Frank said:
tomsax, If you drive your Tesla at 65-70 mph on the freeway for half of the battery capacity, and the other half you drive in city traffic, with the AC on, what range do you get? The EPA range seems to be 221-244 on the Tesla Roadster and I'm wondering how far off the EPA estimate is when you drive given these conditions. You previously mentioned that the 244 EPA range could be achieved by driving 55 mph on level ground and I'm wondering if we can also apply that to the Leaf, meaning the Leaf could achieve 73 miles of range at a constant 55 mph. But I'm also interesting in knowing how the mixed driving conditions of freeway (at normal freeway speeds) and city driving.
Not to over think this as it's getting into the
Engineering forum but I think in summary we can look at the LEAF in the following way:
Power is the energy cost per unit time, as in kWh per h or kW. Therefore, it is possible to talk about what power is required to drive the car at a given speed, v, under given conditions. If you know the car's speed at the time of the calculation, you can then extrapolate how far it can go because if it's using P power and has 24kWh batteries it can go for 24kWh/P hours and thus (24kWh/P) * v miles.
So to figure out the range of the LEAF, at least on paper, you simply need to know what that Power function is; this is what is done on the Tesla site.
In simple terms, Power depends, obviously, on speed, on temperature visa vi climate control, wind speed and direction and whether you're going uphill or downhill: P(V, Tc, T0, Tt, m, W), where Tc is the current cabin temperature, T0 is the starting temperature (e.g. the temperature outside the cabin) and Tt is the target temperature, m is the slope of the current stretch of highway and V and W are vectors with magnitudes of speed and wind speeds and directions.
Of course this is a very complicated function. But it can be broken down into the following components:
1) Rolling Resistance: generally a linear term, which means that as speed increases, it increases proportionally. The Rolling Resistance of the tires attenuates this factor.
2) Acceleration: generally a square term, which derives from the fact that the more Kinetic Energy you put into your vehicle (the more you increase the speed) the more energy you use; you can also recapture Deceleration to the extent allowed through regenerative breaking, but the rest is lost as heat. The mass of the vehicle is also a factor.
3) Climbing / Descending: This term depends on speed with which you apply or remove Potential Energy by pushing your car up or letting your car roll down a slope. It depends on speed and again on mass.
4) Air Resistance: this is potentially the most complicated to calculate. It is also the chief limiting factor of a car's speed because it increases as the
cube of the velocity, meaning if it's, for example, 6.24 kW to maintain a speed of 55 mph, it's 12.86 kW to go 70 mph and only 1.01 kW to go 30 mph and a whopping 27.34 kW to go 90 mph, assuming no wind component and STP (Standard air Temperature and Pressure: 0 degrees Celsius and 100 kilo-pascals). In truth, this calculation, to be totally accurate, would involve calculating the current air density, which is based on the current air pressure, humidity and outside temperature (T0) as well as a tensor for the Coefficient of Drag at all angles of wind direction so that the Wind vector can be combined with the Cd Tensor and Velocity / Speed vector to get an appropriate magnitude of the Drag experienced by the car.
5) Climate Control: this is the only component that is part of base load, meaning it doesn't depend on velocity. Like the radio and headlights and CARWINGS, this is a fixed energy output that is working regardless of how fast the car is going; it is used even when the car is stopped. How temperature plays a part in range is rather complicated, but one could consider the volume of air needed to heat or cool (the cabin volume), the amount of heat lost through the windows or heat added through the windows (depending on whether (T0 - Tc) is negative (heater) or positive (a/c)) and whether the target temperature has been reached. The radiative heat energy lost / gained through the windows should be given as the difference of the quartics, i.e. between T0**4 - Tc**4 (a/c) or Tc**4 - T0**4 (heater), as well as the surface area of the windows of the cabin and the Radiation constant of the grey-body material, in this case Glass: 5.13E-8 W/m**2 *C**4. Now, I've no idea of the window area of the LEAF, so let's just assume it's 15 m**2. This means that if T0 is 95 F and Tc is 75 F, you're adding approximately 948 W of heat energy to your car through the windows (using the Blackbody equations of heat radiation adjusted for glass). Obviously, to maintain the 75 F cabin temperature, you're going to need at least that much energy since A/C is not 100% efficient, and that's with the windows rolled up and not including incident solar radiation.
Of course, those are just rough, ball-park calculations but should give a good idea of what to expect from the LEAF. Hopefully Gudy and the rest of you earlier adopters can give us some better, real-world examples of the LEAF performance.
In the mean time, I'm still speculating...
