I was also puzzled by LP and SP until I read an article explaining that because on a globe, the shortest distance between two points is a straight line, the direction can be found using a piece of string (pulled taut) on a globe passing through the two points involved eg England and Australia. When the string is as short as possible, that is the short path. The long path is 180 degrees from the short path. No other direction will reach that same destination. So the rest of the string can be extended in a straight line all the way around the globe, forming a perfect circle. In fact a great circle.
Now when I hear someone calling “CQ dx long path”, I wonder long path to where? Every direction is both a short path and a long path to a lot of locations, all somewhere along the great circle formed by the string.
Sometimes the polar anomalies caused by the curving of the magnetic field near the globes make paths a little different from the directions taken from pure “global string theory” (!) but those cases are rare. And with antennas that have a 60 degree beamwidth you can never tell.
The simplest directional antennas are bidirectional. So positioning for the short path direction also satisfies the LP.
On the dynamic beams like steppir and ultrabeam, the controllers have a SP/LP switch. This merely swaps the lengths and roles of the director and reflector (on a 3 el yagi) allowing you to check the opposite path in a few seconds, rather than waiting for a rotator to turn a beam around. Good demo of the 180 degree relationship.
73 Andrew VK1DA/VK2DA