Why does a pilot bank up to 5 degrees into the operating engine following failure of the other engine?

Question

If a multi-engine aircraft suffers an engine failure while near minimum control speed (V_mc), 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?

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

The failure of an engine in a multi engine aircraft causes it to yaw towards the failed engine. To counter this, the pilot has to apply the rudder towards the live engine. This is all great as the rudder itself can keep the aircraft balanced.

Even though the aircraft looks balanced with the rudder alone, the application of the rudder puts the aircraft in a side slip. With the rudder applied the force on the vertical stabilizer acts through the aircraft CG to keep the live engine thrust from yawing the aircraft into the dead engine. This causes air flow to hit the vertical stabilizer from a side generating a side force that opposes the rudder force. This side force then puts the aircraft in a side slip towards the failed engine.

To give you an example, think of an aircraft that suffers from a right engine failure. As soon as the engine fails, the live left engine thrust yaws the aircraft into the right engine. The pilot counters this using the left rudder. The rudder creates a force on the left side of the vertical stabilizer which allows the pilot to fly the aircraft without losing control. As the rudder is applied, the nose of the aircraft points to the left causing the relative air flow to hit the aircraft on the right side. The result is a left side force which puts the aircraft in a right side slip. Look at the picture below.

https://www.boldmethod.com/blog/und/how-does-zero-sideslip-work-in-a-multi-engine-aircraft/

The reason why we put in a small bank towards the live engine is to reduce the effects of the side slip. An aircraft in a side slip creates drag which is detrimental to the performance of the aircraft particularly in a climb. When you bank into the engine, the lift component generates a side component which allows you to fly the aircraft in a controlled state with a reduced rudder deflection. The end result is a reduction in the side slip which increases the aircraft performance. This also reduces the minimum control speed of the aircraft, Vmc.