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actual Vmc can be at a higher airspeed given the higher DA, lower power, higher temp, lower pressure, CG, etc. Vmc can also be at a lower airspeed at a lower DA, very cold temp, etc.
Desert, you've got it backwards. Higher DA, lower power, higher temp, lower pressure will all get Vmc to be lower since Vmc is an indicated (calibrated) speed and all of those things will reduce engine power.
You're right. Shouldn't have been in such a hurry.