Roadster Efficiency and Range

[Cobos]

I'm not sure if I'm on a wrong idea here, but it seems a compromise might be useful. Say half the pack is exchangable and is a nice round or rectangular box with standard connectors. If someone wants to make an EV with longer range they either have 2 of those boxes or they have one half swappable and the rest "hardwired" to the car. You might even run without the swappable pack on your daily commute to save weight.

This does add complexity so it might not be worth it, but if PBP is going to set a standard for a swappable pack it seems a smaller formfactor would be the logical solution.

Cobos

 

[graham]

This is actually sort of what I was envisioning for the Model S. They have talked about single battery packs for the low end model and multiple battery packs to get to the 300 mile range. They have talked about swappable batteries. My thought was for swappable to work, it would have to work whether you got the single pack or the multi packs... so it probably only works for the "first" battery. The first battery has to be in a standard configuration and placement. If you have multiple packs, the additional ones never change.

Only a guess of course.

This would give you an initial long range, say the 300 miles they are waving about. If you run out of that, you can quick swap the first battery for another 160 miles. repeat as necessary until you can do a full slow charge.

 

[max_andrews]

Tesla Range Estimates at various speeds

Hi everyone! First post for me here! Sorry if this has been covered before, but I just ran some numbers on real-world range estimates and though i'd share.

The horsepower to sustain a given speed is roughly the sum of the rolling resistance, air resistance, and friction loss at that speed.

Let's let friction loss be 1.5HP at 20MPH, and increase as a function of the square of velocity. I'd like better accuracy here, but this is in-line with some real world corvette numbers I saw so for this example good enough. A quick list:

20mph: 1.5 hp
30mph: 3.4 hp
40mph: 6 hp
50mph: 9.4 hp
60mph: 13.5 hp
65mph: 16 hp
70mph: 18.4 hp
80mph: 24 hp
90mph: 30.4 hp
100mph: 37.5 hp
110mph: 45.4 hp
120mph: 54 hp

Rolling resistance is given as (mass * gravity * coeff. of rolling resistance * speed);
mass in kg, gravity 9.8, for the coefficient of RR we'll assume .01 for low-loss tires, and the speed is m/s. The value this returns is in watts, so we must transform this into horsepower. Here's the estimated horsepower required to overcome rolling resistance at various speeds:

20mph: 1.5 hp
30mph: 2.2 hp
40mph: 3 hp
50mph: 3.7 hp
60mph: 4.4 hp
65mph: 4.9 hp
70mph: 5.2 hp
80mph: 6 hp
90mph: 6.6 hp
100mph: 7.4 hp
110mph: 8.1 hp
120mph: 8.8 hp

Air resistance is a bit trickier. Basically, for output in watts, for formula is [(.5 * p * (V * V) * A * Cd) * V]
V = velocity in m/s (variable)
A = frontal area in m^2 (estimating 1.8 m^2 for tesla)
Cd = drag coefficient (estimating .25 for the tesla)
P = desnsity of air in kg/m^3 (constant at 1.164 assuming 30 degrees ambient)

So for 60mph (27m/s), is would look like this: [(.5 * 1.164 * (27 * 27) * 1.8 * .25) * 27] = 5,200 watts or 7 horsepower. Here's the list:

20mph: 0.25 hp
30mph: 0.85 hp
40mph: 2.03 hp
50mph: 3.95 hp
60mph: 6.83 hp
65mph: 8.64 hp
70mph: 10.86 hp
80mph: 16.25 hp
90mph: 23.05 hp
100mph: 31.64 hp
110mph: 42.10 hp
120mph: 54.71 hp

Now for total horsepower needed, we just combine the three sections for each speed. I've rounded the numbers to the nearest horsepower:

20mph: 3 hp
30mph: 7 hp
40mph: 11 hp
50mph: 17 hp
60mph: 25 hp
65mph: 30 hp
70mph: 34 hp
80mph: 46 hp
90mph: 60 hp
100mph: 77 hp
110mph: 96 hp
120mph: 118 hp

To get the range at each speed, we take the capacity of the battery (53kwh or 71hph) and divide it by the amount of horsepower being used, and then multiply it by the speed to find the distance traveled. For 60mph: [(71hph / 25hp) * 60mph] = 170mi. Here's the list:

20mph: 473 mi
30mph: 304 mi
40mph: 258 mi
50mph: 209 mi
60mph: 170 mi
65mph: 154 mi
70mph: 146 mi
80mph: 124 mi
90mph: 107 mi
100mph: 92 mi
110mph: 81 mi
120mph: 72 mi

So there you have it. This seems to jive pretty well with the EPA highway estimate, which is 225 miles at an average of 48mph.

Of course these values do not take into account acceleration needed to get up to speed, and assume that you are constantly driving at the speed for the entire duration of the drive. If you stop at a traffic light, slow down in traffic, etc, you will lose power getting back up to speed - so in real-world conditions the milage is probably a bit lower than my estimates here. The values for 20 and 30mph of course assume no stops - and we all know if you are going 20 or 30 it's going to be around town with frequent stops. Also, this is where my friction numbers are most sketchy, so don't trust the 20 or 30mph numbers too much. In fact, the EPA highway/city numbers for the tesla are pretty much identical, so my 20mph value is double what it should be. And naturally, if you are doing some spirited driving in the hills with lots of braking and rapid acceleration, your mileage also goes to crap and these estimates no longer apply.

So what you can learn from this is that you can definitely get 225 miles going 48mph, but if you're cruising on 280 or 101 at close to 80mph, don't expect more than about 120 miles of travel before needing a recharge. Hope this is helpful!

 

[malcolm]

Hi max.

Thanks for taking the time to put this together. You may also want to look at this:

Tesla Motors - touch

Interestingly your range figures are on the generous side at very low speeds but a bit too low at high speeds.

But any calculations (even Tesla's) rely on assumptions :smile:

 

[graham]

Of course these values do not take into account acceleration needed to get up to speed, and assume that you are constantly driving at the speed for the entire duration of the drive. If you stop at a traffic light, slow down in traffic, etc, you will lose power getting back up to speed - so in real-world conditions the milage is probably a bit lower than my estimates here.

It also does not take into account the reclaimed power of regenerative braking. For city driving (or highway driving during rush hour in the Bay Area) slowing down does put some power back into the battery pack, which would extend the range somewhat.