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I would argue that no matter what the condition airspeed is the only thing that it is going to keep the aircraft under control if an engine failure occurs. We'll get back to that in a minute.
Assuming however, that you aren't considering engine failure, then the next thing you would be considering is getting to your destination. Obviously, higher groundspeed is essential but that isn't the whole story. You need to look at where your plane will achieve the highest TAS. Most normally aspirated light twins get that somewhere around 6000'-7000' MSL. Then the winds aloft are taken into account to see what altitude yields the highest groundspeed, all things considered.
Once you've analyzed all this stuff the bottom line question is how fast do you want to get to your planned cruising altitude.
If you're climbing into a tailwind you'll want to sacrifice groundspeed achieved by establishing a high TAS in the climb for altitude which gives the best wind component. If you're climbing into the wind, and the higher you go the slower you go, you're better off taking your time in the climb.
Getting back to the engine failure thing though, the most important
thing to keep in mind is that when engine failure occurs there are TWO
issues involved that do not necessarily have anything to do with one another.
Those issues are performance and control. Read below to see how these things
should be considered in a single engine situation.
FACTORS AFFECTING Vmc
There are a number of different factors that have an effect on Vmc, the speed at which control of a multi-engine airplane with its most critical engine inoperative is no longer possible. Before one can properly consider these factors however, one must first understand the difference between performance and control.
PERFORMANCE AND CONTROL:
Performance of an airplane, in very general terms, is the ability of the airplane to climb, to get away from the ground.
Performance is the result chiefly of excess thrust horsepower. Without excess horsepower airplanes don't climb. It therefore follows that anything that can be done to increase the amount of excess horsepower available will increase performance. It is performance that the pilot is interested in when considering flight planning where weight and density altitude are concerned.
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Control, on the other hand, is an entirely different aspect of the game that most new multi-engine pilots confuse all too readily with performance. Control refers to the pilot's ability to command the aircraft about its three axes with unquestioned authority (particularly, in this case, where the rudder is concerned since we're talking about single-engine operations). In a light twin some factors that affect control in a positive manner may have disastrous effects on performance.
INCREASED Vs. REDUCED:
But first, some semantics. When it is said that a particular factor lowers or reduces Vmc this refers to a reduction in the indicated airspeed at which the loss of control occurs. It does not refer to a reduction in the danger presented by the situation. Another common way that this is expressed is to say that Vmc is improved. Conversely, when a particular factor is said to increase Vmc this refers to an increase in the indicated airspeed at which loss of control occurs and does NOT refer to any increase in the safety of the situation.
THE FACTORS THAT AFFECT VMC:
The factors that affect Vmc most dramatically can be found in the Part 23 aircraft certification regulations that pertain to light twins. These factors, as they are listed, represent a major engine failure essentially during rotation for takeoff, perhaps the most critical phase of any flight in a multi-engine airplane. Although it could be argued that this is not an absolute worst case scenario (as one examiner has been known to point out, someone could be shooting at you) this does represent the most serious situation that most of us will ever face.
The factors are as follows:
1. Maximum power on the operative engine (assumes S.L.)
2. Up to 5 degrees of bank into the operative engine (at the discretion of the applicant - the manufacturer).
3. The propeller on the inoperative side is windmilling.
4. The C.G. is in its most unfavorable position (aft).
5. The aircraft is airborne and is out of ground effect.
6. The flaps are selected to their takeoff position.
7. The landing gear is retracted.
8. The cowl flaps are open.
9. The airplane is at its maximum gross takeoff weight.
10. The aircraft is trimmed for takeoff.
Items 1-4 are in their order of importance in terms of their significance in maintaining directional control once the engine failure occurs. The other factors are in somewhat random order but they are still significant in determining the controllability of the aircraft.
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A CLOSER LOOK:
The following is an examination of each of the factors in detail to see the effect of each on both performance and control.
1. Maximum power on the operative engine. This factor assumes two things, first, it assumes that the airplane (engine) is at sea level and, second, it assumes that the engine is not turbocharged (a process that will not be dealt with until later in this discussion). Let's keep this simple. If you did not have a lot of power working on only one side of the airplane there wouldn't be a directional control problem. Therefore, the single most influential factor that affects Vmc is the power that is being delivered by the operative engine. An increase in power in any single engine situation means an increase in Vmc and therefore maximum power may be equated with maximum Vmc. Conversely, if we take away that power we don't have a directional control problem anymore.
Now let's take a look at performance. Obviously, if we take away the
power that is being produced by the single functioning engine we heave
ourselves a very heavy glider with abysmal performance. So, performance
suffers when we reduce power in an attempt to resolve the control issue.
2. 5 degrees of bank into the operative engine. This is easily the second most important factor in the Vmc situation. Banking the airplane into the good engine has the effect of re-directing some of the vertical lift into a horizontal component which reduces the sideslipping tendency that the airplane suffers from in improperly coordinated single engine flight thereby increasing the effectiveness of the vertical stabilizer and with it the rudder. By increasing the effectiveness of the rudder the actual angle to which the rudder tab must be deflected at a given airspeed in order to maintain control is reduced. What this means is that there is more rudder to step on as speed continues to decay. When we run out of rudder we run out of control so the later that occurs the better. This effect is dramatic: Vmc is reduced by 3 knots/degree of bank up to the 5 degree limit. This means that Vmc is approximately 15 knots higher when no bank is used than when it is used.
Performance is also a beneficiary when 5 degrees of bank is used. Because
the airplane is taken out of the relatively high drag sideslip situation
and made to fly straight again the total drag on the airframe decreases
thereby freeing up some of the remaining horsepower on the operative engine
and placing it in the category of excess thereby making it usable for climb.
(See also AOPA Safety Foundation Safety Report Vol. 19 No. 2 for additional
information on this subject.)
3. Windmilling propeller on the inoperative engine. This is somewhat the opposite (though not nearly of the same magnitude) of having maximum power on the operative engine. While the operative engine is producing thrust on one side of the airplane the inoperative engine has a windmilling propeller which produces drag on that side. This
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drag acts in concert with the thrust being produced on the operative side to further
exacerbate the problem of rotation about the airplane's vertical axis. Needless to say this produces a more serious problem than if the propeller were feathered. Since this is the case it can be said that the windmilling propeller increases Vmc.
Performance, in this case, is also affected adversely because of the
drag that the propeller imparts on the airplane. This drag is added to
the rest of the drag from parasitic and induced sources resulting in greater
total drag. Since we know that the airplane always requires some specific
amount of power to fly in the first place, and since this is an added burden
it can be said that the amount of excess thrust is effectively reduced.
Thus, we can see that the airplane's ability to climb on the one engine's
power is reduced and therefore, that performance suffers.
4. Most unfavorable C.G. This effect is far more easily explained in a drawing however, this will serve as a verbal accompaniment to such a drawing. One first needs to understand the basic principle of a lever. Basically, this principle says that a force applied at a distance yields a torque. Further, the principle says that the force must rotate about a central point called a fulcrum. To determine the torque that results from the use of a lever one has only to multiply the force by the distance. It therefore, follows that the greater the distance the greater the resulting torque when the same initial force is used. The distance is called an arm and is not unlike the arm that is calculated for weight and balance purposes.
One additional item of information is also necessary to complete one's understanding of the situation; the fulcrum or, point of rotation, is located at the center of gravity (C.G.). The reason for this lies in the definition of C.G. in the first place. The C.G. is the one point in space about which all of a given object's mass appears to act. That is, if we were to throw a rock into the air while spinning it as we let go of it, its rotation would be about its C.G. Similarly, an airplane has such a point about which all of its mass appears to act and we know this also, as a C.G. Motion through the vertical, longitudinal and lateral axes always occurs at the C.G., thus our C.G. must always be within the manufacturer's tolerances as control of the airplane may be difficult to impossible if it is not.
When dealing with engine-out situations control lies in the amount of torque that can be generated by the rudder about the vertical axis (the fulcrum) of the airplane. The location of the vertical axis, as we saw in the previous paragraph, is at the C.G. The further aft the location of the C.G. the shorter the distance (arm) between it and the tail (the principle residence of the rudder). What this ultimately means is that for a given airspeed a given angle of rudder deflection will yield a smaller torque if the arm is shortened. Since we assume that the operative engine is producing maximum power during this situation the amount of force required to correct the flight path of the airplane is always constant. Therefore, as C.G. moves aft the rudder becomes less and less effective and considering a most aft C.G. we see that we run out of rudder sooner than if we had a more forward C.G. The effect is to increase Vmc.
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Strangely enough however, the aft C.G. has a positive effect on performance.
This is so because the induced drag created by lift production is less
with an aft C.G. Precisely why this is so is rather complicated and can
be found in many books so I shall not drivel endlessly about it here. Needless
to say however, that if the overall drag is reduced there is more thrust
(which directly opposes drag) that can be utilized for climbing since the
engine power output level remains constant.
5. Aircraft airborne and out of ground effect. When considering this factor there are two principal things one must keep in mind; first, ground effect is an area close to the ground where the wing tip vortices are either partially or totally destroyed thereby reducing induced drag and total drag and second, P-factor is a very real participant in the control equation.
When an airplane is in ground effect the wing tip vortices are prevented from forming because as the rotating mass of air swirls off of the wing tip it strikes the ground and is broken up. The net effect of this is that instead of losing the outboard 20% of each wing tip due to the turbulent flow over them one has access to those portions of the wings to help keep the airplane in the air. If more wing area is lifting the airplane it means that a lower angle of attack will be required to keep the airplane flying.
And here's where P-factor comes in. It will be recalled that P-factor is one of the four left turning tendencies in a single engine airplane. This effect is still present in a twin but it is far less noticeable because it is balanced by the other engine's thrust. In single engine operations however, this is not the case. P-factor is increased when angle of attack is increased and so anything that would create a need for a higher angle of attack would necessarily create more P-factor and therefore a greater turning tendency. The introduction of yet another torsional force will, in most cases, make things worse.
Now let's take a look at where ground effect comes into this. If the airplane has lifted off and is still in ground effect its overall lifting efficiency is greater than if it were not in ground effect because of its increased effective wing area. This means that when an airplane rises out of ground effect its minimum angle of attack must increase in order to remain airborne due to the relative reduction in wing area. With this increase in angle of attack comes an increase in P-factor and therefore, an increase in Vmc.
Performance is also adversely affected by being out of ground effect
because the dramatically increased level of induced drag. When drag is
higher the amount of thrust that is required to keep the airplane flying
is greater thus yielding a lower value that can be considered excess. With
less excess horsepower the airplane's performance will suffer.
6. Flaps in the most favorable position for takeoff. This is a somewhat obscure point but it is important to understand since it relates more to aileron effectiveness than rudder
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effectiveness. First, when the flaps are in their normal position for takeoff it further
supports the notion of the overall scenario which is that the engine failure occurs on takeoff. However, there is another issue to be considered here: that of spanwise flow over the wing. When the flaps are extended the air flow is deflected down around the bottom of the wing providing lift and drag as necessary. What is usually not recognized is that air also circulates around the lateral edges of the flap onto adjacent surfaces of the wing. Well, guess what lies adjacent to the flaps. That's right! The ailerons! If the ailerons are treated to increased airflow they will be more effective and can figure quite prominently in the overall control equation. Flaps in the takeoff position therefore, establishes the degree of lateral circulation that will be present during the takeoff roll. It is also worth mentioning at this point that in most cases where light aircraft are concerned the flaps will be UP for takeoff. What this means is that the ailerons will not receive any additional airflow and therefore, control will be affected in a negative fashion.
Performance, on the other hand, is enhanced by having the flaps up.
With the flaps extended the drag on the airplane is increased dramatically
thereby compromising its ability to climb using the available horsepower.
In this case the position of the flaps that benefits control (down) is
in opposition to the position that benefits performance (up), thus making
the authorized position for takeoff a detrimental factor in the overall
Vmc picture.
7. Landing gear up. This one is fairly simple. When the landing gear is down it has the effect of stabilizing the airplane because the protrusions from the bottom of the plane act like skegs on a surfboard. The yawing tendency observed when an engine is lost is slightly reduced with the gear down because of this increased stability and therefore less control input is required by the pilot. The result: Vmc is decreased with the gear down. However, that is not how the airplane is certified. Rather, it is certified with the gear up and therefore, in a less stable condition than if it were down. The effect of having the gear up is an increase in Vmc.
Performance, on the other hand, suffers with the gear down because the
drag is higher leaving less excess thrust to promote a climb. Since the
certification occurs with the gear up we can see that this has a positive
effect on the performance of the plane. Once again, performance and control
are at odds with one another.
8. Cowl flaps open. This is another somewhat obscure point and, I might add, a negligible one where small twins are concerned but on larger ones with say, large diameter radial engines, this can be a very influential factor.
With the cowl flaps open air is permitted to pass through the engine compartment to cool the engine and this is a good thing to have going on during periods of high power output. Unfortunately the cooling process also ends up causing a lot of drag due to the air getting
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tangled up on various parts of the engine as it passes through the compartment. If the
cowl flaps are closed the amount of airflow through the engine compartment is significantly reduced (as anyone who has observed cylinder head temperatures during a climb with cowl flaps closed will tell you). It turns out that when the cowl flaps are closed a substantial portion of the air that would have gone through the engine compartment now joins the boundary layer going around the engine nacelle thereby dramatically reducing drag. So we see that having the cowl flaps open actually can increase the drag by a substantial margin over the cleaner closed configuration. An increase in drag at a given power setting must necessarily result in an increased angle of attack in order to maintain altitude. We said previously that anything that resulted in an increased angle of attack would have a negative impact on control and increase Vmc and that is precisely the case here with the cowl flaps open.
The performance aspect of this actually has two points of view. First,
we could say that the increased drag would hurt performance and this would
be correct. However, the increased engine cooling efficiency that results
from having the cowl flaps open might be a superseding factor that could
outweigh the increased drag. As long as the engine is properly cooled we
might see a higher level of power output and thus an overall improvement
in performance. You will have to be the judge on this point.
9. Aircraft at maximum gross takeoff weight. This is another issue, which has more than one point of view. Both arguments have their merits and multi-engine pilots should at least be aware of what they are. The first point of view suggests that when an airplane departs at maximum gross weight as opposed to any lower weight, the angle of attack required for flight will be at its highest by comparison to any other weight. What this means is that P-factor will also be at its highest by comparison to any other situation. The increased P-factor has the effect of increasing Vmc.
The second point of view asserts that since the airplane is at its heaviest the total lift generated by the wings is also greatest (a fact that is not in dispute). When 5 degrees of bank into the good engine is then added to the situation the resulting horizontal component of that lift will be greater thereby having a greater impact on the reduction of Vmc. In this model Vmc is reduced by departing at maximum gross weight.
When we consider performance however, maximum gross weight clearly is of detriment to the scenario. When airplanes are heavy they don't climb as well as when they're light (this should be an intuitive deduction). Another way of looking at this that is more representative of the facts is to recognize that a heavier airplane will require a higher minimum amount of power in order to fly level at a given airspeed. Since the power output of the operative engine remains constant no matter what the weight of the plane it is obvious that there could not possibly be as much excess horsepower available. So, no matter how you look at it maximum gross weight at takeoff has an adverse effect on performance.
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10. Aircraft trimmed for takeoff. This factor relates primarily
to pilot technique in dealing with the engine failure. It assumes that
the pilot will not handle the situation ideally and that both control and
performance will suffer as a result. Because the pilot will have no aid
of trim during the initial phases of the emergency he will have to make
all the appropriate control inputs entirely by feel and instrument interpretation.
Inconsistency in the application of these techniques and distractions related
to the nature of the emergency will cause a degradation in the controllability
and the performance of the airplane. Put bluntly, the pilot's own inability
to deal with the situation in an ideal fashion is likely to increase Vmc
and decrease aircraft performance simultaneously!
THE CRITICAL ENGINE
Back at the beginning of this discussion you will recall that one of the stipulations in the part 23 certification regulation was that the most critical engine be failed. This is an interesting point because the determinants that decide which engine is most critical vary from airplane to airplane according to how many engines it has and what direction the propellers turn. Obviously, on an airplane that has four engines one of the outboard engines will be most critical because of its location far out on the wing where it has a lot of leverage and would therefore create a greater asymmetry should it fail. Since most of us won't be operating large four-engine airplanes it would be better to focus more on the direction that the propeller turns as the principle determinant of which engine is most critical.
Most American made aircraft have engines that turn clockwise (as viewed from the cockpit). P-factor, it will be recalled, is actually the asymmetric production of thrust over the propeller disk (also known as asymmetric disk loading) caused by the fact that in a climb the descending blade has a higher angle of attack than the ascending blade and therefore produces more thrust on that side of the propeller. On clockwise turning engine this phenomenon occurs on the right side of the propeller thus imparting a left turning moment on the aircraft.
Now, if we look at the airplane from the top and imagine where this
disk loading problem is occurring we see that where the left engine is
concerned it is occurring inboard of the engine nacelle next to the fuselage.
However, if we look at the right engine we see that the asymmetry is being
produced outboard of the engine nacelle further away from the fuselage.
What should be apparent at this point is that if the left engine should
fail there would be two major factors contributing to the directional control
problem. First, the left engine failing would place the operative engine's
thrust on the right side of the plane thereby creating a yaw to the left
and second, the greater length of the lever arm from the C.G. to the point
where the maximum thrust is being generated on the right propeller places
the P-factor at a greater distance from the C.G. than if the right engine
were to fail. Once again, P-factor is a left turning tendency and in the
event of a left engine failure we
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already have a left turning problem and the P-factor simply exacerbates it. This effect
becomes dramatic as the horsepower of the engine and diameter of the propeller increase. What all of this means is that on most American made airplanes the most critical engine is the left one and the certification tests are performed with it rendered inoperative.
TURBOCHARGING:
One final note with regard to turbocharging. Many light twins are equipped with turbochargers, which have the effect of preventing a loss of power as altitude increases by compressing the intake air to sea level density before it is ingested into the engine. Simply put, what this allows the engine to do is burn the same amount of fuel as efficiently at altitude as it would at sea level thereby maintaining its sea level rated power output.
Factor #1 in this discussion was maximum power on the operative engine. If we look at this with a slightly more critical eye we see that when an engine is not turbocharged that maximum power can only be extracted from an engine at sea level and furthermore, only under standard atmospheric conditions of 29.92" Hg, and 20 degrees C. What we may conclude from this is that Vmc must decrease with altitude since the engine is no longer producing maximum power when it is taken to altitude. This is not true when the engine is turbocharged until the engine is taken to what is known as the critical altitude where the turbocharger cannot compress enough air to maintain sea level air density in the intake duct. In other words, when the engine reaches its critical altitude it too will begin to lose power and Vmc will begin to decline.
CONCLUSION:
These are the ten items on which light twin certification tests are
based. Hopefully this discussion will afford you a better understanding
of what these factors are and how they play a role in a Vmc scenario. One
thing that must always be remembered is that performance and control are
not the same thing and when Vmc is the issue the ONLY thing that counts
is keeping airplane right side up! Some procedures that stem from this
fact may not make much sense because they involve a conscious decision
to crash the airplane in a controlled fashion rather than attempt to fly
it around for a landing but that is the reality of flying a light twin.
No matter how abhorrent the thought of intentionally wrecking the airplane
is to you it should be remembered that inflicting damage on the airplane
will prevent it from being inflicted upon you and it might even
save your life!
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