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Saturday, July 27, 2024 | technology

The Physics of Battery-based Electric Vehicles

No matter how much battery capacity improves, the physics says it will not be good enough. But its explosive yield would increase


E lectric vehicles sound wonderful. They get more torque, they're quieter, and they're less complicated than ICE vehicles. Some people think if batteries improve, the problems with low range, long charging times, and tendency to explode into an unquenchable inferno will be solved.

The indisputable laws of physics say that cannot happen. The failure point is the physics of charging. There are three general types of chargers:

    Level          Voltage          Type          Power     
Level 1 120 AC 1.2 kW
Level 2 240 AC 9.6 kW
Level 3 400–800 DC 25–350 kW

Current battery capacities range from 65 kWh to 212 kWh. A Tesla Model 3 or Model Y LR (Long Range) has a 75 kWh. A Mustang Mach-E ER has 91 kWh. So, you might think that with a Level 2 charger it would take 91 divided by 9.6 or 9.48 hours.

But the limiting factor is not just the battery, but the charging system. An AC charger needs a rectifier because a battery can't handle alternating current. A rectifier is about 81.2% efficient. The battery management system also limits the power to prevent overheating. This is especially important for level 3 (public) chargers. A Mustang Mach E ER limits the power to 150 kW, while a Bolt limits you to only 55 kW.

Battery charge times

Battery charge times for common EVs. Data Source

The graph at right shows the problem. Charge times incre­ase linearly with battery capacity. If someone produced a battery with ten times more capacity, it would take ten times longer to charge it.

Suppose you said “No problem, just increase the power of the charger by a factor of 10.” Suppose there was a Level 3 charger that could handle that, say 3500 kW, or 4375 amps at the standard 800 volts. A cable that could handle that current without melting would be too heavy to lift; they'd have to raise the voltage to 8000V to make it practical. Your Mach-E would take exactly the same length of time to charge as it does now.

To be specific, let's assume you could tolerate 1000 watts of heat in a 2-meter cable. With 4375 amps and 800 volts, that means the acceptable power loss can only be 0.028571%. It would require a cable with a cross-sectional area of 38,281 mm2 or 8.69 inches in diameter, which would weigh 1511.7 pounds.

With 437.5 amps and 8000 volts, to get the same amount of cable heating would still require a cable 382.82 mm2 area or 0.87 inches in diameter. It would weigh 15.1 pounds, and it would still be a mighty stiff cable. The point is: you would need huge cables or huge voltage. What we'd end up with is tens of thousands of volts inches away from your car.

That is, of course, assuming the heat dissipation rate in your car is still enough to handle it. Most likely, you're going to need a bigger cooling system now, with more liquid coolant with antifreeze and corrosion inhibitors, a bigger radiator, and a bigger fan. That's because a battery only works between 20° and 40°C and can only handle a 5°C difference between different parts of the battery. If the ambient temp is below 20°C (68°F) or over 40°C (104°F), the battery must be heated or cooled. A radiator leak in an EV is far worse than a radiator leak in an ICE vehicle. The ICE will just seize up. An EV with a 5000 kWh battery would be practically a small nuclear weapon.

Power Availability and Explosive Yield of an Electric Car

An energy of 5000 kWh is equivalent to 4.3 tons of TNT, or 1/232 kT. It would take 3486 of these cars, which just coincidentally is almost exactly the number on that transport ship that caught fire, to equal the energy in the Hiroshima explosion. The Douglas AIR-2 Genie had a W25 nuclear warhead that produced 1.5 kT. So one of our hypothetical 5000 kWh batteries would be 1/348 as powerful as that. Clearly, if energy yield is the important factor, nuclear power is the future for cars.

This would greatly improve safety as well, as people would be strongly disincentivized from having vehicle collisions.

With our current batteries, the numbers are bad. Manufacturers exaggerate the range and give unrealistic charging times. The actual usable capacity is only 95% of the gross capacity, which is what automakers advertise. There are many reports claiming that with ordinary driving, the distance you can get is only 75% of what they claim. The AAA says using the electric heater on a cold day reduces range by another 41%; using the a/c reduces it by 17%. People who live in humid climates know you sometimes need both to keep your windshield from fogging up.

Taken together, this means on a really bad day, you'd get 0.95 × 0.75 × 0.59 × 0.83 of what you expect, or 34.9%—about 1/3 of what the government claims.

As for power availability, in my city the electricity goes out when it rains or snows or when there's a particularly strong wind. It's usually out for a day or so, but sometimes it's out for up to two weeks. Almost everyone here has a backup generator that runs on natural gas or gasoline. If not, after a couple of days your car would have to be towed to a public charging station unless you live in a house and can afford to have a charger installed.

These limitations have practical consequences. Last year I was hoping to downsize. The only suitable place was 40 miles from the nearest grocery store. Given the above numbers, the car would not have been able to make the trip. So I'm stuck in a city I hate with a rusty 22-year-old car that leaks a variety of unidentified brown liquids because nobody knows what the US government is planning to do.


jul 27 2024, 7:31 am. updated jul 28 2024, 7:18 am


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