A.G.,
Sorry for the confusion. I always work in % slope, which is about 2.2 X degrees for the same measurement. 45 degrees is a 100% slope. For convenience, since
launch angle for average golfers is about half club loft angle, and each % slope is about twice degrees, it effectively means I can just use the actual loft angle of the club to represent the approximate slope % on the front of the bunker!)
As to specifics, first, nature does usually decide how deep that bunker will be, unless a flat site and I can build up as much backing fill as I wish. But yes, I actually do use a 7 iron at 150 yards as a proxy when designing for everyday players. I know a tour player would be hitting a lob wedge, but in most cases I don't design for them. Of course, under the "deeper when closer" theory, a hole might have a shallow bunker at 200 yards for the green and a deep one 100 yards, and "appropriately" challenge both, etc.
My only point is that the math details of that bunker matter when designing it primarily as a tempting hazard. For everyday play, if if I theorize that I would like to make it borderline to clear the lip, for a good, but shorter hitting player, to potentially reach the green, then
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it seems to me that a sand bunker 150 yards from the green, on the direct line of play at least, should be <34% slope to implement
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that
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design theory.
I mostly design cape and bay style bunkers, but the theory probably works whether that bank is sand or grass, the ball doesn't care.
If doing flat bottom bunkers with a steep bank, there is obviously the potential for a wedge out lie if just at the base of the slope. Again, no big whup, but in theory, you tend to punish the longer tee shot more, which is actually the better tee shot, whereas the guy who semi fans a drive and finds the front of the bunker has a relatively easy play. Hey, maybe he needs to help and the gca should give it to him? Who knows?
And, as you suggest, so often bunkers are for other functions, including artistic composition, save from worse trouble, aiming devices, or in a few cases, because people think playing out of wet sand is better than playing off of wet turf, i.e., the bunker is a (half assed) drainage solution. But, I usually like bunkers to be appropriate hazard first, then whatever other way it can be useful.
In reality, in most cases its hard to convey the exact slope to bulldozer guys and get any exact percentage. In the end, I'm happy if my bunkers 200 yards from the green are a bit shallower and flatter than those 100 yards from the green, etc. As to the math, I have just logged too many miles on planes over the years, and I occupy my mind with these kinds of riddles rather than watching movies.