Jim Lux wrote in
:

I think that for the purposes of looking at the effect of shorting/not
shorting turns, Wheeler is more than adequate. the key is the fact
that it encapsulates the difference between the Nturns^2 (zero length
solenoid with all turns coincident, fully coupled) and Nturns (zero
coupling) for dimensions that are "practical" for ham use.

And the other interesting thing is that the graph of inductance vs
length for coils of interest here is that it looks pretty linear (and
the fact that the coil stock vendors refer to "uh/inch" kind of
confirms that)

An interesting bit of trivia for the models I created is that the flux
coupling coefficient doesn't vary much with turns for a given diameter
and coil pitch.

When you make relatively large diameter coils of fine pitch, k is higher,
and that creates the conditions for higher loss in shorted turns.

The implication for long loose coils is that k is low, mutual inductance
is low, inductance approaches a constant L per unit length etc.

Sensibly, most air cored solenoids operate in the midrange.

Owen