Ugh, this has gotten convoluted, and alot of generally correct physics applications have been thrown out there some of which aren’t correct for the situation presented.
I’ll try and clarify as succinctly as possible.
First, about the flex of the shaft. This action has no effect on the actual impact of the golf ball. To explain, a golf club flexes an exceptional amount, and each club flexes differently depending on the swing of the golfer, material of the shaft and the length of the shaft. Now, it does contribute to the driving distance. More flex is not always better. The ideal flex condition is one where the club releases all its potential flexed energy at the precise moment before impact with the ball. A club with alot of flex will release that energy at the right time for a golfer with a slower swing. A stiff club will have less flex, but release at the correct time during a fast swing. So, two different clubs in the hands of two different golfers can result in having the same head speed at impact. A long driving golfer is one who has the swing acceleration to force a stiff shaft to flex alot, but still release at the correct point, coupled with a high overall swing speed. The idea of using a club with alot of flex could be bad if the golfer out swings the release of the club flex, causing it to release its potential enegry after the ball is impacted. In short, zut is incorrect. The stored potential energy is not transfered into the ball at impact. It releases its potential energy into swing speed. Ergo, if one is able to accurately deduce the swing speed at impact (as we must assume the mentioned technologies do) the club flex and potential energy has already been transfered into work and is included in the speed reading for a physics analysis.
Second, it is important to mention that neglecting air resistance a club w/ 45° loft and the same club head mass and shaft length will provide the longest drive. But since we aren’t dealing with a air-free environment, and the properly lofted clubs are shorter and weighted differently we can’t say what club would work ideally for a non-dimpled ball. It really is off topic anyways.
Third, wood is not an ideal material for impacting a ball. Golf clubs have stopped being made using it, and baseball bats would as well if you were to ignore MLB regs.
Fourth, a straight drive isn’t neccesarily going to be the longest. The reason being wind and roll. If we assume a still day, which we’ll need to do since the variety of effects on both baseballs and golf balls are too many to discuss, you can assume that a straight drive will be the best for air travel. A draw (slight hook) is ideal for the longest drive condition. The reason being the a draw imparts a slight top hand english onto the ball giving it a tendancy to roll after landing farther than a perfectly straight ball. This is however a razor edge depending on conditions because the amount of backspin effects flight distance. More is not always better. So we’ll neglect this effect for discussion.
Fifth, I have seen baseballs hit 800-900 feet quite often. Where? Well, Wrigley field of course. Often balls that leave the park (eg. beyond the bleachers) hit Sheffield Rd. and roll down Kenmore Avenue. I say this to make a point. We usually consider baseball distances based on strictly flight distance to a point higher than the altitude of impact. So, we rob the homerun hitters of a little distance that we grant golfers.
So from the OP: [list]
[li]We know the longest officially driven golf ball 412 yards[/li][li]To be discussed further[/li][li]Well, it depends on the athlete, but we’ll say some impressive batters manage 100mph, and some impressive golfers likely reach club head speeds (at the precise point of impact) of 125 mph. Neither of these speeds are average of course.[/li]
For point two, lets set some ground rules. We’re going to only consider flight distance, and ignore ground roll. So we’ll subtract 30-50 yds from your general drive. Two, we need to figure out if we want to discuss if the golf ball is pitched, or if its hit of a stationary tee. Or do we hit a pitch golf ball w/ the bat, and off a tee for the golf club?
Some things to consider. A bat is round, and a pefectly hit ball will recieve a higher impulse than a ball hit off a flat surface. A bat typically weighs 30-40 ozs, a golf club 10-15 ozs. The entire weight of the bat is not applied to the ball, only a percentage one can figure using the center of mass, the center of rotation and the parallel axis theorum. More TAM than I plan on doing.
Have at it.