Electronic – getting odd inductances from home made inductor

You have experimentally derived the equivalence that 113 turns yields one inch of coil length, yielding the conversion factor (1 inch / 113 turns). Obviously this tacitly depends on the coil diameter, but is a sound figure for the diameter under which you established the measure.

If you have 113 turns that is one inch. If you have 226 turns that is two inches. and so forth. So Length definitely equals number of turns / 113. Looks to me like you can safely substitute N/113 for l. Just keep in mind this doesn't generalize because of the implicit dependence on diameter built into the 113.

You should probably just ask the second part of your question as a new question. It's way more interesting than the part I'm answering here :-).

If magnetic permeability of ferrite core is unknown - you have to wind it and measure it.

That may be complicated without oscilloscope or multimeter with inductor measurement.

In addition - I think RF ferrite may not work. Radio ferrites are not designed to store so much energy. It probably oversaturate and not work as desired at high current.

It will be even harder to determine if that happens without oscilloscope.

I think it would be easier to use some inductor with few thick windings from ATX power supply or other DC/DC converter and try how good or bad your converter is by measuring power efficiency.

Power input:

$$P_{in} = I_{in} \times U_{in}$$

Power output:

$$P_{out} = I_{out} \times U_{out}$$

Efficiency:

$$n = \frac{P_{out}}{P_{in}}$$

That kind of flyback converter should have 65%-75% efficiency.

However if coil is very badly chosen and you have big power supply - you may blow up transistors because energy must go somewhere when back EMF happens on big transformer. Maybe try with smaller (1A?) power supply first and check transistors temperature.