CALCULATE
AIRSPEED FROM GPS
This note works out a formula to
calculate a plane’s airspeed from GPS readings. The “wind triangle” diagram
shows the relationship between Airvelocity, Windvelocity, and Groundvelocity.
The term “velocity” is used because each side of the triangle has direction as
well as length. Thus “airspeed” is the length of the “airvelocity” side, etc.
Using vector algebra, we can write:
If the plane flies first in one
direction & then in another direction we get two separate wind triangles:
Since
we can subtract the
first equation from the second to obtain:
Square
both sides of the equation to get:
In
squaring the equation we used a type of vector multiplication called the
“scalar product”. The symbol 
denotes the angle between
the vectors 
and 
; while 
and 
denote the lengths of the two vectors. The symbols 
, 
, and
are
defined similarly. Since the plane’s airspeed is the same no matter which
direction it’s going, 
and
are
really just the airspeed “A”:
The
last two steps were accomplished by algebraic simplification and the use of a
trigonometric identity.
This
equation can now be solved for the airspeed:
To
evaluate the equation use the following values recorded in flight:
·
The GPS groundspeeds,
and 
, for two different headings .
·
The angle 
of heading change (from compass).
·
The angle 
of groundtrack change
(from GPS).
The
equation is easier to evaluate if you decide to take data with 
and 
in exactly opposite directions. Then, 
and:
On a recent flight, the following data was recorded for
N3631K at an indicated altitude of 6700ft:
(1) (2)
Heading (deg) 335 155
Track (deg) 333 152
Groundspeed
(knt) 105 133
Thus
. So we can use the last formula instead of the second last
formula. The formula is to be evaluated with:
The
result is: A=119 knots
An
Excel SPREADSHEET has been programmed to do the
calculations.