True Airspeed Calculator

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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
• Background
• Source Code

Instructions

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.)
6. 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.)
7. 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:

• V_TAS = 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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For comments or questions about this web site or applets, contact the webmaster. For the address of the webmaster, look at the first few comments of a Java file. To obtain all Java files, download the True Airspeed Calculator ZIP file. The True Airspeed Calculator ZIP file is available on the Distribution Policy page. Copyright 2001 REA Computing, Inc.