It depends on where you are measuring the voltage... probably you have less current flow so less voltage drop that you see as an increase... no?

TGS for properly sizing a transformer is not so hard.. basically a big transformer is needed for low frequencies because the number of cycles tells you how many times you can use your core per second...

i usualy take the voltage applied divide by 2 for pulsing 50% than divide by Bmax of the core than divide by the crossectional area of the core and than divide by the frequency... this gives the number of turns...

ferrite is usualy bmax 0,3tesla

area is in square meters

frequency in hertz

the 2 is a factor telling we can use only half of the core flux swing because its not ac... if was square ac it would be 4 and if sinewave it would be 4,44

above this voltage at this frequency the core will saturate with the turns you calculated....

with this simple equation you can develop good transformers already

the gap will allow more energy to be stored for a given design suchthat it will reduce the inductance increasing the current so the energy stored also the gap help avoid saturation...

1Henrie is = to 1volt aplied by one second make a current to go from zero to 1 amp...