I had taken the statement to mean that they thought that the biggest impact was wiper motors, not the biggest impact is rain. While the latter often necessitates the former, the wiper motors can be on without there being any rain—I knew a kid in high school who always drove with the wiper motors on. Very bizarre.
I discount the energy costs of wiper motor, headlights, etc. With modern vehicles, those are minimally impactful. I can even go out to measure it in the truck if needed.
Rain in the air impact on aerodynamics has only a couple percent impact on automobile drag (so overall not a large percent on total range). Though we get soaked during a rainstorm, the relative density of the air doesn’t change a lot, and the mass of the rain only matters a little bit.
However, as you noted: a thin film of water on the road will absolutely increase rolling resistance. It will depend a bit on the tire tread. Here’s one example from a research paper where they did experiments on the roads in Poland and Sweden.
You can see that for an 80 kph test, at about 0.65-0.7 mm of rain on the road surface, the rolling resistance is increased by about 40%. It gets even higher at higher speeds. This is in part due to the vehicle pushing water as you mentioned. It’s also because the tire temperature is decreased and that causes lower pressure and thus increased rolling resistance. This is just rolling resistance. This impact will be more noticeable at low speeds since rolling resistance has a greater relative effect on efficiency at low speeds. At higher speeds, drag takes over.
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Humidity doesn’t have a large impact on aerodynamic drag; this is mostly because high humidity air tends to be warmer air and density is more dependent on temperature than humidity, so highly humid air tends to be less dense.
Overall, for an EV, on a no-HVAC drive, something like >95% of the energy gets to the driveline (as opposed to ICEs, which lose about 79% of the energy to heating up the surroundings without producing useful work). Driveline losses cost about 2% - 5%. So about 90% of the energy is delivered to the wheels.
On the highway, about 45%-50% of the total energy expenditure is spent on pushing the air out of the way. If there’s a 4% increase in aerodynamic drag due to rain, that’s a 2% increase in total energy expenditure. 350 miles * 0.02 = 7 miles reduction in range.
For rolling resistance, at highway speeds, about 15% of the total energy expended is due to rolling resistance. If that increases by 50%, that’s another 7%-8% increase in total energy expense, which is about 28 miles reduction in range assuming 350 miles range.
Reducing speed a bit will overcome most or all of that increase in resistance.