redanman:
Your comprehensive explanation of a canine's anatomy and flexion is very interesting as is your mention of; "It's the effect of the magnitude of the third dimension, the "Z" axis, that changes the effect", (whatever all that exactly means). But certainly Tillinghast's ideas and explanations on the use of trees to form and create a "dogleg" golf hole appear to be a bit more straightforward and easier to understand!
To Tillinghast a dogleg hole was simply the formation of some feature, in the example he used--the use of trees one could not hit over ("If it be impossible to carry over this obstruction..."), on one side or another, but on a single dogleg the same side as the hole's curving direction (or in Tillinghast's words 'twisting").
Tillinghast also said; "The trees are permitted to remain along the side for such a distance as may be considered proper for a well-hit shot to exceed."
Do you see what he says there? "......for a well hit shot to exceed."
Presumably that means if a shot is not well enough hit either in distance or direction then it hasn't "exceeded" that dogleg feature (often trees) and therefore there should be no necessary reason for the golfer on his next shot to have a direct or clear shot at a green!
And this is further enunciated by him when he said that a shot that "exceeds" (negotiates) the dogleg would then create a next shot that has the green opened up to it!
"Under normal conditions, a player should be required to drive at least two hundred yards before the barrier to his second shot is removed."
Do you see what he says there? "....barrier to his second shot is removed."
That's all pretty clear stuff.
But what he doesn't say exactly, probably because the implication of it is so clear, as well as the clarity of it in his drawings, that if a golfer does NOT CHOOSE to drive the ball down the inside direction of a dogleg, he can choose to drive it to the outside, presumably opening up the angle to the green somewhat but consequently leaving himself a longer but nevertheless direct shot at the green.
And Redanman and Chip, anyone can see by looking at any of Tillinghast's drawings (as well as those of many other architects), as well as understanding the ideal example he gives--ie, Pine Valley's #1, that it's more than possible to put the ball in the fairway and still to have NOT 'exceeded' or negotiated the dogleg (for a direct second shot to the green).
I realize neither of you like trees on golf courses that come into play in any way, but either disagree with Tillinghast's ideas on the concept of the dogleg or agree with it. Please don't attempt to take his relatively simple explanations and complicate it into something that isn't understandable!
And very definitely dogleg holes are holes containing playable options--you either try to "exceed" the dogleg (get past it) with a longer accurate shot down the inside of of the dogleg or you choose a shorter shot to the outside of of the dogleg creating a longer second shot (with a direct approach to the green)!
And Tillinghast said nothing about using holes like this constantly! He said they're useful occasionally to create "variety" in design. So in the context of Tillinghast's ideas, explanations and uses of dogleg holes I don't know why you mention "beating one drum too loudly."