Where does the 3 for 1 rule of thumb come from?  When I first read the article in the
January The Post-Flight,  I was startled by the statement "A 3 degree glide slope
means that you are descending at a rate of 3 for one, meaning that for every foot
traveled down, you have advanced 3 feet."  It sounded way too steep.  So, I dusted
off my old high school trigonometry and did some calculations to see if I could derive
the 3 for 1 rule of thumb.

 The math is a simple right triangle problem.  The hypotenuse of the triangle is the flight
path, the opposite side of the glide slope angle is the altitude, and the adjacent side of
the glide slope angle is the ground distance.  The ratio of  opposite/adjacent is the
tangent of the angle.  A one foot drop in altitude for every three feet travelled along
the ground results in a tangent of 1/3 or 0.33333333, which corresponds to an angle
of 18.43 degrees.  This is more than six times the normal glide slope angle of 3 degrees!

 The tangent for 3 degrees is 0.052407779.  To descend 1,000 feet at this angle, one
would have to travel 19,081 feet along the ground.  This would be a hard number to
remember and use without the aid of a calculator, but it does provide the basis of the
3 to 1 rule of thumb.  If one were to travel 18,000 feet for every 1,000 foot descent,
and since 18,000 feet equals 3 nautical miles, the result is a 3 to 1 rule of thumb:  For
every 3 nautical miles of ground distance travelled, we will descend 1,000 feet on the
glide slope!  (The 3 to 1 rule of thumb is exact for a glide slope of 3.17983 degrees.)

 The rule of thumb to check glide path quality derives from the same calculations used
to derive the 3 for 1 descent rule of thumb.  Recall that a 3 degree glide slope results
in a ground travel of 19,081 feet to descend 1,000 feet.  Rounding 19,081 to 20,000
results in a 20 to 1 ratio, or  a 1 foot descent for every 20 feet travelled . The distance
in feet an aircraft will travel in one minute is 100 times the ground speed in knots, as
derived from the following calculation:

 feet/minute = (nautical miles/hour * 6000 feet/nautical mile) / 60 minutes/hour

To maintain the 20 to 1 ratio, our descent must equal the forward distance travelled in
feet/minute divided by 20, and, since the forward distance travelled in feet/minute is 100
times the ground speed in knots, we end up with (100 * ground speed) / 20 or ground
speed * 5.  Since, in calm wind, the airspeed on a 3 degree glide slope is almost identical
to our ground speed (to travel 19,081 feet along the ground, we travel 19,107 feet along
the glide slope), we derive our rule of thumb:   Basic descent rate in feet/minute equals 5
times the airspeed in knots, which, if you prefer, can be expressed as ½ the airspeed
times 10.