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I hope some people will find this data useful..

Tonight after work I wanted to run some tests to determine the optimal speed for switching polarity in front of a coil to find the optimal speed.

I took 2 identical single wound coils with iron cores open on 1 end.  Clamped them tightly together..  Ran DC power to one of the coils (making an electromagnet), and put a bridge rectifier on the other coil, going to a load of 3 motors.

I setup the ardiuno and H-bridge to switch polarity on the electromagnet in intervals I specify..  And measuring the input vs output.

The timing was the following format:

Positive charge  on lead 1- negative Charge on Lead 2.  Delay XXX Milliseconds
Then Switch Negative on Lead 1, Positive on Lead 2.  Delay XXX Milliseconds
Repeat indefinitely..

My results are not perfect, but some general ballpark figures and guidelines emerged...

Anything in the microseconds was switching way too quickly..  Like no output or input.. 
From around 1 to 10 millisecond delay between switching was optimal with the least loss.  1 Millisecond gave me 4.439 watts from source-  Output was 4.25 watts.  A loss of .189 watts

As the delay was increased, so was the input and output power, but the efficiency went progressively lower as I increased delay (as expected)..

Staggering the delay timing (example-  1 millisecond positive, 4 millisecond negative) did NOT work well at all. 

As a summary-  for the most efficiency:

1.  keep your magnets spaced as evenly as possible.
2.  For Most efficient (the least loss)  -  aim for switching polarity every 1 millisecond
3.  But getting enough power out of very quick millisecond switching probably isn't going to happen.  You will probably need to sacrifice efficiency for more power output.

  Try also ferrite cores as it is good for high frequency. Iron cores are slow to react.
Air cores will work but less output due to less transfer.