Hit the Road: the Aerodynamics of Cars On-Road
This blog is mainly a summary of what has been done to understand and possibly predict the aerodynamic performance of road cars on road.
While it might sound a bit repetitive to say "road cars on road", the fact is a lot of aerodynamic study of road cars are done in a rather calm wind tunnel. That could result in some significant difference from real-world on-road conditions. If only the straight-line drag coefficient is used to predict a car's fuel consumption over a certain cycle, chances are it will be underestimated. To address this, the concept of "wind-averaged drag" is brought forward.
First of all, for a given ambient wind condition, the resultant velocity and aerodynamic yaw angle can be calculated using the equations below:
The idea of "wind-average" is to use the probability statistics of wind direction and velocity to assign a weighting to each wind condition then calculate the averaged drag. And there are many ways of doing it.
Mr. Steve Windsor of Jaguar and Land Rover Ltd. has summarized three typical methods used for calculating wind-averaged drag: the MIRA, SAE and TRRL method. The table below shows the probability distribution for wind direction and speed assumed by each method.
Now, with a given vehicle speed, the resultant wind velocity (with reference to the vehicle) can be determined for each wind condition. And if the vehicle's yaw sweep data is available, the force coefficient for a particular yaw angle can be looked up or interpolated, hence the force can be calculated. The assumption here is that the force coefficient is a function of yaw angle only.
The wind averaged drag coefficient becomes a bit more interesting here. By definition it is:
While the wind probability is constant for each method, the resultant wind velocity varies with the vehicle speed given. So the wind averaged drag coefficient is a function of vehicle speed. It is still a dimensionless term, but since it varies with vehicle speed, its non-dimensionalization becomes less necessary in my humble opinion.
MIRA and SAE method both assume uniform directional probability, which might not be so accurate. So researchers have incorporated more detailed statistics of wind and highway directions in a particular region to improve their model. Others have sought to take aerodynamic measurements on road to characterize on road wind conditions.
The US Environmental Protection Agency has conducted "Constant-Speed Torque Tests" on road in order to measure the wind-averaged drag. The test vehicle is equipped with an anemometer and its data are correlated to theoretical calculations based on multiple road-side weather stations.
Tesla Motors and EXA Corporation collected aerodynamic data on-road during a typical drive cycle. The recorded fluctuation in yaw angle and turbulence intensity are fed into a transient CFD simulation, whose results help to improve the electric vehicle's range prediction.
Starting from similar projects like this, EXA Corporation has included an "on-road aerodynamics" simulation mode into their latest product. The details of this simulation are not clear but I am guessing that some transient inlet boundary condition (varying yaw angle and turbulence intensity, perhaps) is used.
Similar to what Tesla and EXA Corporation has done, researchers at Durham University has attempted to simulate on-road wind conditions in a model-scale wind tunnel equipped with a Turbulence Generating System. This turbulence generating system uses a set of vertical aerofoils (showing some respect for the British aerodynamicists by spelling it so) ahead of the test section with a mechanism to control and vary their angles of attack (AOA) at different frequencies. With the aerofoils' AOA varying, different yaw angle and turbulence length scale can be achieved in the wind tunnel. The pattern of such variation can be tailored to match a recorded on-road condition for a typical drive cycle. (link)
While these studies have become excitingly sophisticated, I am still wondering how the wind-averaged drag method compares to the more advanced methods when it comes to efficiency prediction model.
While it might sound a bit repetitive to say "road cars on road", the fact is a lot of aerodynamic study of road cars are done in a rather calm wind tunnel. That could result in some significant difference from real-world on-road conditions. If only the straight-line drag coefficient is used to predict a car's fuel consumption over a certain cycle, chances are it will be underestimated. To address this, the concept of "wind-averaged drag" is brought forward.
First of all, for a given ambient wind condition, the resultant velocity and aerodynamic yaw angle can be calculated using the equations below:
V_res = { [V_car + V_wind * cos(theta)]^2 + [V_wind * sin(theta)]^2 )^0.5
Ψ = atan{ [V_wind * sin(theta)] / [V_car + V_wind * cos(theta)] }
Wind Speed (V_w), Vehicle Speed (V_v) and Resultant Speed (V_RES)
courtesy of Steve Windsor
The idea of "wind-average" is to use the probability statistics of wind direction and velocity to assign a weighting to each wind condition then calculate the averaged drag. And there are many ways of doing it.
Mr. Steve Windsor of Jaguar and Land Rover Ltd. has summarized three typical methods used for calculating wind-averaged drag: the MIRA, SAE and TRRL method. The table below shows the probability distribution for wind direction and speed assumed by each method.
Now, with a given vehicle speed, the resultant wind velocity (with reference to the vehicle) can be determined for each wind condition. And if the vehicle's yaw sweep data is available, the force coefficient for a particular yaw angle can be looked up or interpolated, hence the force can be calculated. The assumption here is that the force coefficient is a function of yaw angle only.
The wind averaged drag coefficient becomes a bit more interesting here. By definition it is:
While the wind probability is constant for each method, the resultant wind velocity varies with the vehicle speed given. So the wind averaged drag coefficient is a function of vehicle speed. It is still a dimensionless term, but since it varies with vehicle speed, its non-dimensionalization becomes less necessary in my humble opinion.
MIRA and SAE method both assume uniform directional probability, which might not be so accurate. So researchers have incorporated more detailed statistics of wind and highway directions in a particular region to improve their model. Others have sought to take aerodynamic measurements on road to characterize on road wind conditions.
The US Environmental Protection Agency has conducted "Constant-Speed Torque Tests" on road in order to measure the wind-averaged drag. The test vehicle is equipped with an anemometer and its data are correlated to theoretical calculations based on multiple road-side weather stations.
Tesla Motors and EXA Corporation collected aerodynamic data on-road during a typical drive cycle. The recorded fluctuation in yaw angle and turbulence intensity are fed into a transient CFD simulation, whose results help to improve the electric vehicle's range prediction.
Starting from similar projects like this, EXA Corporation has included an "on-road aerodynamics" simulation mode into their latest product. The details of this simulation are not clear but I am guessing that some transient inlet boundary condition (varying yaw angle and turbulence intensity, perhaps) is used.
Similar to what Tesla and EXA Corporation has done, researchers at Durham University has attempted to simulate on-road wind conditions in a model-scale wind tunnel equipped with a Turbulence Generating System. This turbulence generating system uses a set of vertical aerofoils (showing some respect for the British aerodynamicists by spelling it so) ahead of the test section with a mechanism to control and vary their angles of attack (AOA) at different frequencies. With the aerofoils' AOA varying, different yaw angle and turbulence length scale can be achieved in the wind tunnel. The pattern of such variation can be tailored to match a recorded on-road condition for a typical drive cycle. (link)
Durham University's TGS Wind Tunnel
While these studies have become excitingly sophisticated, I am still wondering how the wind-averaged drag method compares to the more advanced methods when it comes to efficiency prediction model.
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