Which bullet lands first?

Cecil's Columns/Staff Reports
1

In the 1988 column http://www.straightdope.com/classics/a5_201a.html
Cecil discusses which bullet lands first, one that is dropped, or a second one shot horizontally out of a gun. For the more “enlightened” view, he makes note of the curvature of the earth as an influence. He also notes that a vacuum is assumed. This is a bad assumption on Earth. Maybe his arguments make sense on the moon, but I am not aware of any gun ever being taken there. However, I could be wrong about this, given that the NASA control center is in Texas.

At any rate, the aerodynamic effects are significant. In particular, given that the most guns have a rifling effect (the bullets spin when they exit), the direction of the wind, and direction of bullet spin can determine whether the bullet experiences a lift, or a force downwards. I believe this is called the Magnus effect. Imagine watching a bullet travelling away from you (preferably), and you see it spinning clockwise. If the wind is blowing from right to left, the air gets thrown upwards a bit after it passes by the bullet. Tossing the air up puts thrust downwards on the bullet (according to Newton’s Law III in The Principia), and the flying bullet hits the ground first. If the wind is travelling from left to right, the air is thrown downwards after it passes over the bullet, and the bullet is lifted somewhat. This bullet will hit the ground last. This topic is covered very nicely in Acheson’s “Elementary Fluid Dynamics”, p.132. Don’t let the name fool you–it’s not really for Elementary School students.
I daresay that this effect is more significant than the Earth’s curvature for a typical gun. It does require wind, but I also suspect that there is more wind on the planet at any given moment than there is calm. Also, only two directions would have no effect (either into the wind or downwind), whereas all others would feel the effect. Hence, I would consider curvature of the planet to be, at best, a tertiary effect.

Sorry that I took so long to get back to you on this column, but work has been kind of piling up the last twelve years.

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There was an extensive review of this topic here back in June in You fire a bullet and drop one – which host the ground first.

In addition, in Cecil’s July 14, 2000 column, What’s the world’s largest commercially available bra size (revisited)?, Cecil noted that “I handed this question [brassière sizing] to one of my interns, young Doug, along with a bunch of other worthy topics, such as the effect of atmospheric drag on dropped versus falling bullets. You can see what he zeroed in on.” which, at least to me, seems to indicate that Cecil is already hard at work on an update that addresses your concerns and those brought up in the earlier thread.

Of course, since it took you 12 years to come up with your response, it’s only fair to give Cecil the same amount of time to develop his.