Engineering Professor Calculates How Fast The Eagle In The USPS Logo is Going

Random questions that pop in your head while you shower are not necessarily things that should be definitely answered; however, they tend to be great one-liners. Did you know that a single strand of hair can hold up to 3 ounces of weight and this means the typical person’s full head of hair can support up to 12 tons?

Or did you know that the eagle in the USPS logo is moving with about Mach 4.9? Well, thanks to a mechanical engineering teacher, now you know.

Teaching my compressible flow course online is giving me the opportunity to answer some long-standing questions, such as: Just how fast *is* that eagle in the @USPS logo going? Turns out, about Mach 4.9... pic.twitter.com/bICR7BUItb

— Andrew Higgins (@A_J_Higgins) April 3, 2020

Higgins calculated the speed of the eagle by looking at the shock wave it causes by moving so fast. 

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Here is the thing: if something is moving fast enough, one picture of it can tell you a lot about the speed in which it is moving, thanks to the Mach number at which an aircraft is flying can be calculated by.

In this case, the aircraft we are talking about is the all-American eagle that has adorned the logo for the United States Postal Service. 

"Sonic" Eagle

In 1970, the "standing" eagle was adopted as the Postal Service's official seal.

in 1993, the eagle decided to soar. The current "sonic" eagle in question was introduced as the new logo of the USPS to "capture the ethos of a modern era which continues today."

When looked closely, you can see the shock wave the eagle is causing by moving so quickly. Andrew Higgins calculated its exact speed by using some simple formulas.

How to calculate?

As NASA explains, when an object moves through a gas, the gas molecules are deflected around the object. When the object nears or moves beyond the speed of sound, which is about 700 mph or 330 m/s on Earth at sea level, small disturbances in the flow of gas are transmitted to other locations with constant entropy as sound waves.

Small disturbances are transmitted downstream within a cone for supersonic and hypersonic flows, which are demonstrated by the blue lines in the figure below.

This line is called a "Mach line", and if you find the angle difference of the Mach line and the direction of travel, you get the "Mach angle" (α or µ).

It is a relatively simple formula: You determine the speed by using the Mach angle, the speed of sound (a), and an object's velocity (v): sin(µ) = a / v. As you can see, the ratio of v to a is the Mach number (M).

You can see the detailed numbers and formula done by Andrew Higgins down below. 

The exact number is Mach 4.9312753949380048. That's pretty fast!

Of course, Twitter folk wouldn't leave it there, and for good reason too. Two other Twitter users calculated that the eagle is traveling towards us at around 60,000 km/s as per their assumptions by taking the blue shifting in the radial direction in account. 

Additional: The blue-shifted eagle is travelling towards us at around 60,000km/s as per my assumptions and @CosmicRami’s calculations. https://t.co/ifpbtQTtZe

— Stilgherrian (@stilgherrian) April 4, 2020

Mathematics community seems to be thriving thanks to the eagle that many people didn't know was an eagle for a long time. 

its an EAGLE?!

— horsegirl energy (@MissusCharizard) April 4, 2020

There is something to learn for anybody!