Flying Facts About Turbulence and Inertia

Turbulent-Clouds

Going into the Spring and Summer flying season, turbulence is a common concern for pilots of all types of aircraft. Luckily for us, there is a great system in place to alert you about the weather encountered by other pilots through PIREPS. The bad news is that each airplane will react differently to turbulence, and pilots have to keep that in mind when interpreting these reports.

Consider the following case. A Cessna 152 pilot receives a PIREP about light turbulence ahead reported by a B-747. Will the Cessna experience more or less turbulence and why?

You probably guessed that the Cessna pilot had better buckle up. Light turbulence to a big-old Boeing 747 might just be a bad deal for a Cessna 152. Why is that? Well, it all has to do with inertia.

Inertia is defined as “a property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless acted upon by an external force”. You can think of inertia as a resistance to change in motion.

Without getting too mathematical, Newton’s second law (= ma) deals with inertia and reveals that  a heavier object (the 747) has more inertia than a lighter object (the Cessna). In English: a heavy plane is less inclined to be bumped around than a light airplane. OK, this isn’t the most shocking revelation, but let’s imagine our Cessna pilot keeps trudging on. How bad can it get? Let’s do some sloppy bar-napkin calculations to get an idea.

I’m going to assume that the 747 is buffeting along with a quarter G of strain at worst, so let’s say the wing is experiencing momentary accelerations of a = 1.7 m/s2. We know that the 747-400′s max gross landing weight MGLW is a whopping 630,000 lbs, or m = 285,762 kg. So the entire airplane is experiencing a net force of F = 485,795 Newtons. Taking into account the 747-400′s wing area of A = 5825 square feet, we can see that the turbulence is producing F / A = 83 Newtons / sq. foot of force on the wing.

What’s this look like for the Cessna? Well, a C-152 weighs in at 1670 lbs, or m = 757 kg and has a wing area of 160 sq. feet. 83 Newtons / sq. foot which is a force of F = 13,280 Newtons. Some algebra reveals that the Cessna 152′s wing is bouncing in turbulence with accelerations of a = F/m = 17 m/s2 which comes out to about 1.7 G’s, much worse!

Now there are a lot of other aerodynamics factors that I am not taking into account with respect to wing and aircraft design, and this is a pretty quick “hack,” so the numbers aren’t going to be dead-on accurate. If you work in engineering or physics, I invite you to present a more complete picture in the comments below. I look forward to seeing it!

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About the author
Pat Flannigan is a professional pilot and aviation blogger. He has been flying for fifteen years and is currently working as an airline pilot in the United States.

3 Replies to Flying Facts About Turbulence and Inertia

  1. JetAviator7 says:

    Patrick:

    Where have you been, and where did you learn all this mathematics?

    All you really need to know is that get to close behind a Boeing 747 in anything smaller than a C5A and you are in for the thrill of your life, newtons or not!

    But of course here we are talking about “wake turbulence” which has little to do with atmospheric turbulence, something we DO need to think about with the onset of summer and the coming thunder storms.

  2. Hey there! I’ve been a bit behind I know. This one’s the gee-whiz obvious stuff. I’ve got a follow-up coming up that might sound a bit surprising.

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