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Why MountainScopeTM Does Not Use GPS to Display Attitude

We've had enough questions from people about GPS-derived attitude, that we've decided to write up this web page to explain ways this could be done, and why MountainScope does not do it. There is at least one company who advertises this feature.
In a nutshell: GPS does not measure the correct quantities for attitude, and this GPS-derived attitude could be unsafe to use to fly an airplane.

GPS Basics
The GPS system uses orbiting atomic clocks, broadcasting precise time values, to determine the position of the receiver, which uses extensive and complicated math and a database of well-known satellite orbits. Since the only things directly "measured" in the process are time and position on the planet (eg, latitude, longitude, altitude), this means that any other values are derived by extrapolating time and position. For example, ground speed is calculated by looking at two position solutions and the time between them: distance divided by time is speed. Similarly for ground track, using the vector from one position to the next to figure out which direction the receiver moved. Most GPS receivers output position data once per second, so these derived quantities are an average over one second, based on position at the start and end of that second. (for more details on how GPS works, you could visit Wikipedia's page)

Pitch?
Considering how a GPS receiver works, you can see that certain things can be derived. Another example would be climb rate, by comparing two measured altitudes and the time between measurements. Some systems will actually show this climb rate as pitch! This assumes that the axis of the airplane is perfectly aligned with the ascent slope line of the airplane. Anybody who has flown an airplane "straight and level" in slow flight (ie, near a stall) knows that it's easy to find situations where the attitude indicator may indicate a significantly nose-up attitude, while the aircraft's altitude remains constant. With a GPS-derived attitude of this kind, you could be very close to a stall and this "pitch indicator" would still show you "straight and level!"

Roll?
Another quantity that could be legitimately derived from GPS (but at a second level of extrapolation) would be turn rate, by using two consecutive ground course calculations, and the time between those calculations. (Keep in mind, those ground course values were already derived by looking at consecutive position measurements.) Using some assumptions, some companies take the the turn rate and ground speed, and calculate the roll! This requires the assumption of a coordinated turn in addition to the assumption above, where pitch angle matches the ascent line given by the climb rate. Again, any pilot knows that the roll angle may vary for a given turn rate, given differences like winds, etc.

This could work...
The only possibly-accurate way of doing this would likely require 3 or 4 highly-accurate GPS receivers, placed in particular ways at different points on your airplane. Then it would be feasible to calculate the actual pitch and roll of the aircraft. For example, place a GPS in the tip of each wing. Then use simultaneous position measurements to calculate the slope between the two tips of the wings, which could produce a believable roll value. The downfall to this approach would be the accuracy requirements along the altitude axis, which has the weakest accuracy in the GPS system. Something similar could be done for pitch by placing GPS receivers in the nose and the tail of the aircraft.

Summary
The GPS system was created to enable a receiver to calculate its position on the planet, along with any related quantities that can be extrapolated using time. However, the pitch and roll attitude of an aircraft cannot be measured solely by knowing the position of one part of the airplane relative to the planet. Therefore, when you see any device or software purporting to display attitude information based solely upon GPS, you should approach it with a high degree of skepticism, if not ridicule!


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