effect of flap on vmca
 

Consider a particular aircraft with a published vmca speed with flap in the takeoff setting, what effect will an increase or decrease of flap setting have on that speed and why? cheers

None - because Vmca is always given for the take-off flap setting.

I think what you meant to ask was what effect flaps have on Vmc (as oposed to Vmca). My understanding is that the answer is still very little, if any.

FFF
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Differences might be academic but theoretically there is a difference,
accelerated slipstream on the "live" side will increase lift generated also with flap deployment. On the "dead" side the flap will cause less of a lift increase because of the lesser accelerated airflow.
Therefore lift assymetry as a result of engine failure will increase, therefore a stronger roll moment.
Vmc concerns directional control however, so it is arguable as to how increased roll moment will affect yaw.
Roll towards the dead engine will generally increase the yaw towards the dead engine, which will need to be corrected with more rudder deflection.
So as a secondary effect I will say that flap does affect Vmc.
If it is actually noticeable in a real life situation , I don't know.
Vmc is a fairly academic number in itself anyway.
Standard atmosferic conditions, max gross weight
, full pwr working engine, windmilling dead engine, max aft cg etc etc etc.
You will hardly ever fly under those exact conditions anyway, so "published"
Vmc is a best guess indication, not you "true" Vmc for your conditions.
It's just as vague a number as Va.
I don't like anything below Vsse anyway.

In general terms, anything that increases drag will increase Vmc all other things being equal. Anything that reduces drag will reduce Vmc.

As someone else said, the actual IAS is fairly academic as the real Vmc on any given day (as opposed to published Vmca) is anyone's guess.

The use of flap lowers Vmc beacuse your AOA reduces hence a bigger fin area is exposed in the stream flow.
The rudder is the primary control related to Vmc, so assumed the CG remains the same, so the arm, a larger rudder exposure in the airflow ensures a positive controllability also at some knots below the same situation with a lower flap setting.
Generally speaking, many aircraft models have more selectable flap positions within the flap take off range, so the use of a higher one reduces the Vmca,althought it affects other factors as the climb gradient and so on.

Vmca
 

http://gav.customer.netspace.net.au/vmca.htm

The above link is helpful with regard to the question