Flying Off the Grid

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...

 Yes.

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.

 B737 Classic SUGAR Volt Payload Equivalence (kg) Maximum Wt 62,822 62,822 wM Empty Wt 32,821 49,713 wE Zero Fuel Wt 49,713 N/A wZ Fuel Wt 13,109 N/A wF Battery Wt N/A 13,109 wB Payload Wt 49,713 49,713 wP Airframe Comparison Wing Span  (m) 28.9 38.7 dW Wing Area (m^2) 91.0 55.5 aW Aspect Ratio 9.2 27.0 AR Aerodynamic Comparison Lift-to-Drag Ratio 15.0 25.7 L/D Drag (N) 4,188 2,442 fD Service Ceiling (ft) 37,000 37,000 cS Cruise Performance Summary Speed (km/hr) 876 876 vC Range (km) 4,176 4,176 rR Duration (hr) 4.8 4.8 rT Requisite Propulsion Energy Propulsion Thrust (N) 4,188 2,442 fD Power (Nm/hr = J/hr) 3,668,804,800 2,139,044,749 pT Cruise Power (MJ/hr) 3,669 2,139 pT Trip Energy (MJ) 17,490 10,197 eT Lithium-Ion: Specific Energy Estimates Minimum: 0.360 MJ/kg N/A 36,414 Solution 0.778 MJ/kg N/A 13,109 wB Maximum: 0.875 MJ/kg N/A 11,654 Tesla Model S: 0.567 MJ/kg N/A 17,984

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
• Highlighted in yellow are assumptions-of-equivalence between the specifications that characterize the Boeing 737 Classic along side technical parameters assumed for the SUGAR Volt -- specifically wM, wP, cS, vC, rR, and rT.
• Highlighted in blue in the table are the technical consequences of one key assumption -- that the weight of the lithium-ion batteries in the SUGAR Volt wB shall not exceed the maximum fuel load in the B737 Classic wF = 13,109 kg (28,900 lb).
Our efforts must now be devoted to ascertaining the Requisite Propulsion energy for the battery powered SUGAR Volt.  As shown in Wages of Flight, aircraft weight is a major energy consideration.  Both aircraft are assumed to have the same Maximum Weight wM, but we see a significant difference between the two aircraft in wE.  Here's why: The Empty Weight of an electrically powered airplane must include its batteries wB, which means that from take-off through landing, its weight stays the same, wM = 62,822 kg (138,500 lb).
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
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.

Issues Revealed by the Model

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...
 For what it may be worth, I refract every problem through three lenses: Technical Factors Economic Issues Human Considerations Each has its own primacy, and there's a neat word for this analytic discipline, "prescinding" (you could look it up).
Only Technical Factors are addressed here.  Conspicuously absent are Economic Issues and Human Considerations.  Hmm, another puzzle or two perhaps?

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 useInasmuch 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.
• For the SUGAR Volt, that means its landing weight is the same as its maximum weight at take-off mWA more robust landing gear will increase the weight of the airframe, possibly necessitating the inclusion of a retractable center wheel.
• The B737 Classic used in the model enjoys weight-lightening throughout its flight. For simplicity, the model does not take that into account.  Keeping its weight constant at mW ignores any implied savings in Trip Energy eT as an economic benefit for combustion aloft, a subject outside the scope of the puzzle as noted above.

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.

Each battery pack weighs about 6,600 kg (2,800 lb).
Getting the swap-time to under an hour, say, would require dispatching a pair of battery-elevating vehicles, each loaded with fresh battery-packs to meet flight arrivals.
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).

Daily aircraft movements would originate with fully charged batteries at spoke terminals.  Following a rapid turn-around at the hub, each aircraft returns again to the spoke terminal, where batteries are recharged during maintenance intervals.
Thus...
• No charging services are needed at the hub,
• Congestion at gates would be reduced, and
• Flight crews can sleep in their own beds at home.
• Passenger inconvenience is inevitable, but just as inevitable is the decrease in the skies of combustion-propelled aircraft, which are guilty of discharging immense amounts of CO2 and H20 into the upper atmosphere.
Solvers of Green Flight have encountered the most practical way to address charging time...
As described above, with its , 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.

Suppose that the SUGAR Volt were to slow its Cruise Airspeed vC by half (for the sake of simplicity) from 876 km/hr (547 mph) to 438 km/hr (274 mph).
Hey, that's still faster than the most advanced passenger rail trains!
Propulsion Thrust fD will decrease by a factor of 1/4 from 2,442 N to 610 N and Range -- distance between battery chargings -- will increase by a factor of 4 from 4,176 km (2,610 miles) to 16,700 km (10,440 miles).  Of course, the flying time will increase for a 2,000 km hub-and-spoke segment from 2.3 hr to 4.6 hr. But the total CO2 and H20 discharged into the upper atmosphere amounts to -- zero.

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.

You are invited to offer your own comments -- and criticisms -- here.