Calibration Procedure

  The calibration of the University of North Dakota's Citation Aircraft wind system involves four basic components.

    1.)  Determining the offset, if any, between the aircraft heading angle and track angle.
    2.)  Determining the alpha angle calibration coefficients.
    3.)  Determining the beta angle calibration coefficients.
    4.)  Determining the pitot pressure (wind) calibration coefficients.

  Aircraft position information for the calibration procedure can be based on either the real time 25 Hz applanix data file or on the 25 Hz post processed (SBET file) applanix data.  All calibration software module's can use either the real time or post processed input data file.  Currently there are some inconsistencies with the post processed applanix data that is under investigation; hence, the examples given below are based on the real time applanix data file.

  The wind calibration procedure described below involves first determining the heading angle offset and then iterating on the alpha, beta, and pitot pressure calibration steps until the calibration coefficients converge.  The calibration coefficients given below are the result of five iterations of the alpha, beta, and pitot pressure calibration steps.

Heading Offset:  Real Time 25 Hz Data
 
Determining the offset between the aircraft heading angle and track angle can be done by looking at the difference between the heading and track angle during aircraft taxies on the runway.  Runway taxies are typically done at the end of a reverse track calibration flight.  A cross wind on the aircraft can result in an offset between the heading and track angles; therefore, it is important to do aircraft taxies in both directions along the runway.  
  Real-time heading offset on July 11, 2003 (Segment 1)
Figure 1:  The aircraft's heading (black line) and track angle (blue line) versus time for taxies segment 1 on July 11, 2003 using the real time data files.


   Real-time heading offset on July 11, 2003 (Segment 2)
Figure 2:  The aircraft's heading (black line) and track angle (blue line) versus time for taxies segment 2 on July 11, 2003 using the real time data files.


Real-time heading offset on July 11, 2003 (Segment 3)
 
Figure 3:  The aircraft's heading (black line) and track angle (blue line) versus time for taxies segment 3 on July 11, 2003 using the real time data files.


Segment Number
 Heading Angle
 Track Angle
 Heading Angle - Track Angle
1
  180.07111
 180.01495
 0.056157858
2
 -0.08130
 0.016070
 -0.09737
3
 180.05413
 179.99825
 0.055882353

Table 1:  Summary of the time segments for the taxies on July 11, 2003 using the real time data files.


  The heading angle offset is calculated as follows.  The heading angle minus track angle value is averaged for segment 1 and 3 and subtract from the magnitude of segment 2 and then divided by 2.  This gives a heading angle offset of 0.0206764 degrees.  Using 0.0206764 degrees as the heading angle adjustment, the mean difference between the heading and track angle for segment 1 would be 0.0768 degrees and for segment 2 it would be -0.0767 degrees.   They are equal but have different signs.  The reason that both values are not equal to zero is due to a cross wind on the aircraft that has a small affect even on the runway.

  Since the taxies segment plots (Figures 1-3) do not show any systematic bias in the heading angle relative to the track angle, we will assume the calculated heading angle offset is due to noise in the measurement and will take the heading offset to be 0.0 degrees.  Any change in the heading offset values needs to be updated in the "citation_constants.pro" software routine before proceeding with the rest of the calibration steps.

Alpha Angle Calibration:  Real Time 25 Hz Data

  The alpha angle calibration assumes that the vertical wind is zero and will give incorrect results if the true atmospheric vertical wind is not zero.  Typically, the time period selected for the alpha angle calibration is during "porpus"  maneuvers when the pitch angle is changing.  A time period where the pitch angle changes due to aircraft speed changes can also be used for the alpha angle calibration.

  The following alpha angle calibration example was taken over a time segment where the aircraft speed was varied resulting in changes in the pitch angle (Figure 4).  For this example, the alpha calibration slope was 0.0777 with an offset of 5.2588.  The vertical wind speed shows very little change during the time segment (Figure 5) which indicates a good alpha angle calibration.

Pitch Angle During Alpha Angle Calibration
Figure 4:  The aircraft's pitch angle versus time for the time period of the alpha angle calibration on July 11, 2003.  Note that this was done at a constant altitude of approximately 9000 meters.


Vertical Winds during the Alpha Calibration Segment
Figure 5:  The vertical wind versus time for the time period of the alpha angle calibration on July 11, 2003.


Beta Angle Calibration:  Real Time 25 Hz Data

  The beta angle calibration assumes that the X and Y wind components do not change as the sideslip angle changes.  For the time segment illustrated in Figures 6 and 7, the beta calibration slope was 0.0423 with an offset of 0.5195.

Beta Angle Calibration X Wind component (July 11, 2003)
Figure 6:  The X (East) component of the wind versus time for the time period of the beta angle calibration on July 11, 2003.  The black line is for no beta angle correction; where as, the blue line includes a beta angle correction in wind calculation.

Beta Angle Calibration Y Wind component (July 11, 2003)
Figure 7:  The Y (North) component of the wind versus time for the time period of the beta angle calibration on July 11, 2003.  The black line is for no beta angle correction; where as, the blue line includes a beta angle correction in wind calculation.

 
Pitot Pressure Calibration:   Real Time 25 Hz Data

  The calibration of the aircraft's nose pitot pressure is done by flying reverse track legs at three different altitudes and at two or three different aircraft speeds per altitude.  For each reverse track pair (a segment in one direction and a segment in the opposite direction), the horizontal wind is assumed to be constant.  The July 11, 2003 reverse track flight gives a calibration slope of 17.2344 with an offset of -3.6440 (Figure 8).

reverse track calibration (July 11, 2003)
Figure 8:  The nose pitot pressure versus the measured pressure transducer voltage for the July 11, 2003 reverse track flight.  The least squares linear fix to the data points gives a slope of 17.2344 and an offset of -3.6440.


Please contact David Delene at delene@aero.und.edu with your questions or comments.

Citation Aircraft Wind Calculation Page