TimeHorse : I used a shortcut approximation that range goes by the square root of speed, but I can obviously be completely wrong.TimeHorse wrote:Thank you, Carnac the Magnificent.gudy wrote:based on 70 miles at 55mph (with AC on), 95mph would give you about 24 miles of range.
Seriously, how can you with 1 speed / range determine what the range will be at another? Given that range is (speed * 24kWh / Power) and power required to overcome drag is proportional to the cube of the speed, all we can say for sure is there is some quadratic equation (with a reciprocal term, 1/v) that would determine the reciprocal range under those conditions. Solving for such an equation would require 4 distinct speed points with all other variables being equal. 70 mi at 55mph would only give you 1 of those. One could just as easily guess that the equation is v * 24kWh / ((v - 55mph)**2)kW + 18.8 kW, which is 70.2 mi at 55mph and about 1.4 miles at 95mph.
Here's the reasoning :
IF you exclude other drag / friction / losses :
Power required to overcome drag : P = some constant * speed ^ 3
Distance D = t (time) * speed
Time to empty t = C (battery capacity) / P
from these : D = C * speed / P
D = C * speed / ( some constant * speed^3)
D = C / (some constant * speed ^2)
If you increase speed by 95/55 = 1.72 , you'll reduce range by 2.98, hence going from 70 miles to 23.46 miles ...
Of course, drag does not account for 100% of the power you need, and there are also a lot of other factors which go both way (you're discharging the battery faster, therefore reducing its actual capacity, and you have high currents, increasing losses in power transmission).
Sadly, I don't feel like driving at 95 mph in a brand new leaf in the US, so I won't be the one doing the experiment ;p