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If a multi-engine aircraft suffers an engine failure while near minimum control speed (Vmc), one of the solutions is to bank up to 5 degrees into the operating engine to increase rudder effectiveness to maintain control. Why is it up to 5 degrees? What happens if the pilot banks more than 5 degrees into the operating engine?

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  • $\begingroup$ Closely related, maybe a dupe? $\endgroup$ – Pondlife Aug 30 at 3:52
  • $\begingroup$ @Pondlife I don't think this is a dupe. The current question asks specifically about the reason of the 5° mentioned in this answer $\endgroup$ – Manu H Sep 1 at 18:35
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The 5 degrees of bank is to create a side slip component that offsets the skewed thrust line created by the asymmetric thrust, and the rudder input made to counteract the asymmetric thrust.

You have the live engine on one wing that wants to make the airplane turn. You apply opposite rudder to stop the turn. With the rudder moment pushing sideways, you end up with a resultant thrust line that is offset, and the airplane proceeds forward with a lateral skew toward the dead engine even though you think you're going straight. By banking into the live engine, bank angle makes the airplane want to side slip toward the down wing, which is in the opposite direction to the skew effect mentioned above. The 5 degrees of bank is roughly what gives the necessary amount of side slip tendency. Close enough in other words.

The result is that you will be flying with 5 degrees of bank, but actually proceeding straight through the air. The skid ball will be offset into the bank because you are actually still in coordinated flight and the offset location of the ball is the true "centered" location.Skew

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  • $\begingroup$ You're saying in the first paragraph that the bank creates a sideslip component, but then you say in the last paragraph that you're still in coordinated flight. Doesn't coordinated flight mean that there's no sideslip? Can you clarify what you mean there? $\endgroup$ – Terran Swett Aug 29 at 17:08
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    $\begingroup$ You are in coordinated flight; the tail is lined up behind the nose in the airstream, because the sideslip tendency created by lowering the wing is offset by the skewed effective thrust line. Imagine you're in a car on slick ice driving straight, but the wheels are crooked, making the car dogleg sideways somewhat. If you tilted the ice surface laterally, so the car wants to slide downhill, just the right amount, the lateral sliding tendency cancels out the dogleg tendency and the car goes straight along even though the surface is slanted. Sorta like that. I've added a crude diagram. $\endgroup$ – John K Aug 29 at 18:16
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    $\begingroup$ On a marginally power piston twin, the 5 deg bank that is done to cancel out the sideslip induced by the offset thrust line can mean the difference between climbing and no climbing. If you don't lower the wing, the airplane is in fact sidesliping with the wings level, basically being pushed sideways by the rudder you might say, with the resulting drag rise. $\endgroup$ – John K Aug 29 at 18:21
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    $\begingroup$ No slip is taking place; banking produces a sideways force to counteract sideforce from deflected rudder, thus eliminating any turning tendency ( heading change ) . Generally speaking, banking does not cause or cancel sideslip. $\endgroup$ – quiet flyer Aug 29 at 18:50
  • $\begingroup$ I don't think the description is quite accurate. The bank utilizes gravity to offset the side force introduced by the rudder, freeing up sideslip so that less rudder would be required. On another note, I think the OP has a good idea about the VMCA maneuver, but was asking why 5 deg in the regulations (and not 6 or 7 deg)? $\endgroup$ – JZYL Aug 29 at 18:54
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These figures are a regulatory baseline for sizing the ailerons, vertical stabilizer and rudder for an aircraft. The 5° bank limit is done to minimize the load factor on the aircraft while providing a force to counteract rudder input required to maintain a coordinated flight path.

In the event of an engine failure in a non-centerline thrust twin or multi engine aircraft, the operative engine is going to create a strong yawing moment about the vertical axis of the aircraft in the direction of the dead engine. Uncorrected, this results in a forward slip toward the side of the good engine and, when combined with the fuselage blanking airflow over the wing on the dead engine side, a rolling moment also develops about the longitudinal axis in the direction of the dead engine. At low speeds, combined with the high drag created by the slipping condition plus a 50% loss of total available thrust from the engine failure, this can quickly snowball into a departure from controlled flight and crash. The typical action is to apply rudder in the direction of the good engine to counteract this forward slip. However, while the nose will be aligned with the desired flight path doing this, the actual flight path is a side slip towards the dead engine side, which creates excess drag. The only available counter to this is to bank the airplane into the direction of the good engine to counteract the rudder force using the horizontal component of lift. This results in a coordinated flight track parallel to the horizontal axis of the aircraft with a minimum amount of drag.

If excessive bank angle is used to do this, the vertical component of lift is diminished, requiring a greater angle of attack to be imposed upon the wings to stay aloft. This in turn creates more induced drag. The regulations for aircraft design of light twins, therefore, dictated that, in a worst case Vmca, directional control must be maintained with a bank angle NOT GREATER THAN 5°.

Harry Horlings, a former military test pilot and aviation consultant, published this excellent video on the nature of Vmc and what it means to the design and operation of aircraft.

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  • $\begingroup$ This statement appears to contradict itself: " However, while the nose will be aligned with the desired flight path doing this, the actual flight path is a side slip towards the dead engine side, " Banking does not cause or prevent sideslip. $\endgroup$ – quiet flyer Aug 29 at 18:56
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    $\begingroup$ It does prevent it if you have a dead engine and need to apply rudder force to counter the yaw due to asymmetric thrust. If you do a force diagram you will note that the airflow deflecting off the rudder causes a lateral force to be applied to the tail fin. This lateral force will cause the airplane to slip in the relative wind. A slight bank towards the good engine will direct just enough of a horizontal component of lift to counteract this rudder force and prevent a side slip. $\endgroup$ – Carlo Felicione Aug 30 at 14:46
  • $\begingroup$ @CarloFelicione Your above comment is good. I would suggest dropping the word "slip" since it evokes sideslip, which is not the case here. It's also not the lift per se that generates the side force, but close enough. I'm suspicious of lift vs bank as the reason for limiting to 5 deg. At even 10deg bank, the extra load factor is only 1.5% of the level flight lift. $\endgroup$ – JZYL Aug 30 at 20:49
  • $\begingroup$ @CarloFelicione -- re your comment above-- in your example I would say that a more detailed description of "applying rudder to counter adverse yaw" would be to say that the ideally the pilot is applying exactly enough rudder so that the plane is flying with zero sideslip as measured by a yaw string on the nose, despite the dead engine. As you point out the rudder will still be causing a sideforce which will displace the slip-skid ball off-center. The purpose of banking is to prevent this sideforce from causing a heading change-- not to alter the position of the yaw string or slip-skid ball. $\endgroup$ – quiet flyer Sep 3 at 14:04
  • $\begingroup$ (Continuing)-- Yes, due to the interrelationships involved, if we are simply using the rudder as a "steering" control to hold a constant heading, then it's true that too much bank would correlate w/ a slip toward the GOOD engine, and too little bank would correlate w/ a slip toward the bad engine, but the rudder is not really a heading-holding control, and looking at it this way "puts the cart before the horse" and obscures what is really going on. For more see my related answer to related question aviation.stackexchange.com/a/65877/34686 -- especially paragrph beginning "Now, granted" $\endgroup$ – quiet flyer Sep 3 at 14:14
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To maintain straight flight after one engine inoperative (let it be right hand engine), rudder input (nose left) is required to take out the yaw asymmetry from the engines. As rudder is deflected, it produces an aerodynamic side force (to the right), which, if left as is, would push the aircraft into a skid turn. This would not constitute straight flight.

To zero the side force, and to maintain level flight (ball centered), the only recourse is to utilize sideslip to generate opposite aerodynamic side force. This means a sideslip nose left in our scenario, which means even more rudder nose left. As speed is decreased, increasingly larger rudder would be required. At some threshold, rudder would be saturated and level flight would no longer be possible below this speed.

But what if we relax the requirement of level flight? What if we allow a bank angle into the live engine (bank left wing down)? In this case, we are allowing a little portion of the gravity, equal to $W\phi$ for small bank, to help out with the aerodynamic side force. Correspondingly, less sideslip and rudder would be needed. In fact, if sufficient bank angle is used (usually after a few deg), we can allow the aircraft to sideslip into the failed engine (nose right); a nose right sideslip would generate aerodynamic nose left aerodynamic yaw, further decreasing the rudder required.

By allowing banking, we can decrease the speed threshold to which the control surfaces would saturate, thus lowering the minimum control speed (Vmc).

Throughout it all, rudder generates an aerodynamic rolling moment, as does sideslip, which must be countered by roll control. As bank angle is increased, the aircraft will be less rudder limited, and more roll control limited. Under FAR 25.149 (and the old 23.149), a maximum bank angle of 5 deg is allowed for the determination of Vmc. Different aircraft will be limited differently at 5 deg bank; some may be limited by rudder, others by roll control, and still others by stall warning.

For those still not convinced, please refer to the following equations, which must hold true for steady/straight flight:

$$0=N_{engine}+qS_{ref}b_{ref}(C_{n_\beta}\beta+C_{n_{\delta r}}\delta r+C_{n_{\delta a}}\delta a+C_{n_{\delta s}}\delta s)$$

$$0=C_{l_\beta}\beta+C_{l_{\delta r}}\delta r+C_{l_{\delta a}}\delta a+C_{l_{\delta s}}\delta s$$

$$0=W\phi+qS_{ref}b_{ref}(C_{y_\beta}\beta+C_{y_{\delta r}}\delta r+C_{y_{\delta a}}\delta a+C_{y_{\delta s}}\delta s)$$

Even more additional information can be found in AC 25-7C Appendix 6.

What would happen if you fly more than 5 deg into the live engine with OEI, nothing much, unless you are flying at Vmc, which would smaller than $V_2$ and $V_{REF}$.

As to why 5 deg, and not 6, or 7 deg? My guess is that it's a rounded number that offers adequate decrease in Vmc for performance, yet not so much as to introduce large lateral acceleration and a big disparity between (a high) low weight rudder limited OEI speed and (a low) high weight rudder limited OEI speed.

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The rudder is used as needed to prevent sideslip (as measured by a yaw string not the slip-skid ball), and the aircraft is banked as needed to eliminate any turning tendency (heading change) due to the deflected rudder. That's really all there is to it.

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    $\begingroup$ The correct physical explanation of OEI straight flight (would be better if you add gravity). However, I still believe the OP is asking why the regulation states 5deg instead of another number. $\endgroup$ – JZYL Aug 29 at 19:13
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Answer: Increases available rudder travel

Logically, we counter yaw of engine out thrust imbalance with rudder into live engine. But now we have used up some of our rudder travel in that direction.

Alternative: roll into live engine. Slip into live engine. Create side force on Vstab/rudder without deflecting the rudder. Result: Now have more rudder travel available, BUT, plane will drift laterally off course towards the live engine. You can maintain heading by allowing the nose (thrust vector) to compensate the drift, but now you are doing .... a forward slip!

The bank and slip technique certainly centers the rudder a bit more. But to reduce drag (recenter the "ball") the best way is a coordinated turn into the live engine!

But notice to compensate for lateral live engine force vector, control inputs will feature a bit more rudder.

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