A look at the Road Vehicle Model, how it works and some case studies. Building on the release of our Vehicle Model as a simple Excel Spreadsheet we wanted to look at how it works and how it can be used. This all builds on the basic Road Vehicle Power Demand and hence that is a good place to start.
Needs review: this page is a working draft of the Road Vehicle Model description. The intro above references “case studies” that are not yet included below, and the motor efficiency section still uses a fixed placeholder map rather than motor-specific data (noted inline further down). Treat the derivations on this page as in progress rather than final.
Aerodynamic Forces
The aerodynamic forces on the vehicle are proportional to velocity squared and hence become dominant at high speed. FA is the frontal area and Cd is the drag coefficient. ρair is the density of air and we assume 1.225kg m-3
Rolling Resistance
In the simplest terms the rolling resistance is a fixed term dependent on the vehicle mass, gravity and the tyre coefficient of rolling resistance (Rr).
Typical values for car tyres are an Rr ~ 0.006 to 0.01
Acceleration
If we accelerate the car very quickly we need to apply a force to do so.
Also, if we decelerate we have to apply a force to do that.
We sum all of these forces to get the resultant force acting on the vehicle and that required to move the vehicle over any particular drive cycle.
The Drive Cycle
A typical drive cycle would look like this. Here we see speed versus time with data at a 1 second sample time.
It is then simple to look at the speed change and calculate the acceleration.
v = u + at
Having the total force we then multiply that by the vehicle speed and we get the power.
power = force x velocity
Hotel Loads
These are all of the electrical loads on the system, other than those required to move the vehicle.
Typically these will be 12V based, but gradually more and more of these loads are directly from the HV bus. An example is the heat pump.
Total Power vs Time
We then add the Hotel Load power requirement to the power required to move the vehicle. Thus giving us total power required at any point in time. Repeat this calculation over the drive cycle.
Gearing to the Motor
We know the speed of the car, but we really want to know the speed of the motor. In an electric vehicle there is normally just one gear ratio between the motor and the wheels.
The wheel and tyre provide one part of the gear ratio and the belt / chain or gear set provide the second part of that overall gear ration.
For the rolling radius we use an equation that has been built from real tyre data. This then allows you to enter the tyre width, profile and rim size from which the rolling radius is calculated.
That then means for a given vehicle speed we know the rotation speed of the wheel and knowing the gear ratio (T2/T1) then gives us an overall ratio.
The tyre rolling radius calculation is all open and visible within the excel vehicle model.
Motor Efficiency
The final step is to work out the demand at the battery terminals and for this we need to know the motor efficiency.
First of all though we need to define the motor.
We use a simple approach where we ask for:
- Torque (Nm)
- Power (kW)
- Base Speed (rpm)
- Maximum Speed (rpm)
From these for numbers we can calculate the torque versus rpm and power versus rpm relationship of the motor.
The motor efficiency versus torque and speed looks like this. At this point we have used a fixed map, but will over time allow the user to select a motor type.
For now we have created a rough surface equation that maps to this. Thus allowing the model to run in a spreadsheet.
Hence we know the power demand versus time at the battery terminals. However, some big assumptions, the biggest is perhaps that this is an energy model that in the first instance assumes the vehicle can match the speed versus time trace.
We will build on this page so that we eventually create a full description of this model. Thus allowing you to understand and estimate the impact of vehicle design on battery pack requirements and hence design.
Battery Power Demand
Once we know the power demand versus time at the motor and the motor and inverter efficiency we then know the demand from the battery. This is a power versus time trace and we need to know the current.
Vehicle Model
A simple ground transport vehicle model in a Microsoft Excel spreadsheet. This works from the basic forces and equations of motion to calculate acceleration, steady state power / energy consumption through to drive cycle requirements.
See also: Electric Vehicle Range Calculator, Auxiliary Systems Power Consumption in Electric Vehicles, Cold Climate EV Range