Efficient loop formation requires the caster to move the rod in a Straight Line Path to the target.
First of all remember this: The line will follow the path of the rod tip. If the rod tip deviates from a straight line, so will your flyline. There may be circumstances were it is desirable to not cast in a straight line, but that is something I want to talk about later.
For now remember to keep track of what your rod tip does when you make a cast. There are 4 different paths that the rod tip can make when you make a cast. All of these paths result in a different loop shape.
“The first is the nearly STRAIGHT LINE PATH of the rod tip. This path generates a narrow LOOP and accurate placement of the fly. A narrow loop will show a top and bottom leg separation of approximately 20 inches. The top and bottom leg of the loop will also be in the same plane, that is to say that the top leg should always be directly above the bottom leg for maximum efficiency. Another advantage of the narrow loop is its ability to penetrate a wind. The smaller and tighter loop has less surface area and increases resistance to the wind ”
The second path the rod tip can travel is in a CONVEX PATH. The path of the rod tip in this instance travels in a large upward arc as opposed to a near straight line path. A convex path of the rod tip opens up, or widens the loop, decreases wind resistance and compromises accuracy.”
“The third path the rod tip can travel in is a CONCAVE PATH. The path of the rod tip in this instance travels in a downward arc. This path will form a closed or TAILING LOOP and commonly leads to the dreaded wind knot. The tailing loop will severely compromise full TURNOVER of the loop and accurate placement of the fly.”
Last but not least is the LATERAL PATH of the rod tip. In this instance the path of the rod tip no longer moves in a single plane but instead swings out to the left or right from the straight line path to the target plane. Know as the "Swinging Loop," the top leg "swings out" to the left or right of the bottom leg of the loop. The swinging loop is a casting fault.”
When I was in the early stages of learning how to cast a flyline, this essential was a revelation for me. Concentrating on what the rod tip does when you make a cast really gives you a sense of the control over the flyline we all strive for.
Just as a bit of a relief for before all of you go out to practice: The straight line only occurs during a part of your cast. The picture below is an excellent illustration of what to aim for. The picture is part of an article about SLP by Jason Borger and can be found here http://fishfliesandwater.com/casting-mending/slp-straight-line-path-of-the-rod-tip/