Vehicle Dynamics Primer
One of my goals for this project is to put together a car that handles very well yet maintains good ride comfort. I started reading the references I could find both in printed forms as well as on the web. Straight up, I was struck by how questionable material was published. Many of the folks writing appear to fall into one of two camps; they understand some effects but misunderstand the causes or they have an inventory of ‘solutions’ to sell and shape the problems around their ‘solutions’. Much of the stuff is pretty misleading.
I am, by education, an electrical engineer however I have engineered some rather large extreme mechanical structures in my career. As I attempted to understand vehicle dynamics, I needed to step back to first principles and apply some very simple tools to understand the dynamics. Force-Vector diagrams and properly understood layers of abstraction are the tools I used.
To define Force-Vector diagrams as I am using them: A drawing showing all of the forces applied by and to the object as well as their direction. With these diagrams, all forces and their directions MUST sum to zero. I truly believe that if folks actually drew them as they discuss suspension dynamics, as opposed to simply using prose, many misunderstandings would be eliminated.
The second is simplified modeling or Layers of Abstraction. If you are attempting to analyze and improve the suspension system on a car for instance, you can’t start with the entire system. Cause and effect will end up interrelated and confused, so optimizations, and even a good basic grasp of interrelationships will not be possible. One needs to analyze the system piece by piece, purposely ignoring other factors later combining additive or unrelated pieces and only then start layering on interrelated and effects. The more simplified the model, the further removed your analysis will be from reality. There is nothing wrong with that, as long as you accurately access where you are and where the shortcomings of your model are. You need to guard against jumping to the conclusions that one simplified piece will provide. It is a very common issue for designers to attempt to force reality to match their abstraction.
I needed to work through a series of force-vector diagrams applied to various simplified models to ensure that I understood what was happening to the model vehicle. The Book “Race Car Vehicle Dynamics” by Milliken was invaluable to me. Below is a somewhat organized and polished summary of that work. I hope that it helps others. If someone finds a hole in my process, please let me know.
Thanks
Leo
Basic Definitions:
Velocity.
Velocity is the speed of an object in a specified LINEAR direction (known as a vector.) (http://en.wikipedia.org/wiki/Velocity)
Acceleration.
Acceleration is a change in Velocity. It is NOT necessarily a change in speed. A vehicle going around a constant circle at a constant speed IS accelerating because the direction vector is changing. Acceleration is measured in the change in velocity over a set period of time ( i.e. the change in feet per second, per second.) (http://en.wikipedia.org/wiki/Acceleration)
G Force.
Gravitational Force really has two definitions for these simplified models.
1)
The attractive force between the Earth and another object that is stationary or moving at a constant velocity parallel to the earth. In this definition, the car is NOT moving or accelerating toward earth (which would cause an acceleration of 32 ft./s each second), it is at a static distance, so gravity is simply applying a force at a vector. The units of this measurement of force are Pounds, Kilograms (or their derivatives), it’s also known as 1G at sea level. The vector of this force is straight down towards the Earth’s core.
The attractive force between the Earth and another object that is stationary or moving at a constant velocity parallel to the earth. In this definition, the car is NOT moving or accelerating toward earth (which would cause an acceleration of 32 ft./s each second), it is at a static distance, so gravity is simply applying a force at a vector. The units of this measurement of force are Pounds, Kilograms (or their derivatives), it’s also known as 1G at sea level. The vector of this force is straight down towards the Earth’s core.2)When a vehicle is accelerating, it is being subjected to additional forces similar to gravitation (see above). These forces are proportional to the static weight of the object and how fast it’s velocity is changing. These forces are also specified as weight, however because these forces are proportional to the static weight of the object, it can be also specified relative to weight due to gravity (i.e. a 1G turn). As this force is a reaction to acceleration, the Vector is opposite the direction of acceleration (i.e. the vector is to the right on a left turn, to the front on braking)
When a vehicle is accelerating, it is being subjected to additional forces similar to gravitation (see above). These forces are proportional to the static weight of the object and how fast it’s velocity is changing. These forces are also specified as weight, however because these forces are proportional to the static weight of the object, it can be also specified relative to weight due to gravity (i.e. a 1G turn). As this force is a reaction to acceleration, the Vector is opposite the direction of acceleration (i.e. the vector is to the right on a left turn, to the front on braking)Under Construction
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