True Airspeed Calculator
The True Airspeed Calculator will allow a pilot to accurately determine
the true airspeed of an aircraft using a GPS or loran unit. The airborne
procedure requires approximately 10-15 minutes of stabilized flight to
collect groundspeeds in three separate directions, and the ground procedure
requires only a few minutes to type those groundspeeds into the calculator.
Instructions
- In the aircraft at the desired altitude, set the aircraft power to
the desired setting (e.g., 75 percent). Configure the GPS or loran
unit to display groundspeed.
- Turn to one of the cardinal headings (north, east, south, or west)
and allow the aircraft to stabilize at its trimmed airspeed. Record the
cardinal heading and the groundspeed readout from the GPS or loran.
- Turn to another cardinal heading and allow the aircraft speed to stabilize.
The indicated airspeed displayed on the aircraft's airspeed indicator
(KIAS) should be identical to the indicated airspeed
in the previous step. If it is not, you may be in an updraft or downdraft
and may need to allow the aircraft more time to stabilize at its trimmed
airspeed. Record the cardinal heading and the groundspeed readout.
- Turn to a third cardinal heading and allow the aircraft speed to stabilize.
Again, the indicated airspeed should be identical to the previous airspeeds.
Record the cardinal heading and the groundspeed readout.
- On the ground, enter the recorded groundspeeds into the input boxes
in the left half of the True Airspeed Calcualtor. Enter the groundspeed recorded
while heading north in the top box, the groundspeed recorded while heading
west in the left box, etc. As you enter the groundspeeds in the input boxes
on the left, the groundtrack display on the right will show lines representing
the legs of the airborne test. When you have finished entering the three
groundspeeds, the groundtrack display will contain a no-wind representation
of your groundtrack. For example, if you first flew north, then east, then
south, the line displayed would go up first, then right, then back down.
(If any of the directions are opposite to the previous direction, its line
will draw on top of the line for the previous direction, so it will look
as if only two lines have been drawn.)
- If the groundspeeds are not entered in the same order as the legs were
flown in the air, the groundtrack representation will not be accurate.
To fix this problem, click the mouse in the input box where the first-flown
groundspeed is entered and then press and release the control key (Ctrl)
on the keyboard. Repeat the same procedure for the input box where the
second-flow groundspeed is entered, then the same for the last-flown groundspeed.
At this point the groundtrack display should contain an accurate no-wind
representation of your groundtrack. (On some browsers, pressing the control
key may not be necessary; clicking the mouse in the input box may be enough
to change the order in which the legs are displayed.)
- The calculator determines the wind and the aircraft's true airspeed by
making an initial guess and then continuing to make better guesses until
the solution is found. If you want the calculator to display only the final
solution, uncheck the "Show Iterations" checkbox. Leaving the
checkbox checked will cause the calculator to display each guess as it is made
so that the groundtrack display becomes an animation starting with the
calculator's initial guess and ending with the final solution. (Since the calculator
makes a new guess every tenth of a second, there is not a significant performance
penalty to leaving the checkbox checked so the calculator's progress can be
observed.)
- Click the "Compute" button with the mouse. This will cause
the calculator to begin the guessing process and eventually determine the true
wind and aircraft airspeed, usually within seconds. The groundtrack display
will now contain a wind-corrected representation of your groundtrack, and
the values for true airspeed and the wind will be displayed below the groundtrack
display.
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Background
In the February 1995 issue of Kitplanes magazine, David Fox presented
a method for determining the true airspeed of an aircraft using a loran
or GPS unit and a pocket calculator. David explained that the classical
way of determining groundspeed (flying a measured course in opposite directions)
could result in errors if a crosswind exists. The new method presented
by David involved flying three groundtracks perpendicular to each other,
recording the groundspeed on each track. As an example, the first track
(not heading) could be north, the second east, and the third south. The
first groundspeed is recorded as V1, the second (perpendiclar
to the first) as V2, and the third (parallel to the first and
perpendicular to the second) as V3. The true airspeed of the
aircraft is given by the formula:
- VTAS = SQRT( V12 + V22
+ V32 + V12 * V32
/ V22 ) / 2
The wind components in the direction of the first and second tracks
(north and east in our example) are given by the formulae:
- W1 = ( V1 - V3 ) / 2
- W2 = ( V2 - V1 * V3
/ V2 ) / 2
Although the True Airspeed Calculator uses the same basic principles as
David's method, there are some differences. David's method requires that
specific tracks be flown, the Calculator requires that specific
headings
be flown. Because of this, the underlying equations are more complex and
not as easily solved. Although the equations can eventually be reduced
to a quadratic equation which can be solved
exactly, it is more difficult
and error-prone. The Calculator does not attempt to reduce or solve the equations,
but uses iteration to improve on an initial guess until the solution is
found. While solving the equations would be quicker and more exact, iteration
was chosen because:
- its speed and accuracy are sufficient for this type of application,
and
- it provides a series of ever-improving solutions which can be displayed
on the screen for the user's enjoyment.
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