Vmca
The Critical Engine
There are a number of reasons why one engine may be designated more critical than another. Services supplied from that engine are one reason and then there are aerodynamic considerations that I will cover here.
Span Wise Distribution of Lift
The slip stream behind the upgoing blade of an engine will impinge on the aerofoil at a higher angle of attack than the down going blade. This means there will be greater lift and thus drag behind the up going blade. For aircraft where all props rotate in the same direction the drag due to the wing will be displaced in one direction. Therefore, the engine on the side to which the drag is displaced will be more critical because the drag will have a greater moment arm and will assist in the yawing moment generated by the operating engine. (eg. clockwise prop rotation when viewed from the rear means the left engine is critical.)
Assymetric Blade Effect
When the propellor disc is tilted relative to the airflow the upgoing blade will have a slightly less angle of attack on the airflow than the downgoing blade. Thus the downgoing blade will generate slightly more lift and thus the thrust centre line will be shifted towards the down going blade. This means there will be a greater yawing moment when the engine on the upgoing blade side of the aircraft fails.(Assuming props all rotating in same direction)
d - distance travelled by downgoing blade
u - distance travelled by upgoing blade
d > u therefore Vd > Vu and therefore Thrust(d) > Thrust(u)
Torque Effect
The torque of the engines will tend to roll the aircraft in one direction. The critical engine in this case will be the one that when failed leaves the greatest net rolling moment towards the failed engine.
Air Minimum Control Speed
In general the definition of the Vmca is the minimum airspeed for directional or lateral control with:
(a) Maximum permissibile power on all operating engines
(b) Critical engine windmilling
(c) Full rudder deflection or some nominated amount of pedal force whichever occurs first
(d) 5 degrees of bank away from failed engine
(e) Flaps in takeoff position
(f) Most rearward CofG
(g) Minimum gross weight (**Some regulations require max gross weight and I am not sure why. I will explain why min gross weight is worse for Vmca later)
Factors Affecting Vmca
Temperature
An increase in temperature means an increase in density altitude and thus decrease in engine power(for turboprops) and thrust. Less thrust means less yawing moment and lower Vmca.
Altitude
Higher physical altitude means higher density altitude and affects Vmca in the way described in Temperature
Centre of Gravity
An aft CofG means a smaller moment arm for the rudder to work on and thus leads to a higher Vmca.
Flap Position
With the flaps down the drag induced behind the operating engines will be greater and is a favourable effect. Thus raising the flaps will increase Vmca.
Ground Effect
Ground effect increases the lift generated by the wing, therefore, the required vertical and side components of the tilted lift vector (as described in Angle of Bank) can be produced at a lower airspeed. Thus being in ground effect lowers Vmca.
Angle of Bank
The most obvious way for the pilot to oppose the asymmetric yawing moment is, of course, to use the rudder to generate a counter moment. However, although the yawing moments are now balanced, there is an unbalanced sideforce, which unless checked will generate a centripetal acceleration on the aircraft and so curve the flight path. This has two undesirable effects, firstly the effective angle of attack(AoA) of the rudder will be reduced as the aircraft moves sideways through the air and secondly, this sideways movement induces a lot of drag which decreases performance. It is possible to generate the balancing sideforce alternatively by banking the airplane towards the live engine and allowing a component of its weight, W Sin (AoB), to act to oppose the sideforce due to rudder. This technique has the advantage that sideslip is suppressed and drag is reduced, note also the rudder requirement will be reduced (compared to wings level) because the effective AoA of the rudder increases as the sideslip is arrested.
The astute amongst you will reason that increasing the angle of bank further than initially required will generate a side slip towards the operating engines and thus increase the effective AoA of the rudder generating a larger sideforce and allow the rudder pedal force to be reduced thus allowing a lower Vmca due to the now greater pedal travel available. While this is true there is now a performance penalty. Thus there is an optimum angle of bank, normally 3-5 degrees, which gives the greatest control increase for a small loss in performance. What must also be remembered is that at all times we are trying to achieve control of the aircraft first and climb performance second.
Effect of Weight
As weight is increased, the lift required to balance the weight also increases. When the AoB is introduced, the side force component is also greater. This means a greater AoA on the rudder and thus less pedal force required. Therefore, higher weights lead to a reduction in Vmca. However, with wings level higher weights actually increase Vmca due to the higher AoA required to remain level or climb and this increases assymetric blade effect.
SUMMARY
The big point for flying in an assymetric condition is to have correct technique. You must get the AoB on the aircraft immediately a failure occurs because it improves controllability AND performance. This is critical. After that bear in mind all the other factors affecting Vmca in your subsequent decision making.
Quick one for the instructors you can widen the gap between actual Vmca and stall speed either by extending flaps partially, which decreases stall speed, or sticking the toe behind the depressed rudder pedal to limit rudder travel, which artificially raises Vmca to a faster speed...
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