Defining Drag as Information Theory

День тому

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.

КОМЕНТАРІ: 19

@nelsonphillips Рік тому

The rest of the script: Now we can change the idea that complexity of the model increases the coefficient, to the complexity of the fluid flow induced by the object influences the coefficient. Therefore, its the information carried by the fluid that is important. This idea ties in well with the frontal area being a parameter of the drag force equation | because you increase this parameter and you increase the amount of air impacted by the vehicle. So yeah size is important, because that larger amount of air is about to carry more information. But, it doesn’t tell the whole story with this parameter | and that is because the wake of the vehicle is where the disturbed complex air sits. With a large vehicle it is inherently going to have a larger wake along with the high pressure zone at the front, which the reference area is hinting at because force = pressure * area. However, it becomes more apparent how the size of the wake is impactful when seeing formula one cars, | or really any other open wheel cars in the wet. The wake size is much larger than the vehicle itself and therefore also its influence. Basic stuff really, now we understand that complexity is important and inherently more air can carry more information. So if the wake is larger and is more complex then it will be because the car or object produces more drag. But this is still a bit abstract and we don’t really know what this larger and more complex looks like. For an analysis the drag needs to be visualised in some sense, so there needs a way to map information onto the air flow. Downforce is usually visualised though low pressure regions on the underside surfaces, or negative z-axis | because low pressure is the dominate influence. Drag is in a sense opposite, | where we would want to identify both high and low pressure regions, in the x-axis. The less difference is the aim so drag forces tend to be much smaller and its a bit more complex as skin friction becomes important particularly with low lift aerofoils. Looking at a coefficient of pressure plot around a wing profile downforce is dominated by the low pressure, drag is more of a combination. When the high pressure air at the stagnation point accelerates out of that region it drops in pressure developing thrust on the forward surfaces reducing drag. Then if the pressure gradients are to high because of acute geometry | it can cause laminar flow separation. This geometry in a sense has a local wake with recirculating flow, with an inherent increase in flow complexity and therefore drag. Normally flow separation is avoided at all costs, but then there was formula ones f-duct that reduced the size of the rear wing wake. For an aerofoil separation removes most of its lift and increases drag, which is almost all of its function. A formula one rear wing primary function is to generate as much downforce as possible which tends to lead to relatively high drag. A low drag air plane wing would typically have lift to drag ratio of at least 15, a formula one rear wing is about four to eight depending on downforce. This high drag is a product of the low pressure present of the backward facing surface. Separation for a high downforce wing reduces this significantly even though the air is now more complex. This is the trade off between larger less complex laminar wake or a more complex turbulent wake for car designed for aerodynamic performance. For a vehicle that doesn’t have high aerodynamic performance needs | it would then want to look more like a wing with a highly tapered rear, hence a teardrop shape. But it isn’t always possible to have a nice tapered rear with an integrated trailing edge. The trailing edge is then distributed around a perimeter of the cars rear. An example is the hatchback or its analog the ahmed bluff body. These shapes will inherently have a surface adjacent to either structures vortex and fully three dimensional turbulent re-circulation in a wake that is a lower than atmospheric pressure. The three dimensional complex flow averages out and has basically been discussed, as its the general wake. A vortex structure is a little different. The flow having a structure means it is less complex than the turbulent air. This lower entropy vortex is created through a pressure gradient.

@nelsonphillips Рік тому

When looking at a vortex with total pressure it doesn’t highlight features well because it is including all the parameters static and dynamic pressure that makes up energy in an air flow, excluding temperature and density. This is because a vortex is still laminar flow with the lower pressure masks changes in momentum. For such a dramatic change in how the flow is behaving total pressure doesn’t describe the flow but only the fact that disturbed flow exists in that field. In a similar way calculating the circulation around an airfoil will give a good way to calculate lift for potential flow. But that isn’t able to give a value for drag for an airfoil, as its drag is dominated by surface shear stress values. In an absurd and ideal sense potential flow says downforce is free or at least has super low entropy. This suggests the vortex structures present at the rear of cars represents drag caused by low pressure laminar flow on a rear facing surface, like a rear window. Which it does as this is the definition of induced drag. This induced drag is present as entropy in the large wake mentioned before. So the point is information theory introduces probability into an aerodynamic analysis through the concept of entropy. Placing an object in a fluid stream increases the probability the flow will end up being more complex and thus increasing drag. A part from the drag coefficient the reynolds number is another magical non dimensional number that fits nicely here. The longer the object is in the fluid flow the greater the probability the fluid will become more complex. Which is exactly what happens in boundary layer growth caused by the shear stresses from the body fluid interaction. Then another, for those who know the Strouhal number became important for 2022. There are many of these numbers and each can be broken down in a similar way. This is the basic idea of information theory for fluids. There exist research papers using shannons entropy for fluids with similar approaches, so there is some reading for those interested. Currently, this theory is not necessarily a predictive tool but an analysis tool. Really it hasn’t been developed enough, though I wouldn’t be surprised that similar methods are used in industry. The Lattice Boltzmann method is a newer method for fluid simulation which is likely going to be more popular because its computational better. In a sense Machine Learning does this scalar manipulation, both either implicitly and explicitly, going by how many papers referencing entropy its becoming more explicit that not. However, that is its a bit hap hazard at the moment as there isn’t a general theory of information at the moment. Anyway this is about racecars…. Now I’ll use these methods described in the theory to analyse the airshaper model to identify problematic areas of high drag and illustrate some solutions. Together there are about three specific areas on the car I will look at, that will use different methods to identify for their informational content. First I’ll look at the rear wheel, then sidepod leading edge, followed by the halo and helmet regions. Open wheel racecars have the inherent problem of exposed high drag wheels. These have a large high pressure region on the forward surface, high shear stress regions caused by their rotation, with a large and complex wake. They’re all bad. There cannot really be any direct wake control measures | as the geometry is fix. Not mentioned before in the theory is the multi body approach needed here. Basically its changing the state of air impacting other geometry caused by something usually upstream. Using the logic defined earlier, low entropy air impacting another piece of geometry would be less likely add as much information to the air than if the air was originally high entropy. Exactly like the slipstream effect for a trailing car. Therefore, looking for up stream geometry is required to approach this problem streamlines can be used for this. Influencing the high pressure field in front of the wheel is a bit more specific | rather than aiming low entropy air at the wheel. Seen on the corresponding chassis there is a high pressure region that reaches across the rear engine cover, | forward of both the rear wing and wheels. If this high pressure region can be altered to accelerate air over this body work, | the high pressure field can be reduced in size thus reducing the rear wheel drag. A way to do this would be to delay the tapering of the sidepods closest to the rear wheels. The leading edge of the sidepods is particularly messy, showing unnecessary complexity above the inlet, next to the chassis. The wall shear stress maps shows a high value wrapping up over the side of the chassis, | followed by low value behind the leading edge, | indicting flow separation and turbulent flow. The line integral convolution on the surface gives another visual aid for following the direction and path of the air. Even more clearer with this is the separation above the sidepod. This closeup view suggest the high pressure air infront of the inlet escapes above the sidepod because the bottom leading edge is further forward than the top. The inner edge at the interfaces to the chassis is quite blunt, thus the pressure gradient is too large | wrapping the air up in a bubble of separation. So, rounding that corner off would be a first step in addressing this. If the lower edge is going to be so far forward then it might be an idea to bring that round further forward thus delaying and pushing out the pressure gradient from that corner. Also while we are here the rear view mirror stay. The interaction between the mirror body, stay and sidepod isn’t very coherent suggesting misaligned stays, but I think it is rather the mirror shape. The hint it the air is rotating correctly down the sidepod drawing laminar air down. However, the mirror will always have some sort of influence on drag, but without doing a detailed study with numerous iteration its a bit hard to know what to fix other than copy other solution found on the real world cars. This image here is a good view of all the flow around the cockpit. The size and shape of the separation of the sidepod inlet is quite apparent. A cross section of the velocity magnitude show how much energy is taken out of this virtual windtunnel. It stretches right along the side pod and therefore would have a significant influence on drag. Around the cockpit and helmet there are mandatory safety features that you can’t do much about but subtle changes can be influential. A change to the halo model was the sharpening of the horizontal trailing edge. This reduces the size wake and changed its shape removing some rotation, likely reducing its drag. The problem now is a corresponding negative downstream effect produced. The wake is now significantly smaller but also higher. Lifting the turbulence above the helmet. Resulted in significant separation on the helmet because of the large and sharp driver cooling inlets on the helmet. This sequence of images across the cockpit illustrates the energy being removed for the air that is slowing it down to the cars speed. In conclusion reducing drag is a matter of adding lots of little things together removing bits of low entropy air. Delaying the sidepod tapering, making sure all the radius on leading edges are large enough and avoiding tripping the air. Anything that isn’t producing downforce needs its wake reduced as much as possible.

@The666opal111 Рік тому

@@nelsonphillips Thats fucking PogChamp dud. forsenScoots

@markmateo7074 Рік тому

This is the first time I've seen an video that links race car aerodynamics to information theory. This was really interesting!

@nelsonphillips Рік тому

yep, this is original content.

@benburris4735 Рік тому

Was curious about this as a layman for application on combustion chamber and port design for IC engines. Thanks for showing a pointer for me too look into. Cheers!

@cudedog 7 місяців тому

Wow, amazing analysis.

@afoxwithahat7846 Рік тому

Thank you very much, I have trouble trying to visualize all this

@rolandotillit2867 Рік тому

If you could do something that increases drag, but lets you run less rear wing because it makes the floor work better, that would be a worthwhile compromise. Body drag is massively influenced by the rear wing, anything you can do to run less rear wing is a plus in these regulations. All efforts should be to get the best floor performance possible, regardless of the drag penalty it imposes, then you can reduce drag tremendously by running very small rear wing. The main difference between this generation rear wing and the previous generation cars, is the endplate used to be on both the suction and pressure side, now it is only on the suction side. This means that the vortex behind the rear wing has a more spanwise wake. This gives the rear wing the potential to influence the tire wake, something the previous generation cars couldn't really do because the wake from the rear wing was more streamwise. I would argue that feeding more high energy air to the rear wing endplates(to energize the boundary layer in this stagnant region), and beam wing will improve floor performance to the point where you can run a smaller rear wing angle. Enough for a net gain in drag reduction.

@Jpifr Рік тому

Fantastic content ! Only thing is my brain is going to explode... Plus my mind is thinking of the car moving the air and not the air moving around the car so I had to move my brains 190° so I could get that the air is loosing energy although in reality the track it's the opposite I guess

@nelsonphillips Рік тому

aerodynamicists are terrible at always talking about air as if it moving as opposed to the car. Experiments have the air moving.... when doing interviews in F1 they do this 99.9% of the time and only very seldom do they correct themselves....

@ARBB1 6 місяців тому

How interesting

@ricca228 9 місяців тому

9:12 Where did you get those illustrations?

@nelsonphillips 9 місяців тому

Some Salient Features of the Time -Averaged Ground Vehicle Wake Author(s): S. R. Ahmed, G. Ramm and G. Faltin Source: SAE Transactions , 1984, Vol. 93, Section 2: 840222--840402 (1984), pp. 473-503 Published by: SAE International

@ZenBeepBop 4 місяці тому

I don't get ANY of this.. but I really want to. I'm not old enough for university yet, is there somewhere I can get started so I can come back to more complicated concepts like this?

@nelsonphillips 4 місяці тому

To understand this you really need the topics of engineering maths, calculus and probability. Advanced high school maths covers it, so if you learn calculus up to integration most of this should be understandable. However, the concept here is a bit out there and is original thought on my behalf. To learn this formally it would come under the subject statistical thermodynamics. This is one of the three most difficult engineering subject and is mostly postgraduate level. If it takes you ten years to get a basic grasp of the subject you're not doing too bad.

@rocketman99 Рік тому

Very nice , read up Variational lift theory it is similar to your approach

@nelsonphillips Рік тому

interesting read that. Initially thought that it isn't similar, but then if you translate this into 2d it is close. They still have a problem with boundary layer interaction. I wonder if my method would work better in this regard....

@rocketman99 Рік тому

@@nelsonphillips most likely , information theory approach talks about reynolds number pretty well