The Effects of High Altitude on Topspin
The path of a ball is not just a simple question of ballistics and gravity -- it's a bit more complicated than that, as the "spin" that makes golf balls slice and curve balls curve depends on the altitude at which the ball is moving. In other words, if you're planning on factoring topspin into your home run record attempt, you'll need to know how high up the diamond is first.
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Topspin
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Spin occurs when a ball that is ordinarily thrown straight is given some degree of rotation. As the ball rotates, its path changes --- this allows for the slice of a golf ball and the way a curve ball breaks. If you imagine a dot drawn perpendicular to the line of throw, topspin occurs when the spin is such that the dot rotates towards the thrower, and backspin occurs when the spin is in the opposite direction; the dot appears to rotate away.
Magnus Force
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The ability of topspin to change the trajectory of a ball is the result of a physics property known as the Magnus effect, or Magnus force. The additional rotational velocity imparted by the spin causes a thin layer of air directly over the surface of the ball -- the boundary layer -- to separate, creating a low pressure region that draws the ball in the direction of the spin. In the case of topspin, the Magnus force draws the ball downwards.
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Other Factors
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A moving object is impacted chiefly by two factors: atmospheric drag and the Magnus effect. Both of these are directly related to atmospheric density, which is lower at higher altitudes. As a result, the ball travels a greater distance due to reduced drag, and the effect of the curve is lower due to the reduction in the Magnus effect. Where topspin is concerned, the combination of reduced drag and a lessened downwards pull on the ball means that it travels substantially greater at higher altitudes. Humidity is also a possible factor; higher altitudes tend to have less humid air, resulting in a lighter ball that naturally carries farther.
Real-World Effects
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One easy way to look at the real-world effects of high altitude on spin is by comparing the performance of pitchers and hitters at Denver's Coors Field, a mile above sea level. At Coors Field, balls curve a third less than they do at sea level, resulting in curve balls that stay fair when they would otherwise have broken foul. According to Major League Baseball, the lessened atmospheric drag results in balls traveling 9 percent farther than they would at a lower altitude.
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References
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