Some thoughts, if I may ..
after doing a assumed temp takeoff with a V1 cut, that you cannot set MCT once airborne before flaps are up?
I presume that you are distinguishing between “can not” and “may not”.
Unless there be a systems constraint, then “can not” ought not to apply. But it isn’t quite as simple as that.
For the OEI analysis, the presumption is that TO thrust is maintained until the end of the third segment, ie when flaps eventually are tucked away. If you choose to reduce thrust, then you will reduce the achieved performance and, if the takeoff is (especially) terrain critical, you may just put yourself into an uncomfortable situation.
Perhaps you are confusing the OEI and AEO cases ? The RTOW numbers are based on a V1 failure etc., ie an OEI continued takeoff. If, as is the usual situation, all the engines continue to produce useful noise, then there is no reason why (presuming there is no noise abatement constraint or similar requirement) you cannot reduce thrust shortly after takeoff at a convenient height PROVIDING THAT you operate the aircraft AEO so that the achieved climb profile remains above the calculated OEI profile. This is pretty simple philosophical stuff and ensures that you are able to revert to handling a post-V1 failure without finding yourself below the OEI profile and, potentially, in a world of hurt.
I believe that MCT has a 10 min limit on the CFM engine..
As noted in (a) subsequent post(s), the standard deal is 5 minutes at takeoff thrust (10 minutes if you grease the OEM’s palm with an appropriate quantity of silver) but continuous operation, subject to necessity, for MCT/METO.
VMCA......
Not really. For a rated thrust takeoff (either the full deal or derated) Vmc is for the rating. If you then run further down to an ATM case, the Vmc remains appropriate to the rating and there is no reason why you can’t play with the throttles. However, if you choose to push the thrust up in the event of a failure, that should be done carefully and steadily, lest the thrust ramp up be more than you can easily control – I recall a fatal investigation in which I was involved, many years ago, where this was the probable cause of the (unnecessary) subsequent crash, burn, die sequence.
which was normally a 5 min. limit but with one engine inoperative it was a 10 min. limit.
What the AFM says you can do is a matter of that which is provided by the certification (normally 5 minutes for the OEI cleanup) and options the aircraft owner/operator may choose to purchase from the OEM.
While the presumption is that the thrust selected for takeoff (presuming that the sums are worked correctly) will be adequate, should you really need a bit extra, I think most of us would be of the view that you take what you might need, subject to handling caution as noted above.
With a fixed derate you can use a lower VMCA
No, that’s not quite the case. If you are at either full rated or derated thrust, you get a single Vmc (although different for each of the ratings) which is determined during the certification exercise. There is no choice, as such, involved along the way. It is a case of what you see is what you get.
which perversely in some situations can allow you to lift more
Nothing perverse involved. On a short runway, V1 often is constrained by either Vmcg (typically) or Vmca (via distance/Vr/V2 considerations in the analysis) so that, whatever min V1 you are stuck with, determines distance requirements and may well require a lower weight to fit the takeoff into the physical runway available.
Where the derate may be useful, in such a case, is in being able to schedule a lower min V1 which, in turn, may improve the distance numbers sufficiently to permit taking a higher TOW.
but in the case of an engine failure limits the amount of thrust you can apply
Really just a case of follow the AFM’s limitations and normal pilot competence should win the day.
5 minutes is TO is usually adequate - 10 minutes is not needed for most airports - only those with obstructions relatively close to the departure end
Actually the other way around - keystroke error, I presume ? Close in obstacles will be covered by the 5 minutes rating. The 10 minute rating becomes useful where 5 minutes would leave you still wanting some more grunt to clear the far obstacle. The additional time usually is employed to drive the third segment height up above the critical obstacle or sufficiently so that the fourth segment is able to clear the obstacle. Doesn't always work out that way in the analysis but that's the general gameplan.
Flaps down has a stabilizing effect on VMCA.
We always need to be very careful with student level throw away lines. A bit like the old "which is critical of Vmcg/Vmca". All depends on the aircraft – for some it’s this, for others it’s that.
As always, when talking engine stuff, I urge readers to listen attentively to our engines folks, such as tdracer.