”Another factor of importance I knew because I was a pilot. Add three inches to a six-foot-long propeller and you’ll reduce the revolutions per minute the motor will turn it at by least three hundred… Pushing a long rod through the air takes more effort than pushing a short one. I ran tests and found I could get 25 percent more speed at the fly using a six foot rod than I could with one that was nine feet long.”
Lee Wulff
I like to browse through the books in my library now and then, and today it has been the turn of Lee Wulff’s Trout on a Fly, published in 1986. Lee was famous for using six foot rods for atlantic salmon… and being very good at catching them. I underlined the quote above more than sixteen years ago, when I did my first read of this fine work.
Lee’s statement was one of the first casting mechanics issues I started to analyze as an would-be casting geek. Unfortunately Lee doesn’t explain what those tests he mentions were, but something seems to be wrong.
A rod is a lever —a third class one, to be precise— and the longer it is the more force it takes to rotate it with the same velocity. This is what Lee confirmed with the propeller of his plane. But what I miss in Lee’s statement is something fundamental: by reducing the length of the propeller, do we increase the speed of the plane?
In fly casting we are after line speed, which comes from rod tip speed, the higher the latter the higher the former. With a short rod we need less force to rotate it, so its angular velocity increases but —and this is a big one— the rod tip speed decreases in the same proportion, as the distance covered along the same angle of rotation by the tip of a short lever is always shorter than the distance covered by the tip of a long lever. It will take more time for the long one to describe the same angle, but its tip will cover more distance as well: rod tip speed remains the same.
Think of shifting gears in a bycicle: the gear ratio that gives the higher speed is that which asks for our legs to pedal slower and with more —not less— force.
In casting neither very short nor very long rods will give us the higher line speed and distance. The problem is that each caster has to find that middle ground that suits him.
onemorelastcast.net 
From a mechanical perspective I would also argue that a longer rod is “easier” to move in something closer to a straight line. Even if both didn’t bend the shorter rod would be producing more of an arc? At least in my mind. So a very long rod would require too much effort, a very short one would be a disadvantage.. The answer, as you say lies in the middle and one suspects that “The middle” differs for every caster..
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“Even if both didn’t bend the shorter rod would be producing more of an arc?”
Unfortunately “arc” in conventional fly casting lingo has nothing to do with “arc” in geometry.
In casting, “arc” refers to the angle the rod is rotated during the casting stroke, and if we rotate a short rod and a long one of the same action through the same angle both will give the same loop width.
A very long rod requires a lot of force to rotate, and maybe you don’t have it; a very short one requires a lot of angular velocity to get the needed rod tip speed, and maybe you can’t generate it.
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Lee fished dryfly on his short rods and as far as I know never caught a salmon in Scotland on one.
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Well, I don’t have the reference at hand, but he managed to catch a salmon in Scotland casting with his bare hands. Just an anecdote.
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