<<We recently enlarged the air intake in the cowl of our legacy from 2.5"
(factory standard) to 3.5" (the same diameter as the fuel servo.)  For you
Continental folks, the Lycoming cowl has a third intake hole just for engine
air below the prop.  We also moved the hole up closer to the prop to take
advantage of ram air.  To our surprise, we got no boost in MAP and lost a
few kts. airspeed.  Presumably the intake hole is now too big.  Does anyone
know the formula for calculating the diameter of the air intake for a fuel
injected engine (or know where we could find it?)>>

I've been doing research on the same subject and couldn't find information
directly related.  Instead I used information for cooling inlet calculations
and concluded that a reasonable inlet size would result in a velocity ratio
of 0.4.  That is the velocity of air within the inlet at its mouth is 40% of
the free air velocity.  I did this calculation for the max-cruise condition
to get the size.  Then the trick is to gradually increase the area (a
10-degree included angle cone is reasonable) so that more  pressure recovery
can be accomplished in the inlet.  For my Lycoming with a -10 servo that
velocity is only about 130 ft/sec, much less than the free-air velocity.
The throat area (NOT the area of the lip) for my ES worked out to 7.9 sq in.
compared to 9.6 at the servo inlet.  A smaller inlet probably would work as
well or better and the recommended maximum velocity ratio was 0.7.  I picked
0.4 as it would move to a higher velocity ratio at takeoff and climb and I
didn't want to compromise those conditions with an inlet that was too small.
The pressure recovery with this type of design was listed as 0.75 to 0.85.

I would welcome any more expert opinions as I am about to create the inlet
configuration on mine.

Gary Casey