 Copyright ©2019 by Paul Niquette. All rights reserved. The puzzle provided a
table of parameters for modeling an
electrically powered airliner as a replacement
for a popular fossil-fueled airliner in the
present fleet. Solvers were asked a
simple feasibility question: Can
lithium-ion
batteries really do the job?
The table has been expanded below to
facilitate the solution to the
puzzle and results in a simple technical
answer...
Accordingly, an aircraft like SUGAR Volt, which applies the Boeing Truss-Braced Wing, can be powered in some future design by rechargeable lithium-ion batteries to operate in place of fossil-fueled commercial airliners like the Boeing 737 Classic.
Technical
Model for an Electrically Propelled Airliner
Solvers of many puzzles in the collection (for example Which Way, Amelia?) have confirmed the definition of a 'model' as an ordered set of assumptions.
Nota bene, a combustion-propelled aircraft gets steadily lighter and faster as its fuel is burned, while discharging immense amounts of CO2 and H20 into the air.Another significant difference is Wing Span dW. The SUGAR Volt wing is more than a third longer than the B737 Classic wing. That gives it nearly 3:1 advantage in Aspect Ratio AR. Now, Lift-to-Drag ratio L/D varies according as the square-root of AR, which gives the SUGAR Volt more than a 1.7-to-one aerodynamic advantage over the B737 Classic. With both aircraft in steady flight at the same speed, aerodynamic Lift = Weight wM. Therefore, Drag fD = wM / (L/D) for each aircraft. We see in the table that the 1.7-to-one advantage in L/D results in a one-to-1.7 advantage in lesser Drag and therefore the requisite Propulsion Thrust for the SUGAR Volt, with its Truss-Braced Wing. We turn now to estimating Requisite Propulsion Energy for the SUGAR Volt. Solvers surely recall that one Joule (of energy) equals the work done by a force of one Newton applied through a distance of one meter; thus 1 J = 1 N-m.From the Cruise Performance Summary in the table, one can derive an extreme cruise-flight ('trip') at speed vC = 876 km/hr (548 mph) over full Range rR = 4,176 km (2,610 miles) and observe that its Duration is rT = 4.8 hr for both aircraft. The Propulsion Thrust for each aircraft to overcome aerodynamic Drag force is given by fD = 4,188 N for the B737 Classic and fD = 2,442 N for the SUGAR Volt. This, along with Cruise Power pT and Trip Energy eT confirm the aerodynamic Cruise Performance advantage for the SUGAR Volt. Solvers of Green Flight know that both Lift and Drag -- vary according as the square of Airspeed. Inasmuch as Lift = Weight, Lift is a constant wM, and only Drag can vary. That means the Lift-to-Drag Ratio itself L/D varies inversely with the square of Airspeed (compensated by pitch and power controls).Requisite Propulsion Energy is simply a matter of multiplication, fD x rR, which produces values for eT = 17,449 MJ and 10,197 MJ for the B737 Classic and SUGAR Volt respectively. Lithium-Ion Specific Energy Estimates range from 0.360 MJ/kg to 0.875 MJ/kg. In between we find the solution to the puzzle at 0.778 MJ/kg which can be accommodated within the 'budget' of Battery Weight wB = 13,109 kg (28,900 lb). As a check, we have ascertained that the Specific Energy of the batteries in the Tesla Model S amounts to only 0.567 MJ/kg, requiring wB = 17,984 kg, which suggests that the weight of infrastructure for the lithium-ion batteries in a road vehicle must be included in the Specific Energy estimates for the batteries. Feasibility Study The Flying Off the Grid puzzle is directed at an immense and vexing problem for the airline industry resulting from the environmental impact of aviation on global climate. The elementary 'model' set forth above offers a technical feasibility study, comparing a representative fossil-powered, jet-propelled airliner with one research proposal for a future battery-powered, electrically-propelled airliner. A business -- competitive -- study might call for compliance with a recommendation made in The Rational Process...
Landing Weight Our solution above took notice of the general fact that an electrically-powered machine does not give up any of its weight during use. Inasmuch as specifications for many of today's airliners include a limit for landing weight, the jettisoning of fuel can be required for mitigating various incidents aloft that necessitate unplanned early landings.
Charging Time On the ground parked at the passenger gate, the battery-packs in the SUGAR Volt's nacelles under the wings will necessarily be plugged into 'the grid' -- perhaps through a dedicated power substation at the airport terminal. The required electrical charging energy will be somewhat more than the 10,197 MJ calculated in the model, which can mean as much as 3.0 MWh for charging each SUGAR Volt. That will take up to five hours, based on the charging time for the lithium-ion battery pack on a Tesla Model S. Battery-swapping systems might be considered, but such would be complex indeed... ...beginning with a conceptual design for the airframe that accommodates a quick-change feature for battery packs or, alternatively, exchanging the whole battery nacelle aerodynamically latched under the wings.Far more practical is a mandated policy that expands and exploits hub-and-spoke routes... ...which limit flight segments to less than one-half of the aircraft's maximum range. In the model, rR = 4,176 km (2,610 miles), so the SUGAR Volt would be assigned to spokes of, say, 2,000 km (1,250 miles). Solvers of Green Flight have encountered the most practical way to address charging time... As described above, with its Truss-Braced Wing, slender and thin like that of glider, has an Aspect Ratio AR = 27. Since Drag fD varies according as the square of Airspeed vC, we can determine the effects of Slowing Down. Critique of the
SUGAR Volt
Published descriptions
of the SUGAR Volt say
that, to
meet the 'ultragreen'
requirement (the
UG in
SUGAR),
the aircraft
will
apply
hybrid-electric
propulsion technology.
Each of its two engines integrates the battery-powered electric motor with a coaxial, turbo-fan engine that burns jet fuel. Two in-flight operating modes are proposed: The turbine engines are called upon for take-off propulsion and for climbing, then for cruising at constant altitude, the turbines are idled and electric motors take over the responsibility for propulsion.In formulating the Flying Off the Grid puzzle, your puzzle-master (that would be me) rejected the hybrid-electric concept out of hand. Here's why... Foremost, it violates the most important objective -- to ascertain the feasibility of a battery-powered airliner that does not use combustion in the sky ("off the grid").Solvers of Carbon Footprint noted that a hybrid vehicle operating "off the grid" is propelled by the combustion of fossil fuel over every mile it travels. Its battery mainly supports two fuel-saving stratagems [1] shutting off the engine during prolonged stop-and-go driving and [2] recapturing energy from the application of brakes, especially in driving down hill. These stratagems are judged here to be inappropriate for the SUGAR Volt, so the complexities of hybrid propulsion have not been considered for Flying off the Grid. |
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