Summary of methods to determine true air speed (to calibrate ASI)
Peter Chapman
-- AS PART OF THE PROCESS TO CALIBRATE THE AIR SPEED INDICATOR
Pilots of homebuilt aircraft may be interested in determining the
errors in their indicated air speeds. Speed over the ground can be
determined with the aid of map & stopwatch, or a GPS. Compensating for
wind converts ground speed to true air speed, which in turn is
converted using density altitude to determine what the IAS should be.
A major difficulty is trying to compensate for wind, as perfect
no-wind conditions are hard to find, especially if one isn't lifting
off at the crack of dawn. Over the years I heard of various
wind-compensation methods, not all of which sounded like they would be
mathematically accurate. This write-up is the result of compiling and
comparing the various methods that I've heard of, to help decide how
to calibrate the airspeed indicator on the homebuilt I co-own. This
document is not exhaustive, but should give the reader a useful
overview of some of the methods that have been tried.
I have no insight into the world of professional test flying, as my
own qualifications or lack of same are: Private pilot (200hrs),
skydiver, paraglider pilot, co-owner of a Zenair Zodiac homebuilt,
degree in aeronautical engineering (but haven't been working in the
field for years).
GENERAL TECHNIQUES
Results can naturally be more accurate when more data points can be
taken, and the more accurately the tests can be flown -- maintaining
constant airspeed, heading (or ground track, depending on the test),
altitude, and engine power. The job becomes more difficult if there's
turbulence or rising and falling air. Holding all values constant
becomes mathematically impossible. If there is thermal activity, it
may be better to focus on holding a constant airspeed, as chasing
altitude in a thermal would require putting the nose down and
increasing speed.
Some test methods require tracks to be flown, while others require
headings. The aircraft's equipment affects which is more convenient. A
directional gyro helps to fly accurate headings, although it may
precess in the time it takes to fly a few test legs. A GPS will
provide accurate track information. Whether it is more difficult to
maintain, on average, a steady ground track or a heading when there is
turbulence and varying winds is another issue, which my personal
experience cannot answer, as my new GPS hasn't yet been used in an
aircraft.
A test run is flown for each indicated air speed for which a
correction is desired. Indicated air speed errors result from errors
in measuring pitot and static pressure, and internal instrument
errors. The methods described here will account for the combined
errors from all these sources. The instrument errors can also be
determined separately by ground tests: A manometer of clear plastic
tubing is made, with a difference in water (or other fluid) level
corresponding to a particular pressure, which corresponds to an air
speed that should be shown. (One source on manometer testing of ASI's:
Kitplanes July '89, "How to Calibrate Your ASI" by Jim Weir. Also
found on his web site at:
http://www.rst-engr.com/
A more detailed source of calibration info is at an RV aircraft
builders' site:
http://members.xoom.com/_XMCM/kevinhorton/ssec.html
)
FIVE METHODS OF COMPENSATING FOR WINDS
#1) 'OPPOSITE HEADING RUNS' (OR 'OPPOSITE TRACK RUNS')
This is an old and often mentioned method. True air speed is
calculated by averaging the ground speed from runs along ground tracks
or headings 180 degrees apart. Sources have suggested using a 3 to 5
mile course, measured accurately on a topographic map. Nowadays two
GPS waypoints could be used. Ground speed is calculated by time over
the course divided by distance.
A fair bit of detail on this method follows, so it may be worth
skipping to method #2 if attempting to quickly review the different
methods available.
Typically flight along opposite headings -- not ground tracks -- is
called for, which means that the flight is actually between two
parallel lines a specified distance apart, rather than between two
points that same distance apart. The airplane is allowed to drift with
any crosswind component. The FAA's Amateur-Built Aircraft Flight
Testing Handbook (AC 90-89) may favour flying a heading rather than a
ground course, but does not make the distinction clear.
Sources often don't distinguish between three ways to carry out this
method of runs on opposite headings:
1a) Fly the track (between the start and finish points). Use
GPS ground speed. Or use time divided by course distance.
1b) Fly the heading (perpendicular to parallel start and
finish lines). Use GPS ground speed.
1c) Fly the heading (perpendicular to parallel start and
finish lines). Use time divided by distance between start and finish
line on the chosen heading. Or determine the component of GPS ground
speed along the heading direction.
For a pilot, flying a ground track (#1a) may be intuitively wrong when
attempting to determine true air speed. The plane is clearly losing
out on some speed towards the target point by having to correct for
drift. But flying a constant heading is no better if the pilot simply
uses GPS ground speed for calculations (#1b). By flying a heading
where there is a crosswind, the ground speed will increase by a
similar percentage as the ground speed would have decreased if flying
a constant track. Even when averaging runs in opposite directions, one
method will slightly over-estimate true air speed from ground speed,
and the other will slightly under-estimate it. For a 100 mph aircraft
in a 10 mph crosswind, the errors are about 1/2 %.
The most accurate version is #1c: The key is to measure the ground
speed perpendicular to the start and finish lines, that is along the
chosen flight heading. This component of the ground speed is
unaffected by any crosswind component. Only in this way does flying
headings become superior to flying a ground track.
If the wind is a pure crosswind, then its effect is entirely removed
by method #1c. If there is a pure head or tailwind, its effect is
entirely removed by averaging the speeds from runs in opposite
directions. If, however, there is a combination of crosswind and head
or tailwind, the method provides a very close approximation to the
true air speed. For the 100 mph aircraft in a combined 10 mph
crosswind and 10 mph tail or headwind (i.e., 14.1 mph on a heading 45
degrees from the course direction), the error in estimating true air
speed is a negligible 0.05 %.
If doing method #1c the old fashioned way, the stopwatch is clicked
when the start and finish lines are crossed. With a GPS, some geometry
work would be necessary after the flight, to determine what component
of the speed along the track actually flown is in the direction of the
chosen heading. Airspeed and track information for each leg can be
gathered at different levels of detail. A pilot could simply jot down
the track direction and ground speed from time to time when flying the
leg, averaging them later. Or data could come from the entire leg
flown. The test run would be determined by flying a heading, marking a
start and a finish waypoint with the GPS some minutes apart, while
recording times for these events by stopwatch. If the GPS has a moving
map then it likely has a track log feature that records a steady
stream of time and position data. If downloaded to a computer, mapping
software can be used to determine an average track and speed.
Sources that describe using time over a measured course don't always
note how easily errors can occur. Even over a 5 mile course, a 1
second error in timing becomes 1/2 mph error at 100 mph, or 2.2 mph at
200 mph. It becomes important to mark the time accurately, which is
more an issue of determining when the start and finishing line have
actually been crossed, than just how quickly one can punch the button
on the stopwatch. Without careful attention, it may look as if a point
or line on the ground is being passed, when it is still only 85
degrees below and not 90 degrees. The greater the height, the more
difficult it is to be accurate.
No matter which version of the opposite heading runs method is used,
accuracy is improved if the runs can be flown into and out of the
wind, with as little crosswind as possible.
By using the version of the method that uses the component of ground
speed along the chosen course heading (#1c), the calculations are
nearly mathematically correct for determining true air speed. Other
versions of the method are less accurate for most wind conditions, but
may be sufficient.
#2) 'AVERAGED HEADING TRIANGLE'
EAA's Experimenter magazine, Dec. '97, reprinted a method that had
been printed in the Rans company's newsletter. The pilot flies three
legs with headings 120 degrees apart. The true air speed is the
average of GPS speeds from the three legs. The method is only an
approximation, which the article does not state. For a couple sample
calculations with different wind directions and a 100 mph aircraft in
a 10 mph wind, the error was about 1/4 %. It is as if the method
average out the errors the simpler versions of method #1, which were
seen to vary between zero and 1/2 % for the same aircraft and wind,
depending on the wind direction.
(The article's correction factors for density altitude are wrong, by
the way, since they say to multiply by values which are the air
density ratios rather than the square root of the air density ratios.)
#3) 'THREE GROUND SPEEDS AND TRACKS' (OR 'THE CIRCLE OF VECTORS')
By flying three legs in different directions, and recording both
ground speeds and tracks, wind velocity (speed and direction) and true
air speed can be determined without approximation. Some trigonometry
is necessary, but the equations are available on a spreadsheet. While
headings need to be maintained accurately, it does not matter what the
chosen headings are, so an accurate compass swing is not necessary.
Best results are found for headings 90 to 120 degrees from each other.
I have also called the method 'the circle of vectors' because of a
helpful diagram in the article proposing the method. Doug Gray wrote
the PDF document found at:
http://www.hlos.com.au/~doug.gray/home.html
#4) 'THREE TRACKS AT 90 DEGREES AND PYTHAGORAS-LIKE FORMULA'
This method uses one leg in one direction, a second leg at 90 degrees
to the first, and a third leg in the opposite direction to the first.
Tracks are flown, and only ground speeds are recorded. A formula that
has parts resembling the Pythagorean theorem determines a
mathematically correct true air speed. I haven't done the derivation
myself but the method is apparently correct. The formula is:
true air speed = (square root(A^2 + B^2 + C^2 + A^2 * C^2 /
B^2) )/ 2
where A, B, and C are the ground speeds for the three legs in
the order described above.
This formula was presented by David Fox in the Feb. 1995 issue of
Kitplanes (which I haven't seen), and is referred to in notes
associated with the web sites for method #3 and #5.
If headings were flown instead of tracks, the formula would only be an
approximation. (For a 100 mph aircraft with a 10 mph wind
perpendicular to the two runs that are in opposite directions, the
error is 0.91%. When the same wind is parallel to the two runs, the
error was a miniscule 0.005%. But method #1 produces better
approximations if one can correctly guess the wind direction relative
to its two runs.)
#5) 'THREE HEADINGS AT 90 DEGREES AND ITERATIVE CALCULATION'
Only ground speeds need to be recorded in this method, but three
headings at 90 degrees to each other must be flown. Data is entered
into a Java applet from Craig Cox at:
http://www.reacomp.com/TrueAirspeed/index.html
It iteratively calculates the true airspeed and wind velocity. The
program shows results to whole number values only, but more accuracy
can be attained by multiplying all inputs by 100 (and dividing the
output speeds by the same amount).
Both Doug Gray's and the iterative method are recommended at the
following site, which has a number of useful flight testing resources
and links:
http://members.xoom.com/kevinhorton/rvlinks.html
OTHER ERROR SOURCES
While some of the simpler methods are only approximations, their
errors may be acceptable when considering other errors in the
measurements. Error sources include:
1) Selective Availability (SA)
Selective Availability causes a GPS's reported position to slowly
wander in a pseudo-random manner. The speed error with SA turned off
is small, about 0.1 mph. While I don't have confirmed numbers
available, one web site said that the SA-induced errors are 'typically
0 to 3 mph when at rest (but can be more), and typically plus or minus
1 mph when travelling over 60 mph'.
The motion added by SA is actually independent of the GPS user's
speed, but when the user is moving fast enough only the error motion
parallel to the user's path with have much of an effect on the
displayed speed. (An SA "crosswind" has less effect on reported speed
than an SA "headwind" or "tailwind".) So while flying the error
introduced may usually be less than 1 mph. From time to time the
wandering motion will happen to be both rapid and in line with the
aircraft's track, so GPS speed errors could occasionally be at least
as high at 3 mph, assuming the above information on position wandering
is correct.
Repeating airspeed calibration tests at different times, at least 15
minutes apart, can improve test accuracy. Just taking multiple data
points during a 5 minute run may not be sufficient, as the speed and
direction of the position wandering may be similar throughout. While
more detail is available on GPS related web sites, the period of the
most significant SA wandering is very roughly on the order of 10 or 15
minutes.
2) Display Error
Some GPS's only show speed to whole mph (or kts or km/h) when above a
value of 100, resulting in another plus or minus 1/2 unit inaccuracy.
3) Variations in wind velocity, and inability to fly a perfect flight
path.
All the flight test theory in the world may feel rather academic when
one is bouncing around in a small, low wing loading homebuilt. One may
want to climb somewhat to get above low level mechanical turbulence,
wind shear, and thermals.
4) Compressibility
Compressibility effects are usually ignored, but one might want to
look into the issue when dealing with a high speed homebuilt. The
difference between compressible and non-compressible calculations of
speed from pitot pressure differ by less than 1% if under 200 mph and
in the lower atmosphere.
TRAILING BOMB or CONE
One method of calibrating airspeed without using ground speed (and
therefore having to compensate for wind) is the 'trailing bomb' or
'trailing cone' method. Instead of measuring static pressure on the
aircraft, where it is so easily influenced by local pressure changes
in the airflow, static ports are placed on an object trailed behind
and below the airplane. Normally this is regarded as a method for
professional flight testing only, but it can be done at home with 50'
of soft tubing, a plastic funnel, and other simple parts. A
description can be found in Sport Aviation, March 1977. ("A study of
Cruise Performance of the T-18" by Howard Henderson and Peter Roemer.)
Comments and additions welcome!
Peter Chapman
Toronto, Canada November 1999
p.ch...@utoronto.ca (my permanent e-mail)