# Tesla Roadster 0-60 Calculation



## ignoramus (Nov 17, 2012)

For a Roadster that weighs 1235 kgs and a motor that has a peak power capability of 185kW to 215kW. I calculate theoratical acceleration as follows:

Kinetic Energy at 60mph (96.5 kmph) is 0.5*1235*26.5*26.5 = ~430kJ

I am assuming a straight-line power delivery to the wheels as torque is constant from 0 rpm. So the average power would be half the max power. So assuming the peak power is 185kW, the average would be 92.5kW and it takes 4.6sec to impart 430kJ to the car (neglecting inefficiencies, which can be quite a bit). Yet, the real tesla can do much better than that. 

The only explaination that could I think of is that the power-delivery curve is not a straight line and the torque at low-speeds actually exceeds the peak-torque thereby imparting more power/energy than the peak rating? 

Or, are my numbers simply wrong?


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## major (Apr 4, 2008)

ignoramus said:


> For a Roadster that weighs 1235 kgs and a motor that has a peak power capability of 185kW to 215kW. I calculate theoratical acceleration as follows:
> 
> Kinetic Energy at 60mph (96.5 kmph) is 0.5*1235*26.5*26.5 = ~430kJ
> 
> ...


Your method is wrong. K.E. says nothing about acceleration. It is simply the energy associated with the mass at a particular speed. You can deduce that 92.5kW can be delivered for 4.6 seconds to change the system energy by 430kJ but it is incorrect to assume that is the only way to change the speed from 0 to 60mph. In fact, you could not deliver 92.5kW at 0.

You need to use the F = ma relationship.


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## ignoramus (Nov 17, 2012)

major said:


> You can deduce that 92.5kW can be delivered for 4.6 seconds to change the system energy by 430kJ but it is incorrect to assume that is the only way to change the speed from 0 to 60mph. In fact, you could not deliver 92.5kW at 0.
> 
> You need to use the F = ma relationship.


The 92.5kW is the average of a straight line that starts at 0(at 0 speed) and ends at 96.5 kmph (final speed, peak power 185kW). 

I also agree with you that a straight-line power delivery is not the only way to take the car from 0 to 60 but in the case of a roadster which uses a AC drive and from what I understand from the graphs, the power delivery is a straight-line upto the synchronous speed(~6000 rpm) (I assumed that 60mph is below that 6000rpm).

If I use the F=ma method. The power required to propel a mass from 0 to 60mph would be P = m*a*V = 1235*6.79*26.5 = 222kW(0 to 60 in 3.9 sec). If I take that 222kW number and half it to 111kW and compute the time it takes to give the car a KE of 430kJ, then it would give me ~3.9sec

All the above calculations still don't consider any inefficiencies.

I am sure I am making a silly mistake somewhere but don't know where ...


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## Jordysport (Mar 22, 2009)

I thought i would have a crack at this, 

ok so the tesla produces 270Nm of torque and Peak Power of 185kw if we assume that peak power will occur at roughly 270Nm which it most defiantly will.

Power = RPM * 2 * PI * Torque / 60000 to find RPM

which is 6542 rpm approx, so our motor map will look something like this: *(in attachments)*

Then simply put into an Iterative spreadsheet for speed. All based on F = M*a

*(in attachments)*

Inputting all the data from the wiki page gives results of 

0-60 in 5.57 seconds and 0-100mph in 9.89 seconds and a top speed of 122mph (gearing limited) 

Which is not far off  (for the original Tesla there appears to be MANY variants)


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## ignoramus (Nov 17, 2012)

Jordysport said:


> I thought i would have a crack at this,
> 
> ok so the tesla produces 270Nm of torque and Peak Power of 185kw if we assume that peak power will occur at roughly 270Nm which it most defiantly will.
> 
> ...


Nice graphs. So, your calculations add an extra second to my theoratical 4.6, which looks reasonable as rolling resistance and air-drag don't matter for much at such high accelerations. 

Also, I just realised that the 185kW could be mechanical power and not electrical so the inefficiencies would be just in the transmission (which may not be too high)

Roadster's graphs - http://webarchive.teslamotors.com/performance/acceleration_and_torque.php

How can real numbers be better than theoratical/calculated one's? Unless they are computed wrongly


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## Jordysport (Mar 22, 2009)

ignoramus said:


> Nice graphs. So, your calculations add an extra second to my theoratical 4.6, which looks reasonable as rolling resistance and air-drag don't matter for much at such high accelerations.
> 
> Also, I just realised that the 185kW could be mechanical power and not electrical so the inefficiencies would be just in the transmission (which may not be too high)
> 
> ...


I Summary with all equations and calcs......shit in shit out. in other words your results accuracy are only as good as the accuracy of the inputted data. 

eg CdA i couldn't find the value quickly so took Cd 0.35 * width * height. 

I didn't see those graphs i just made mine relative to the numbers but you could map the motor better to get a higher accuracy. furthermore this is all assuming a perfectly smooth and perfectly flat road surface with completely still air which is impossible to achieve in real life. but there is only so much you can do. 

You can't say that RR & Drag force are too small to worry about at high acc. Acc is not related to drag force its Velocity.
eg at 60mph the tesla's drag is 15% of the power!


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## subcooledheatpump (Mar 5, 2012)

Just going to throw in some info 

The Tesla Roadster has a top speed of 125.6 MPH with the optional 225/45/R17 tires, With the standard 175/55/R16, it has a top speed of 118.6 MPH. The difference in tire size also affects the torque since the tires are in a way like a final gear IE; a larger tire means you go further with fewer rotations but less forces are acting to move the vehicle, and vice versa with smaller tires.

These top speeds also assume 14000 RPM electric motor speed, 2.6538 gear ratio and 3.12 final ratio, 8.28 overall ratio(gear ratio and tire sizes available on the tesla motors website)

The website also states the Roadster has 273 ftlbs torque at 0 to 5400 RPM, Roadster sport has 295 ftlbs at 0 to 5100 RPM

power for the roadster is 225 kW at 5000 to 6000 RPM
Power for the roadster sport is 223 kW at 4400 to 6000 RPM

Have fun calculating


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## ignoramus (Nov 17, 2012)

Jordysport said:


> I Summary with all equations and calcs......shit in shit out. in other words your results accuracy are only as good as the accuracy of the inputted data.
> 
> eg CdA i couldn't find the value quickly so took Cd 0.35 * width * height.
> 
> ...


My bad, I shouldn't have said RR and drag-force are insignificant at such high accelerations, in a general sense. I meant to say that it is the case for current problem at hand. Like you said, 15% would only make the results worse by 15% not the large discripency that I see in my numbers to that of real stuff.

I suppose, what I am trying to say is that if the real number is 3.9sec then theoratical ones should be ~3 or less to account for all the real-world losses, RR, Cd stuff etc.


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## Brute Force (Aug 28, 2010)

It's worth noting that the top speed for the Tesla Roadster is governed.


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## Jordysport (Mar 22, 2009)

Brute Force said:


> It's worth noting that the top speed for the Tesla Roadster is governed.


By max RPM yes, 14,000 RPM. 

Ok, I've done a much more accurate analysis of it just for fun . and assuming perfect traction the Tesla Sport Performance as follows: 

0-60 - 3.59
0-100 - 8.95
Top Speed - 126mph 

Obviously i then had to take into account tractive force, and the only unknown value was COG height, so based on a perfect launch done to achieve 3.7 seconds to 60, the COG height would be 38.5cm off the ground which isn't unrealistic, that results in traction issues up to 48 mph (2.93 seconds) after which full throttle can be applied. 
With this setup now it achieves 

0-60 - 3.70
0-100 - 9.04
Top Speed - 126mph.

Here is the spreadsheet i made for it  you can change values and it should all change fine.


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## ignoramus (Nov 17, 2012)

Jordysport said:


> By max RPM yes, 14,000 RPM.
> 
> Ok, I've done a much more accurate analysis of it just for fun . and assuming perfect traction the Tesla Sport Performance as follows:
> 
> ...


Yep, I found my mistake. It was in my assumption that the car reaches 60mph before it enters the constant power-region. 

Thanks to Jordysport's detailed spreadsheet, I now know that it enters constant-power region at about 48mph there by increasing the average value of the total power applied. Instead of half the peak power (213/2 = 106.5kW in this case), the average power is higher at 127kW thereby bringing the system's KE to the required level faster and hence shorter acceleratioin times. 

Thanks, Jordysport.


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