banktoturn,

It was a low aspect ratio wing of about 3 that Horner was using. The square tips gave more effective span and lower induced drag. With a really high aspect ratio wing (or even a moderately high one I guess) the shape of the wing tip starts to be a non player with respect to induced drag. There may be some other drag components of the wing tips that change with shape though.

The figures are not totally clear in the book, the figure that shows the tip shape and center of the vortex is just showing the difference in spanwise location of the center of the vortex. There are some other figures with wing shape and you put the together and allegedly come up with Horners conclusions. The figures in the Horner book are hand drawn and don't reproduce well, it is difficult to see some of them in the book! There isn't any kind of wind tunnel data that I would like to see on the subject.

I am sure other sources have better data but I don't have any at hand.

I know when wing tips were a subject at work we would talk about all the neat good stuff and pull out some old reports and end up with the same old shape for the fighters. Of course the high aspect ratio heavy lifters pulled out reports for their airplanes and got different answers.