Multi-Engine: Zero-Sideslip
The zero-sideslip is necessary for a pilot to maintain control of an aircraft and have the greatest climb performance during an engine failure in a twin.
Aerodynamics | February 10, 2022
A multi-engines published Vmc speed is of high importance to the pilot of a multi-engine aircraft.
The reason for this high importance is that a pilot risks losing control and potentially entering a Vmc roll if they allow a twin-engine aircraft to go below its Vmc speed during an engine failure.
To be specific, the Vmc speed of a multi-engine aircraft is:
The sea level calibrated airspeed at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the aircraft with that engine still inoperative and then maintain straight flight at the same speed with an angle of bank not more than 5°.
The only downside to this definition is that it does not consider that the Vmc speed of a multi-engine aircraft changes based on a large handful of conditions. Similar to how a single-engine aircraft's stall speed changes based on: power setting, the center of gravity, flap setting, etc.
A multi-engines published Vmc speed will change whenever the current conditions differ from the preset conditions listed under Part 23.149:
Additionally, while in this configuration, the following must be true:
Since it is improbable for any given day and configuration to precisely match the preset conditions for determining Vmc, a multi-engine rated pilot should understand how Vmc changes for each condition.
A standard atmosphere is defined as:
Therefore, the published Vmc speed is determined when the aircraft is at sea level, with an outside static pressure of 29.92 and a temperature of 15 degrees celsius.
An easy way to relate all 3 of these elements together into one easy-to-use number would be to use Density Altitude.
Remember density altitude considers the aircraft's altitude above (or below) sea level, the pressure altitude (Static pressure), and then is corrected for non-standard temperature - any temperature different from the standard atmosphere. In other words, density altitude is the altitude the aircraft "thinks" it's at.
Vmc decreases as density altitude increases because the amount of thrust produced decreases as density altitude increases. Therefore, the amount of rudder authority required to offset the asymmetrical thrust created by the still-functioning engine is decreased.
At a density altitude of 0ft, the actual Vmc speed will match the published Vmc speed.
If the density altitude is greater than 0ft, the actual Vmc will be lower than published.
If density altitude is less than 0ft, the actual Vmc speed will be higher than the published Vmc speed.
Note: Multi-engine aircraft with turbocharged or supercharged engines will not experience a decrease in Vmc as altitude increases. This is because turbocharged and supercharged engines can maintain the same amount of thrust output at higher altitudes.
Since a multi-engines critical engine is defined as the engine that will have the most adverse effect on aircraft performance and controllability if it were to fail, it makes sense the FAA requires the published Vmc speed to be based on the critical engine failing.
While a few factors determine which engine is the critical engine, it can be simplified down into one question: What engine requires more rudder force to overcome if the other engine were to fail?
On most conventional twins, this would be the left engine.
With the left engine failed, the rudder requires more force to overcome the right engine than it would require to overcome the left engine if the right engine failed.
Therefore, with the critical engine failed - The actual Vmc will match the published Vmc.
With the non-critical engine failed - The actual Vmc will be lower than the published Vmc.
If your aircraft is non-conventional and has counter-rotating propellers, no matter what engine has failed, the actual Vmc will not change from the published Vmc.
Multi-engine pilots are taught to "raise the dead" during training.
What this means is if an engine failure were to occur, a pilot should raise the dead engine by banking into the operative engine. For example, a pilot should put the aircraft into a left bank if the right engine has failed.
While in a bank, the horizontal component of lift generated by the bank takes the place of the yaw force generated by the rudder. If the aircraft were to have no bank, the yaw force created by the rudder would put the aircraft into a side slip.
While in a sideslip, the amount of rudder deflection required increases, which in turn increases Vmc. Therefore, with a bank into the operating engine, Vmc will be decreased.
To prevent claims of an unrealistically low Vmc speed during certification, the manufacturer is only allowed to use a maximum of 5 degrees of bank toward the operative engine.
The sensitivity Vmc has to an aircraft's bank angle is exceptionally high. Tests have shown that Vmc may increase by more than 3 knots for each degree of bank less than 5 degrees. Therefore, loss of directional control may be experienced at speeds almost 20 knots above published Vmc when the wings are held level.
Higher bank angles greater than 5 degrees would help lower Vmc since the higher bank angle would reduce the required rudder deflection. However, too much bank can result in a large sideslip and require a greater angle of attack to maintain the same vertical component of lift, which may result in a stall.
During multi-training, pilots are taught to establish a "zero-sideslip" for best performance. The 5 degrees of bank does not inherently establish zero sideslip or best single-engine climb performance. Therefore, pilots attempting to get the most performance by establishing a zero-sideslip should expect Vmc to be slightly higher.
In summary:
At 5 degrees of bank, the actual Vmc speed should not change from the published Vmc.
Greater than 5 degrees of bank, the actual Vmc speed would be lower than the published Vmc speed. However, climb performance may begin to degrade, and a stall will become more likely. It is not recommended to go above 5 degrees of bank.
Less than 5 degrees of bank, the actual Vmc speed will be higher than the published Vmc speed by about 3 knots for every degree less than 5. Most likely, a zero sideslip will be achieved between 0-5 degrees, and a pilot should be expected to operate somewhere in this area.
The most unfavorable weight for a multi-engine aircraft is when it is the lightest.
As a multi-engines weight increases, the amount of inertia and momentum it has is increased. This increase in momentum and inertia increases the resistance an aircraft has to external forces, resulting in a lower Vmc speed.
Therefore, at lightweights, the yaw and roll associated with an engine failure would be increased compared to the same aircraft at a heavier weight, resulting in a higher Vmc speed.
Since multi-engine aircraft are certified at the lightest, most unfavorable weight, the following can be expected:
At the lightest weight, the actual Vmc speed will match the published Vmc speed.
At heavier weights, the actual Vmc speed will be lower than the published Vmc speed.
Note: Early certification of multi-engine aircraft did not specify the weight at which Vmc had to be determined. Therefore, many manufactures calculated Vmc at the heaviest weight resulting in the previously mentioned effects on Vmc to be reversed. In this case, actual Vmc matched published Vmc at the heaviest weight and increased as weight decreased.
The most unfavorable center of gravity on a multi-engine aircraft is an aft center of gravity.
As the center of gravity of a multi-engine aircraft moves from fore to aft, the distance or arm between the center of gravity and rudder is decreased. This results in the rudder becoming less effective.
To compensate for this loss of effectiveness, the airspeed required to maintain directional control is increased. Therefore, the further aft the CG - the greater the Vmc speed.
Since Vmc is calculated with the furthest aft, most unfavorable, CG, the following can be expected:
At the furthest aft CG, the actual Vmc speed will match the published Vmc speed.
At the furthest forward CG, the actual Vmc speed will be lower than the published Vmc speed.
It would be wise to remember that the factors that affect Vmc are simply certification requirements and may not have very much effect on Vmc in real-world practice.
Such as the case of being airborne and out of ground effect.
You can make the case that being in ground effect, or even on the ground, would help lower Vmc, but in real-world practice having an engine failure in ground effect right after takeoff would hopefully result in a pilot aborting takeoff and landing about 2 seconds after the engine failed.
The margin is very thin for ground effects actual effect on Vmc, and the number of resources available explaining its effect is even less.
Since the research available is pretty small, I will not attempt to explain ground effects' ability to change Vmc until a good source can be found.
However, based on what can be found, the general consensus is that while in ground effect, the following occurs:
Being in ground effect does affect Vmc. However, it is up for debate if being in ground effect increases or decreases Vmc.
While out of ground effect, there should not be any difference from the actual Vmc speed to the published Vmc speed. This is because the aircraft is tested and certified while out of ground effect.
During certification, both engines are set to takeoff power, and then one engine is failed.
In this configuration, the amount of asymmetrical thrust is greatest, and Vmc would be the highest. It is a statement of fact that the amount of thrust produced by the functioning engine has the greatest effect on a multi-engine aircraft's Vmc speed compared to all of the other factors. Since Vmc is published with a high power setting, having a high power setting can not increase the actual Vmc beyond the published Vmc speed.
However, a lower power setting can reduce Vmc by a substantial degree.
Since Vmc is based mainly on the amount of asymmetrical thrust produced by the still-functioning engine, if the functioning engine's thrust, and subsequently the asymmetrical thrust, is reduced, such as when power is idle, Vmc would probably be much lower. Maybe even lower than the aircraft's stall speed - effectively making it no longer a factor. Therefore:
At high power settings, the actual Vmc speed will be equal to the published Vmc speed.
At low power settings, the actual Vmc speed will be much lower than the published Vmc speed.
Multi-engine students should be taught that if a Vmc roll or loss of control is about to occur during an engine failure, the best course of action would be to reduce the power on the remaining engine. By reducing power on the remaining engine, the aircraft's ability to climb will be removed entirely. But the chance of losing control and entering a Vmc roll will be significantly reduced.
This requirement is another one of those requirements for certification and not necessarily capable of changing Vmc.
Arguments can be made that if correct rudder trim is inputted, it can effectively increase the amount of force produced by the rudder and reduce actual Vmc speed compared to the published Vmc.
However, the effect that trim has on Vmc is probably negligible and is not really consider a "true" factor that affects Vmc speed.
Generally speaking, multi-engine aircraft are designed to take off with their flaps set to zero and their cowl flaps open.
This is what is considered as "Flaps In Takeoff Position."
A multi-engine aircraft's Vmc speed and climb performance will be the greatest while its flaps (not including cowl flaps) are set to zero.
This is because when flaps are extended, the wings create more lift and drag than with flaps retracted.
If an engine were to fail, the wing behind the failed engine would produce less lift than the side with the operating engine.
This is because the operating engine will accelerate more air over the wing than the side with the failed engine.
This accelerated air causes two things to occur:
With the flaps extended, these effects are even more pronounced.
The increase in drag directly behind the operating engine essentially fights against the operating engine and reduces the tendency for the aircraft to yaw towards the dead engine.
Since the aircraft has a lower tendency to yaw into the dead due to the increase in drag, the amount of rudder required to offset the asymmetrical thrust produced by the operative engine is reduced. Therefore, the aircraft's Vmc speed is reduced.
However, this increase in drag hurts the aircraft's climb performance. Therefore, many manufacturers and pilots elect to have their aircraft takeoff with flaps fully retracted as part of their normal operations. Many manufacturers also have pilots put the flaps up if an engine failure occurs to reap the benefits of the increased climb performance.
Since Vmc is calculated with the flaps in takeoff position, the following can be expected:
With the flaps set for takeoff, the actual Vmc speed will match the published Vmc speed, and climb performance will be the greatest.
With the flaps extended, the actual Vmc speed will be lower than the published Vmc speed, but climb performance will be diminished.
Cowl Flaps are also tested in the takeoff position.
Generally, for takeoff, cowl flaps are to be in the full open position to promote proper engine cooling at the high power settings and low airspeeds found during takeoff.
With the cowl flaps open, Vmc will be the lowest.
This is because cowl flaps increase an aircraft's directional stability - similar to the landing gear.
However, cowl flaps also increase drag and therefore reduce aircraft performance while they are open.
Since multi-engine aircraft are certified and tested with cowl flaps in the takeoff position, the following can be expected:
With the cowl flaps open, the actual Vmc speed will match the published Vmc speed.
With the cowl flaps closed, the actual Vmc speed will be higher than the published Vmc speed, and performance will be increased.
When an aircraft's landing gear is retracted, its directional stability is slightly reduced.
When an aircraft's landing gear is extended, the gear will aid in directional stability. This increase in directional stability will help offset the asymmetrical thrust produced by the remaining engine and effectively decrease Vmc. However, with the gear down, the ability to climb on one engine will be penalized.
For this reason, many multi-engine manufacturers include putting the gear to be up during an engine failure.
Since Vmc is determined with the gear retracted:
With the gear up, the actual Vmc will not differ from the published Vmc speed.
With the gear down, the actual Vmc speed will be lower than the published Vmc speed, with the ability to climb reduced.
A majority of twin aircraft require the propeller controls to be in the full forward position for takeoff.
At the full foreword position, the pitch or bite of the propeller is minimal, resulting in a very small blade angle. Some pilots describe this condition as a low pitch / high rpm blade angle. This provides the greatest amount of thrust, which is desirable during takeoff.
However, if the engine were to fail with the propeller controls in the full-forward, the propeller will begin to windmill - the free rotation of the propeller in the air stream absent any engine power.
This windmilling condition causes an increase in drag on the failed engine resulting in an increase in Vmc due to the greater yaw force towards the dead engine. Vmc is highest when the critical engine propeller is windmilling at the low pitch / high rpm blade angle.
To combat this increase in Vmc, manufacturers design constant speed props to feather - the ability to rotate the propellers parallel to the free airstream. Feathering inhibits the propeller's ability to rotate and thus reduces drag and Vmc.
A multi-engine aircraft published Vmc speed is determined with the critical engine windmilling in the takeoff position unless the engine is equipped with an autofeather system.
However, without an auto feathering system, the following would occur:
With the engine windmilling, the actual Vmc speed will match the published Vmc speed.
With the engine feathered, the actual Vmc speed will be lower than the published Vmc speed.
