Regenerative Braking Physics Question

[Nords]

Graham's Toyota Prius
"The harder you press the accelerator, the more torque the ICE produces. This increases both the mechanical torque though the ring and the amount of electrical power generated by MG1 for MG2 to use to add still more torque. Depending on various factors such as the battery state of charge, the road grade and exactly how hard you press the pedal, the computer might draw extra power from the battery to boost MG2's contribution. This is how highway passing acceleration is achieved with only a 70 horsepower ICE in such a big car. On the other hand, if power demand is not that high, some of the electricity produced by MG1 may be used to charge the battery, even while accelerating! The important thing to remember is that the ICE both drives the wheels mechanically and drives MG1 forwards enabling it to generate electricity. What happens to that electricity and whether more electricity is taken from the battery depend on complex factors which may be beyond our ability to fully figure out."

Translation:
"The car has a continuously variable transmission, but the battery boost means that you can still peel rubber accelerating uphill without worrying about a clutch."

Of course you can see the battery charge indicator drain right before your eyes, but by the time it gets low you're already going 75 MPH.

Or so I've heard.

 

[clifp]

I watched the energy consumption display, and it went from 1.7 kWh at rest to 2.9 kWh at the top speed of 100+mph, then dropped down to 2.4 kWh at rest again.

So, the car expended 1.2 kWh to get to that top speed and recovered 0.5kWh or 42% of that energy. That's not bad considering the energy irretrievably lost in the moving part friction, tire rolling resistance, and aerodynamic drag.

By the way, 1.2 kWh is the energy that can lift this 4,800-lb car a height of 660 ft. And in order to charge the 85 kWh battery from empty by regen braking, you need to coast the car from a height of no less than 47,000 ft.

The above numbers give me a better perspective on the amount of energy that is required to push a car at highway speed. It's huge.

47,000 foot that is a big mountain. My house is 1,000 feet above sea level and I spend a lot of energy moving the Tesla up the hill a once or twice a day.

In another video they pointed out that 1.2 KWH cost about $.10 in Florida where they film a lot of the drag racing videos. From a sheer entertainment value a dime to a 1/4 mile drag race in a Tesla is hell of a bargain.

Too bad it take $100K upfront investment to spend the dime.

 

[Nords]

Too bad it take $100K upfront investment to spend the dime.

But being able to use the phrase "Ludicrous acceleration" is worth it!

 

[NW-Bound]

47,000 foot that is a big mountain. My house is 1,000 feet above sea level and I spend a lot of energy moving the Tesla up the hill a once or twice a day...

Tesla says that the 85kWh battery can move the Tesla 320 miles at a constant speed of 55 mph. Seeing that this same amount of energy can lift a 4,800-lb car up 47,000 ft gives an idea of how much it takes to move a car sideways at highway speeds. And 55mph is not fast.

Here's some more simple calculations for one to get some insight. Imagine a long ramp of 320 miles, sloping down such that one end is 47,000 ft higher than the other. Take a Tesla, put it in Neutral (if it has that mode), and the car will coast at a constant 55mph down the ramp.

This ramp that has the car converting potential energy to exactly cancel out the aero drag and rolling friction has a slope of 2.78% or 1.6 degrees. That shows that the Tesla has a fairly low drag. When I coast down a 6% slope in my RV, I am not stupid to put it in Neutral, but in Drive, man, the darn thing hardly accelerates from 70 mph. Its aero drag is that bad!

Back to the Tesla, that constant 55mph down that slope means the drag is 133 lbs at that speed. On level land, the power to fight that 133-lb force at the speed of 55mph is 20 hp.

The aero drag effect on cars is huge. My RV only gives me 8-8.5 mpg at low elevations near sea level, and I generally drive at 60 mph. On trips in the high Western states like Colorado and Wyoming, I had as high as 9.5-10 mpg. When one considers that drag is proportional to air density, and that air at 7,000 ft is 80% as dense as at sea level, the result is not surprising.