Of course there is a bit of science (aka physics) related to fly casting, and you really don’t need to understand it in order to throw good loops. But… Here’s a little taste.
Good efficient loops are nice and tight; with sharp arrow-like points. Their value is less resistance and greater accuracy. But like so many things in life, tight loops are not always what you want. In fact sometimes you want just the opposite, for example; when throwing large heavy flies or multi-fly rigs with split shot. Hopefully, my diagrams below help you understand how this works.
In order to throw tight loops the rod tip must follow a straight line. As the rod bends deeper which is typically caused by more line out beyond the rod tip, greater application of power, or both, the rod tip must continue to follow a straight line. Use a smooth acceleration; think of the word zzip. Spell the word with more “Z”‘s as the the length of line you are casting increases. End each stroke by flicking the rod tip followed by a crisp stop.
Fortunately, I am reminded how this stuff works when watching students go from no loops to beautiful loops. The best method to success is through hands-on casting practice. Practice adjusting the variables (Power, Stroke, Pause) along with the constants (Firm Wrist, Straight Line Path, No Slack, and Crisp Stop).