The yaw angle is the difference in direction between the direction of movement and the direction in which the car is pointing. A few similar topics that may go hand in hand with this study are the roll and pitch angles of the vehicle. The yaw angle is about the rotation in the z-axis (vertical axis), the roll angle is about the rotation in the x-axis (through front of the car and out the tailgate), and the pitch angle is along the y-axis (from the right car doors to the left car doors). All axis pass through the center of mass of the vehicle.
Yaw specifically comes into play when cornering or when cross-winds are introduced. The greater the yaw angle is the sharper the car turns.
One purpose of this study is to figure out the optimal yaw angle that will generate the most speed while our vehicle is cornering. The second purpose is to research and decide on an optimal aero-body of the car to achieve our goal of increasing speed.
An experiment conducted on a vehicle aerobody was done in a wind tunnel testing out different pitch angles. The yaw and pitch angles being defined as the direction of the wind relative to the direction that the front of the car was pointing. The way that they tested it was by keeping a consistent yaw angle of 60 degrees when testing out pitch. The took a pressure reading for each aerobody model (10, 20, 30 degree pitch respectively) and were able to come up with a Reynolds number for each model. A Reynold’s number being defined as:
They then plotted the Reynolds number against the coefficient of drag for each model. Shown here:
This shows that a 30 degree pitch angle produces the least amount of coefficient of drag. Therefore a 30 degree angle would be optimal.
A similar experiment was done to get an optimal yaw angle. This time the pitch was kept consistent and the yaw angles of 50, 60 and 70 degree models were experimented on. Using the same definition of Reynold’s number a similar graph was produced:
This shows that a 50 degree yaw angle may be optimal when attempting to reduce drag.
An interesting article that questions the validity of a so called “optimal” angle suggests that there isn’t an optimal angle because the wind and speed of the vehicle is every changing. So how can manufacturers plan for this. Theoretically there is an optimal angle at which the wind would flow over the body of the car but we cannot control the direction and speed of the wind. An important thing that is mentioned in this article is that the greater the speed of the vehicle the less of a yaw angle will be created. For example, if you tie a string out the back of your vehicle and there is no wind the the string will tail directly behind the direction of motion. This is a 0 yaw angle. Now, picture a crosswind perpendicular to your motion - the string wouldn’t stick directly out the right/left of the car it will lag behind because of the draft you create with your movement effectively decreasing the yaw angle. So speed, in most cases is your friend. Even though the article I am referencing is about bicycles it still applies. For pro cyclists that travel faster they experience a 3-7 degree yaw angle and for the average person - we would experience a 10-12 degree yaw angle because we are travelling much slower.
Since we are designing a vehicle that will be driving at typical everyday speeds we should design our aerobody accordingly.
Another study done by an aerodynamicist suggests that yaw angles actually have an effect on lift. But oddly, shown by this study different shapes had very similar effects of lift at yaw, shown below:
The plot shows the increase in yaw angle from 0 to 15 degrees plotted as a function of length which is then plotted against the coefficient of lift “Some small components and local changes to edge conditions can have an effect on lift at yaw by the action of flow interference and separation. However, from full-scale tests on a wide range of cars, shown in Figure 16, it can be seen that, even with this variability, the increase in lift at yaw is broadly similar.” The only time there was a discrepancy with these similarities was when the people performing the studying started introducing square edges instead of curves in various places.
You might be asking what does lift have to do with cars. As air moves faster around the car the a lift force is produced lifting the tip of the car off the ground as gravity is negated. We aren't building a plane so it’s probably a good idea that our vehicle doesn’t leave the ground at any point. There are a couple ways to counter this. One way being keeping the cars low to the ground will allow less air to flow underneath the vehicle thus negating the effects of lift. Another way is to just drive faster to produce a ground effect.
Another interesting and relevant topic that came up in my research is the a study that was done on rear slant angles in a wind tunnel. Here is a figure displaying the different aero bodies that were tested.
Below are a few tables with results from the simulations performed for this study.
This study can be found at this link if you are interested in seeing some of the math done to get these results: https://jeaconf.org/UploadedFiles/Document/d86c5fa8-2e77-4d47-b51d-5926832848ef.pdf
The study concluded that a 20 degree rear slant angle had the highest rating of crosswind sensitivity and a 0 degree model had the least.
Other things to consider:
Drag is generated by three different forces, and ultimately our goal is to reduce drag as much as possible.
Frontal pressure - effects of the car pushing through pre-existing air
Rear Vacuum - effects of the air not being able to fill the space that the car just took up
Friction against the outer part of the vehicle
Frontal pressure builds up, but just like any other high pressure area the air wants to flow back to atmospheric pressure - so our goal is to design an aerobody that does two things to counter this phenomenon. One, we need to have minimal pressure build-up at the front of the car, which we can do by limiting the amount of surface area that the hits the air head on. Two, we need to provide an easy way for the air to quickly flow away from the front of the car in a way that reduces turbulence as much as possible.
Sources:
Basic overview - https://www.youtube.com/watch?v=1GEQwWGUEBI
https://www.cyclist.co.uk/news/1796/cycling-science-yaw-angles-explained
https://www.mdpi.com/2311-5521/6/1/44/pdf
https://jeaconf.org/UploadedFiles/Document/d86c5fa8-2e77-4d47-b51d-5926832848ef.pdf