AHRS, Air Data Computers, and Magnetometers
Keith Thomassen, PhD, CFII

Aircraft with modern glass cockpits no longer need vacuum-pump-driven spinning gyros to determine attitude. They instead have Attitude and Heading Reference Systems (AHRS) to determine the aircraft pitch, roll, and yaw, and have Air Data Computers (ADC) to give you altitude and airspeeds. Magnetometers are used to determine your magnetic heading and give supporting information to the other devices. This article is intended to give pilots a better understanding of these 3 key devices, how they work and what information they generate and display in the cockpit.

Figure 1

Figure 1. Schematic of a glass cockpit, the G1000, with AHRS, ADC, and magnetometer.

The schematic in Figure 1 of the G1000 system is typical of a glass cockpit, which shows the central role of the AHRS. It shows information flow paths and dependencies among these items. Note that the AHRS gets information from the ADC and magnetometer, and uses your position and velocity solutions from the GPS.

With these components your GPS can generate roll commands to follow heading legs with an autopilot, and can determine when you reach your baro-corrected altitude to sequence from the 3 flight legs that end at an altitude (see article on Flight Legs). On a Primary Flight Display (PFD) you can have tapes for altitude, airspeed, and compass heading, and display a pitch ladder, bank scale, and slip-skid indicator.

So how does all this work, and what do these things do? Without getting into the weeds on these topics, which you can easily do since they are highly technical, we'll discuss some basic concepts and principles at play. Key technologies in these devices are various Micro Electro-Mechanical Systems (MEMS) sensors. There are MEMS used in accelerometers, in rate gyros and in magnetometers. They are small, typically between 20 microns and 1 mm. Each device incorporates computer chips with the MEMS in their applications to process data and generate signals to the navigation system.

For an ADC, you need sensors for temperature and pressures, but your angle of attack and vertical speed (changing static pressure) also come into play to generate the proper output. Unlike older mechanical pressure instruments (like altimeters), modern pressure sensors are solid-state based, using either bonded strain gauges, capacitive devices, or piezo-resistive elements. But we won't get into the weeds, so suffice it to say you need sensors to measure both the static and dynamic (pitot) pressures. For air data calculations you also need to measure temperature.

You can measure the outside air temperature with a probe designed to extract all the energy from the air that strikes it, by bringing that air to rest to recover both its kinetic and thermal energy. At rest on the ground, it measures the true outside air temperature (OAT) but when in the air it adds whatever extracted kinetic energy of the air (Ram Air Temperature) that strikes it, giving you the total air temperature (TAT).

If the kinetic energy is totally recovered in an adiabatic (slow) manner, a simple formula including your Mach number and the adiabatic index (from the theory of gasses), gives the ratio of TAT to OAT. Alas, you can't recover it all so a fudge factor is inserted in the formula to improve accuracy. The TAT probe is different from an OAT probe that does not attempt to recover the ram temperature. At a Mach number of about 0.2 the difference in these temperatures becomes important.

So what can you calculate and display from those measurements? Using the International Standard Atmosphere (ISA) model, static pressure at the aircraft can be converted to pressure altitude using an equation for the barometric law that relates altitude changes to pressure changes. From the pressure altitude and the local barometric correction, your baro-altitude is determined. That altitude is entered into your altimeter and Electronic Flight Information System (EFIS) displays and sent to your GPS and ADC.

An ADC can determine the pressure altitude, vertical speed, calibrated airspeed, true airspeed (TAS), and density altitude (DA). By vector subtraction you can also calculate the wind vector (speed and direction) if you get a velocity vector along your flight path from your GPS. Wind vectors are now commonly displayed on EFIS and GPS units, but to my knowledge only the Chelton EFIS will display DA and ISA on a Multi-Function Display (MFD), as shown in Figure 2. There is a DA calculator in the Garmin Touchscreen Navigators (on the Utilities page) but you can't select DA on the data displays on the 4 corners of the GPS moving map (but you can choose Wind).

Modern solid-state magnetometers are a huge improvement over the wet compass for displaying your magnetic heading, and they eliminate the compass errors during turns and acceleration. These devices sense the earths' magnetic field vector to determine your magnetic heading, which is the horizontal component of that field.

Figure 2

Figure 2. The Chelton EFIS system displays the Wind, DA, OAT, ISA, TAS, and GS (ground speed) on its MFD display, unique among modern GA glass systems.

As an aside, the magnetic North Pole is actually moving northward towards Siberia at the moment, at a fairly fast rate (34 miles per year, compared to the 20th century average of 10 miles per year), giving rise to the changing magnetic declinations that are giving errors for charted courses on airways, runway numbers, and GPS values for their computed courses. VOR's are calibrated infrequently, so the airway value on the map is only correct then and starts changing at that moment. GPS units use current values of declination and know where the waypoints are on airways, from which they can determine the current magnetic course of that segment.

The term MEMS is a general one, and there are different sensors for different applications. In an accelerometer, a force may change a capacitance (say by the piezoelectric effect) to produce a voltage. In a rate gyro a force due to the Coriolis Effect (centrifugal force) applied to a sensor gives a voltage proportional to your angular rate of turn, while a magnetometer could use the Hall Effect (the deflection of current carrying electrons by a magnetic field) or the Magneto Resistive Effect (change in resistance in the presence of a magnetic field) to determine the magnetic field.

We'll again stay out of the weeds and simply say that there are solid-state devices that can do all these things, and fortunately are useful in a variety of other applications that have led to their rapid development and lowered costs. For example, accelerometers are used to trigger the release of air bags and magnetometers are appearing in smart phones for map orientation and in vehicle navigation displays. For a simple “how they work” article click here. .

Magnetometers are 3-axis devices to determine the magnetic field along each axis, relative to its mount in the aircraft (which may be changing). If your aircraft were level and not pitching and rolling, you would simply need to determine the direction of the horizontal component of the earths' field. But that isn't the general case, so if you determine the magnetic field on each of the 3 axes of the device, you will also need to know your pitch, bank, and yaw angles to determine the local horizontal field direction. Consequently, you need that information from the AHRS, as shown in the connections between these devices in Figure 1, and a computer chip to do the computations.

Finally, let's look at an AHRS. There are many variations in design by the different manufacturers, generally proprietary, so we'll again talk general principles. From a pilot perspective the object is to determine aircraft attitude (and in the process eliminate vacuum driven spinning gyros). An AHRS does that, and more.

An AHRS device uses 3-axis MEMS accelerometers and rate gyros, in combination with a 3-axis magnetometer to perform the tasks. AHRS units get rotation information from rate gyros that are accurate in the short term, but the cumulative updates of angles leads to accumulating errors in the long term. In contrast, accelerometers and magnetometers provide accurate long-term attitude calculations and can be used to error check and correct the rate gyro solutions.

So why use an accelerometer? When you turn and bank it is because there are vertical and horizontal forces (acceleration is proportional to the force causing it) so accelerometers supplemented by a magnetometer can tell you how your attitude is changing.

But the accelerometer and rate gyro sensors suffer vibrations and magnetic noise errors, so must be filtered on an appropriately long time scale to give useful signals. Consequently they cannot be used for short-term changes. But they make a good combination with the rate gyros for the reasons just stated. These pitch and roll changes bring the aircraft to a new place, and your GPS knows where that is, so your PVT solutions (position, velocity, and time) from the GPS are another way to correct those evolving AHRS solutions.

In summary, an AHARS using these 3 different MEMS can provide a wealth of pilot information on a PFD display. Figure 3 shows the Chelton PFD and Figure 4 has the G1000 PFD. They both have speed, and altitude tapes, and indicate your compass heading and vertical speed. There are pitch ladders and bank scales to show pitch and roll. They both have flight path markers (white circle on Chelton, green circle on the G1000, each with stubby wings and a tail) that show your vector velocity in space, which is generally not aligned with your aircraft axis. (You’re not going where you’re pointing).

Figure 3

Figure 3. The Chelton PFD with altitude, speed, and compass tapes; it also has a bank scale and pitch ladder. The white circle with wings and a tail is your flight path marker. The green diamond is your magnetic ground track, while the white triangle is your heading. The magenta arrow left of the flight path marker is the split out needle of an HSI, and the 5 dots range over the full scale deflection of the needle. The glide slope indicator and vertical speed arrow are also shown.

Figure 4

Figure 4. The G1000 PFD with altitude, airspeed, and vertical speed tapes; it also has a bank scale and pitch ladder. The green circle at the point of the flight director cheverons is your flight path marker. An HSI is displayed showing your course and magnetic heading.

They both have slip/skid indicators below the white heading triangle under the compass scale. The Chelton also has a green diamond next to it to show your ground track, which is slightly right of your heading. It also has a “winged V” mark above and right of the path marker denoting the axis of the aircraft (here, pitched above the horizon and pointed left of the path marker to correct for winds from the left). The horizon is the white line marking level flight. When the center dot of the Chelton path marker is on that line you are in level flight, an excellent aid in maintaining a level turn. The HSI presentations on both devices come from both the magnetometer and a course (GPS, VOR, ILS, etc.) that you’re trying to follow.

So there you have it. A revolution in glass panels for General Aviation has taken place, and central to those devices are the AHRS, ADC, magnetometer, and of course the WAAS aided GPS. These first 3 are generally less well understood than other common instruments in our aircraft, but this short set of descriptions may be the launch point if you want to dig deeper in the technical underpinnings of each.