race cars

Brembo Racing Brakes Heat Transfer Numerical Analysis 1 – Introduction of the problem

The goal of this overall project is to simulate brake rotors. In this article, the problem is introduced, simplifying assumptions are listed, and the benefits of a relaxation factor in central differences are demonstrated.

Brake Model

Abstract This is the first writing in what will be a series of papers on the numerical analysis of brake rotors used in race cars. The purpose of this writing is to describe the goal of this series, to introduce the problem, its background, and the method that will be used to solve it. The most basic initial model will be introduced, along with a list of simplifying assumptions that were used, and the initial results it produced. Being the first writing in a series, the topic is covered more broadly, and many aspects of the topic are introduced at once. This resulted in a longer writing than what is anticipated for future writings. A detail of the mathematical model will be released at a later date.

Summary The goal of this paper was to introduce the topic of the series and release preliminary results. The limits of the current code were mentioned, and the effects were discussed. Iterations, error, maximum temperature, and temperature distribution were observed with changes in relaxation, step size, and residual. The maximum max temperature was 1,166K while the minimum max temperature was 1,158.7, a deviation of only .6%. It was observed that adding a relaxation factor significantly improved performance. For a residual of E-5 and a step size of .00025m the version without a relaxation factor took 188,642 iterations while with a relaxation factor only 9.905 iterations were necessary. The initial temperature guess also had a large effect. By guessing 1000K across the rotor before the first iteration, 22,294 iterations were necessary, while using the average temperature of each row as the guess for that row before the first iteration required only 16,264 iterations. Error was somewhat erratic without relaxation, but with relaxation it was found that error was directly related to step size, and the size of the grid. It was found that the solution was first order accurate, and that as residual was decreased...

Simple Weight Distribution/Transfer 1

I show how to find the center of gravity on a race car according to the weight distribution at the wheels. Future related articles will show weight distribution during acceleration etc.

Formula 1 car dimensions and weight distribution during acceleration

I remembered that that 2011 F1 Regulations state a certain weight distribution for the cars and I decided to find the aproximate CG location based off that. It is a simple matter of Statics.

sum of forces in the x direction are zero

sum of the forces in the y direction are zero

sum of the moments are zero

The regulations state a certain minimum weight on the front and rear axle, and after averaging the leftover weight I came up with 2889N on the front and 3389N on the rear. Besides averaging the extra weight over both axles, let's also assume a 3m wheelbase.

no forces in the x direction

summing forces in the y direction

summing the moments

simultaneous equations

weight distribution of an f1 car

Therefore the front axle is 1.62m from the CG, based on the assumption that the remaining 7Kg not specified in the regulations is...

Testing My Aerodyanamics Article Example

This article tests my previous example used in Aerodynamic Coefficients: Lift. The results from known car data validate the theory and example from the older article.

race car aerodynamics forces lift drag

I cracked open my copy of Race Car Vehicle Dynamics (R146) by Milliken and found something very similar to the example I made in my article Aerodynamic Coefficients: Lift. Let's take the data from Milliken's example and see if my method gets the same outcome. In his book he states the Chaparral 2J has: Tire Friction Coefficient: 1.3, G's on skidpad:1.7 Weight: 2500lb His example is simpler than mine so I can start halfway through my earlier example.  

Newton's Law F=ma

Friction force

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Normal Force Required

Downforce

His book says the downforce was 770lb. Looks like it works!

Aerodynamic Coefficients: Lift

This article talks about airfoils, lift coefficients, lift, angle of attack, and more. A cool example is shown to demonstrate the application to auto racing, using an F1 car going around 130R at Suzuka.

Airfoil simulation using XFOIL

The technology of race cars is a vast topic involving many disciplines. As tempting as it may be to dive right in to multi element wings and Navier-Stokes it is important to have a solid grasp on the fundamental topics. One of these topics is Aerodynamic Coefficients. Before talking about the properties of fluids, I would like to talk about the aerodynamic coefficients and later show the dependence on fluid properties. If you are reading this I will assume you know what lift is. You should be able to look at an airplane wing for example, and know that a wing with flaps engaged has more lift than a wing with the flaps up, and that a wing at a high angle of attack will create more lift than a wing with a low angle of attack. Let’s take that intuition and show why it works. We know that the faster the airflow over a body the greater the force exerted on the body. We also know that the more dense the fluid, the greater the force exerted on the body. Try paddling an oar in the air and see how far you will travel. These two properties describe the dynamic pressure (*2):

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where rho is the density of the fluid.

Intuition tells us that based on the equation, the higher the dynamic pressure, the greater the lift and drag. It is also apparent that velocity has a greater effect on the dynamic pressure than the density, due to the...

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