Re: How can your conclusion on the speed of a falling rifle bullet be true?

The question: "How can your conclusion on the speed of a falling rifle bullet be true? You conclude the speed of a falling bullet to be 91mph at return to shooter. With a greater density and less drag than a falling human (terminal velocity about 120 mph), your conclusion makes no sense."

It is perhaps counterintuitive to think of a bullet's falling more slowly than a person, but it all has to do with the amount of drag that is developed by the thing that is falling, and the drag depends to a very great extent on the way that a nonspherical object is falling. Bullets are largely cylindrical in shape, and for a bullet that is falling with its long dimension parallel to the ground the coefficient of drag, C_d, is about 1 (see fluidmech.net or scienceworld), while if the bullet is falling with its front face toward the direction of fall C_d is about 0.3 (see nasa.gov), and if the blunt back end of the bullet is facing the fall C_d is about 1.0 (see the same page as previous). (The Reynolds number for the velocities we are discussing is on the order of 10⁴.) Skydivers can also take on two very different positions, either head down, or more or less horizontal. For a head-down falling person C_d is about 0.7 ( see indiana.edu or hypertextbook), and for a horizontally falling person C_d is about 1 to 1.3 (see engineeringtoolbox.com).

Let's make some calculations based on these numbers. See jumpshack.com for a useful calculator. For a bullet we will use a "mass" of 0.033 pounds (about 230 grains) and a horizontal cross-sectional area of 0.25 inch² but a circular cross-sectional area of 0.155 inch². For a person we will use a "mass" of 180 pounds, a heads-on cross-sectional area of 110 inch², and a "spread-eagle" cross-sectional area of 775 inch². You can change any of these numbers and see what differences the changes make. Here is a table summarizing the input data and the resulting terminal velocities:

Several of the sources given above indicate that a person in free fall obtains a terminal velocity of about 120 mph, which is reasonably close to our 116 mph for a horizontal fall, so obviously when the previous answers say that a free-falling person obtains about 120 mph the assumption is for a "spread-eagle" position. In addition, a body like a bullet will not fall stably with either its front or back ends pointing in the direction of fall, so the bullet will stabilize into a "flat" fall and obtain about 88 mph, which is reasonably close to the previously given figure of 91 mph. (I have looked for two days for a site that discusses the falling orientation of roughly cylindrical bullets, and I know there's a site out there somewhere because I have seen it sometime in the past, but I have not succeeded in finding it now!)

I would say that the previous conclusions about terminal velocities are true.

John Link, MadSci Physicist