engine. He cuts me off, tells me I am wrong and that an aircraft that is heavier has to fly at a higher angle of attack to generate the same amount of lift which increases P-Factor which will be cause the opposite effect of increasing Vmc with an increase in weight. I could see where he was saying and it basically boiled down to me saying I hadn't thought about it like that, and never thought to quantify the forces. Anyone with more experience care to weigh in? He wasn't disagreeing with me, nor I with him but it was a matter of how strong each one of these forces was. A google search has yielded people saying both things, and I'm sure this is something that could vary from aircraft to aircraft, so if that is your approach lets just consider a PA-23-160.

 

[cezzna]

Less asymmetric thrust due to higher weight, less opposite rudder required, rudder authority 'lasts longer' or keeps plane straight to a lower speed, ie lower Vmc

 

[TwoTwoLeft]

Kind of splitting hairs here.... Yeah, but he's also forgetting that with in increase in AOA comes an increase in induced drag. Symmetric drag, induced or parasite actually lowers Vmc (assuming zero sideslip is established). So once again, it all comes back to available horsepower & P-factor. What is going to affect these two the most?

Density Altitude...

One thing to remember about Vmc, its just a number. That number is based on a set of specific (least desirable) conditions that will produce a loss of directional control. The biggest role weight plays with Vmc is it's location (CG). When you make the airplane "heavier" this can only happen in a few selected locations. The airplane doesn't just uniformly gain mass to it's airframe. In this situation, to purely talk about weight with out acknowledging it's distribution makes the argument invalid.

 

[Houston]

He cuts me off, tells me I am wrong and that an aircraft that is heavier has to fly at a higher angle of attack to generate the same amount of lift which increases P-Factor which will be cause the opposite effect of increasing Vmc with an increase in weight.

Ask him to show you his reference.

 

[Houston]

Take a look at what aviategw had for a reference:

http://forums.jetcareers.com/threads/vmc-and-weight.12482/

 

[CoffeeIcePapers]

Take a look at what aviategw had for a reference:

http://forums.jetcareers.com/threads/vmc-and-weight.12482/

ATP training material isn't really a valid reference, IMO. How about this? AFH:

The precise condition of zero sideslip (bank angle and
ball position) varies slightly from model to model, and
with available power and airspeed. If the airplane is
not equipped with counter-rotating propellers, it will
also vary slightly with the engine failed due to P-factor

P-factor does have some effect on the bank angle required for zero sideslip, which will change Vmc by some factor. How much? Who cares.

 

[TwoTwoLeft]

For training purposes, the aircraft specific POH/AFM is where you should look. That's where the specific criteria for your aircraft on which Vmc was based is located. For an older Beechcraft there is an operating supplement available. Not sure about the older pipers. I havn't got my hands on an Apache or Twinkie POH.

 

[Houston]

ATP training material isn't really a valid reference, IMO. How about this? AFH:

I saw that, but it doesn't support what the DPE stated when he accused durind of not knowing what he is talking about.

P-factor does have some effect on the bank angle required for zero sideslip, which will change Vmc by some factor. How much? Who cares.

The people who participate in the certification of aircraft. The change is what makes the difference between Vmca and Vmcg.

 

[Dugie8]

The whole point of having the "What affects Vmc" discussion is to show that most everything that would "lower" Vmc also lowers your performance.

 

[USAviationRecruiter]

It's about inertia. The greater the inertia of the aircraft the less likely it will be for the operating engine to roll it over, ie. lose directional control. The Vmc weight factor is a trade-off with stall speed.

 

[Houston]

It's about inertia. The greater the inertia of the aircraft the less likely it will be for the operating engine to roll it over, ie. lose directional control.

Can you reference something that supports that supposition?

 

[JustinS]

Can you reference something that supports that supposition?

Well the laws of physics kind of prove this... When an object has more mass, it takes a larger force to change its trajectory through the air. However, the engine power produced single engine does not increase just because the weight of the airplane is increased to MTOW. I teach this as one of the reasons why weight has a positive effect on Vmc. However, the negative effect on performance is more considerable...

 

[J Cole]

Hmm...very interesting. I had not heard of that particular argument before.

I am also unfamiliar with the concept that a lighter aircraft would require less horizontal component of lift. Could you elaborate?

As far as the lighter weight of the aircraft increasing VMC, Justin is right. More mass equals more inertia and more inertia means that more force will be required to act upon the aircraft to make it change direction. An example I used when explaining this concept to multiengine students was to compare two pickup trucks driving down a gravel road - one with the bed filled with sandbags and the other empty. Driving the same speed, which truck would be moved more by the bumps?

I believe that the DPE may also be right, however. A higher angle of attack would increase the effect of P-factor, causing an increase in VMC, but only in certain cases. The question is: which force would overcome the other? I believe this would be different in just about every type of aircraft (and affected with the same type of aircraft by any number of variables) and could probably only be solved in a case by case basis by an aeronautical engineer. Perhaps in some cases, the forces would cancel one another out.

However, I do feel compelled to point out some problems with this argument:

1. This argument would obviously not be true of pure jet aircraft - since P factor is either not present or is insignificant.

2. This argument would not be true of an aircraft with counter rotating propellers, as P factor would actually place the center of thrust closer to the center of gravity in the event that either engine would fail. This would mean that an increase in angle of attack would actually decrease VMC.

3. In the case of a conventional multiengine with propellers, it would only be true in the event of the failure of the critical engine. If the non-critical engine failed, an increase in angle of attack would again cause the center of thrust to be moved inward, towards the center of gravity.

For these reasons, it might be a useful thing to point out to students, but I think it would be largely irrelevent in a discussion of VMC.

 

[Houston]

Well the laws of physics kind of prove this... When an object has more mass, it takes a larger force to change its trajectory through the air. However, the engine power produced single engine does not increase just because the weight of the airplane is increased to MTOW. I teach this as one of the reasons why weight has a positive effect on Vmc. However, the negative effect on performance is more considerable...

What you're teaching is a very common answer. However, think about this. Vmca is at a steady state. No matter how much force it might take to get that mass moving, eventually, it gets to a steady state.

I believe if you look around, you won't find any publication that gives that as the reason. However, there is a whole lot of training material that says it has to do with the horizontal component of lift. I could close my eyes and see John and Martha standing there explaining it, but I don't want to subject myself to those kind of flashbacks.

All of the rest of the items you mentioned are certainly true and very important points.

 

[Houston]

it might be a useful thing to point out to students, but I think it would be largely irrelevent in a discussion of VMC.

It depends on what level of testing the student is attempting to pass. The great majority of AME students are going for that rating on a commercial or flight instructor certificate. Here is a part of the flight instructor PTS:

Task C: Flight Principles-Engine Inoperative (AMEL and AMES)
References: FAA-H-8083-3, FAA-S-8081-12, FAA-S-8081-14; POH/AFM.
Objective: To determine that the applicant exhibits instructional knowledge of the elements related to flight principles engine-inoperative by describing:
1. Meaning of the term “critical engine.”
2. Effects of density altitude on the VMC demonstration.
3. Effects of airplane weight and center of gravity on control.
4. Effects of bank angle on VMC.
5. Relationship of VMC to stall speed.
6. Reasons for loss of directional control.
7. Indications of loss of directional control.
8. Importance of maintaining the proper pitch and bank attitude, and the proper coordination of controls.
9. Loss of directional control recovery procedures.
10. Engine failure during takeoff including planning, decisions, and single-engine operations.

Unfortunately, the AFM, which is one of the references listed does an inadequate job of discussing that subject.

 

[J Cole]

It depends on what level of testing the student is attempting to pass. The great majority of AME students are going for that rating on a commercial or flight instructor certificate. Here is a part of the flight instructor PTS:

Unfortunately, the AFM, which is one of the references listed does an inadequate job of discussing that subject.

You misunderstood my last comment (understandable - I didn't quantify it very well). I had actually meant that the P factor issue would be largely irrelevant. I would still absolutely teach the effects of weight and center of gravity on aircraft control. But I believe the main reason for weight affecting controlability is still inertia related.

 

[TwoTwoLeft]

No, weight affecting controllability is primarily CG related.

 

[shdw]

I am also unfamiliar with the concept that a lighter aircraft would require less horizontal component of lift. Could you elaborate?

Since L sin (bank angle) yields the horizontal component of lift. Assuming bank angle remains the same, if total lift required decreases, such as the case of a lighter aircraft, then so does the horizontal component of lift.

 

[shdw]

It's been ages since I've spent time on multi engine dynamics, so pardon my need to steal from other sources to build an argument. What follows I hope gives some food for thought to the two sides of the argument we see here. From page 294 of AFNA:

Once defined, the minimum directional control speed is not a function of weight, altitude, etc., but is simply the equivalent airspeed (or dynamic pressure) to produce a required yawing moment with the maximum rudder deflection.

And page 585 of Mechanics of Flight:

Because some bank angle is typically used to establish Vmc, the insight gleaned from Eq. (5.10.5) exposes an important and nonintuitive feature of the Vmc problem. Whereas many performance metrics, such as takeoff distance and climb, suggest that high gross weight is the most demanding operation condition for the minimum-control airspeed problem, it is light gross weights that are most dangerous. Even for a fixed approach speed, when an airplane is banked at a small fixed angle away from the failed engine, the rudder deflection needed for lateral trim increases with decreasing gross weight.

Emphasis not added by me.

The point of my posting these two seemingly conflicting quotes is not to claim one or the other correct. In fact, either statement is correct. Depending on how you choose to lay out your argument, or subsequently, how it was presented to you, will have an impact on which one of these two quotes you read to be correct.

So why are they both correct?

The first quote deals with Vmc independent of bank, or a crude 2D picture where one force acts to spin you one direction and the other acts to stop the spin. In this case weight is not important.

The second deals with Vmc when banked flight is introduced. This leads to our 3D picture and a condition where weight and CG play integral roles in Vmc. Which role is more important is an argument I will avoid because I believe it of little importance. What matters is they both matter, that we realize they both matter, and that we fly an accurate speed probably given to us from the POH.

 

[shdw]

It's about inertia. The greater the inertia of the aircraft the less likely it will be for the operating engine to roll it over, ie. lose directional control.

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Can you reference something that supports that supposition?

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For those of you on here allergic to math, I know we have many! Skip to the last paragraph. <3​

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Where:​

W = weight​

Delta sub r = rudder deflection​

Cw = weight coefficient​

rho = density​

Sw = planform area of the main wing​

delta sub r sat = rudder saturation angle​

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This formula is how you solve Vmc for the rudder. The control saturation angle is different and must be determined independently for each bank angle. The weight coefficient is found by rearranging the lift formula so Cw equals weight divided by 1/2 rho V squared Sw.​

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What this all means is the above formula contains both a weight and a velocity term, or it contains inertia. Like the other argument going on here, you can explain this in more than one correct way. Choosing to include or exclude inertia (or HCL) in the explanation does not make or break it's validity. The key is to accurately lay out the guidelines (definitions) for your argument and take care not to mix and match as you see fit.​