CU‐Boulder ECEN5017/USU ECE6930  

Acceleration Capabilities of the Tesla Roadster

The specifications for the Tesla Roadster are available online:

http://www.teslamotors.com/roadster/specs

The goal of this problem is to verify analytically the 0-60 mph acceleration time ta of the Tesla Roadster. Throughout the problem, use the specifications from the “Performance” and “Dimensions” tabs, for the standard (non-sport) roadster. Note that some answers may be obtained via multiple approaches; full credit will be given for any correct approach.

a) From the website, retrieve the following information and convert to the given units:

Maximum engine Torque Temax [Nm]

Maximum engine power Pemax [kW]

Engine rpm at base speed nebase [rpm] (take from upper range of torque rating)

Maximum engine rpm, nemax [rpm]

Maximum Speed vmax [m/s]

Curb Weight (mass) Mv [kg]

Front Area Av [m2] (estimate from dimensions)

Battery capacity [kWh] (estimate from rated charging power and time)

Range [mi]

b) Calculate the following:

Approximate base speed vb

x = vmax/vb

c) Given the results of parts (a-b), plot the approximate vehicle tractive force Fv [N] and power Pv [kW] vs speed curves of the Tesla roadster for speeds between 0 and 60 mph. You may assume that the maximum power rating remains unchanged across this range of speeds. Label the force and power at 0 MPH, base speed vb, and 60 MPH.

d) Using the results of (a)-(c), solve approximately for the time, ta, taken to accelerate from 0-60 mph in the Tesla roadster. For this, assume that the roadster is tested on a flat, concrete or asphalt road and that the vehicle body type is well modeled as K-shaped (as detailed in lecture) for aerodynamic drag calculations. How does your calculation compare to the reported value from the website?

e) Under the same assumptions as above, and assuming the roadster drivetrain is 100% efficient, estimate the following:

Maximum continuous speed to achieve the rated range (ignore all acceleration)

Energy required to accelerate from 0 to 60 MPH in the rated time. Give the result in kWh and in percent of battery capacity.