How long does it take for an electric car to get 60 mph? (Comparison of various cars)

[jumpjack]

I have some literature data for EVs:

kg W Nm sec-to-60mph
Chevrolet Volt 1715 63 130 9,0
smart fortwo electric drive 900 55 130 12,9
Mitsubishi i-MiEV 1185 47 180 13,5
Citroen zEro 1185 49 180 13,5
Peugeot iOn 1185 47 180 13,5
Toyota Prius Plug-in 1500 60 207 10,7
Renault Zoe 1392 65 220 8,0
Renault Fluence Z.E. 1543 70 226 9,9
Nissan leaf 1595 80 280 11,9
Toyota RAV4 EV (US only) 1560 115 296 8,0
Tesla S 1999, 225, 430, 120, 5.9
Tesla S Perf 2108, 270, 440, 125, 5.4
Tesla S Perf Plus 2108, 310, 600, 130, 4.2

These are for ICE vehicles:
Fiat Stilo: 1488 kg, 255 Nm, 11.2 s
BMW M3: 1885 kg, 400 Nm, 5.3 s
Citroen C3: 1126 kg, 133 Nm, 14.5 s

I'm looking for formulas which allow me to calculate 0-60 mph time given mass, torque and power.
All formulas I found give impossible results like >60 seconds!

Any help?

[RedDevil]

W should be kW for kiloWatt.
Feed your formulas with kiloWatt (Watt * 1000) and you'll get acceptable results.

Any chance you could add a Tesla model S to that list?

[jumpjack]

Unfortunately I'm not allowed to edit my post.
Anyway I already used kW rather than W, it's a typo...

Tesla S 1999, 225, 430, 120, 5.9
Tesla S Perf 2108, 270, 440, 125, 5.4
Tesla S Perf Plus 2108, 310, 600, 130, 4.2

[RedDevil]

Okay

Let's do some number cracking.
First let's assume that the power can be used 100% to generate acceleration. Of course there will be losses, but those are hard to factor in.
If the power is calculated as to the wheels, the losses should not be too big, if at all.

We need to know how much energy is required to reach a certain speed.
It takes one joule (??) to speed up one kilo from a standstill to one meter per second, or 3.6 km/h. ...
(EDIT: that 's not right, obviously. Made the rest of the post obsolete. Removed that.)

[RedDevil]

Forget that last post. I goofed up right from the start.

It takes one Newton to speed up one kilo from a standstill to one meter per second, or 3.6 km/h, in one second.
It will travel half a meter doing that, so one Newton over half a meter means just half a Joule was spent.

We need to go 60 miles per hour, that is 96.56 km/h or 26.8222 m/s.
The relation between speed and energy is quadratic, so we need that squared times half a Joule to find how many joules we need to speed up one kilo to 60 mph: 359.72 Joules

The Tesla S weighs 1999 kg, so it needs 719,072 joules to reach 60 mph from a standing start.
It produces 225,000 Watt (Joules per second).
So according to this formula it needs 3.19 seconds to reach 60 mph.

That's a lot less than the 5.9 it actually needs.
Of course the driver adds extra weight. Say 5%. That would slow it down to 3.24 seconds.

It cannot use all its power when it is still moving below a certain speed; the wheels would spin.
Say it would accelerate at 6 m/s² until it can use full power, from where the acceleration slows down. At 225 kW and 2100 kg (add driver) that would be at 17,8 meters per second, say after 3 seconds.
It would have spent, on average, half the power it has during those 3 seconds so that adds 1.5 seconds to the time we calculated earlier, so 4.74 seconds.
Still more than a second faster than the actual acceleration time.

There are additional factors.
Maybe the traction control jumps in, there is friction in the tires from deforming while accelerating, there is wind resistance, rolling resistance, rotational mass to speed up.
If that all combines to 20-25% of the whole then we've done it! Accuracy

[NachtRitter]

Also, isn't the power figure provided (the 225kW) typically at the motor, not at the wheels (e.g. hp vs bhp)? The Tesla drivetrain is likely more efficient than a typical ICE drivetrain, which has a 15% "rule of thumb" loss, but since they are using a differential & half shafts vs in-hub motors, there's still some loss there. Along with the losses you note, it may make the total % loss more reasonable.

(On the other hand, maybe the power rating is under-reported... Tesla Model S Cranks Out 428 Horses At The Wheels: Video)

[niky]

Very hard to take a roller-dyno of an electric car at face value. Rollers have a problem with cars that produce lots of torque right at the get-go... and with no gears and an electric motor, the Tesla produces a crapload of torque at the get-go... which is why we typically dyno newer cars in fourth or fifth gear (helps give you a longer pull to get the turbo spooled up, too).

Also have no clear read-out of torque versus rpm and/or road speed... which is much more important. Also no word of SAE corrections, which would have been silly to apply, since it's not a gasoline motor... ...but some machines do this automatically, anyway.

Granted, the performance of the Model S in terms of 0-60 does suggest it really makes that much power at the wheels. That is one hot momma.

[Mustang Dave]

I read an article recently about some Austrian (as I recall) engineering students who built an electric car. It looked like a miniature Formula 1 car. It had an electric motor driving each wheel. 0-60MPH time was 2.4 seconds - quicker than a Bugatti Veyron's 2.5 seconds. Top speed was just over 60MPH.

[RedDevil]

Originally Posted by Mustang Dave

I read an article recently about some Austrian (as I recall) engineering students who built an electric car. It looked like a miniature Formula 1 car. It had an electric motor driving each wheel. 0-60MPH time was 2.4 seconds - quicker than a Bugatti Veyron's 2.5 seconds. Top speed was just over 60MPH.

See http://ecomodder.com/forum/showthrea...tml#post396094
Four wheel drive on slicks, 135 hp/100 kW weighing just 145 kg, TC/thrust vectoring per wheel, max torque all the way: results in 2.15 seconds to 100 km/h (62 mph). Hard to beat...