Ask A Scientist© Environmental Earth Science Archive

 >   name        Lori
 >   status      student
 >   age         40s

 >   Question -  What is the earth's rotational speed at different points on
 > the globe?
 >What formula can I use to determine it?
 >
 >I've tried the one submitted by Grayce,which is C=2 x Pi x R x Cos((Pi x
 >L)/180), and my calculations for latitude of 34 comes out at 1037.4553mph
 >not the 860mph as on her example. Am I doing something wrong? I tried
 >using the same calculation for the equator and that result is 1037.51mph.

To answer the question you are asking is trivially easy.  The question I
think you meant to ask is a little more involved, but not much.

The earth's rotational speed is one revolution per day.  It doesn't matter
where on earth you stand, that is the rotational velocity.  I believe that
you mean to ask the TANGENTIAL velocity of any point on the earth due to the
earth's rotation.  To compute this approximately, you need to know two
things:  the latitude of the point on the earth's surface, and the
circumference of the earth.  For ease of calculation, we will assume that
the earth is a perfect sphere.  This is a pretty good approximation;  the
surface IS extremely flat, and the oblateness at the equator is only a
factor of about 0.3%.

I came up with a formula similar to the one you cite.  One possible source
of error in using this formula is that it converts the degrees of latitude
into RADIANS, which you need to do if you're calculating cosines in a
spreeadsheet.  Some calculators default to calculating trigonometric
functions of angles measured in degrees.  If you are calculating the cosine
of the angle in degrees, you don't need the factor of pi/180 used in the
formula.  Be aware that the formula as written gives the velocity in
distance per DAY, and you need to explicitly multiply by day/24h to find the
value in distance per hour. Doing that, I get 860.16 mi/h at 34 degrees
latitude.

In doing this, I convert the latitude of 34 degrees to 0.593 radians.  The
cosine of an angle of 0.593 radians is 0.829; multiply this by your
equatorial velocity number and you'll get 860 mph.  If you make the mistake
of calculating the cosine of 0.593 DEGREES, you'll find that it is 0.999946;
multiplying this by the equatorial velocity gives 1037.48 mph.  I'll bet
that's what you did.

So, the short answer to your question is either that you shouldn't convert
to radians when you use the formula, or that you should calculate the cosine
from the latitude in radians.

Richard E. Barrans Jr., Ph.D.
Assistant Director, PG Research Foundation
Darien, IL USA
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