It's not that easy to calculate the number of turns for a winding.
If you have a standard magnetic circuit such as a dual rotor or a single rotor with a laminated core, you can with practice get quite close if you know the grade and area of the magnet and the air gap.
With an open magnetic circuit such as Hugh's 4 ft machine it is more difficult. you can not easily predict what flux density you have at a given point. It can be done by computer modeling and finite element analysis, but if you want to go that route it will take you even longer.
Most of us make a test coil, measure its voltage and resistance and predict the output from that.
That's the beauty of using a published design, someone else has done the hard work for you and you know it will work first time.
After you have built a few alternators you will be able to predict better using the results of previous experience.
You are right, that 4ft machine does not use laminations. The idea is for anyone to be able to build it. Suitable material for laminations is not always easy to come by.
I think the reasoning is that it uses the same size magnets as the big 8ft mill and they are a common magnet available reasonably cheaply. It could have used smaller magnets with a dual rotor .
I am not sure that I have answered your question, if not come back.
Flux