Sonic Boom Lines

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Original publication date: February 1992 (But it should have been done in April. :-)
Heurikon Technical Hallucinations

Sonic Boom Lines
by Jeffrey Mattox (Copyright 1992, 2009)

On maps and globes of the Earth, the locations of the equator, the Arctic and Antarctic circles, and the tropics of Cancer and Capricorn are clearly shown.  These circles indicate certain characteristics of the apparent journey that the sun makes over the Earth’s surface each year.

There are two other conjured circles on the Earth’s surface that few people know about.  They are called “sonic boom lines,” and they indicate the latitudes where the Earth’s surface velocity is equal to the speed of sound.

Breaking the Barriers of Credulity

You know that an aircraft produces a boom whenever it accelerates above the speed of sound (approximately 760 miles per hour at 57°F).  The window-shattering sonic boom that occurs when the aircraft “breaks the sound barrier” is caused by an atmospheric shock wave that extends from the aircraft to the ground.  We rarely hear sonic booms today because FAA regulations prohibit all aircraft from flying at supersonic speeds over inhabited areas.

However, despite FAA and public desires, the rotation of the Earth causes many parts of the surface to spin at velocities that exceed the speed of sound.  Since the circumference of the Earth is roughly 24,000 miles, the surface speed at the equator due to the rotation of the Earth is about 1,000 miles per hour (well above the speed of sound).

mathUsing simple trigonometry, it is easy to compute the latitude where the Earth’s surface is moving at precisely the speed of sound (see figure).  At sea level and zero degrees Celsius, that latitude is 44 degrees, 21 minutes, and a circle drawn around the Earth at that latitude is a sonic boom line.  Of course, there are two such lines; one in the Northern Hemisphere, the other in the Southern Hemisphere.

Unlike the equator and tropics, the exact locations of the sonic boom lines vary according to local altitude and air temperature.  For example, using Heurikon’s altitude (978 feet above sea level) and average atmospheric conditions (11.83°C), the sonic boom line moves to 43° 04' 55" north latitude.  Although these effects are very small, they are enough to make the exact locations of the boom lines laborious to determine and in continuous flux.  That is why cartographers refuse to put these lines on their maps.

Cone Heads in Our Nether Regions

Technically, the sonic boom lines are the intersections of an imaginary cone with the Earth’s surface.  That cone (the surface of which represents all points that are rotating at the speed of sound) extends parallel to the Earth’s poles and pierces the Earth at the two sonic boom latitudes.  The supersonic atmospheric regions that are directly above locations on the Earth’s surface that are themselves outside (but near to) a sonic boom line are called, curiously, the “nether regions.”  Those small areas dissipate the sonic boom shock waves into outer space, thus preventing the shock waves from causing a continuous, annoying boom to listeners on the surface.

The Earth’s motion around the sun and the sun’s motion through the cosmos do not affect the sonic boom phenomenon nor produce one of their own.  This is because sound waves cannot travel through the vacuum of outer space.

lobby Heurikon Hyperbole

If you examine a map of Wisconsin, you will see that the northern sonic boom line comes near to the Madison area.  In fact, the altitude- and temperature-adjusted line (at 43° 04' 55") goes right though the center of our building, piercing the flagpoles, front doors, central corridor, rear doors — even the picnic table.  The wide maroon stripe in the middle of our lobby carpet lies directly over the boom line!

Is it merely a coincidence that our building straddles the northern sonic boom line, and should we be concerned?  Dunno.  Go figure.