# How to compute drag coefficient for falling book? [closed]

The book measures 20 x 20.3 x 1.4cm and I'm assuming it's sealed shut so the pages don't flap open. Mass is 450g.

I want to understand how quickly it would fall if dropped straight down from 10km altitude. I've used a value for drag coefficient for a flat plate perpendicular to the air flow that I got from NASA (1.28) but I'm guessing that a falling book would spin round, slowing its fall, so this value is probably not right - is this likely?

So I'm wondering if it's possible to estimate the drag coefficient to any degree of accuracy. I don't have access to a wind tunnel and I'd rather not drop it off a tower as an experiment. :)

• Umm.. if the book tumbles and spends part of its time falling with say the spine pointing straight down, won't the average speed be much faster than suggested by your description? Nov 1 '19 at 16:32
• I don't get the downvotes, this is less ridiculous than other questions on the site, and makes for an ok though experiment. Nov 2 '19 at 12:42
• Brings to mind a new possible question :"what is the purpose of a book"-- similar to "what is the purpose of a propeller" Nov 3 '19 at 0:37
• Try physics.se for relevant answer as well. Nov 3 '19 at 23:03
• @AEheresupportsMonica and others: this question is being discussed here: aviation.meta.stackexchange.com/q/3978/1467
– Federico
Nov 25 '19 at 9:40

You have a very thin book. The answer depends on how you initially drop the book.

# 1. If you drop it flat about its front

It will very closely approximate a flat plate; in this case, the pressure drag will overwhelm the skin friction drag. Hoerner, Fluid Dynamic Drag has some empirical data on the drag coefficient of a bluff body (near 2.0):

To retrieve the 3D coefficient, dimensionalize it with the frontal area.

# 2. If you drop it broadside

The skin friction drag would dominate. You can approximate it via the flat plate friction drag. For a single side, the drag coefficient looks like (from Anderson, Fundamentals of Aerodynamics):

# 3. If it tumbles

Your book may also tumble at some point due to random perturbation about its major principal axis. This changes the drag even further; but once again, Horner has some empirical correction formula.

The book's pages won't flap open, but it will bend unpredictably, because its density is so close to that of paper (vs. hardboard) that it must be a paperback. So you can't assume that it's a flat plate. Even if you fling it like a frisbee so centrifugal force holds it flat like LightSail 2, during a 10 km drop, air friction will overcome that and let it tumble chaotically.

I know of no drag measurements for variously curved thin plates at arbitrary angles of attack. You might need to drop half-ounce paperbacks late at night in a tall building lobby to estimate lower and upper bounds for CD.

• Thanks - it is in fact a hardback with 2mm board. Nov 6 '19 at 13:58
• Huh. Densities for hardboard that I found were a good deal less than for paper, but if these numbers come from your actual measurements, then you'd know! Nov 6 '19 at 15:03