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Anyways, back to Critical Density Altitude.
First, let's review Vmc (minimum controllable airspeed.) Simply put, Vmc is the published calibrated airspeed at which a multi-engine aircraft is still controllable if an engine has failed. A different way of looking at this is that Vmc is the lowest airspeed at which the rudder provides enough force to counteract the yaw due to asymmetric thrust from the operating engine when that operating engine is set to full power. When an aircraft is certified with a speed for Vmc, several other operational parameters are met to obtain that published calibrated airspeed (FAR 23.149 anyone?)
Throughout your multi-engine training, you may have been taught that there are several factors that affect Vmc. One of them being density altitude. You see, when density altitude increases (meaning that there is a lower air density) the propellers take less "bite" from a column of air and therefore will produce less thrust. This results in less P-Factor from the imbalance of thrust produced by the descending blade of the propeller versus the ascending blade. Due to the fact that less yaw will be now be produced by the operating engine (since there is less P-Factor and thrust produced), Vmc decreases, even though the published calibrated airspeed for Vmc stays the same.
As you may have put together while flying a multi-engine airplane, Vmc and the single-engine power-on stall speed are usually very close and sometimes even the same value. But as you increase your altitude (which results in a lower air density and an increased density altitude) even though Vmc may decrease, we must remember that our indicated stall speeds do not change. So at some point, Vmc and the this indicated single-engine power-on stall speed (which we will call Vs) will be exactly the same. The point at which this occurs is known as the "Critical Density Altitude."
From the graphic above, we can see that Vmc (depicted above as a grey line) gradually decreases as density altitude increases. While the indicated single-engine power-on stall speed (depicted above as a blue line) stays exactly the same at every altitude. At a certain density altitude, Vmc and the single-engine power-on indicated stall speed (Vs) will be exactly the same, this is the Critical Density Altitude. I am fully aware that it may be confusing to designate a new stall speed (Vs,) but remember, we are now using TWO engines during normal flight in a twin-engine airplane. The airplane will not stall in a typical power-on stall scenario with only one engine operating, a topic that I will write about later.
Once an airplane reaches its critical density altitude, if the airspeed is brought below the singe-engine power-on stall speed with the operating engine set to full power, the airplane will stall and loose directional control at the same time. This is because we are below Vmc for that specific density altitude. As you may realize, this is extremely hazardous! Loosing directional control while stalling the airplane can lead to a spin or other uncontrollable flight condition.
At a density altitude lower than the critical density altitude, if we lost an engine and set the operating engine to full power, we would loose directional control prior to stalling the airplane (as depicted by the shaded grey and white area.) This is because there is enough yaw produced by the engine to overcome the force of the rudder, meaning the speed for Vmc is a higher value. Thus we would reach Vmc prior to stalling the airplane.
At a density altitude higher than our critical density altitude, the opposite occurs. If we lost an engine and set the operating engine to full power, we would stall the airplane prior to loosing directional control (as depicted by the shaded blue area.) This is because there is not enough yaw produced by the engine to overcome the force of the rudder. As a result, Vmc is lower than the indicated stall speed. Make no mistake though, the possibility of loosing directional control once the aircraft is stalled is still a possibility. Since you are risking the possibility of stalling the aircraft while plenty of yaw is being produced by the operating engine, a spin may occur if lack of recognition of the potential stall and proper control inputs are not utilized.
One more thing. Remember, Vmc and the single-engine power-on stall speed are usually very close. Careful consideration must be used to avoid any condition that would put the pilot in either a single-engine power on stall or Vmc condition. Be safe, fly safe, and always utilize an appropriately rated Multi-Engine Instructor (MEI) whenever you may question your own understanding of Vmc or your multi-engine flying skills.
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