Commercial, Embedded Avionics

New Research Produces Open Source FMS Formula

By Woodrow Bellamy III  | December 1, 2015
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[Avionics Today 12-1-2015] New research from a Canadian aeronautical science university has provided the avionics industry with an open source reusable mathematical formula that provides the replicable calculations of an Airbus A320 Flight Management System (FMS) to provide the most optimal air speed to use while in cruise flight mode. In a soon-to-be-published study by the American Institute of Aeronautics and Astronautics, Concordia University researcher Luis Rodrigues produced a general purpose open source FMS to help pilots, manufacturers and operators determine how to use FMS inputs to generate an aircraft cruise speed that minimizes fuel consumption and flight time.
Rodrigues and co-author Jesus Villarroel, an engineer with flight simulator company TRU Simulation and Training, believe the FMS formula could have a wide range of potential uses both educationally and at the industry research and development level. 
Airbus A320 flight simulator cockpit. Photo: Airbus.
"Many researchers have previously published papers on FMS algorithms. Those have been suggested and produced since the end of the 1970s, looking at cruise speeds and altitudes that provide the most economically efficient operation of an FMS-centered aircraft. But what I haven’t seen before is actually an analytical solution that gives you a formula. This is really what is new in this work," Rodrigues told Avionics Magazine.
According to Rodrigues, the main objective of the research is to propose optimal and suboptimal control solutions to the cruise economy mode problem, which occurs within an FMS on flight operations that take place below the "drag divergence Mach number." Rodrigues says that the problem occurs as an optimization of a function of the FMS that trades off the fuel and time-related costs of a flight using a flight crew supplied cost index to produce the aircraft's optimal cruising speed. 
"The big advantage is that the formula depends on parameters and those parameters will be different for different aircraft, so all we have to do is plug in different numbers for different aircraft in the formula," he added. 
The formula is the square root of a sum of two terms, one of them depends on the weight of the aircraft, and the formula can be used with data from a specific aircraft, similar to a traditional FMS. 
While Rodrigues and Villarroel have no idea of knowing whether the formula will be useful to some of the world's biggest FMS or airframe manufacturers, a Montreal-based aerospace navigation research company has already shown interest in it and will soon test it out in one of their flight simulators. 
"We are already collaborating with them and trying to adapt our FMS to their aircraft — a Piaggio Avanti aircraft. So we are now using their flight simulator to program our algorithm and see how it compares with what the real FMS would do in the aircraft," said Rodrigues.
There are also other potential uses, including bringing it into play on general aviation aircraft, which do not feature FMS. 
“This … is really a tool for pilots. At the end of the day, those are the people who benefit because it’s a tool to help the pilots decide what should be the target point for the speed at which the aircraft is cruising,” said Rodrigues. 
Rodrigues also believes his formula could help the aviation industry reduce carbon emissions. 

“One of the big challenges that society is already [facing] is to reduce the carbon footprint of emissions from the atmosphere from everywhere, including transportation systems,” Rodrigues adds. “The all-electric aircraft is something that has been talked about and I do believe it will happen in the future. Between now and then, we have to make do with the aircraft that we have, the best we can do is try to use new designs or to use software such as that for the FMS that helps reduce emissions.” 

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