Understanding inductors with non closed/looping iron cores
The air gap is significant and is the definer of the inductance but, the main thing about using an &quot;open&quot; ferrite core is that all the winding turns remain highly coupled to each other (unlike in a pure air core). This means that you can still take advantage of the relationship of inductance being highly proportional to turns squared.
So, there is a good &quot;winding&quot; benefit but, \$A_L\$ is much reduced because of the very dominant air gap. Nevertheless, being able to rely on \$L \propto N^2\$ is a useful thing especially if you wind your own.
And, of course, with such a massive (and dominant) air gap, temperature related variations in permeability are virtually non-existent (unlike a closed ferrite core). The ability to deal with large magnetic field strengths (ampere turns) is also another rich benefit compared to ungapped core designs.