How far did the Mick hit it?

Also had an interesting email discussion recently about the distance that Mickey Mantle's famous "565" foot homerun in April of 1953 actually travelled. Along with this are other claims of prodigous Mantle blasts.

After reading these claims I went back and looked at what Adair says in his book The Physics of Baseball about how far a ball can be hit. Based on his model he says that in order to hit an 85mph fastball 400 feet you need a bat speed of 76mph. To hit one 450 feet you need a speed of 86mph. He estimates that under normal conditions this is the limit to how far a ball can be hit. If however, the fastball is 95mph add 10 feet. If the batter pulls the ball add another 15 feet. If it's 100 degrees add another 20 feet. With a 10mph wind add another 40 feet. Hit it in Colorado and add an additional 10-15 feet. Add them all up and if everything is going your way the ball could go 550 feet.

Since his book was published in 1990 I assume that a bat speed of 76mph must be modeled after what were perceived norms for the time. With the increase in weightlifting it is probably not uncommon to get velocities of 85mph for guys like Bonds and Sosa although I haven't seen any data on this at all (incidentally I wonder if increased swing velocities account for the increase in broken bats that announcers and players often comment on). And with every increase in velocity you multiply the force (f=mv^2).

Sosa's homerun in Florida in July was projeted at 484 feet. Adair estimates that Mante's homerun went between 511 and 520 feet because we know Mick's blast cleared a 55 foot wall by 5 feet, 460 feet from the plate and then glanced off a beer sign. So he estimates that the ball would have landed 60 feet past the sign given an angle of descent of 45 degrees.