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VMCa and VMCg - HELP

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Old 30th Oct 2002, 23:22
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VMCa and VMCg - HELP

Not sure if this is the correct place for this question.. but here goes.

I have always believed VMCa to be a lower speed than VMCg from a performance and PoF point of view, due to the shorter moments between the landing gear and fin on the ground compared to the moment between the CG and the fin when in the air.
two other instructors from two reputible schools have agreed, but my instructor at my school and the notes I have say that VMCg is a lower speed than VMCa.....the explanation given being "VMCg has got to be lower cos your not in the air yet !!"
He also backed this up with a diagram from a text book....but i am not convinced.

Anybody know any better ??

Thanks in advance

Last edited by spitfire747; 27th Nov 2002 at 07:33.
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Old 31st Oct 2002, 00:50
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I would tend to agree with your assessment that VMCa is Lower than VMCg.
It’s double Jeopardy when on the ground since the CG will be forward of the main gear this means that:

1) The turning moment about the main gear due to asymmetric thrust on the ground with the critical engine inoperative will be greater than in the air due to the relative positions of the CG and main gear.

2) The restoring arm between the Rudder and the Main gear whilst on the ground will be lower than the arm between the Rudder and the CG whilst airborn.

Good Luck with the Performance Exam

Cypres

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Old 31st Oct 2002, 02:46
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Vmca and Vmcg

An important factor to bear in mind is that for most aircraft Vmca is essentially determined by a static force balance and can be relatively easily approximated analytically. Whereas Vmcg is by its nature a dynamic manoeuvre and is not at all amenable to analysis. Therefore one cannot make a firm statement about the relationship between Vmca and Vmcg.

If one just considers the static force balance in the yawing plane, then care must be taken to include all the sources of yawing moment. In particular, when considering moments about different points (such as wheel and c.g.) all the relevant differences should be accounted for.

For the Vmca case, the moments concerned are, as noted, the engine-generated yawing moment and the rudder generated restoring moment. Considering only these factors, Vmca would be the lowest speed at which these two are equal.

For Vmcg, if one considers moments about the main gear (using the inboard wheel) it does appear that the engine moment is increased and the rudder moment decreased, as you suggest. But if one continues to consider the c.g. as the point of reference then the moments are seen to be equally balanced. As a body is in equilibrium about all references points at once, it is clear that there is an error in the logic.
The problem is that in choosing to take moments about a wheel, account must be taken of other factors. In particular, the acceleration of the aircraft down the runway generates a considerable inertial moment.

The actual reasons why Vmcg is often lower than Vmca are far more complex than these. Factors which come into play are:

1. Vmcg is a dynamic manoeuvre where the restoring force is applied after the disturbance, and must be capable of more than balancing[ the engine moment. This generally will require a larger rudder moment than for Vmca and so a higher speed.

2. Vmcg is conducted at or near zero angle of attack; Vmca is conducted at low speeds and high angles of attack - often at or near shaker/stall warning. For many aircraft rudder power is a powerful function of angle of attack, and the reduced rudder effectiveness for Vmca requires a higher speed to generate the same moment.

3. Vmca is defined as a static trimmed speed (ignoring the other Vmca requirements for simplicity). Vmcg is the speed at which the engine is assumed to fail; by the time the pilot has applied full rudder the speed may have increased several knots, and so the speed at which the moment balance occurs is slightly higher than the declared Vmcg. This tends to relatively lower the value of Vmcg.

4. Vmca may well be limited by factors other than rudder power; the aircraft must be trimmed in all axes and so other controls may actually be limiting. They may also be producing significant yawing moments themselves, further complicating the balance. These tend to increase Vmca.

5. Vmca is helped by a high directional stiffness (Cn-beta or Nv) and a low sideforce coefficient (Cy-beta or Yv) as these combine to allow a high beta for a given bank limit and a high restoring force due to beta. Vmcg is broadly neutral for these parameters - high stiuffness reduces the initial deviation but makes correction more difficult. Low sideforce again reduces the deviation and reduces the correction. For Vmcg these aerodynamic factors can be lost in the landing gear effects.

If one combines all these factors then often item 2 is an important reason for Vmca being a higher number. But it is by no means required to be that way.


(Incidentally, my current aircraft has Vmca higher than Vmcg)
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Old 31st Oct 2002, 06:38
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Cor blimey. I always presumed that it was a straightforward case of 'VMCG is lower because the traction of the nose wheel helps to keep it straight if an engine fails on the runway'.
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Old 31st Oct 2002, 16:58
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I think what mad scientist means is that he doesn't know the answer! Sounds good though.....

I must say that I think most of it will be over our heads unless we did an aeronautical degree..... But my interpretation of Vmca and Vmcg since I have recently been studying it for ATPL, is that.....


Vmcg must occur before V1, and Vr must be a min of Vmca1.05. So Vmcg will always be less than Vmca since to get airbourne requires in regulation that Vmca is higher than Vmcg.

Since Vmcg is determined by aerodynamic forces being able to control an a/c, it would always be below Vmca since Vmca requires more than just aerodynamic control but ability to maintain altitude.

Vmcg would also mean being able to control the a/c with the nosewheel off the ground, hence the moments would be around the CofG so moments around the nosewheel become invalid as a calculation. Thus we must always take the moments around the CofG.

We must always take the most limiting factors for safety, so the above would make sense.

But hey, I am just a student at the moment and Scientist's explaination sounds much more detailed and ambiguous! I do wish I understood fully what he was talking about!

But remember for exams and etc.... that Vmcg will be less than Vmca.

There is also Vmcl that is for the landing configuration that takes factors such as descent and different arms because of CofG movement with flaps and gear movement.

A question I came across asked order of V speeds and two of the answers were:
Vmcg, V1, Vmca, Vr, V2
Vmcg, V1, Vr, V2

the later being stated as the correct answer. Weird! I guess you have to ask the CAA for that one.

It does seem a very academic question and one that would be open to debate in the same manor that scientists can't work out the age of the universe. Vmcg before Vmca works for me. What works for you????????
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Old 1st Nov 2002, 00:47
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TMOH:
Vmcg must occur before V1, and Vr must be a min of Vmca1.05. So Vmcg will always be less than Vmca since to get airbourne requires in regulation that Vmca is higher than Vmcg.
Sorry, not true. (The part in italics)
Try Vmcg=80kts, Vmca=75kts, V1=Vr=90kts, V2=95kts.
That should meet all the relevant Vmcg and Vmca driven requirements, and is physically plausible. Just because Vrmin is 1.05Vmca does not mean that Vr=1.05Vmca. You cannot use the regulations to deduce the values of e.g. Vmca, Vmcg, Vs or Vmu, because these are all things which determine the minima - they do not define the values themselves.

To take a really extreme example, V2min is 1.2Vs (or 1.13Vsr, but lets not go there for now). But V2 can be any value greater than that. If I want to define V2 as 200kts, because it's a nice round number, I'm allowed to. The takeoff performance will, of course, be diabolical if I do so, but there is nothing in the regs to stop me.

Apart from anything else, there are many limits placed on the takeoff speeds, and the actual published speed must respect all of them. Without knowing which was the limiting factor for given conditions, simply knowing V2, say, gives at best only a vague idea of the underlying aerodynamics.

A question I came across asked order of V speeds and two of the answers were:
Vmcg, V1, Vmca, Vr, V2
Vmcg, V1, Vr, V2
the later being stated as the correct answer. Weird! I guess you have to ask the CAA for that one.
The reason is that they are testing your grasp of mathematical logic as much as anything. The regulations require the following:
V1>Vmcg
Vr>V1
V2>V1
(if you ignore the possibility of some of these being "greater than or equal to")
The regs also require V2>Vmca
(actually in this as in other cases it may be a factor as well, but the logic is valid anyway)
So the second of the two options is clearly correct. What about the first one. To know that V1<Vmca<Vr I would have to have a requirement (indeed two) placing Vmca relative to those two speeds. Knowing Vmca is less than V2 doesn't help; for all I know it could be <Vmcg, given the regulatory requirements. So while the second set of V-speeds is mandated, and hence must always be true, the first is not mandated, and may or may not be true. That's why they said the second one was the right answer.

And finally...
indeed I do not know the answer, because there is no answer, or rather the answer is the classical engineer's answer: "It depends"
The balance of the factors does tend to result in a higher Vmca than Vmcg for most aircraft. But there is no simple reason why this is so, and therefore there are exceptions, and it would be dangerous to assume otherwise. Of course, since both numbers are required to be demonstrated in test, and are presented in the aircraft pubs, I see no reason to make an assumption; just look the numbers up!

Luke:
Cor blimey. I always presumed that it was a straightforward case of 'VMCG is lower because the traction of the nose wheel helps to keep it straight if an engine fails on the runway'.
Actually, since no credit is permitted for nosewheel steering in the FARs, Vmcg is demonstrated with the nosewheel steering inop'ed and the wheel free to castor. In any event the nosewheel is actually slightly destabilising, and it is the mainwheels which stabilise the aircraft on the ground (which is why they are fixed and the nosewheel free to move for a tricycle gear)

Last edited by Mad (Flt) Scientist; 1st Nov 2002 at 01:01.
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Old 1st Nov 2002, 08:20
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The Mad Scientist is right, and it shows how complex even a simple question can become. For the JAA exams it is usually assumed that Vmca is lower than Vmcg because of the old CAA specimen graphs for the L1011.



One of these, shown above, gives the values for Vmcg and 1.05Vmca at different density altitudes. It is then a simple matter to remove the 1.05 factor to compare the speeds.

In the example above Vmcg shows as 110.5kt, 1.05Vmca as 112kt and therefore Vmca is 106.5kt, 4kt lower than Vmcg.

Last edited by Alex Whittingham; 1st Nov 2002 at 16:30.
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Old 1st Nov 2002, 10:45
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To Mad Scientist,

All I can say is thank you...... Your second reply makes much more sense to me. I can see clearly now as they say. But I am interested to know how you know so much about this particular area in detail. This kind of detail is not covered in ATPL training as far as I know. Really, all they want is that you know the basic relationship of the V speeds. I would love to know this kind of detail that is lacking in ATPL training courses!
By the way, the last time I checked, V2min is now 1.13Vs or 1.08Vs for 3+ engines. Changed as recently as 10 months ago. But I could be wrong so check for yourself. Then again, I am sure you know way more than just that and are simply trying to talk layman! One day I will understand the lingo more fully, but until that day I am but a student.
Atleast I will know the answer now when I take the exam in 4 days!

Cheers
JD
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Old 1st Nov 2002, 15:10
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Hey there S747, how's it going at LGU? It seems an age since you posted the "handing my notice in" post....
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Old 2nd Nov 2002, 02:17
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TMOH
By the way, the last time I checked, V2min is now 1.13Vs or 1.08Vs for 3+ engines. Changed as recently as 10 months ago. But I could be wrong so check for yourself. Then again, I am sure you know way more than just that and are simply trying to talk layman! One day I will understand the lingo more fully, but until that day I am but a student.
Aha! I'm afraid another "it depends" is the answer here. There are now 2 ways to determine stall speed, and which way you determine stall speed will affect the factors used for all quoted speeds.

The old way was to simply conduct the stalls and measure the minimum speed in the stall. After correcting for various factors (such as stall entry rate, residual thrust, etc.) the resulting speed was declared to be the stall speed, Vs. This is commonly called the "minimum speed" or "Vsmin" method.

The new way is to conduct the stall tests as before, but to correct all speeds obtained to the speed that would have been required for 1-g level flight. As an aircraft is usually falling out of the sky at the stall, i.e. producing less than 1-g of lift, this correction results in a higher speed than the older method. The resulting spped is the "1-g stall speed" or Vs1g. This speed is then further corrected to obtain the so-called "reference stall speed" or Vsr.

The new way is a more academically accurate way of determining the stalling speed, as it should be far more repeatable and can be linked more directly to the maximum lift producing capability of the wing. Unfortunately, the resulting speed is invariably higher than the Vsmin method would produce.

If the authorities were to mandate this new stall speed methodology, with no other changes to the regulations, the result would be to drive stall speeds up by some 6% or so (on average) and therefore V2, Vref etc would also be impacted in many cases.

But the old V2, Vref etc were safe - as demonstrated by long service experience. Therefore it was reasoned that provided the same V2 etc resulted, it was permissible to reduce the regulatory factors for those aircraft where the manufacturer elected to use the Vs1g analysis method.
Consequently, the rules are currently V2>1.2Vs or V2>1.13Vsr (for <3 engines), depending on the aircraft and analysis method used.

Afraid I can't lay my hands on the precise FAR/NPA numbers at the moment - it was a proposed rule the last time I bothered checking, but one that could be elected following discussion.


And to answer your other question: my name would have been "Mad (Flight) Scientist" but that exceeded the allowable number of characters. I'm currently a "flight scientist" (or in UK parlance aerodynamicist) for a (the??) Canadian aircraft manufacturer with a background in S&C primarily. So working out these numbers is what I do for a living (at least when people are watching!)
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Old 4th Nov 2002, 21:11
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Thanks everyone for your detailed explanations but luckily the question did not come up in todays Perf exam

And TheDove - Its ok and LGU, not the best for notes, so if you are thinking of starting, get OXFORDS notes.

Just did PoF, Perf and Airframes so Gotta go ....... got BEER to drink
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Old 14th Nov 2002, 16:53
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Vmca Vmcg

Interesting reading. However one question and one observation. First the question:-

If the Vmcg and Vmca are indicated speeds why do they reduce with increase in altitude (especially density altitude)?

And the observation, (which is in addition to all that has been said about turning moments on the ground etc):

Vmca may also be less then Vmcg because the flexibility is available of putting on slight bank (5 degrees) to counter yaw due critical engine failure. This is not available on the ground hence lesser control deflection and hence lesser aerodynamic pressure or less IAS for the same effect is required .

However I just saw the graphs of an MD-11 in which the Vmcg is lower.
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Old 14th Nov 2002, 17:01
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Because as the air gets thinner the thrust on the remaining engine reduces. This makes the asymmetric thrust easier to control.

As to your observation, I use this in class to explain my statement above although, as you can see, there's much more to it.

The determination of Vmca also allows more freedom of manoeuvre. Vmca is determined so that the heading change during the recovery from an engine failure at that speed is not more than 20º whereas Vmcg has a more restrictive limit of no more than 30ft deviation from the centreline.

Last edited by Alex Whittingham; 14th Nov 2002 at 17:34.
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Old 19th Nov 2002, 16:04
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Thanks Alex that sorted out one doubt!
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Old 23rd Nov 2002, 00:05
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Vmca, Vmcg from an Operational Viewpoint

Vmcg is less than or equal to Vmca. I looked through my reference library but could not find any definitive information on it. I do remember from way back in a FlightSafety HS-125 training session this topic surfaced and the answer was that it had to do with the nose wheel. On the ground you have nose wheel steering, ground contact and the rudder. Once you are in the air you only have the rudder.
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Old 23rd Nov 2002, 00:30
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25.149(e)

VMCG .... is the calibrated airspeed during the takeoff run at which, ..., it is possible to maintain control of the airplane using the rudder control alone (without the use of nosewheel steering)
italics added for emphasis.

ATPMBA: nosewheel steering has nothing to do with VMCG as prescribed by FAR25; it may make it possible to control the aircraft in practice at lower speeds, but you may NOT take credit for it. This allows for such events as wet, slick runways or engine failure AT rotation, where the NWS is pretty useless.

The reason you cannot find a definitive statement in the literature regarding VMCA vs VMCG is that one cannot be made; there are too many variables and the manoeuvres are different. It would be like trying to state a fixed relationship between Vs and Vmu. They have similarities, but no hard and fast rule can be applied.

And incidentally, you have more than just rudder in VMCA - you have bank (and hence beta), a pretty powerful influence on VMCA, and also the possibility of roll control limitations.
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Old 27th Nov 2002, 07:31
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Thanks to all who have contributed to this post, peoples views have been very interesting and I have come to the conclusion there is no definite answer due to the numerous variables that are applicable.

From all the JAR/CAA feedback I have got, there is no question that directly asks these two to be put in a specified order, so I assume there never will be.

Thanks again
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Old 1st Apr 2004, 10:06
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The following limits were defined earlier.

QUOTE:

V1>Vmcg
Vr>V1
V2>V1
(if you ignore the possibility of some of these being "greater than or equal to")
The regs also require V2>Vmca

UNQUOTE

If Vmca is less than Vr, then we begin flying at a speed which guarantees controllability in the air.

If Vmca was higher than Vr, we begin flying at a speed which controllability in the air is not guaranteed.

(and there could be quite a spread between Vr and V2; this leaves a grey area, as the regs state Vmca must be less than V2, but not by how much)
e.g. Vr = 120
V2= 135
Then Vmca could be 134. What happens between 120 and 133?
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