[nanwynnfan]

I'll respond to that jtur posit simply because there have been so many arguments over bat speed, contact force, force dissipation and exhaustion ... and all culminating in debates over the maximum distance a human being [prime MLB batter] can possibly hit a pitched baseball.

We've all heard of the Mickey Mantle blast alleged to be @ 565' and there are MLB parks with painted seats to mark remorable HRs that struck them; they serve as measured, verified "distance" markers.

I've been guided by two elemental speed factors, at least one of which is considered a relative "given" - the speed of a pitched baseball.

Tiger pitcher Joel Zumaya, @ 103 mph is NOT my model. I default to 80 mph because it is the speed of the pitched baseball at the instant it collides with the forward-moving bat that counts in the equation.

So, a pitched baseball, at that instant, will be a bit below its release speed of 85, 90, 100, 105 mph; and not all pitches are fastballs, so 80 mph seems areasonable figure.

Having read Dr. Adair's book on the physics of baseball and other paper on the subject, I get the simplified, elemental formula that impact speed is comprised of two elements:

-the pitched ball forward speed at impact mutiplied by a factor of .25, so that 80 mph * .25 contributes 20 mph to collision force;

-the bat speed contributes a factor of 1.2, so that a bat speed of 70 mph contributes 70 * 1.2 or 84 mph to collision force, the sum in this case being 20 [ball] + 84 [bat] or 104 mph. [I would refer those who would question of bat spped to Dr, Adair's "The Physics of baseball," pages 29-34 ... and page 37, with Ted Williams as primary model.

-the second factor is the immediate dissipation of the forces of both bat and ball the instant after contact, which is tremendous. If the ball leaves the bat at 104 mph contact speed, as any fan knows, even the most vicious line drive travelling far enough to be a HR will enter the stands as a speed far less than 104 mph, more like 40-60 mph, enough to make surprised fans scatter, with the more resolute getting a souvenir [aided maybe by a glove].

-the arc of the drive and gravity work on the forward flight speed of the batted ball's flight, a rainmaker high drive might drop into the seats with as little forward speed as 10-25 miles per hour, a moderate drive @ 25-35 mph, and a vicious liner > 35 mph. That final speed at descent, averaged with initial blast-off speed gives a solid rule-of-thumb means of calculating average forward speed of batted balls over the course of their trip.

-the final element in distance is flight time; and although some very high "blasts" seem to hang up there forever, the fact is that 5 seconds is about max for a very high arcing blast with a final descent speed of @ 15-25 mph.

If we take our 104 mph contact shot with that final descent speed of 25 mph and a hang time of 4.2 seconds, we have a batted ball travelling 397.'

If a trailing breeze adds a tenth of a second to the flight, it'll go @ 407'.

If a batter with bat speed of 74 mph strikes the same ball with the same trailing breeze, he'll get 422' aided by a split second of added flight time and bat speed.

I used 70 mph as my base > average, talented batter example for a number of reasons:

-NOT to underestimate bat speed contributions in equations;[also considered Dr. Adair to be pretty darn knowlegeable; and took into consideration bat weights, woods, etc, sine Ted's prime];

-show how hard it is to improve on excellence ... spinach etc. will not jump start bat speed at the highest levels of performance by very much, even 7% may be too generous;

At the bottom line, physicists and mathematicians who have studied this far more deeply than I have "capped" maximum HR batted-ball distance by a gifted human being @ 475' [conservatively] to 515' [generously] with neutral atmosphere and maximum ball bat contact contributions.

I'd have guessed a bit further, but an idealized example seems to bear Dr. Adair [@ 500'] out:

-Pitched ball @ 100 mph [release and start @ 103-105 mph] * .25 = 25 mph

-Bat speed 80 mph [Clark Kent emerging from phone booth] @ 80 mph * 1.2 = 96 mph;

-Collision force [speed] 25 + 96 = 121 mph;

-Lower type liner, flight time @ 4.4 seconds ...= 519.49'.

[Maybe the guy on tv was swinging an aluminum bat]. Another consideration is the non-linearity of bat speed augmentation, the jump from 55, 60, 65 mph being geometric, not arithmetic. This would be supported by small returns on maximum effort among the very best.