Another Vmc question

[Houston]

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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.​

Are you under the impression that formula supports a hypothesis that Vmca varies with weight due to inertia?

 

[shdw]

Are you under the impression that formula supports a hypothesis that Vmca varies with weight due to inertia?

Yes. Being that contains both mass and velocity, the two very terms used to calculate an objects inertia's, it proves inertia existence in this discussion.

Really, we do not need a formula to know this though. If you are referring to an objects movement in space changing, or it's resistance to movement, as is the case here, you are talking about inertia. Whether you choose to acknowledge it or not in your explanation, as said before, won't change the validity of the statement.

 

[shdw]

Are you under the impression that formula supports a hypothesis that Vmca varies with weight due to inertia?

Emphasis added.

For what it's worth, the very existence of the weight term implies inertia's existence. After all weight is just mass times gravity, where gravity is the acceleration.

 

[Houston]

Yes. Being that contains both mass and velocity, the two very terms used to calculate an objects inertia's, it proves inertia existence in this discussion.

Totally irrelevant to the question. Let me simplify it into a single question again.

Why does Vmca go down as weight goes up?

 

[JustinS]

Totally irrelevant to the question. Let me simplify it into a single question again.

Why does Vmca go down as weight goes up?

Inertia... My answer remains the same... This was taught to me during my commercial multi, and this is what I taught my examiner on my MEI initial.

Let's do an exaggerated example... You have a ping pong ball rolling down the hill, and out of nowhere a force exerts 10 pounds of force 90 degrees to the ball's direction. The Ping pong ball's direction changes a LOT! i.e. high Vmc.

Now, lets take a bowling ball going the same speed down the same hill with the same force of 10 lbs exerted on the bowling ball at a 90 degree direction to the direction of the ball. The bowling ball's trajectory is not changed nearly as much. i.e. low Vmc

Hence inertia has an effect. Now I don't know what kind of airplanes you guys are flying, but the plane I fly you can go from 3700 lbs to 3,350 lbs over the course of a flight. That's 350 lbs! Inertia is a valid argument...

 

[Houston]

Inertia... My answer remains the same... This was taught to me during my commercial multi, and this is what I taught my examiner on my MEI initial.

Then let me ask you this. Given that Piper Aircraft Inc. has published that it's due to the horizontal component of lift and not momentum, why did they get it wrong? One would think that with all the aeronautical engineers at Piper that they could come up with the same answer you are teaching. The King School (John and Martha) teach something different than what you teach. They, like Piper Aircraft Inc. teach that it is the horizontal component of lift, without any mention of momentum. Why do you think they have been teaching it wrong for so many years?

 

[JustinS]

Then let me ask you this. Given that Piper Aircraft Inc. has published that it's due to the horizontal component of lift and not momentum, why did they get it wrong? One would think that with all the aeronautical engineers at Piper that they could come up with the same answer you are teaching. The King School (John and Martha) teach something different than what you teach. They, like Piper Aircraft Inc. teach that it is the horizontal component of lift, without any mention of momentum. Why do you think they have been teaching it wrong for so many years?

That would be correct as well. I would say we are both right. If we imagine a situation without bank and ball set, then that would certainly change in what way weight causes Vmc to change correct? Awesome info in here, thanks for enlightening me.

 

[Houston]

That would be correct as well. I would say we are both right. If we imagine a situation without bank and ball set, then that would certainly change in what way weight causes Vmc to change correct? Awesome info in here, thanks for enlightening me.

Can you think of any published author that has every written that momentum is the reason or a reason?

 

[JustinS]

Can you think of any published author that has every written that momentum is the reason or a reason?

I'll dig up something tomorrow.

I definitely agree with you about the increased component of horizontal lift for the same amount of bank set at a higher weight causing Vmc to decrease.

Try this now. Wings level, rudder to center the ball. (Yes I am aware we're in a slip now...) Now tell me if we're in this situation with a heavier weight. Will Vmc be less or more than at a lighter weight, and why? It certainly cannot be due to the horizontal component of lift generated by a bank angle if we're holding wings level. Both our arguments are valid and correct so we're splitting hairs. I am on the same page as you guys, and I agree. Thanks for sharing this knowledge, I'm excited to teach my first multi student these things.

 

[Houston]

I'll dig up something tomorrow.

Don't rush. Take your time. It's an important learning experience.

Try this now. Wings level, rudder to center the ball. (Yes I am aware we're in a slip now...) Now tell me if we're in this situation with a heavier weight. Will Vmc be less or more than at a lighter weight, and why? It certainly cannot be due to the horizontal component of lift generated by a bank angle if we're holding wings level.

You are hitting on a great point. That is the difference between Vmca and Vmcg and the associated misconception of what Vmcg is.

To begin with, Vmc does not change with weight when the wings are level. Vmcg is in fact, the wings level Vmc. It is used in certification. Vmca is with up to five degrees of bank.

The FAA is largely to blame for the great misconception because of the poor way they write about Vmcg. Here is one quote from FAR Part 60 "Minimum Control Speed-ground (Vmcg) using aerodynamic controls only (per applicable airworthiness standard) or alternative low speed engine inoperative test to demonstrate ground control characteristics." So, when you ask someone what Vmcg is they give an answer like "it's the slowest speed at which you can control the airplane on the ground if one engine is inoperative". Then you have to ask them if they could control an airplane at ten knots if they lost an engine. Of course they could. So, then what is Vmcg? They use the term "on the ground", but they throw in "using only rudder", which means that you would have zero ground friction. That is a situation (thankfully) that most of us never fact in a lifetime.

Thanks for sharing this knowledge, I'm excited to teach my first multi student these things.

An instructor who is excited about teaching is perhaps aviation's most valuable resource.

 

[shdw]

Try this now. Wings level

If the wings are level weight does not play a roll.

Weight becomes a factor as soon as you're banked.

Why does Vmca go down as weight goes up?

I've already answered this, but perhaps rewording it, devoid of formula, will help.

When the aircraft is partially banked weight no longer acts parallel to it's vertical axis. Instead, it acts to some degree, equal to the bank angle, off vertical. The result is a portion of weight acting along the lateral axis and a portion acting along the vertical axis. Since yaw is both a transitional action along the lateral axis (inertia part here) and a rotational action along the vertical axis (moment of inertia part here), we can conclude that inertia, in both traditional and rotational senses, is present.

Why don't we find explanations like this in our traditional aviation books? Simple, inertia isn't a force and it isn't something previous subject material has covered. And they definitely haven't introduced the 6 degrees of freedom. In other words, there would be more to explain than simply reexplaining an already touched on topic like HCL. Keep in mind, inertia exists in any object that has weight and moves along the x, y or z axis (transitional). Similarly, moment of inertia exists in any object that has weight and is moving about the x, y or z axis (rotational).

Interestingly, I've read and reread the sections pertinent to this discussion in almost a dozen aerodynamic books over the course of our discussion here. Not one mentions inertia. Not one mentions HCL. Why? I'm not certain, but I'd guess it's because they are not there to provide the reader with memory aids. What we are arguing here is just that, a memory aid aimed to assist in correlating these ideas to help the reader better remember them.

For what it's worth, I would still stick with teaching HCL as well. For the reasons mentioned above, but also because mentioning inertia carries with it some baggage that an intuitive student may cling to later on. For example, explaining Va's shifting with weight and, remembering our chat about inertia, concluding that the heavier airplane is more sluggish. For thrust causing an acceleration, sure. For Va going down, nope. What's the difference? Transition. Rotation. Still, a problem I'd rather avoid so I'll stick with HCL to explain this, but I won't claim the inertia explanation wrong either.

 

[Houston]

I've read and reread the sections pertinent to this discussion in almost a dozen aerodynamic books over the course of our discussion here. Not one mentions inertia. Not one mentions HCL. Why? I'm not certain, but I'd guess it's because they are not there to provide the reader with memory aids.

So then, following that supposition, the reason Piper Aircraft Inc. states it is HCL would mean they are there to provide memory aids?

 

[shdw]

So then, following that supposition, the reason Piper Aircraft Inc. states it is HCL would mean they are there to provide memory aids?

Can you provide a link?

I can't comment till I see who wrote it and context of the publication.

 

[Houston]

Can you provide a link?

I can't comment till I see who wrote it and context of the publication.

Piper Seneca POH. A condensed version can be found here:

http://ehfc.net/SenecaIIManual.pdf

Also, could you elaborate on what you consider to be a "memory aid".

 

[J Cole]

Interesting stuff. I want to flesh out the HCL issue a little bit more, since I had never heard of it up until now. My understanding is as follows: a multiengine aircraft with an engine out, the wings level, and the ball centered is actually in a mild slip due to off centerline thrust. This slip reduces performance by increasing drag. We can negate this slip if we slip the aircraft in the opposite direction. This slip creates a horizontal component of lift (HCL) opposite the slip to stop the sideslip problem. Using this slip (aka "bank and ball") also has the added benefit of reducing the amount of rudder necessary to stop yaw - which improves controllability and reduces Vmc.
Now, a heavier aircraft will have a greater lift vector than a lighter aircraft. This means that, given the same bank angle, a lighter aircraft will have a smaller HCL than a heavier aircraft. This means that a heavier aircraft will require less rudder pressure to maintain control at a given bank angle than a lighter aircraft (hence the lower Vmc at a higher weight). However, all of this must assume a constant bank angle. If a pilot in a lighter aircraft simply compensated for the shorter lift vector by increasing the bank in "bank and ball", this effect would be negated because the HCL would be increased to match what it would have been in a heavier aircraft. Therefore, if we can assume a perfect technique is used (which may be impossible - I'm not sure), then I believe that the HCL argument is invalid.

For what it's worth, I would still stick with teaching HCL as well. For the reasons mentioned above, but also because mentioning inertia carries with it some baggage that an intuitive student may cling to later on. For example, explaining Va's shifting with weight and, remembering our chat about inertia, concluding that the heavier airplane is more sluggish. For thrust causing an acceleration, sure. For Va going down, nope. What's the difference? Transition. Rotation. Still, a problem I'd rather avoid so I'll stick with HCL to explain this, but I won't claim the inertia explanation wrong either.

I actually believe the explanation of inertia in Vmc translates nicely to Va. As you stated, inertia is not a force. Rather it is defined as an objects resistance to force. An object with more inertia will require a greater amount of force to move it (or, more correctly, cause it to accelerate). Therefore, a heavy twin will require more force to cause it yaw then a lighter aircraft - thereby increasing its controllability. In Va, a heavy aircraft requires more force to displace it from its original position - causing an acceleration (g force).
Anyway, great discussion.

 

[JustinS]

If the wings are level weight does not play a roll.

I full heartedly, and respectfully disagree. Weight physically plays a roll in Vmc wings level. I am extremely baffled as to how this conversation has gone just as far south as a conveyor belt conversation... When the laws of physics dictate that a heavier airplane will have more inertia causing its direction through space to change less readily with the same force from the engine applied. I find this, and the other explanation of the horizontal component of lift together and separate to be extremely valid. Someone please explain to me how inertia has no validity...

 

[shdw]

Piper Seneca POH. --- what you consider to be a "memory aid".

I had a feeling you were going to list a POH. You've never seen anything written inaccurately in those have you? Bare in mind I agree HCL is accurate. My contention is that so is inertia. You ask for a source that explicitly points it out, I don't have one. Do you have a source that explicitly discounts it?

Memory aid being something that the learner can use to correlate two ideas. If they understand the concept of inertia, or you demonstrate it by having them push on objects, then they can correlate the two different ideas. Inertia is now the memory aid. Likewise for HCL.

 

[shdw]

I actually believe the explanation of inertia in Vmc translates nicely to Va.

And you're not alone, this concept is used all the time to explain Va. Va deals with rotational acceleration not transitional. You might make an argument for moment of inertia if the rotation point were about some point other than CG. Since CG is the rotation point, however, that would be a difficult argument to make.

Va is Vs * sqrt (n). Since Vs goes down with weight as per L = 1/2 rho v2 S rewritten to Vs = sqrt( L / rho S) then so must Va. Recall lift equals weight so solving for Vs is really sqrt (W / rho S).

An easier way to think of it is drawing two aircraft flying the same speed at two different weights. The lighter aircraft will be at a lower angle of attack and as such will have a larger angular distance to travel before reaching stall. Moving the control surface to it's limit will impart some acceleration. The longer that acceleration is allowed to happen the greater the force will become. In other words, the lighter aircraft will have to fly slower so it's AOA matches that of the heavier aircraft.

 

[shdw]

I full heartedly, and respectfully disagree. Weight physically plays a roll in Vmc wings level.

Ok so we have a pole sitting perfectly balanced on a frictionless pivot point. We have another pole, 5 times heavier, sitting perfectly balanced on another frictionless pivot point. If you were to walk to the end of each of the poles and give them a push, which one would be harder to rotate?

Since the pivot points are frictionless they would be equally easy to rotate. Since the friction force is F=ma, mass would play a role if friction played a role. However, since an aircraft is not attached to the ground it's pivot point is frictionless and makes this a sound example of weights role in the wings level Vmc scenario. If that doesn't satisfy, here:

Equation (5.10.5) for fixed airspeed and thrust contributions, the control deflection required for lateral trim at zero bank are independent of aircraft gross weight.

Note that their mention of lateral forces refers to movement of the lateral axis around the vertical axis. In other words, they are talking about yaw. The next sentence you will see includes bank angle and gross weight:

On the other hand, the derivatives of these control deflections with respect to bank angle are directly proportional to gross weight.

The sentences in this paragraph precede the paragraph I quoted in reply 19 on this topic.

 

[Houston]

Just checking. Anyone yet been able to come up with anything from a published author, and aircraft manufacturer, or a noted school that says the reason Vmca changes with weight is because of anything other than the change in the horizontal component of lift?