Guiding Solar Impulse around the world thanks to mathematics

Solar Impulse

Between 100-150 billion flight-path possibilities were analysed in 2014: this is how mathematics is serving one of the most incredible adventures of our time

One of the key challenges of the round-the-world flight that Solar Impulse and Altran are being faced with is managing long-haul, non-stop flights of up to 120 hours and transoceanic crossings of between 7,000 and 10,000 kilometres (4,400 to 6,200 miles). Over those long stretches, the Si2 solar plane will have to adapt to tricky weather conditions. Because of their inherent instability, those conditions can lead to potentially hazardous situations for the aircraft. It is on the ground, at the Mission Control Centre (MCC), through a special system of mathematical calculations developed by the Altran team that the plane's flight-paths for this extraordinary odyssey are traced.

Between 100-150 billion flight-path possibilities were analysed in 2014: this is how mathematics is serving one of the most incredible adventures of our time.

The mission of the Altran Flight Strategy Team at the MCC base is to explore the flight possibilities and develop optimised strategies so that the Flight Director receives a constant flow of information for the decision-making process. Altran innovative calculation system was designed to simulate optimum take-off opportunities and ensure smooth flight connections, as well as to access the margins of security and level of risk. The solutions are detailed from every angle and discussed with the three other MCC specialist teams: Meteorologists, Air Traffic Controllers, and Flight Engineers.

“Altran has developed calculation systems that are innovative in their ability to both analyse massive amounts of weather data and anticipate flight parameters precisely at all times. This enables the Flight Strategy Team to study and develop the best strategy for any given flight, and to live the flight before the aircraft even gets off the ground”, explains Philippe Salle, Chairman and Chief Executive of Altran.

As Altran Head of Strategy and Forecast for Solar Impulse, Christophe Béesau and his team also provide maps and charts that are incorporated into the pilot’s operational flight plans. In addition, the Altran Team ensures the constant input of information to MCC control screens, presenting current and projected flight conditions. This enables the MCC to monitor flights at all times and anticipate any potential difficulties.

Flight strategies, which are tailored to meet the specific flight requirements on a given day, may be called into question at any time because of shifting weather conditions, air traffic constraints or mechanical problems involving the plane. The Altran Simulation Team carries out specific-case studies which serve in the drafting of emergency plans that can be implemented at a moment’s notice and updated when the plane is in flight.

“Pilots must be guaranteed optimal flight security and preparation despite extreme conditions in this challenging adventure”, explains Christophe Béesau.


Using math to obtain maximum anticipation

Reducing uncertainty is a long process. With an aircraft that is particularly sensitive to weather conditions, the slightest variation can rapidly become a major issue for the flight parameters. The flight strategy must be developed to ensure an optimal management of risks of potential variations in critical parameters such as thethe thickness of high-altitude cloud cover, the exact wind speed and direction, or moisture in the air masses to be crossed.

Since Edward Lorentz’s famous speech introducing the notion of the “butterfly effect”, we know that forecasting the weather becomes more difficult as the prediction horizon increases. Because the systems of differential equations that govern weather are unstable, every one-day extension of the forecast horizon theoretically requires considerable efforts.

Nevertheless, Altran has developed calculation systems specially adapted to meet the needs of the Solar Impulse without using supercomputers. By looking at the problem from a different angle, it was possible to obtain another set of equations and focus research on enabling the data to speak for itself, and extracting hidden yet significant information. Altran was able to develop a non-standard approach to information processing by considering the plane as a probe for exploring future weather data; an approach that has completely turned “standard” logic on its head!

Inversing this paradigm offers new data-processing possibilities for the answers required. Precious information to keep the pilot one step (and a few extra turns of the propeller) ahead when climbing into the cockpit!

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