How brute-efficiency enables practical electric flight

Anytime the topic of electric aircraft comes up, the immediate response by the middle-brow (and some high-brow) is that it’s obviously impractical due to the mass-sensitivity of flight and the obvious energy density (or they usually intend “specific energy”) advantage of gasoline and jet fuel over batteries. And this is not a totally wrong claim.

This Wikipedia page is a convenient reference:

Aviation Gasoline has a specific energy of 44MegaJoules/kilogram given the high heating value of burning gasoline (high heating value includes the heat energy in water vapor, low heating value does not). A nice safe Lithium Iron Phosphate battery might only pack around 123Watt-hours/kg, or 0.44Wh/kg. Literally a factor of 100 difference in pound for pound energy density and therefore range (or, even worse, they’ll tell you, because the fuel weight is lost during flight). So obviously electric flight is a non-starter. But is it?

A typical gasoline engine might consume about 285grams of fuel per kWh of mechanical power. A turboprop like the PT6 might consume 308grams of jet fuel per kWh. Efficiency in the range of 27-28%.
Electric powertrains can achieve, under cruise conditions, efficiencies on the order of 95% (98% discharge efficiency from the battery and 97-98% from the motor, maybe 0.5% loss from the controller, etc… and note that the longer you take to discharge from the battery, the more efficient it is). (Less for very high power take-offs, etc.)
Electric powertrains are therefore a factor of 3 more efficient. Secondarily, a high end electric car battery can achieve about 275Wh/kg or 1MJ/kg. Next-generation chemistries (solid state lithium, lithium-sulfur, lithium metal anode, etc) that are available in sampling scale are 400Wh/kg, with some labscale cells achieving 500Wh/kg or even 650Wh/kg. Lets use the sampling level of 400Wh/kg, or about 1.44MJ/kg as you could actually probably build a large battery out of these cells today if you had enough pull. Now the difference between burning fuel and battery electric is down to a factor of 9.
Now comes the other huge factor, often ignored: Lift to drag ratio.
A Cessna 172 or a Piper Cub J-3 might get a lift to drag ratio of 8. The best sailplanes (Eta, Concordia, and Nixus) can get about 70, so about a factor of 9 better. And similar speeds as the Cessna and Piper Cub, too!

The full equation for an electric aircraft is:

Range = E* (1/g) (overall efficiency) (L/D) (battery weight as percentage of total weight).

So if the specific energy is 0.5MJ/kg, overall efficiency is .95*.85 (95% for battery and motor, 85% for propeller), L/D of 20 (about the same as a modern airliner), and 25% battery weight percentage, g is 9.8m/s^2, and therefore the total equation is:
0.5MJ/kg*(1/(9.8m/s^2))*(0.95*.85)*(20)*(0.25) = 206 kilometers.
A more aggressive aircraft may use 1MJ/kg batteries, a lift to drag ratio of 50, and a battery weight percentage of 35%:
1MJ/kg*(1/(9.8m/s^2))*(0.95.85)*(50)*(0.35) = 1442 kilometers.
Now we are getting somewhere!
A Piper Cub J-3, of which 5500 are in flying order today (and very popular in the Alaska bush), gets a range of about 354 kilometers.

A really aggressive approach would use a lift to drag ratio of 70, 400Wh/kg (1.44MJ/kg) batteries, and a battery weight ratio of 50% would get: 4153 kilometers of range. That’ll get you transatlantic distances without additional cleverness.

Antares 23E has L/D = 60.

Another version of the Antares, the Antares 20 with a lift to drag ratio of 56, was used as the basis for an electric airplane with enough batteries for a 450km range.

Now, all this being said, there’s a huge advantage to, at the end of the day, choosing much lower battery mass and structure mass, or picking cheaper chemistry (lithium iron phosphate instead of state of the art lithium ion) and structural materials (automotive grade carbon fiber or even fiberglass instead of state of the art aerospace carbon fiber) and getting by with a 1000km range instead, or with a much greater payload fraction. But it’s important to know what the limits are.

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4 Responses to How brute-efficiency enables practical electric flight

  1. Jim Davis says:

    Why would a high L/D only apply to electric aircraft?

  2. Ben Brockert says:

    It seems like you’re arguing that no one should be flying planes like a Cessna 172 or a Piper Cub J-3 and instead should be in a motor glider, but visiting any GA airport suggests that the market does not agree.

    I’d enjoy having an electric motor glider, though. My scheme is that you also cover it in solar panels; it would give you a bit of range extension, but more usefully it would mean that you could fly somewhere, let it bask for a day or two, and then fly again. Not practical for commercial flight, but fun for touring.

  3. Chris Stelter says:

    @Jim Davis: High L/D doesn’t apply purely to electric aircraft, but the same argument could be applied to electric cars: all those tricks to make a Tesla Model 3 have low rolling resistance and high aerodynamic efficiency could be applied to conventional cars, so why aren’t they? And the answer is that, well, the forcing function for efficiency just isn’t as strong. Second, a lot of internal combustion engine vehicles have lots of ancient heritage. Third, sailplanes are sort of niche and weirdly, lots of the aerospace community is less aware of sailplane tech and thus diffusion of techniques is slower than you’d think (although diffusion isn’t absent entirely!). Fourth, the Celera 500L is an ostensibly diesel electric aircraft with sailplane-like efficiency. Also, the two around-the-world flights, the Rutan Voyager and the Virgin Atlantic GlobalFlyer, both use extremely sailplane-like designs.

    @Ben: Partly because of how incredibly slow general aviation changes. Piper Cub J-3 was literally produced in 1938. Cessna 172 was first flown in 1955, but is based on the 170 and 140 which first flew in the mid-1940s immediately after WW2. There are regulatory (and tort) reasons for this, which are beyond the scope of this thread. Doubtless you’d see a lot more efficient designs if we started from scratch, and indeed, modern touring motorgliders are definitely a thing, like the Stemme S-12, and you see modern electric planes look like gliders, like the Beta Alia (whose prototype variant demonstrated 622km range, basically with an electric car battery but still with vertical lift pod fairings attached).

    Wingspan constraints are a thing, which sailplanes address by “simply” removing the wings for transport.

  4. Agammamon says:

    What I’m seeing here is – for the same airframe you’re going to get more range for the mass of engine/fuel with an FF powered airplane.

    I’m not aware of anyone who is claiming electric flight *can’t* be done today, just that it’s not practical, cost-,wise, with current tech.

    Too many compromises – want range, sacrifice payload or increase cost. *Right now* you get more plane per dollar with an FF powerplant.

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