Mathematical Proof The Eagle In The USPS Logo Is FAST!

The logo for the United States Postal Service is a mean-looking eagle. But a true fluid dynamics geek might look at it and realize that eagle is moving so fast it’s causing a shock wave. But just how fast is it moving? [Andrew Higgins] asked and answered this question, posting his analysis of the logo’s supersonic travel. He claims it’s Mach 4.9, but, how do we know? Science!

It turns out if something is going fast enough, you can tell just how fast with a simple picture! We’ve all seen pictures of jets breaking the sound barrier, this gives us information about the jet’s speed.

Mach Lines

How does it work?

Think about it like this: sound moves at roughly 330 m/s on Earth at sea level. If an object moves through air at that velocity, the air disturbances are transmitted as sound waves. If it’s moving faster than sound, those waves get distributed downstream, behind the moving object. The distance of these waves behind the moving object is dependent on the object’s speed.

This creates a line of these interactions known as a “Mach line.” Find the angle difference of the Mach line and the direction of travel and you have the “Mach angle” (denoted by α or µ).

There is a simple formula for determining the speed of an object using the Mach angle, the speed of sound (a), and an object’s velocity (v): sin(µ) = a / v.  The ratio of to a is known as the Mach number, (M). If an object is going exactly the speed of sound, it’s going Mach 1 (because v = a).

Since Mach number (M) is v / a, we can plug it into the formula from above as 1 / M and use [Andrew]’s calculation shown in the image at the top of the article for a Mach angle (µ) of ~11.7°:

\bf \sin ( \mu ) = \frac{1}{M} \\ \\ M = \frac{1}{\sin(\mu)} \\ \\ M = \frac{1}{\sin(11.7)} \\ \\ M = \frac{1}{0.202787295357} \\ \\ M = 4.9312753949380048

The real question is, did the USPS chose Mach 4.93 as a hint to some secret government postal project? Or, was it simply a 1993 logo designer’s attempt to “capture the ethos of a modern era which continues today”?

Hacking The United States Postal Service (Kinda)

The United States Postal Service (USPS) is fixture of American life with its roots going back to colonial times. It operates the largest civilian vehicle fleet in the world, delivering about half a billion pieces of mail a day. As with any system of that size it’s always interesting to peek and poke at to see how it works. Unfortunately, it’s not as fun to hack as the phone system once was, but that didn’t stop some hackers pranksters from giving it a go.

So how do you “hack” the mail? Simple, by testing its own rules. The folks at [Improbable Research] did just that and some of the results were interesting enough that we thought we would share them with you. They started with testing valuable items to see how honest USPS employees would be. First they attached a $20 bill to a post card. Yep, it showed up just 4 days later, and the money was still there. So they decided to see if sentimental items, that normally would be refused by the postal service, might skate through.  They were able to send both an un-boxed single rose, and a human tooth (in a clear plastic box) without issue. Both arrived just fine, despite the rule that human remains are not allowed to be shipped via USPS.  We’ll let you read some of the other items they tried.

So the next time you’re in Hawaii, forget about sending that generic, boring post card back home. Instead, slap some stamps on a coconut to let your friends know exactly how much fun you’re having.

With that said, we wouldn’t be doing our job looking out for our readers if we didn’t mention that before you try anything too outlandish, you can be fined for abuse of the postal system, even as a recipient. There was a fair amount of fallout when those guys sent a camera through the mail. Have fun, but not at someone else’s expense.