Electric vehicles – Analysis of the forces applied on a vehicle and static factors on power consumption

Every vehicle presents its own specifications and power conversion is definitely determined and communicated by the car maker but most of this information is also set by basic physics formula and thus, can be put in equation so varying entry parameters can be taken into account while calculating evolving values.

A car as a system itself

On a car, multiple forces apply and have to be integrated in estimation and computation to transform the theoretical result into a more realistic one to improve reliability of the algorithm and the overall API.

Some of those forces could be considered as constant but several are depending on other element and are varying over time and the context.
Here are the description of the forces that would apply on the vehicle, we can differentiate those that are directly related to speed and those that are quasi-constant.

Weight and reaction force

The weight of the vehicle is directly linked to its masse and can be calculated by equation that will be used later.
The weight is varying if the masse evolves and in a vehicle, it can be done by modifying the load of it.

Also, this force is oriented to the ground (center of Earth) and thus, it can affect as a resisting force while being on a hill and going up, on the contrary if going down helping the car and acting as a thrust that is usually convertible using regenerative brake system.

Reaction force is directly the result of the weight and inertia of the vehicle on the wheel and tires on the opposite direction of the weight.

Thrust

The thrust if the force produced by the engine or electric motor which is converting energy from various source into energy of movement.
Thrust is depending on driver activation and the force is transmitted on the ground by the tires.

Downforce and lift

Related to the speed, the downforce and lift are applied to the vehicle on opposite ways but rely mainly on the effect of air upon the vehicle and its body.
Downforce is pushing the car on the ground acting as another force in the same direction as the weight.

Lift is by definition, lifting the vehicle by putting a force in the opposite direction as the weight, obtained from the aerodynamic effects.

Rolling resistance

This force is a ground reaction that applies on each tire and is depending on the material, the structure and also the shape of the tires but also of the ground the vehicle would be in contact with. A coefficient without unit is describing the relationship surface to surface for the two components and can vary while the surfaces change (precipitation, rugosity, temperature…).

Air drag

Air drag, or aerodynamic drag, is composed of multiple element related to the action of air that is going through or over the vehicle’s body.
It obeys to fluid law of physics and is globally opposed to the vehicle direction and is also based on varying elements such as vehicle’s speed and air speed but also on several information linked to the vehicle specification such as the drag coefficient which has to be reduced on any vehicle but especially on electric ones in order to obtain extended range on long journey at constant and relatively high speed.

Air drag is composed of multiple forces that are taken into account of this drag coefficient and it includes the form drag (related to the shape of vehicle, it is the most important part of the air drag), internal drag, skin friction, interference drag and other drags mainly related to aerodynamics.

Power usage by speed

In a basic context, the vehicle will behave following basic curves that are set by factual car specifications, the main information is the power usage depending on the speed on a flat road and without any additional parameters like slope, weather or any additional configuration of the car that would affect the power usage.

This characteristic can be represented by a simple curve, here for example, the curve of a well-known vehicle which is the Tesla Roadster:

This curve’s shape is not really universal for all vehicles but mainly for purely electrical with a single stage gearbox (then, it would have different curves if multiple stages would have to be integrated), but it is mainly the case for actual electric vehicles.

Also, it is important to notice that this curve is different for every vehicle and even every configuration of a specific model as a similar model can be configured with a bigger battery that would be impacting the weight of the vehicle and also the electric motor used for example. In order to be accurate, it would be required to adjust and keep the reference in a dedicated approach for each vehicle, model and configuration and if there would be some variation like new model or a specific equipment.

Also, this amount might vary by the drive mode activated but also by the limitation put by the vehicle in case of low temperature or low power level in the battery as it will limit the power that can be extracted or regenerated in the system.

Power usage by auxiliary elements

In car and especially in the most recent ones, several components require power to be whether taken from the battery of generated by a generator which fulfill this function.

Power drawn by the auxiliary elements can be estimated and are varying based on external parameters (environment) but also on the user’s choices, among those, we can take into account:

  • Air conditioning
  • Seats heating or cooling
  • Lights
  • Screen and display luminosity level
  • Activated features (computation required more power for on-board computer)

Other specifications usable as estimable elements

As we’ve seen, many forces are depending on speed but also on other parameters directly linked to the vehicle itself. Car makers are rarely communicating all parameters of their car while it surely helps to adjust estimation and calculus required to obtain practical results, among those we can extract:

  • Static friction and mechanical conversion of the car itself
  • Rolling resistance coefficient determined by the tires and the weight of the vehicle (also known as Crr-Static)
  • Rolling resistance added with the speed or hill/slope information (Crr-Variation)
  • Air drag related to the drag coefficient: depends on the many parameters of the environment and by car specification
  • Weight and other forces applied can be computed as well

Those factors would help to better estimated and measure the potential impact of other factors and calculate with improved precision being able to adjust the impact of those car related factors and integrating new parameters in the basic calculation.

In the next posts focused on the analysis, we’ll deal about others factors and more precisely for the next one, the configuration of the car and describing the dynamic factors of the car that can affect the performance, the calculation and thus the power usage for a specific trip.

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