Air resistance is proportional to v^2.

My dad told a story once where he was driving out west borrowing one of his brother's cars with a broken speedometer. After he got back he said to his brother, "the car just seemed to top out at a certain point" and his brother said "yeah, that's about 85 mph" (the national speed limit was 55 mph at that time). So at 85 mph the air resistance equaled the force the engine could apply and the car wouldn't go any faster.

Force is proportional to square of speed but power = force*speed so proportional to speed^3.

That's not how this works.

First, the force that is proportional to the square of the speed is the drag force, which means it's the force you need to supply just to keep the speed from dropping. Power = force * speed is a different "force" - it's the force produced by the engine.

Second, power output of an engine typically has an RPM where it peaks. Past that point, more speed means less power output, which means much less force output, because the force is the power divided by the speed. But force needed still increases as the square of speed.

It's exactly how it works and the math is not complicated.

Suppose you have a vehicle w/ 3 m^2 frontal area, drag coefficient of 0.3 and it's travelling at 30 m/s. Using this calculator https://www.symbolab.com/calculator/physics/drag-equation you can find that will require about 500 N of force (use density of 1.225). The power at that operating point is the product of speed and force, or 30 m/s * 500 N = 15 kW.

Now let's change the speed to 40 m/s. That bumps the force to about 900 N. Now we would calculate power as 40 m/s * 900 N = 36 kW.

Changing these numbers to horsepower we get 20 hp and 48 hp.

The force goes with the square, the power goes with cube. There are assumptions here - for example, if you have a headwind this statement is no longer true because the speed in the drag equation is the air speed of the vehicle (goes up with headwind / down with tailwind) but the third speed factor is the ground speed of the vehicle (because that's based on the physics "work is equal to force times distance" and power is the rate of work).

The graph of an internal combustion engine's power at wide-open throttle vs. engine speed is irrelevant, unless you are trying to figure out which gear ratios would let the engine make enough power to drive the vehicle under those conditions.

That's how top speed works.

Either that or you're limited by revs - in other words, there's enough net torque that, in the highest gear, the engine is running at redline before wind resistance stops you accelerating.

You don't see that much these days, though, as having your highest gear that short is just leaving fuel economy on the table on the highway. If you can pick up speed going uphill without changing down at least one gear, you're wasting fuel to pumping losses on flats/downhill.

However, ICE is more efficient at higher free speeds unlike electric so there’s a higher sweet spot.

How so?

There's quite a lot of energy needed to just turn the engine over in an ICE car so if you are driving a 5L car at 20mph most of the fuel use is just turning the engine rather than driving the car. Faster, more goes to driving the car.

ICE engines have an efficiency map of output torque/RPM and (up to a point) higher torque usually means more efficient use of fuel. In most ICE vehicles the engine efficiency gains balance with the drag efficiency losses between 40 and 50 mph.

More so that ICE has really bad efficiency at city driving due to lack of regen braking and engine idling.

EVs (and hybrids) with regen braking remove this lost efficiency in city driving, leaving you with an energy usage curve that scales more directly with aerodynamic drag due to speed.

EVs are more efficient at low and high speeds than ICE, they just have small “gas tanks” so the high speed losses are more noticeable.

The use of AC / Heat will also just burn through your battery or your gas at a much faster rate.

Does heating in internal combustion engine cars really affect fuel consumption? My assumption was that most cabin heat was waste heat from the engine, that would otherwise be vented out? Given the dismal efficiency of ICE, shouldn't it be enough to keep a cabin warm even in quite cold climates?

The engine by itself produces a lot of waste heat. But modern engines are more efficient and take a while to warm up (especially diesels, but small turbos like Honda 1.5 too) so cars sometimes implement resistive heating to heat the cabin quicker.

Also some cars have independent heating that can be used to heat up the car up without running an engine. Not sure how exactly it works but I think it uses special battery.

AC compressor of course takes a lot of power.

Which ICE cars use resistive heating? I've never seen an alternator large enough on an ICE car to do it. (I'm also skeptical of how well that'd work on a 12v electrical system)

Hybrids will commonly have them so they can run climate control independent of the engine (at least until the HV battery gets too low) and also bring coolant temp up faster. It seems like they are usually called the PTC heater or supplemental heater.

Ford also seems to offer them as an option (e.g. as part of the cold weather package)for a number of their straight ICE vehicles like the Bronco sport, Escape, or F-150.

See this https://shops.audi.com/en_GB/web/zubehoer/p/retrofit-solutio... for example. I can only assume it's resistive, since it doesn't start the engine - but it might be a system for running the AC heatpump without engine, maybe. Also now that I think of it, window defrost is resistive.

I would guess system like this would be rare in US, because you are allowed to have remote start on your cars.

edit: never mind, it burns fuel https://www.auditech.org/acont-1427.html

Electric window defrosters are really low wattage - because its just trying to raise the temperature of the surface of the glass by a few degrees. Generally IIRC no more than 25-30a - which is a fair bit on a car with a 100a alternator - but less than for example the blower for the air conditioner.

I never thought I'd see the return of the gasoline heater. I wonder if its offered in the states.

Block heaters can be used to heat the engine coolant (and afterwards the cabin) with or without running the engine. I doubt any cars have special batteries for these (even a drive battery of a non-plugin hybrid is somewhat small to be useful); block heaters that don't require external electricity simply use the car's fuel in an auxiliary burner.

Heat generally won't, in a modern ICE, that will capture a lot of the engine heat, though there are still electric and auxiliary heaters.

Slight nitpick: Using heat won't affect gas consumption of an ICE car. The heat is waste heat that otherwise would be dissipated through the radiator at the front of the car. Turning on the heat diverts coolant to a heat exchanger (tiny radiator) in the ventilation system that warms the air in the cabin.

Old trick for people that had cars with somewhat inadequate cooling systems: open the windows, turn on the heating to full helps to cool the engine.

However note that sometimes the A/C will be on at the same time as the heater in order to dry out the air.

This is one of those stupid facts that lives rent-free in my head. "If you want 'dry' hot air you need to dry it before sending it to the heater. The primary purpose of the A/C is to dry the air(this also happens to cool it), there is already an A/C unit in the ductwork, profit" But I decided to fact check myself and was not able to find much information. I did find one page that said this mainly occurs on the "defrost" setting, which makes sense as this is what is used when you don't want your windows to fog.

Regarding conditioning/drying the air instead of cooling it: the first modern air conditioners were invented primarily to dry the air, cooling was a side effect. The term "air conditioner" itself originally referred to moisture content as I understand it.

Thanks. Learned something today!

Heating for ICE vehicles is free because it redirects engine heat.

If your engine is overheating, one of the things you should do is turn the heater on max.

And since overheating usually happens on a hot day, open your windows and try to point the ac vets out them too.

The heat pump in the Tesla Model Y definitely uses electricity, but it is somewhat efficient. Much much more efficient than early model Nissan Leafs for a night and day comparison.