A generic electric car on a 3D road. Cold air, a cold battery and a warm cabin all draw on the same pack. Typical figures are approximate.
Energy use--
Range (full pack)--
Cost / 100 km--
CO2 / 100 km--
Range of a full pack versus outside temperature (your other settings). Dashed lines: resistive heater and heat pump.
Selected heaterResistiveHeat pump
Energy use versus speed at your temperature, against the same car at 20 C.
NowOther heater20 C
Question 1: at which speed does the cold cost the most range in percent? Question 2: how much range does a heat pump give back at each temperature? Each answer is computed with the model and then re-checked with a time-stepped 100 km run.
Choose an experiment.
These run live on your current settings.
The science
Power needed at the wheels
P = (Crr m g cosθ + ½ ρ CdA (v+w)² + m g sinθ + m a) v, with Crr the rolling coefficient, m the mass, ρ the air density, CdA the drag area, w the headwind, θ the slope and a the acceleration. Battery power is P / η when driving and P · η · 0.9 when braking (regeneration), never more than the pack will accept.
What gets worse in the cold
Air density, ρ = p / (R T): 1.20 kg/m³ at 20 C but 1.39 kg/m³ at -20 C, so drag is 16 % higher at the same speed. Moist or snowy air and wet roads add a little more (not modelled).
Tyres stiffen and the road gets wet or slushy, so Crr rises roughly 0.4 to 1 % per kelvin below 20 C plus a road factor (wet 1.12, packed snow 1.6). These are approximate and depend on the tyre.
Cabin heat: Q = UA (Tset - Tout) - occupants with UA about 90 to 100 W/K at motorway speed (shell, moving air, fresh air). A resistive heater turns 1 kW of electricity into 1 kW of heat; a heat pump moves heat, COP = η2 Th / (Th - Tc) with η2 = 0.42 of the Carnot limit, capped at 4.5, so it falls from about 3.5 at 10 C to about 2 at -10 C.
Battery: usable capacity falls about 8 % at -10 C and 13 % at -20 C (approximate), internal resistance rises as R = R20 e0.02 (20 - T), so the I²R loss grows, and the pack accepts less charge, so regeneration is cut. Pack heating below 10 C is added to the auxiliary load.
Drivetrain: gearbox oil is stiffer, efficiency is lower by 0.06 % per kelvin below 20 C.
Why short winter trips hurt most
Heating is a roughly constant power (kW), not a force. Energy per kilometre is power divided by speed, so at 50 km/h the same 3 kW costs twice the Wh/km it costs at 100 km/h. The experiment tab measures this.
Simplifications
Pack voltage is held at 360 V (real packs sag with state of charge); battery temperature is assumed to follow the outside air, softened by the heater term.
One generic car (1850 kg with two occupants, CdA 0.575 m², 75 kWh): no brand or model. Efficiency, UA and temperature coefficients are typical approximate values, not measurements.
No altitude, humidity, battery pre-conditioning while plugged in, windscreen demisting or waste-heat recovery.
Cost and CO2 use your electricity price and grid intensity with 90 % wall-to-pack charging efficiency. They are illustrations, not tariffs.