However, if you let your engine have more power at higher density, I will make my rudder more effective at higher density to counter for that!
I beg to differ.
As a twin instructor (you say in your public profile that you are a FI and CRI, so I assume you instruct on twins), I am horrified that you don't understand this, and the consequences of it.
The rudder will have exactly the same effectiveness, regardless of altitude, at a given IAS. This is because IAS is a measure of dynamic pressure, and control effectiveness is directly related to dynamic pressure. I think you may be confusing IAS with TAS here. If you increase pressure but maintain TAS, then yes, rudder effectiveness will increase. If you increase pressure but maintain IAS, then TAS will decrease, but rudder effectiveness will not change.
I accept that you teach on turbo-charged aircraft, therefore this doesn't apply to your current type. But it is a fact that, as pressure altitude increases (in a normally-aspirated aircraft), so Vmc reduces. The implication of this is that, as we continue to climb, Vmc eventually reduces to a point where it coincides with Vs. As instructors, it is
vital that we understand this, since we regularly (at least once with each student) have to demonstrate Vmc - and if we this at too high an altitude, without being aware of the implications, we risk running out of rudder at the same time as we stall, resulting in a spin.
This is a well-known fact. Not directly relevant to our discussion, until you reverse it. The reverse situation is that, as pressure altitude decreases, so Vmc increases. Contrary to your last post, I believe that Vmca is measured at sea-level in ISA conditions, but I don't have documentation to hand to prove it.
But, whether that's true or not, Vmca must be measured in some kind of atmosphere. And, whatever atmosphere it is measured in, it's only necessary to add a millibar or two to that atmosphere to increase Vmc to something above Vmca (albeit only marginally).
Therefore, if we are to make a go around, the first thing in my crew concept is "g.a., set pwr for take off, set flaps...
That's interesting. My company's procedures are quite different. For an all-engine go-around, we raise the drag flap immediately, then wait for a positive rate of climb. Then we raise the gear. Then we raise the flap. Plenty of time for an engine failure to occur in there! (Although, if an engine failure were to occur at such a critical time, the EFATO drill would involve raising gear and flaps immediately after selecting full power, so the situation would only exist for a matter of seconds.)
FFF
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