Speculation continues to mount regarding the fate of Malaysia Airlines Flight 370. After a week has passed with no knowledge of its whereabouts, “This is now the greatest aviation security mystery in aviation history,” as I stated on Los Angeles CBS Radio, Government Security News, and Fox News.
Assuming the plane did not crash, we can look to science, Breguet specifically, to help us project where the Boeing 777-200ER was physically able to fly. As reported in The Wall Street Journal and Reuters, we can calculate the widest circular sweep of the seven-hour maximum range for the Boeing 777-200ER aircraft.
Who is Breguet?
Let me introduce you to a French Renaissance aircraft designer and aviation pioneer, Louis Charles Breguet. Born in Paris on January 2, 1880, and passed away in Saint-Germain-en-Laye, France, on May 4, 1955, Breguet in 1919 founded the earliest French airline, organized over five years, 1919-1923. Today, Breguet’s airline is known as Air France.
Making it interesting how Breguet's connection to the missing Malaysia Airlines Flight 370 ties us back to similar international aviation safety mishap and 'black-box' search and investigative circumstances surrounding the formerly missing Air France 447 mystery.
Breguet, an aircraft manufacturer during the Second World War, developed the classical Breguet Range Equation. Breguet’s range is now the scientific standard and engineering principle used for determining the possible range of a flight. International aviation safety and security investigators are casting the widest possible net to locate the plane (or any wreckage and debris, if it crashed), given the apparent “about-face” of Malaysia Airlines Flight 370 flying hundreds of miles off-course. This is based on radar surveillance and international reports of transponders and satellite data and information, such as ACARS (Aircraft Communications Addressing and Reporting System) periodically pulsating a hint of evidence.
Why Breguet Matters
“So far no one has a solid “theory of the case,” as lawyers say,” reports The Washington Post.
To provide some accurate scientific information to media, I used The Wall Street Journal’s widely-accepted 2200 nautical mile (or 2500 mile) circular range of possible flight for Malaysia Airlines Flight 370 using Breguet’s Range Equation.
Let’s briefly fast-forward to three weeks ahead inside my current spring semester Mechanical Engineering 318 Jet Propulsion and Mechanical Engineering 305 Thermodynamics classes at Howard University. A dozen extremely bright (and I might add very brave) kids are taking their last undergraduate technical elective prior to their May 2014 graduation with a bachelor’s degree in mechanical engineering. An additional dozen kids enrolled in my Thermodynamics class are entering their second-year mechanical engineering curriculum with a brief introduction to Monsieur Breguet. These students can now understand why Breguet's proven engineering principle is as relevant for them to learn today, as it was for me 20 years ago, when I had my similar training at the University of Cambridge, Department of Engineering’s Whittle Laboratory, and also when I taught a similar jet propulsion class at MIT’s Gas Turbine Laboratory.
An upcoming lecture in my Jet Propulsion and Thermodynamics classes is about air-breathing propulsion “figures of merit,” comparing “specific impulse” and “overall efficiency,” which is encompassed by Breguet’s Range principle. Breguet showed us how the specific impulse is directly related to the overall efficiency of Rolls-Royce Trent 800 engines used by Malaysia Airlines on the Boeing 777-200ER. Breguet’s Range principle has three-primary sources of efficiencies of fuel burn combustion, thermal temperature distributions, and propulsive processes, which are altogether attitude dependent on air density and outside temperature during flight.
Malaysia Flight 370’s Normal Operation. Try to imagine the Boeing 777-200ER operating Malaysia 370, flying with two huge Rolls-Royce Trent 800 turbofan engines, at normal cruise flight speed, U, traveling 480 nautical miles per hour, before suddenly disappearing from radar at 35,000 feet (10.7 km), just 40 minutes into flight.
The aircraft has four primary forces, which are: (i) an upward lift, L, (ii) a downward weight, W, (iii) a forward thrust, T, and (iv) a backward drag, D. The lift-to-drag ratio, L/D is a Boeing 777-200ER key design parameter. Weight opposes the lift, which is also closely-aligned to the drag, D (as an inherent function of the lift-to-drag ratio, L/D), and which is also equally-aligned to the thrust, T (defined as a ratio of the aircraft’s fully-loaded weight, W, to the aircraft’s aeronautical design parameter, L/D).
As a result of steady fuel burn by the engines at normal cruise speed, U, at 480 nautical miles per hour, the aircraft weight is constantly decreasing during flight. This weight change over time is a negative ratio of the aircraft’s forward thrust, T, to the engines’ specific impulse, SI. This specific impulse is an inverse measure of the engines’ fuel burn. Additionally, the specific impulse is a direct measure of the overall efficiency of the engines.
Assuming constant specific impulse, SI, and the aircraft’s aeronautical design, L/D, during normal cruise operation of the Boeing 777-200, the proportional change of the fully-loaded aircraft weight, W, equals a negative ratio of the marginal flight time to a product of the aircraft’s design, L/D, and the engines’ specific impulse, SI.
Breguet’s Flight Time. Breguet found the total time of flight, t, of an airplane is a function of three factors:
(i) the Boeing 777-200ER aeronautical engineering designer’s key aircraft parameter, L/D (that is, the lift-to-drag ratio is about 17);
(ii) the Rolls-Royce Trent 800 propulsion engineer’s specific impulse, SI (which is a dimensionless time of about 2 hours (specifically involving a ratio of the engine's fuel heating value to gravitational acceleration multiplied by the engine's overall efficiency) at 35,000 feet (10.7 km) flight altitude at normal cruise flight speed traveling 480 nautical miles per hour); and
(iii) the Boeing 777-200ER structural engineering designer’s proportional change in the aircraft weight. In other words, the proportional change in the Boeing 777-200ER’s fully-loaded weight is a structural load ratio of the aircraft’s initial (zero fuel) weight (Wi) at 419,100 pounds (190,500 kilograms), to the aircraft's final weight (Wf) at 504,900 pounds (229,500 kilograms), which includes Boeing 777-200ER's seven-hours of fuel loaded at the origination of Malaysia Flight 370.
For those patiently following along thankfully and most appreciatively, Breguet’s total flight time is t = (L/D) X (SI) X log (Wi/Wf) = (17) X (2 hours) X (0.19) = 6.5 hours. I recently described how to calculate this flight time on Los Angeles CBS Radio.
According to The Washington Post, “If the plane stayed airborne for seven hours that would suggest that it flew until it ran out of fuel, or close to the limit of its range. That’s about how long a plane with fuel for a six-hour flight to Beijing can fly.”
Breguet’s Range. Breguet advised us to take the normal cruise flight speed, U, at 480 nautical miles per hour and multiply it by Breguet's total time of flight, t, described above. Marvelously, one obtains the Breguet Range = (U) X (t) = (480 nautical miles per hour) X (6.5 hours) = 3120 nautical miles. Using this absolute maximum range, we can determine how far Malaysia 370 may have flown, altogether depending on how much fuel may have been on-board.
The Brequet Range is consistent with The Wall Street Journal's updated outer circle, extending further at 2781 nautical miles (or 3200 miles), and flying about 6 hours at 480 nautical miles per hour.
Breguet’s Range principle allows one to tie together the overall efficiency of the Rolls-Royce Trent 800 engines mounted to the Boeing 777-200ER flown as Malaysia Flight 370 to determine the 6-7 hours of possible flight time, as has been widely-reported. That is approximately 5 hours of flight time from Kuala Lumpur, Malaysia, to Beijing, China. Plus, airline operators typically allow 2 additional hours for Beijing air traffic control delay (including one hour for a diversion, if necessary).
Merci, Monsieur Breguet
As recently stated in my earlier post “Boeing 777 airplanes do not vanish or fall out of the sky” on LinkedIn.com, “Our most compelling mystery in aviation safety and security history remains an ongoing and essential approach to discussing advanced aviation technology and education, as well as, considering the public understanding of science and technology, and most of all, facilitating the diverse cultural participation in aviation safety and security global workforce experts working through the aftermath investigation of an airplane crash.”
“Besides all the talk of satellites, pings, transponders, circuit breakers, and so forth, what investigators also have on their side are basic scientific principles,” I said to The Washington Post.
“Planes don’t just vanish and don’t just fall out of the sky. They go up and they come down.”
“Like everything else in this world, planes are bound by fundamental rules of science — things like fuel burn, lift, weight ratios and, not the least, gravity.”
We all owe a great debt of gratitude to Louis Charles Breguet for his pioneering innovations in aircraft design, and for his fundamental aviation range theory. This is now aiding the international effort focused on solving the “Missing Malaysia 370 Mystery” – “The Triple M Story” of aviation security history.
The baffling nature of a missing Boeing 777-200ER incident and the global level of interest and intrigue, not to mention the proliferation of theories and speculations that are running rampant, surely tests our patience. This has naturally heightened the participation and engagement of people from all walks in life all around the world.
We are reminded that this is still an ongoing investigation. We all hope to have some answers very soon, that will enable us to better understand aviation security threats, whether accidental or intentional, so as to avoid this kind of mystery in the future.
“It’s just a matter of time,” I've publicly cautioned as, “People should be thinking more in terms of weeks and months,” before we all really know completely all the truths behind this "greatest aviation mystery in aviation security history" and its aftermath of human recovery.
So, above all, thoughts and prayers still must continue to go out to the grieving families and friends of the 239 loved ones on board Malaysia Airlines Flight 370.
UPDATE -- Read More at BBC News: Missing plane: How did a U.K. firm track the plane?
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