Defining Drag as Information Theory

Drag on a racecar is largely considered a lower priority than downforce. The drag budget is usually determined by engine power and the percentage of full throttle in a lap, which would mean lower drag is required for less available power. Reducing drag can be most similarly thought of in terms of weight reduction, applied through small incremental improvements. However identifying drag is probably more difficult than both downforce and weight improvements.

This video will go through the principles of drag in terms of information theory and apply them to the results of Airshapers latest version of their formula 1 model.

So what contributes to a cars drag?

We’ll start with the drag force equation. Where the drag force is equal to half the coefficient of drag multiplied to the air density, frontal area and velocity squared.

The only parameters we have control over | are, the frontal area and that magical coefficient number | that condenses all the other aerodynamic properties into one non dimensional number. As the frontal area cannot really be altered that much | as it space is dominated by the chassis, wheels and wings. Out of each of these elements the rear wing becomes the only part of the car that is tunable for drag reduction. The frontal area of the wing can change according to whether the car is running at a low or high speed track, DRS applies this concept changing the second elements angle. A decease in the wing increases top speed at the expense of downforce and cornering speeds. Therefore, if most of the frontal area is set and so inflexible | we are going to need to dig into that magical coefficient to reduce the drag.

Its pretty interesting that the complexity of a formula one cars aerodynamic drag can be reduce to this number. There isn’t really any clues given as to how to reduce this number | as its non dimensional. Its just pure information, as such we are going to need to map this information onto something. Obviously the information is bound to how the air flows over, under and around the car. Airshaper includes this scale in their report, illustrating how the drag coefficient changes relative to tested objects. Apparent is that adding complexity tends to result in a higher number, for example an exposed person on a bike relative to person inside a cabin. Then the of value 0.91 is for this car | with all its downforce creating bits can be compared to a generic truck. But then | the truck has a much larger frontal area, and that would mean it is more likely to require more power to maintain an equivalent speed.

So now we have the first important idea, complexity. A basic introduction into information theory will show how this idea sits in the theoretical context. For information theory has an idea | entropy as a probability measure of complexity, this is derived from Ludwig Boltzmann’s entropy in thermodynamics (kg⋅m2⋅s−2⋅K−1 ) but the non dimension or more general version. For thermodynamics and its second law, the concept states that energy tends to flow from high temperature to low, that is from low entropy to high. Boltzmann’s entropy formula is the probabilistic definition of this equation based off the number of states, in his case corresponding to how an ideal gas reaches equilibrium. Information, as derived initially by Shannon using the general non dimensional version of Boltzmann entropy, is the quantifiable amount present relative to an event, high probability events have low informational content. Information entropy expands on this and is the information of a random random variable that can be used to understand how frequently a measurement needs to occur to represent a signal or in this case a geometry. That is, a low entropy geometry will have a lower probability of being represented because features are less likely to be captured. To put it another way, a complex geometry has low entropy and will have a higher probability of being represented through a larger number of random samples. Its basically increasing the poly count of your model for CFD meshing. All this means is that the objects drag coefficient has a corollary to the entropy of that objects geometry. However, this isn’t enough to definitively conclude information depicted this way is the reason an objects specific coefficient needs that amount of energy to push through the air.

But, we can say based on information theory and the notion of entropy there is a suggestion, reducing the complexity of the model will reduce the coefficient. Obviously there is more to it than that | because also indicated on this scale, there is the appearance of simpler shapes with values higher than one thats more complex. For example there wouldn’t be many that would say the sphere is more complex than the teardrop shape. So is it actually the complexity of the shape or the only other thing, the fluid? Well it can only be the other thing.

The rest is in the comments. ... https://www.youtube.com/watch?v=tkjIdiEcJbc