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Copyright 1997-2001 jsd

17   Multi-Engine Flying

Q: In an underpowered twin, what is the role of the second engine?

A: It doubles your chance of engine failure, and it will fly you to the scene of the accident.

17.1   Normal Operations

In normal conditions, operating a twin is not very different from operating a heavy, high-powered, complex single. Even so, the weight, power, and complexity may be more than you are accustomed to. In particular: Normal multi-engine takeoff procedures are discussed in section 13.6. Most of the rest of this chapter is devoted to the procedures and principles of engine-out flying.

17.2   Engine Out Scenarios

This section discusses some of the things you might observe when an engine fails, and what you can do in response.

17.2.1   Rejected Takeoff; Balanced vs. Unbalanced Field

Airliners are not allowed to take off unless the available runway exceeds the balanced field length; that is, the runway must be sufficiently long that even if an engine fails at the most critical point during takeoff, the airplane can either stop on the remaining runway, or continue the takeoff and get safely airborne on the remaining engine(s).

In contrast, general-aviation light twins are not required to restrict themselves to balanced field takeoffs. Suppose you lose an engine during the takeoff roll on a short runway. Even if your plane would have done fine on a long runway, on a short runway there will be a period during the middle of the takeoff roll where you can neither stop nor continue safely on one engine. In such a case you must shut down the good engine and apply the brakes. It is much better to hit the trees at the end of the runway when you are ``almost'' stopped then to hit them when you are ``almost'' at full flying speed. This seems obvious on paper, but when you are in the cockpit it takes a lot of willpower to actually shut down the good engine. Think about this. Promise yourself that you will do it right.

17.2.2   Climb

For our next scenario, suppose you are at a reasonable altitude, climbing with full power on both engines. Then one engine fails. One of the first things that you will notice is that the single-engine rate of climb is not half of the two-engine rate of climb. No, indeed! The reason is simple: as shown in figure 17.1, when an engine is shut down, you are not splitting the difference between two-engine performance and level flight; you are splitting the difference between two-engine performance and a zero-power descent.

Figure 17.1: Two-, One-, and Zero-Engine Performance

The power curves in the figure are roughly representative of a Piper Apache, a well-known light twin trainer. Point A corresponds to the two-engine best rate of climb, 1150 fpm at 86 knots. Point B corresponds to the single-engine best rate of climb, 160 fpm at 82 knots. (These numbers apply to a fully-loaded aircraft at sea level in the clean configuration.) We see that the single-engine rate of climb is less than 15% of the two-engine rate of climb.

At density altitudes above 5000 feet the Apache cannot climb at all on one engine. Also, if the engines, propellers, and paint job are not quite factory-new, the performance will be even less than these book values suggest.

You must not allow yourself to think that just because airliners can climb with an engine out, your favorite light twin can climb with an engine out.

It is legal to operate a light twin with anemic or nonexistent single-engine climb performance. In such cases, engine failure at low altitude is perhaps the most critical situation that arises in general aviation with any appreciable frequency. Like a single-engine aircraft with partial power failure, you need to make a forced landing. The problem with the twin is that (because of the asymmetric thrust) if you mishandle the situation, your chance of getting into a spin is much higher than it would be in a single.

On the other hand, even if you are not climbing, you are probably not descending very fast. You can treat it as another ``noisy glider'' situation as mentioned in section 15.1. If you start out several thousand feet above the ground, you can probably travel dozens of miles while gradually descending. Look around and find a nice place for a forced landing.

17.2.3   Slip String

Generally, the best way to fly any airplane is to keep the airflow aligned with the fuselage. Alas, in a multi-engine airplane with asymmetric thrust, it can be rather tricky to perceive just what the slip angle is. The most direct way to get information about this angle is to use a slip string.

To create a slip string, tape a piece of yarn to the nose of the airplane, in front of the center of the window where you can see it. Leave a foot or two of yarn dangling free, so it will align itself with the airflow.

In typical aircraft, the fuselage accelerates the sideways flow, more than it accelerates the fore-to-aft flow. This increases the sensitivity of the string. That is, the angle of the string is larger than the actual slip angle.

Even in ordinary single-engine airplane, slip strings work surprisingly well. The straight-back component of propwash decreases the sensitivity somewhat, and the helical component of propwash biases the string slightly to one side.

The slip string is commonly referred to as a ``yaw string'', even though it measures the slip angle, not the yaw angle (i.e. heading) or yaw rate. As discussed in section 19.6.3, the slip angle measures the angle between the fuselage and the relative wind, whereas yaw is defined relative to some fixed spatial direction. Heading and heading change (i.e. yaw rate) are easy to perceive by looking out the window, while it is not easy to perceive slip angle except by reference to a slip string. Heading can also be perceived using the directional gyro (heading indicator), and yaw rate can be perceived using the rate-of-turn gyro or by observing the rate of motion of the directional gyro.

The inclinometer ball is often referred to as the slip/skid instrument, but that is a misnomer. It measures inclination. As we shall see in section 17.2.5, it is quite possible for the airplane to be inclined but not slipping. Again: there is no good way to determine the slip angle without a slip string.

17.2.4   Coordination

For our next scenario, imagine that you are in level flight at cruise airspeed at a comfortable altitude. Let's also suppose that your airplane has a slip string installed. Then (surprise!) an engine fails. To simplify the discussion, let's suppose the right-hand engine2 is the one that quits. You will immediately notice that the airplane will develop a slip angle. In this case, the airplane will yaw to the right, shown in figure 17.2. This is because the drag of the airplane is more or less symmetrically disposed, while the thrust is now quite asymmetric. As always, two forces with a lever arm between them create a pure torque.

Figure 17.2: Engine Out — Torque due to Asymmetric Thrust

This torque will produce an initial heading change. This will be a pure yaw; that is, it will change the direction the airplane is pointing without any immediate change in the direction the airplane is going. You will observe that the slip string is off-center to the right, indicating an asymmetric airflow. Then, after a short time (a second or so), the torques will come back into equilibrium, because of the airplane's natural yaw-axis stability (as discussed in section 8.2). That is, the uncoordinated airflow hitting the rudder will create a torque that opposes the asymmetric thrust.

Figure 17.3: Engine Out — No Pilot Action

At this point, you could either (i) sit there and be a spectator, as shown in figure 17.3, or (ii) press on the left rudder pedal to center the slip string, as shown in figure 17.4. From the point of view of directional control, your choice doesn't matter very much. That is, in case (i) the airflow strikes the whole airplane (rudder included) at a nonzero angle, while in case (ii) the airflow strikes the airplane at a zero angle, with the rudder deflected. In either case, the amount of tail force produced is approximately the same. The most important difference is that the airplane will climb better in case (ii), because the airflow will be aligned with the fuselage.

Figure 17.4: Engine Out — Correct Compensation

Let's see what happens after the yaw-axis torques have returned to equilibrium. Let's assume for now that you are keeping the wings level. In case (i), the airplane will make a steady turn toward the dead engine. This is obviously a boat turn, due to the uncoordinated airflow striking the fuselage, as discussed in section 8.10. This will be a genuine CM-turn (as defined in section 8.8), changing the direction of motion of the center of mass; the heading will follow the CM-turn in order to maintain a constant slip angle.

What is perhaps more surprising is that even in case (ii), if you keep the wings level the plane will make a CM-turn toward the dead engine (toward the right in this case). It will not turn as rapidly as in case (i), but it will turn nonetheless. The reason is that the rudder force, in addition to creating a torque, is creating an unbalanced force. This force is changing the direction of motion of the center of mass. A possible (but non-optimal) way to stop this turn would be to apply even more pressure on the left rudder pedal, which would create a wings-level non-turning slip, as will be discussed below in conjunction with figure 17.5. For now, though, let's consider the correct strategy, which is to keep the slip string centered and apply a bank (to the left, in this case) to stop the turn. This is shown in figure 17.4. This uses a leftward component of lift3 paired with the rightward rudder force. Once again we have a pair of forces with a lever arm between them, i.e. a pure torque. This lift/rudder pair cancels the thrust/drag pair discussed above.

To reiterate: when engine trouble develops, the first result of the asymmetric thrust is to make the airplane yaw toward the dead engine. The airplane changes its heading immediately (whereas only later does it gradually change the direction it is going). That is, a slip angle develops immediately. If you don't deflect the rudder, the slip angle will grow until the uncoordinated airflow striking the rudder develops enough torque to stop further yawing. This is the basic yaw-axis stability mechanism as discussed in section 8.2. The result is that the airplane does not spin around and around like a Frisbee — it just develops a few degrees of slip angle and then stabilizes.

17.2.5   Perception and Initial Response

If an engine fails suddenly, the initial yaw toward the dead engine is usually quite noticeable. On the other hand, if it fails gradually, the initial yaw (heading change) may be harder to perceive than you might have guessed. It is especially hard to perceive if it occurs during a turn — the turn just proceeds a little faster or slower than normal. The subsequent boat turn may not be super-easy to perceive, either.4
There are three basic ways to perceive and deal with the slip and yaw.
  1. If you happen to have a slip string installed, the procedure is simple. If the string is deflected to one side, step on the rudder pedal on the opposite side, until the string is centered. The mnemonic is: ``Step away from the string''.
  2. A less-elegant, less-accurate technique is to use the inclinometer ball. If the ball is deflected to one side, step on the rudder pedal on the same side. The mnemonic is: ``Step on the ball''. Center the ball, then (to establish zero slip, as discussed below) relax the pedal force to let the ball go off center about one-third to one-half of its width.
  3. A third technique (which is really the most common technique) is to roll the wings level and then apply the rudder as needed to stop the boat turn. The advantage of this procedure is that it can be done without reference to instruments. The main disadvantage is that it doesn't help you regain or retain control in a turn.5 (There are rare situations where even though an engine has failed you might want to be turning.) Then, once you've got the wings level and the turn stopped, you should establish the optimal zero-slip condition, by raising the dead engine a few degrees and releasing some of the rudder pressure.6
At this point, you will find yourself maintaining a rudder deflection and a bank angle, both toward the side with the working engine. Use the rudder deflection (not the bank!) to identify which engine has failed. The mnemonic is: working foot, working engine; dead foot, dead engine. Specifically, if the right foot is not being used to deflect the rudder, bend your right knee. Raise that knee an inch or two, pat it a couple of times, and say ``right engine has failed''. (More on this later.)

To maintain zero slip, you will need to bank the plane very slightly toward the working engine. The mnemonic is: raise the dead. This also implies that the inclinometer ball will be slightly displaced toward the working engine. This correct procedure (figure 17.4) requires slightly more aileron and slightly less rudder than you would need for wings-level, ball-centered, non-turning, uncoordinated flight (figure 17.5).

Having the slip string centered but the inclinometer ball not centered may seem a bit counterintuitive, so let's examine the aerodynamics of the situation a little more closely.

The asymmetric thrust produces a yaw-axis torque, which cannot remain unopposed. The rudder is part of the solution, but remember that while the rudder is producing the desired torque it is also producing a force. We need the forces to be in balance, as well as the torques.

Suppose you try to maintain zero bank instead of raising the dead. Initially the airplane is not in equilibrium, because the rudder is producing an unbalanced force toward the dead-engine side. There are then two possibilities:
  1. Suppose the sideways force remains unbalanced. This will cause the airplane to turn. This will be a wings-level, coordinated turn. I call this a pseudo boat turn. Unlike an ordinary boat turn, the airflow is coordinated along the fuselage, but unlike a regular turn, the horizontal force is not coming from the wings.
  2. Suppose you push a little harder on the rudder pedal, establishing a slip toward the dead engine. The ball is centered, the wings are level, and the rate of turn is zero. (Any two of those things implies the third, regardless of engine status.) The forces are in balance because there is enough uncoordinated airflow over the fuselage to create a sideways force that balances the rudder force. In this situation, as shown in figure 17.5, you are using the fuselage as an airfoil. The problem is that the fuselage has a really poor lift-to-drag ratio. The sideways fuselage lift force is accompanied by a huge drag force, which steals energy from you. It would be much better to use the wings, as previously discussed in conjunction with figure 17.4.
Figure 17.5: Engine Out — Wings-Level Nonturning Slip

The proper technique is counterintuitive, because in any normal situation, proper coordination implies that the rate of turn will be proportional to the amount of bank. (See section 11.5.2, for example.) With an engine out, though, proper coordination requires a slight bank when you are not turning.

The amount of bank for a typical airplane can be estimated using the following argument: The lift-to-drag ratio of the airplane is roughly ten-to-one. In level flight the thrust must therefore be one tenth of the lift. The lever arm between the wings and the rudder is typically about three times the lever arm between the thrust and the drag. Since the torques must cancel, the rudder force (and the horizontal component of lift) must be one third of the thrust, and therefore one thirtieth of the lift. We conclude that the horizontal component of the lift is one thirtieth of the total lift. One thirtieth of a radian is two degrees — not exactly a huge bank.

To find out exactly how much bank you need to maintain coordinated airflow over the fuselage, it helps to use a slip string. At a safe altitude, set up for single-engine flight at VYSE. Apply enough rudder pressure so that the slip string indicates zero slip angle. Bank as required to maintain nonturning flight. Experiment with slightly greater or lesser rudder pressure, to see what produces the best climb performance.

You will discover that in optimal single-engine flight, the inclinometer ball is not centered, but the slip string is centered. The airplane is inclined, but it has zero slip angle. Make a note of how much inclination is indicated by the inclinometer ball; typically it will be off-center by one-half or one-third of its diameter. You can use this information to set up a good approximation of engine-out coordinated flight during subsequent flights when you don't have a slip string installed.

The inclinometer ball measures the inclination of the wings relative to the E-down7 direction. The inclinometer is sometimes referred to as a slip/skid ball, but that is a misnomer8 because the slip string (as discussed in section 17.2.3) provides your only direct information about the slip angle.

Achieving zero slip is the key to optimal climb performance.9 The idea is to have the airflow aligned with the fuselage. Centering the inclinometer ball is not what determines performance. Practice with the slip string until you learn how much inclination is required for a given amount of asymmetric thrust.

17.2.6   Yaw Control at Reduced Speeds

So far, we have discussed engine-out climb rate (section 17.2.2) and discussed the value of maintaining coordinated flight (section 17.2.4). We now begin a discussion of airspeed. As you might imagine, this is rather important.

So, let's consider what happens when airspeed variations are added to the previous scenario. Let's assume you start out at cruise airspeed and gradually decelerate. Again, to simplify the discussion, let's assume the right engine has failed.

The amount of asymmetric thrust does not depend on airspeed; it depends only on the power output of the engine. In contrast, the amount of force the rudder produces depends on the airspeed squared, and on the rudder's angle of attack. Therefore as you decelerate you will need progressively more rudder deflection in order to maintain zero slip. If you do it right, the sideways force developed by the rudder will remain unchanged, and the bank angle will remain unchanged (for now).

At some point you will run out of rudder deflection. The pedal (or the rudder itself) will hit the stops. You will be unable to maintain zero slip.

Now, suppose you continue to decelerate beyond this point. As a slip develops, the airflow hits the tail and rudder at an angle. This gives the tail/rudder an angle of attack over and above whatever angle of attack you created by deflecting the rudder. You are using the slip angle as a substitute for additional rudder deflection. Up to a point, this higher angle of attack allows the tail/rudder to produce a higher coefficient of sideways lift, allowing it to produce the required force in spite of the lower airspeed.

In addition to the air hitting the rudder, you now have the uncoordinated airflow hitting the fuselage. You are relying on the rudder to produce at least 100% of the torque needed to oppose the asymmetric thrust. The air hitting the fuselage makes a small unhelpful contribution to the torque budget, and (more noticeably) contributes to the sideways force budget, producing an undesirable boat turn. This boat turn is in addition to the pseudo boat turn that the rudder is producing, so you will need to increase the bank angle to maintain nonturning flight.

Obviously there is a limit to this process. If you keep increasing the rudder's angle of attack, at some point the rudder will stall. Remember, the amount of asymmetric thrust does not depend on airspeed, whereas the absolute maximum amount of force the rudder can produce depends on the airspeed squared. Therefore, for any nonzero amount of asymmetric thrust, there must be some airspeed below which the rudder cannot develop enough torque. At that point there will be an uncontrollable yaw toward the dead engine. The airplane will spin like a Frisbee.

You might think you could improve the situation by releasing the rudder pedal, thinking this would reduce the rudder angle of attack. Alas, it won't work. It will just cause the airplane to establish a greater slip angle. Remember the rudder needs to produce a certain amount of force to oppose the asymmetric thrust, and the airplane's natural yaw-axis stability will adjust the tail/rudder's angle of attack, trying to create the necessary force.10

If the rudder stalls, it will be about as unpleasant as anything you can imagine. There will be a sudden uncontrollable yawing motion. Because of the yawing motion, the wingtip on the side with the good engine will have a higher airspeed than the wingtip on the other side. Because of the difference in airspeed (plus the difference in propwash patterns) the good-side wing will produce much more lift, so you will get an uncontrollable roll. As the inside wing drops, it will probably stall (since you were already at a low airspeed). You are now in a spin. There is no guarantee that it will be possible to recover from the spin; multi-engine airplane certification regulations do not require spin recoveries.

On some planes (such as an Apache, a common trainer) low-speed engine-out performance is limited by the rudder, as described above. On some other planes (such as a Seneca, another common trainer) you don't need to worry about the rudder because the wings will stall first.11 This is not much of an improvement, because a stall with asymmetric power is also rather likely to result in a spin.

To prevent such nasty things from happening, you need to maintain a safe airspeed. The manufacturer gives you some guidance in this regard, as is discussed in the following section.

17.2.7   Minimum Control Speed — Definitions

The symbol VMC denotes ``minimum control airspeed''. There are at least four different definitions of this term, including:

FAR 23 (the certification requirements for typical general-aviation12 airplanes) gives a very specific definition of VMC, namely:
  FAR 23.149  Minimum control speed.
    (a) VMC is the calibrated airspeed at which, when the
critical engine is suddenly made inoperative, it is
possible to maintain control of the airplane with that
engine still inoperative, and thereafter maintain
straight flight at the same speed with an angle of bank
of not more than 5 degrees.  The method used to simulate
critical engine failure must represent the most critical
mode of powerplant failure expected in service with
respect to controllability.
    (b) VMC for takeoff must not exceed 1.2 VS1, where
VS1 is determined at the maximum takeoff weight.  VMC
must be determined with the most unfavorable weight and
center of gravity position and with the airplane airborne
and the ground effect negligible, for the takeoff
configuration(s) with--
    (1) Maximum available takeoff power initially on each
    (2) The airplane trimmed for takeoff;
    (3) Flaps in the takeoff position(s);
    (4) Landing gear retracted; and
    (5) All propeller controls in the recommended takeoff
    position throughout.
FAR 1 (the ``definitions'' section) defines VMC as ``minimum control speed with the critical engine13 inoperative''. It does not specify any restrictions as to weight, configuration, altitude, et cetera.
The FAA Practical Test Standards for the multi-engine rating call for demonstrating ``VMC'' in a particular way that emphasizes losing yaw control without stalling the wing or rudder, even though (as discussed below) for many airplanes VMC (under definition I or II) is limited by wing stall and/or rudder stall.
In common parlance, pilots apply the term VMC to the airspeed where the airplane (multi-engine or otherwise) becomes uncontrollable, no matter what the reason, no matter what the configuration, and no matter whether any engine is inoperative.
Note that none of these definitions require that the airplane exhibit a positive rate of climb at VMC.14 Also note that during a VMC demonstration, the pilot is not required to optimize the climb rate or to maintain zero slip — although zero slip may be an advantage if it can be achieved.

The VMC number in the Pilot's Operating Handbook is determined according to the FAR 23.149 definition. This airspeed is marked with a red radial line on the airspeed indicator, and is sometimes called the FAR 23.149 redline airspeed.15

There are various ways to lose control; whichever happens first determines where the manufacturer sets the redline:
In some airplanes, under some conditions, you can maintain control, even with an engine out, right down to the point where wing stalls. This is discussed below in conjunction with figure 17.6. A stall with asymmetric thrust could be rather sudden and nasty.
In others (with a smaller rudder, larger wing, and/or higher-thrust engines), there will be conditions under which the rudder will stall before the wings do, as is discussed below in conjunction with figure 17.8. A rudder stall could be very sudden and very nasty.
In yet others (larger rudder: area but a shorter tail-boom, so that the rudder is closer to the wings), there will be situations where neither the wing nor the rudder is stalled, but the boat-turn forces are so large that it requires more than 5 degrees of bank to counteract them and maintain nonturning flight. The airplane would be perfectly controllable if the bank were not limited to 5 degrees. Since a bank of 15 or 20 degrees is not particularly dangerous, the 5 degree limitation must be considered arbitrary. If your airplane, at a given weight and altitude, does run up against this limitation, the resulting ``loss of control'' is neither sudden nor nasty. The airplane will just make a gentle boat turn toward the dead engine, as is discussed below in conjunction with figure 17.7.
Possibility (c) is in some ways attractive, but you have no guarantee that this is what will happen. Rudder stall depends on slip angle, so you may be wondering why FAR 23.149 should mention a bank angle as opposed to a slip angle. Bank does not cause slip.16 If you want to establish any connection between bank and slip, you must consider:
  1. bank angle (i.e. the angle between wings and horizon)
  2. slip angle (as indicated by the slip string)
  3. rate of turn
  4. asymmetric thrust
If any three of these are zero, the fourth is guaranteed to be zero. More generally, other things being roughly equal, given any three of these you can estimate the fourth. The problem is that other things are generally not equal — depending on weight, airspeed, airplane design, et cetera, five degrees of bank could correspond to a large slip angle or perhaps no slip angle at all. So this regulation is not 100% logical.

Some people seem to assign a near-religious significance to the ``5 degree bank'' mentioned in FAR 23.149. However, the real significance is quite limited: One thing we learn from this is that you should not use bank angle or anything else as a substitute for proper airspeed control.

For that matter, airspeed control requires a little thought, too. Perhaps because FAR 23.149 uses words like ``most critical'' and ``most unfavorable'', people commonly assume that it is always possible to control the airplane at redline airspeed, no matter what. This assumption is wrong — dangerously wrong — in many airplanes. For example, there are some airplanes where the certified takeoff configuration19 calls for the flaps to be extended, and the FAR 23.149 redline is essentially equal to the stalling speed in the takeoff configuration. Then if you operate with the flaps retracted, you will lose control of the airplane at an airspeed well above redline.20

Specific procedures for dealing with engine failure are discussed below, in section 17.3.

17.2.8   Effect of Altitude, Weight, etc.

FAR 23 tells us that the airplane, when operated under a particular set of circumstances, can maintain directional control at redline airspeed. The question is, what happens under other circumstances?

Let's discuss an example. Consider a non-turbocharged airplane for which the handbook calls for flaps retracted during takeoff. Then, under standard conditions (takeoff configuration, maximum weight, etc.), the situation is shown in figure 17.6. The single-engine stall speed for the example airplane is shown by a black vertical line in the middle of the figure. The FAR 23 redline is shown as a bright red tick mark on the airspeed axis. The manufacturer had to set it a knot or two above the stalling speed, since that is what limits the low-speed handling for this airplane in this configuration.

Figure 17.6: Speed & Altitude affect Directional Control (basic)

Also, in this figure, the magenta curve shows the airspeed below which the rudder cannot develop enough force to oppose the asymmetric thrust. Thirdly, the dotted cyan curve shows the airspeed below which the boat turn forces are so large that it would require more than 5 degrees of bank to maintain nonturning flight.

Since the example airplane is not turbocharged, as altitude increases there is less thrust available on the good engine. The required amount of rudder force declines accordingly. This is why the magenta and cyan curves trend to the left as they go up. Note that in this configuration, for this airplane, rudder performance is not a limitation — the wing stall is the only relevant limitation.

Now, suppose that several things change: The new situation is shown in figure 17.7.

Figure 17.7: More Flaps, Less Weight, etc.

Let's consider what happens under these new circumstances. The reduced weight will lower the stalling speed. Similarly, extending the flaps lowers the stalling speed. This is indicated by the black line, which moves to the right as we go from figure 17.6 to figure 17.7.

The amount of torque developed by the engine depends on altitude in the same way as before, and is unaffected by the weight, flaps, and other variations. The amount of force the rudder can produce is also unaffected. Therefore the magenta curve is the same in the two figures.

At the reduced weight, less lift is needed for supporting the weight of the airplane. As always, the horizontal component of lift, at any particular bank angle, is proportional to the weight of the airplane. Therefore, at any particular bank angle, you have less ability to oppose a boat turn. This is one reason why the cyan dotted curve moves to the right as we go from figure 17.6 to figure 17.7.

Limiting yourself to less than full rudder deflection does not reduce the amount of torque that must be produced in order to oppose the asymmetric thrust; it just means that the airplane will establish a slip to create the necessary force.22 In this slipping condition, the fuselage produces a boat turn on top of whatever pseudo boat turn the rudder is producing, so you will need more bank to oppose the turn, and you will run up against the bank limitation sooner. This is the second reason that the dotted cyan curve (the bank limit) moves to the right.

And of course, if you limit yourself to a smaller bank, you will run up against the bank limit sooner. This is the third reason that the cyan curve moves to the right as we go from figure 17.6 to figure 17.7. Conversely, if you allow yourself a large bank (15 or 20 degrees) you can push the dotted cyan curve very far to the left, as indicated in figure 17.8.

Figure 17.8: More Bank

Finally, let's consider what happens in different airplanes. For example #2, let's take an airplane where the wing has a very low stalling speed. For such a plane, figure 17.6 never applies; figure 17.7 (or figure 17.8, depending on bank angle) applies even at max weight with the flaps retracted.

For example #3, let's go to the opposite extreme and consider an airplane that has somewhat smaller wings. To compensate, the manufacturer specifies that flaps are to be extended in the certified takeoff configuration. The result is that the certified performance of the new plane is identical to the performance of example airplane #1, as shown in figure 17.6. The interesting wrinkle is this: if you fly the new airplane with flaps retracted, the performance is as shown in figure 17.9. Note the higher wing stall speed. The airplane will become uncontrollable at an airspeed well above the FAR 23.149 redline.

Figure 17.9: Certified Flaps Not Used

Let's summarize this information into a form that is perhaps more directly useful when you are actually in the cockpit, planning or performing engine-out maneuvers. For more information on engine-out procedures, see section 17.3.

17.2.9   Effect of Center of Mass

We know that we have to pay careful attention to the location of the airplane's center of mass, since it has a big effect on the angle of attack stability; see for example section 6.1.1.

This leads us to wonder what effect center-of-mass position has on VMC. There are two possible answers:

  1. CM location has no effect whatsoever if you use the unwise wings-level technique depicted in figure 17.5.
  2. CM location does matter if you use the recommended procedure depicted in figure 17.4. As the CM (or, more precisely, the center of lift) moves aft, VMC increases.
In both cases, you need to create a torque to oppose the asymmetric thrust. You create it using a pair of forces with a lever arm between them. One force comes from the rudder.

In case (1), the rudder force is paired with a horizontal force due to air hitting the side of the fuselage. This fuselage horizontal lift depends on the shape of the airplane, but does not at all depend on the CM location.

There is a deep theorem of physics that says that for any two axes parallel to each other, the torque around one is the same as the torque around the other (provided there are no overall unbalanced forces on the system). In the zero-bank case, it means that VMC can't depend on center of mass location (unless the airplane is actually turning, i.e. being accelerated sideways).

To understand the basis of this theorem, refer again to figure 17.5. Let's pick two pivot points A and B somewhere along the rudder/wing lever arm, as shown in the figure. (You can, if you wish, imagine them to be two possible locations of the center of mass; the CM is no better or worse than any other pivot point.) When we calculate the total torque around each pivot point: The total torque around A is exactly the same as the total torque around B. The total torque is the only thing that affects VMC, and that is the same no matter what pivot point is used.

In case (2), the story is slightly different. The rudder force is paired with the horizontal component of lift from the wings, tail, et cetera. This component arises because you are in a slight bank, as illustrated in figure 17.4. The location of this force depends indirectly on the CM location, according to the following chain of reasoning:
The large vertical component of lift must be located very close to the center of mass, to oppose the force of gravity; otherwise the airplane would be out of equilibrium in pitch.
The small horizontal component of lift is located at the same place as the large vertical component.
Here's another way of saying the same thing: the location of the lift vector depends directly on the shape of the airplane, but you have to adjust the shape of the airplane in order to keep the center of lift located very close to the center of mass. Note that we are not talking about the lift of the wings alone, but the lift of the entire airplane including the tail. In the particular example illustrated in figure 17.4, the center of mass is located rather far forward. The tail has been adjusted to produce a negative amount of lift in order to maintain equilibrium in pitch. The horizontal component of lift depends directly on this contribution from the tail, which in turn depends on CM location.

As the center of lift moves aft, the lever arm between it and the rudder gets shorter. This means you need more rudder deflection and more bank to oppose any given amount of asymmetric thrust.

17.2.10   Effect of Drag (e.g. Landing Gear)

To reiterate: in engine-out flight you have two problems: impaired rate of climb, and asymmetric thrust which can lead to uncontrollable yaw if you're not careful.

You may be thinking that it is possible to counteract the asymmetric thrust using asymmetric drag. Technically, that's true, but as we shall see, it isn't particularly practical.

An unrealistically good type of asymmetric drag is shown in figure 17.10. A source of additional drag (a small parachute) is attached far out on the wing (on the working-engine side). Because it has a long lever arm, a modest amount of drag force will create a significant amount of yaw-axis torque. This will help you maintain directional control. Of course, the drag will exacerbate your rate-of-climb problems.

Figure 17.10: Asymmetric Drag (Useful, but Unrealistic)

If the parachute is attached at a different point, the results will be different. If it is attached near the working engine, as shown in figure 17.11, its contribution to the yaw budget will be exactly the same as if you had throttled back the working engine; added drag is the same as reduced thrust. The effect on climb performance is also the same as if you had throttled back. Obviously, using the throttle is more convenient and practical than adding asymmetric drag.

Figure 17.11: Asymmetric Drag (Useless)

Now we can do a more detailed analysis of how the landing gear contributes to the yaw-axis stability and equilibrium. Let's take the gear-up situation as a starting point, and see what differences arise when you put the gear down.

With the gear up, the forces are in equilibrium: thrust balances drag. With the gear down, there is extra drag. Eventually equilibrium will be restored somehow. Let's assume26 the airplane just slows down, so that the extra drag of the gear will be balanced by reduced drag on the rest of the airplane.

So we have two new forces: a rearward contribution from the gear, and a forward contribution from the reduced drag on the rest of the airplane.

First, let's see what happens when the slip angle is zero. In that case the two new forces are oriented right along the line between them. This contributes nothing to the yaw-axis torque budget, because the forces have no component perpendicular to the lever-arm between them.

Figure 17.12: Extended Landing Gear (Worse than Useless)

Next, let's see what happens when (as shown in figure 17.12) a slip angle has developed. Once again, the new force on the wheel will be mostly a drag force, rearward in the direction of the relative wind. The other new force (the reduced drag on the rest of the airplane) will act in the opposite direction, centered at a place called the center of lateral effort.

Now we have a pair of forces with a component perpendicular to the lever arm. This will create a yaw-axis torque. The torque will grow in proportion to the slip angle. On most airplanes the nose wheel is far ahead of the center of lateral effort, so this will make a negative contribution to the yaw-axis stability.

As a final refinement, we consider the fact that when the wheel meets the air at an angle (as shown in figure 17.12), it acts a little bit like an airfoil and produces a force perpendicular to the relative wind, i.e. a sideways lift force. This force grows in proportion to the slip angle and makes another negative contribution to the yaw-axis stability.

To summarize this section: Of course, during the descent and landing phases, there are some obvious advantages to extending the landing gear.

*   Other Scenarios

The foregoing assumed that you maintained level flight at constant engine power, with non-constant airspeed. But this is just one of several possibilities:

The first three cases usually make a negative contribution to yaw-axis stability; they create a torque when the slip angle is nonzero. The fourth case is even worse: it creates an unhelpful torque even when the slip angle is zero.

17.2.11   Roll Control

Whenever one or more engines are producing power, propeller drag will cause a rolling moment, as discussed in section 9.5. You will need to deflect the ailerons to the right to compensate.

Losing an engine will cause additional roll-axis problems on top of all your other problems. That's because the working engine creates more propwash over its wing, producing more lift on that side. You need to deflect the ailerons toward the working engine to compensate. Many airplanes have aileron trim to help you deal with this.

17.2.12   Critical Engine

On a typical twin, you will notice that the left engine causes more yaw trouble than the right engine does. There are several reasons for this, including helical propwash, twisted lift, and possibly P-factor.

First: Helical propwash was discussed in section 8.4 in connection with single-engine airplanes. The multi-engine story is partly the same and partly different. To be specific, let's consider a plane where the engines rotate clockwise as seen from behind.

In some airplanes, a lot of propwash hits the tail, and you need to apply right rudder to compensate, just like in single-engine planes. If your airplane requires right rudder during the initial takeoff roll, it must be due to propwash; it can't be due to twisted lift (because there is no lift yet), and it can't be due to P-factor (because the prop disks are not inclined).

In other airplanes, in normal flight, most of the propwash misses the vertical tail, as shown in figure 17.13. This causes no problems, so no compensation is required. Even with one engine out, as long as you are able to maintain zero slip, most of the propwash misses the vertical tail, as shown in figure 17.14.

Figure 17.13: Normal: Helical Propwash Has No Effect

Figure 17.14: Engine Out: Helical Propwash Still Has No Effect

Figure 17.15: Slip: Helical Propwash Has An Effect

If you don't apply enough rudder to maintain zero slip, more of the tail will move into the propwash, as shown in figure 17.15. (At low airspeeds, you could easily have a situation where you can't apply enough rudder to prevent this.) Since the vertical tail sticks up, not down, the propwash from the right engine will be rotating in such a way as to reduce rudder effectiveness.28 If possible, you should apply additional right rudder to compensate.

It is a bit ironic that propwash affects the yaw-axis torque budget more when you already have a big slip angle. Normally you don't allow that to happen unless you are forced to, so this effect is usually only noticeable at low airspeeds — such as a VMC demonstration, or a crosswind takeoff (especially a crosswind from the left).

In a plane with four propellers, the tail will be much more affected by the propwash from the inboard engines than from the outboard engines. By using the engines one at a time, and in various pairings, you can shed a lot of light on the effects discussed in this section.

Secondly: As mentioned in section 17.2.11, propeller drag creates a rolling moment and requires right aileron no matter which engine is running. This aileron deflection will produce a certain amount of twisted lift, even though the magnitude of the lift vector is the same on both sides, as discussed in section 8.8.4. You will need to apply right rudder to compensate. This will be most noticeable in high-power low-airspeed situations.

Thirdly: P-factor (asymmetric disk loading) makes a small contribution to the yaw-axis torque budget. I measured this in a light twin, as discussed in section 8.5.4, using both engines. The effect was small, but could be observed if you looked closely. With only one engine, the effect would be half as large.

I also calculated from theory that when the airspeed decreases from cruise to VMC, the corresponding increase in angle of attack causes the center of effort of the propeller disk to move to the right by about one inch. That's not zero, but it's not very much, either.

Most of the effects that people blame on P-factor are really mainly due to a combination of adverse yaw and helical propwash.

To summarize: Some yaw contributions are unbiased, requiring rudder deflection depending on which engine is out. Working foot, working engine. These include the asymmetric thrust (as diagrammed in figure 17.4) and the increased lift over the working engine's wing (as mentioned in section 17.2.11).

Some other contributions are biased to the right, requiring right rudder no matter which engine is out. These include helical propwash acting on the tail, propeller drag acting via twisted lift, and P-factor. These are what make one engine more critical than the other.

Terminology: The engine you most regret losing is called the critical engine. In a twin where both engines rotate clockwise, that will be the left engine. With the left engine out, you will run out of rudder authority sooner, because the biased contributions add to the unbiased contributions. (If the right engine were out, the biased contributions would work in your favor, reducing the amount of left rudder required.)

Some twins have counter-rotating propellers. (That is, one engine rotates clockwise while the other rotates counterclockwise.) In that case both engines cause equally much yaw trouble, and either (or neither) can be considered the critical engine.

17.3   Engine Out Procedures

Engine failure is an emergency. You might want to review the general discussion of emergencies in chapter 15.

Make sure you know the emergency checklist for your airplane. Not all airplanes are the same. The following discussion applies to a ``generic'' airplane, and serves to illustrate some important concepts, but should not be taken as a substitute for airplane-specific knowledge.

During takeoff, it is important to be able to detect any problems promptly. Early in the takeoff roll, you should glance at the gauges (RPM, manifold pressure, and fuel flow) to make sure the readings are normal — and that both engines are the same. Make sure the airplane ``feels'' like it is pulling straight, i.e. no unusual steering effort is required to keep it going straight.

If anything funny happens while there is adequate runway remaining ahead of you, close both throttles immediately and stop straight ahead. In a high-powered airplane, such as an airliner, there will be a point where it is not possible to stop on the runway but it is possible to accelerate and fly away safely on one engine.

In contrast to airliners, typical light twins use a smaller fraction of the runway for a normal takeoff, yet have worse single-engine performance. As a consequence, there is a time even after liftoff when it is better to close the throttles and re-land on the remaining runway. Indeed, even if the remaining runway is not quite enough, you might want to land on it: Suppose that because of density altitude or whatever, your aircraft has poor single-engine climb performance. You will sustain vastly less damage if you land and slide off the end of the runway at low speed, rather than making an unsuccessful attempt to climb out on one engine.

In many light twins, the climb performance is OK with the landing gear retracted but very poor with it extended. Therefore a common rule is the following: when there is no more useful runway ahead, retract the gear. If an engine fails before that point, you know you are committed to landing; if it fails after that point, you know you are committed to climbing.

17.3.1   Procedure: Low Altitude

Once you are airborne and assured of single-engine climb performance, the following checklist applies to our generic airplane at low altitudes: three things, five things, four things. Specifically: Now let's spell each item out in more detail, for the case where your initial speed is above VMC: Here are the same items again, for the where you have a fair bit of initial altitude, but your initial speed is below VMC:29 In the case where your initial altitude and initial airspeed are both rather low, it may not be possible to regain VMC by diving. In this case the procedure is rather simple: you have to close the throttles and make an immediate landing.

Reading about these things is good, but not sufficient. You really should to up with an instructor and practice these things. Practice until the right actions become routine. Review it at least once every six months.

17.3.2   Procedure: Higher Altitude

Finally, here is the procedure for the case where you have a reasonable airspeed and a reasonable altitude, say 1000 feet AGL or more. You should not be in any big hurry to feather the offending engine. If the problem is minor, restarting will be a lot easier if the engine is not feathered. The checklist should be: Take a systematic approach to debugging. Start somewhere on the panel and then check everything you come to, systematically.

It doesn't hurt to be logical, but remember that in an actual emergency, you will be much less logical than you normally are. Unless it is obvious what the problem is, check everything, in order. Don't just check the things that come to mind. Systematic habits are more likely to stay with you.

After you've checked everything once, then try applying logic. What was the last thing you fiddled with before the failure? Did you just shut off the fuel boost pumps? Maybe you should switch them back on; look at the fuel pressure... or did you miss the boost pumps and turn off the magnetos instead? Did you just switch from the inboard to the outboard tanks? Maybe you should switch back, or switch to crossfeed.

Remember that you may be unable to climb or even maintain altitude on one engine. See section 17.2.2 for a discussion of this.

17.3.3   Airspeed Management

The airspeed that gives the best single-engine rate of climb is referred to as VYSE. The value of VYSE for standard conditions (max weight, sea level, etc.) is marked on the airspeed indicator by a blue radial line, and is commonly called blueline airspeed.

If an engine fails, you should (except in certain special situations) maintain a speed at or above VYSE. Maintain thine airspeed lest the ground arise and smite thee.

One exception to the foregoing rule: If you need altitude to avoid an obstacle, you'll be better off at VXSE (best angle of climb) as opposed to VYSE (best rate of climb). In typical trainers, the single-engine performance is so anemic that VXSE will be only slightly slower than VYSE, for reasons illustrated in figure 7.8. Indeed, if you are above the single-engine absolute ceiling, the climb rate is negative and VXSE is slightly faster than VYSE.

Another exception: The optimal airspeed on final approach is typically less than VYSE. You're not climbing, so you don't need to worry about climb performance (unless you need to go around, as discussed in section 17.3.4).

Yet another exception: Suppose your airplane has enough single-engine climb performance that the zero-climb speed VZSE is significantly slower than VYSE. (See figure 7.7.) Further suppose you lose an engine at night at low altitude over a dark forest, at a very low airspeed. You don't want to dive all the way to VYSE, because that could take you into the trees. A much more modest dive will produce a speed above VZSE. Thereafter you can accelerate in level flight, or climb at constant airspeed. In this scenario you don't need best rate of climb as long as you have some rate of climb.

Another relevant airspeed is the minimum control airspeed, VMC. As discussed in section 17.2.7, you could get into big trouble if the airspeed gets too much below VMC. At any speed above VMC you should apply full power on the good engine and accelerate to best-climb speed. Don't be shy about diving to get to best-climb speed; remember the airplane might not be able to climb or accelerate at all at lower speeds.

At speeds below VMC, you will be forced to use less than full power on the good engine, to keep the yaw from getting out of hand while you accelerate to VMC. Losing an engine at an airspeed below VMC is a really nasty situation which (for obvious reasons) most people don't practice during training. To recover, you have to partially close the throttle on the good engine, which takes a lot of willpower. You don't have much time to think. Then you have to dive, cashing in quite a lot of altitude to get the needed airspeed. The usual procedure calls for accelerating to VMC plus a few knots, to give yourself a little margin, before returning the good engine to full power.

17.3.4   Engine-Out Go-Arounds

The first thing to be said about engine-out go-arounds is that you should make every possible effort to make sure that you do not ever need to perform one. The most common reason for a go-around is that you are about to land long and run off the end of the runway. Therefore, if at all possible, fly to somewhere that has a really long runway before attempting any engine-out landing.

The second thing to be said is that for typical airplanes there is a certain height above the ground — often a surprisingly great height — below which an engine-out go-around is simply not possible. The reason for this is simple: the typical approach speed is quite slow — not only below VYSE (best-climb speed) but near or even below VZSE (zero-climb speed, as defined in figure 7.7). If you try to climb out at low airspeed, the rate of climb may well be negative. In order to accelerate from approach speed to any reasonable climb speed, you will need to cash in quite a lot of altitude. You will also consume time (and altitude) while you retract the landing gear, et cetera. In a Seneca, the decision to go around must be made above 400 feet AGL; below that altitude, you are going to touch down. If the runway is obstructed, land on the taxiway, or the infield, or whatever. If you have enough runway to touch down but not stop, consider doing a touch and go (which works better if you leave the gear down). Also consider landing anyway, with the expectation of going off the end at low speed; this is vastly preferable to hitting obstructions at high speed during an unsuccessful go-around.

17.3.5   Low-Speed Engine-Out Demonstrations

There are several key ideas I want my students to know about low-speed engine-out performance, including:
If you are ever in a position where you can descend to a safe landing without using high power on the good engine, by all means do so. This is not a game where you get extra points for climbing when you don't have to.
The rest of the discussion assumes you need the maximum achievable power from the good engine.
Starting from moderate speeds, as you slow down you will need more and more rudder to maintain coordinated flight. This is the coordinated regime. The amount of bank needed to maintain nonturning flight is basically constant.
There comes a point where you run out of rudder authority and cannot maintain coordinated flight. As the speed decreases further, the slip angle automatically increases, and more boat turn gets added to the pseudo boat turn. This is the uncoordinated regime. The bank angle must increase as airspeed decreases if you want to maintain nonturning flight.
You can maintain control down to VMC (i.e. FAR 23.149 redline) in the takeoff configuration.30
If you persist in engine-out flight down to sufficiently low airspeed, at some point the wings and/or rudder will stall and you will be very sorry.
If you are below VMC, you should reduce power on the good engine, dive to regain VMC, and then re-open the throttle on the good engine.
If you are below VYSE, you should dive to regain VYSE, obstructions permitting.
To clear distant obstacles, you want to dive to achieve VXSE as soon as possible. To clear nearby obstacles, you don't want to dive below their altitude, obviously. For a combination of obstacles, you face some tricky tradeoffs. The best solution is to make sure you never get into a low-altitude low-airspeed situation.
The aircraft manufacturer is supposed to specify a minimum safe speed for intentional engine cuts, denoted VSSE, which is typically quite a bit higher than VMC.

To demonstrate these key ideas, you should start in the takeoff configuration at a speed at or above VSSE. Then cut one engine, and gradually decelerate. This will demonstrate idea #1 immediately. If there is a chance you will reach VMC before you have a chance to demonstrate idea #2, it is a good idea to artificially limit the available rudder deflection, perhaps by blocking the pedal with the toe of your other shoe. We do not wish to demonstrate idea #4. After demonstrating flight slightly above VMC (idea #3), return to VYSE (idea #6) and then resume normal flight.

To demonstrate a portion of idea #5, we use a separate maneuver. Starting with both engines at idle, perform a power-off stall. Recover to VMC, then using only one engine, recover to VYSE.

The FAA commercial pilot multi-engine practical test standard (``PTS'') contains a ``task'' called ``ENGINE INOPERATIVE — LOSS OF DIRECTIONAL CONTROL DEMONSTRATION''. The requirements are a bit confusing. For one thing, the PTS speaks of banking ``for best performance and controllability'' but doesn't say how to trade off performance versus controllability. Best climb performance typically requires less bank than best ultra-low-speed controllability.

Among many examiners, the traditions concerning this task are as follows:
  1. Start at a safe altitude and safe airspeed. The PTS calls for VYSE plus ten knots.
  2. The PTS calls for flaps set for takeoff. However, there are some planes (such as a Seneca) where the certified takeoff checklist calls for zero flaps, and where redline is essentially equal to the stalling speed. In such planes you can lower the stalling speed by extending the flaps, which will make the demonstration safer and easier. Most examiners are happy to permit this. Call it ``short field'' takeoff configuration if you like. In other planes (such as an Apache) where the stalling speed is already well below redline, don't bother extending the flaps.
  3. Reduce power on one engine to idle. Do not actually stop or feather the engine.
  4. Depress the rudder to establish zero slip. This gives best performance.
  5. Bank to establish nonturning flight. This will be a very shallow bank.
  6. Block the rudder motion to ensure that you run out of rudder before the airspeed gets close to the edge of the envelope. Stay away from redline and wing-stall speed, whichever is higher. The PTS calls for staying 20 knots above the wing-stall speed.31
  7. Gradually decelerate.
  8. After you run out of rudder deflection, the unwritten rule is that you should not increase the bank. That means the airplane will start to turn. The turn is your signal that it is time to begin the recovery phase. You are not being asked to demonstrate key idea #2.
Before the checkride, you should discuss these unwritten rules with your examiner, to make sure you are both singing the same tune.

The airspeed limit is needed to ensure safety. The artificial limits on rudder deflection and bank are needed so that you can demonstrate a nice gentle boat turn, by pretending to run out of control authority; otherwise the airplane would be controllable at all safe airspeeds and there would be nothing to demonstrate.

Note that in everyday (non-checkride) flight, if you run out of rudder authority at a speed above redline (and if you are sure you want to be flying so slowly) you would just smoothly enter the uncoordinated regime and increase the bank.

You should not do demonstrations the way FAR 23.149 seems to suggest: Full-blown FAR 23 VMC determinations should be left to professional test pilots. For that matter, not even test pilots dare to experiment with loss of control at low altitude. They are not crazy; they experiment at a series of safe altitudes and then extrapolate.

A single-engine aircraft is required (by FAR 23.49) to have a stalling speed of 61 knots or less, and in certain models it is quite a bit less. This is important for safety in case of a forced landing. In contrast, a twin with sufficiently good engine-out performance is exempt from this restriction. The theory is that a twin that can climb on one engine should never need to make an off-airport landing.
We won't discuss aircraft that have centerline thrust, e.g. the Cessna 337 Mixmaster.
This means total lift, including the contributions of the wings, horizontal tail, et cetera. The center of lift will be located quite close to the center of mass, for reasons discussed in section 6.1.3.
The effects are reduced if the working engine is developing less power (because of small engine size, high altitude, and/or reduced throttle setting), the airspeed is high, and the rudder is large. Conversely, in a twin with a small rudder, a large engine, full power, and a low airspeed, a sudden failure will definitely get your attention.
If you forget to roll the wings level before using the rudder to stop the heading change, you could easily find yourself stepping on the wrong rudder. For instance, if you are in a turn to the right and the left engine fails, you might be tempted to stop the turn by stepping on the left (wrong!) rudder.
To know how much bank and/or how much inclinometer ball deflection corresponds to zero slip, you can (a) recall from your training flights what configuration corresponds to best performance, (b) recall from flights with a slip string what configuration corresponds to zero slip, or (c) let the inclinometer ball go off-center by half its width, which is usually ``close enough'' to the right answer.
See section 19.4 for a discussion of E-down and related concepts.
The confusion is understandable, since asymmetric thrust is about the only way you can maintain an inclination without being in a slip of some kind.
... or cruise performance, for that matter — engine-out or otherwise.
In fact, an undeflected rudder produces a less stall-resistant shape, which will probably stall at a higher airspeed.
If redline (as defined in the following section) is down near the bottom of the green arc, it is a good guess that wing stall is what limits the airplane's low-speed controllability. Conversely, if redline is much higher than the bottom of the green arc, you can guess that rudder stall is what limits the low-speed controllability (unless the redline is artificially high because of the arbitrary 5 degree bank limit in FAR 23.149).
A very similar regulation, FAR 25.149, applies to transport-category aircraft (e.g. airliners).
The notion of ``critical engine'' is discussed in section 17.2.12.
If the airplane weights more than 6000 pounds, FAR 23.66 requires the airplane to be able to climb with one engine inoperative, at an airspeed ``equal to that achieved at 50 feet'' after takeoff. Even this does not require climb at VMC.
There are of course other redlines: at the high end of the airspeed indicator, on the tachometers, etc., but they are not relevant to the present discussion.
... except perhaps in a minor way that is not relevant here. See section 11.5.6 for a general discussion of slip angle versus bank angle.
There are many airplanes that are quite nicely behaved even under conditions that require more than 5 degrees of bank in order to maintain non-turning engine-out flight.
That's right: there is no guarantee that 5 degrees is safe. It is commonly assumed that ``the manufacturer must have tested a 5 degree bank because that is the maximum allowed''. But in fact, best control might be achieved at 2 or 3 degrees, and there is no reason to assume that the manufacturer ever tried more than that. Remember, in non-slipping flight the bank required is quite modest (and independent of airspeed), and there is not much that the manufacturer can achieve by slipping that could not be better achieved by more rudder deflection.
This means the takeoff configuration as specified in the Pilot's Operating Handbook or Airplane Flight Manual. Remember that these documents are legally part of the airplane. You can't have a certified VMC without a certified takeoff checklist.
In this example, we are assuming that wing stall (not rudder stall) is what limits low-speed handling.
This option is available to us because, for this airplane, the certified takeoff configuration did not call for flaps to be extended.
If there were an unbalanced torque, the airplane would not only turn, it would accelerate around the yaw axis.
We are talking about rather modest bank angles, perhaps 15 or 20 degrees, that would not get you into trouble in other circumstances.
It may be a good idea to check the wing's stalling speed by performing a stall with both engines at zero thrust. The zero-engine stalling speed won't be quite the same as the one-engine stalling speed, but it should be a useful estimate.
I have done calculations that indicate that for certain light trainers, the wings will almost always stall before the rudder, but you absolutely should not assume that this is true for all airplanes in all circumstances.
At the end of this section, other possibilities will be considered.
One could imagine designing an airplane with the landing gear so far aft that they were behind the lateral center of effort, in which case they would increase yaw-axis stability.
The propwash from the left engine is actually helpful.
It's a little hard to see how this situation could arise in the course of normal flying. However, (a) such a situation is sometimes created as part of a training exercise, and (b) it could arise if the pilot mishandles an engine-out situation, squandering the initial airspeed.
In other configurations, you can maintain control down to redline or VS, whichever is higher.
In airplanes where VMC is at or near VS, VS + 20 may seem like a generous or even excessive margin of safety. In other airplanes, however, VS + 20 is not nearly enough. You need to be careful, since there are plenty of airplanes where VS + 20 is near (or even below) VMC. A better criterion might be to stay above VS + 10 and above redline + 10, whichever is higher.

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