JeffK
Well-Known Member
Using 576 kW from a 102.4 kWh battery, a 77 kW battery should be able to output 433 kW. Assuming 70% efficiency, that means 303 kW on the wheels. I think the Model 3 will weigh approximately 1950 kg, including 75 kg for the driver. And the Model S can accelerate at up to 1.2G, if we say 1.1G for the Model 3, that probably isn't far off.
Using this information, we can calculate the time used on 0-60 mph (or 0-26.8 m/s).
First, we need to know at what speed the car is no longer traction limited:
v = P / ma = 303 kW / (1950 x 10.8 m/s^2) = 14.4 m/s
The time taken to do this acceleration is:
14.4 m/s / (1.1 x 9.8 m/s^2) = 1.34 seconds
Below 14.4 m/s, power is slowly building, as the car struggles to put down the power without spinning the wheels. Above this speed, all 303 kW go into accelerating the car. Going from 14.4 m/s to 26.8 m/s, additional energy needs to be inputed:
E(14.4) = 0.5 x 1950 kg x (14.4 m/s)^2 = 202.2 kJ
E(28.6) = 0.5 x 1950 kg x (26.8 m/s)^2 = 700.3 kJ
The difference is: 700.3 kJ - 202.2 kJ = 498.1 kJ
And the time taken to supply this additional energy is:
498.1 kJ / 303 kW = 1.64 seconds
The complete 0-60 mph acceleration will take 1.34 s + 1.64 s = 2.98 seconds.
BUT, the US method of measuring acceleration uses 1 ft rollout (30.5 cm). The above calculations do not take this into account. The time to accelerate through 1 ft is:
s = 0.5at^2
t = sqrt(s / (0.5a)) = sqrt( 0.3045 / (0.5 x 1.1 x 9.8)) = 0.23 seconds.
The time for 0-60 is thus 2.98 seconds - 0.23 seconds = 2.75 seconds.
I think the likely official number for the Model 3 is 2.8-2.9 seconds.
It's been thrown around that the Model 3 is 20% lighter so I'm going to suggest the weight of the Model 3 P75DL is closer to 1725 kg or less.
I'm sticking with 2.6 seconds 0-60.