Race monkey and mathematics

[lz2lps]

Decided for fun to create an imaginary character called "race monkey" . He is supposed to be modeled after me for number of reasons:
1. I am born in the year of the monkey
2. I am a code monkey (software developer)
3. I like monkeys
4. He is not very smart, but likes to read and watch articles/lectures written by smart people. He is fascinated with how stuff works...

Here is what grabbed his attention while watching a lecture on YouTube:

Mathematics and secrets of the universe

Here is a big secret of the universe actually, coming your way. When you try to apply mathematics to various problems, you often have a question like this: "How can something happen? Is it possible to do/write something like this?". A very good first approach is to suppose that you can, and see what the consequencies are. Then later on, you can say - "Alright, then maybe I should try this, because this seems to be what has to happen" and then you go backwards. Mathematicians will never tell you this, because they like to cover their tracks. They say: "Well it obviously goes like this, you know. You can obviously define this formula, and that formula and life is going to work out so simply". But what they don't show you often is that first step is saying this: "Suppose the problem is solved. What has to happen?"

EE 261: "The Fourier Transform and its Applications" Prof. Brad Osgood Electrical Engineering Department Stanford University The above text is extracted from this video at 40 min 51 sec Youtube: Lecture 2 | The Fourier Transforms and its Applications P.S. (Lyubomir) With little imagination one can see that the above statements are relevant not only in mathematics. but are general. Obviously I know that if i don't write it down somewhere (my local file system or paper that i can't find later in the chaos, are not reliable enough) i will not remember it or understand it. So enjoy...

[lz2lps]

Mathematics, Derivatives and race monkeys

[Lyubomir]Lets first define some terms used in the article: 1. Ride height (link) "Ride height is a term I'm sure most F1 fans have heard at one time or another. It is essentially the distance between the base of the car and the ground. The main reason for a low ride height however, is for aerodynamic reasons. Lowering the ride height increases a car's downforce without any significant increase in drag."

2. Lift and Drag (What is CLA in the aeromap) The two components of Aerodynamic force that we are mainly interested in that relate to performance are drag and lift. Drag and lift add together as vectors to give the resultant total aerodynamic force, and this is the net effect of all pressures acting upon a body, such as a wing. For drag, Cd is used, for lift, Cl is used. where: - rho is density of the air - V is speed of the vehicle. - A is the reference Area upon which the sum of the pressure changes is deemed to act. (You can now see why the car needs most of its power to reach higher speeds. The drag increases the the square of the speed). Positive Cl*A values represent total downforce, while negative Cl * A represent lift. [Article Start] The real deal - what are derivatives Let's say that we have a function of two variables. We'll express it as the following: The most obvious example of a function of two dimensions is a downforce map, which is a function of front and rear ride height. This is illustrated overleaf in figure 1. As can be seen, as rear and front ride height changes, the function values change, and behave in the way we would expect. So when we say that we have a function of two variables, before you head for the hills, just think of an aeromap. Now let's us consider a slice of this function along, say, the front ride height. We are also going to consider a point at, say, a rear ride height of 16.4 mm. This is shown in figure 2. You will notice that at 16.4 mm mark I have illustrated the tangent to this slope. The tangent represents that point, which the function will do at that instantaneous point. As you can see, the slope is increasing so, if we increase the rear ride height, the CLA will go up and vice versa when the rear ride height decreases. Think of it this way - you're turning a car and you let the steering wheel go. The tangent is the path you take. This tangent is also referred to as a derivative of z with respect to rear ride height or dy/dx. So, consequently, derivatives are tangents. It's that simple. This is the beating heart of calculus and, as you can now appreciate, is something your teachers didn't devise as a form of intellectual torture. This also has real-world applications. The treatment we gave to the rear ride height slice is exactly the same as if we were apply it to the front. This is the basis of the idea of partial derivatives. All it measures is the change in z over, say, x while keeping y constant, and vice versa. The notation we adopt for this is as follows: The astute reader will recognize that for this to be valid it must be evaluated at the coordinates described in equation (2). Before leaving the discussion, i want to close the subject by ramming home what the derivative physically means. When the derivative is positive, whenever x changes z accelerates away and vice versa. This is why derivatives are used to describe stability, because it tells you what happens when a variable changes. Remember a car is stable when we turn the steering wheel and the car understeers (the car or derivative is opposing the change) and is unstable when we turn the steering wheel and the car swaps ends (the derivative or a car is propelling the change). The last bit on our maths primer is the chain rule in several variables. If we have, say, z = fn(x,y) and x = fn(t) and y = fn(t) then we may write: Stability Index Evaluation 2 by Danny Nowlan Racecar Engineering Magazine, August 2009

[oldredracer]

I think I studied with Prof. Osgood's dad. Is this him?

http://home.comcast.net/~steveham21/turbo.mpg

[lz2lps]

I don't know, Paul. Looks like him

I see that you know a thing or two about the Turbo encabulator. Did you read the 7th volume of "Zit Shrift ver Electrotechnica Stanisher Danablitze" by David Bluemenstein?

It is mentioned here (4min 6 sec):

http://www.youtube.com/watch?v=REy5hOep96E

P.S. Here is your video on YouTube:

Turbo encabulator

[oldredracer]

Originally Posted by lz2lps

I don't know, Paul. Looks like him

I see that you know a thing or two about the Turbo encabulator. Did you read the 7th volume of "Zit Shrift ver Electrotechnica Stanisher Danablitze" by David Bluemenstein?...

I had to read the English translation, but how I love it when he talks to me that way!

He had me at sinusoidal deplanaration.

[oldredracer]

As I was saying...

[GEORGE]

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[oldredracer]

Originally Posted by GEORGE

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Try to keep up, will ya?

[lz2lps]

Paul, that is one scary black board

Today race monkey decided to leave the mathematics alone and do some research on engine acoustic spying. Few months ago I read few articles about engine acoustic analysis. So decided to make a comparison between the engine acoustics and data recorded by a data logger installed in my car. There was a topic (For comparison only.) in this forum that helped me decide to go from reading about it to doing a little “research”. The logger has 3 axis accelerometer, 5Hz GPS. I connected RPM (sampling rate 100Hz) , TPS (throttle position sensor), and the brake swich, using the car's factory sensors that are used by the ECU. This is the theory and looks very simple: Originally Posted by ”SAE Paper 983047: Reconstruction of Formula 1 Engine Instantenious Speed by Acoustic Emission Analysis написа: ” The sound perceived by a spectator in the stands consist largely of the pressure waves generated by the opening of the exhaust valve in each cylinder. These pressure waves travel along the exhaust pipes and propagate in the air. The sound perceived by a stationary observer is also strongly affected by the well known Doppler effect. If the sound is recorded by a microphone placed inside the vehicle (e.g. using the audio channel of the in-car camera) the Doppler effect is absent, and all the disturbances due to an external noises is minimized because of the short distance between the engine and microphone. It is possible with that rich sound source to reconstruct the instantenious engine speed signal for an entire race, if desired. These SAE papers contain more details: 983047: Reconstruction of Formula 1 Engine Instantaneous Speed By Acoustic Emission Analysis 2002-01-3330: Formula 1 Engine Evolution Analysis Using the Engine Acoustic Emission (lz2lps: BRM P57, Ferrari 312, Ferrari 310B, Ferrari F2001) 2002-01-3321: Comparison Between Formula 1 and Cart Engine Performance Based on Acoustic Emission Analysis

The theory is that the intensity spectrum of the sound, recorded from an onboard camera,contains components connected with the cyclical ignition of the fuel mixture. The frequency of exhaust valve openings has direct relationship with the engine speed. The onboard video that I used for the acoustic analysis: Side Mirror The audio spectrogram (click the image for larger view): This was the first thing that I created before opening MoTeC's i2Pro and loading the data logged at the same time, as the video. Note the calculated RPM. I haven't changed them after looking the real logged data. Here is my logger : DL1 + DASH2 This I think, is the only video that barely shows how I mounted the display. It takes me 5-6 minutes to mount/unmount it. The car's original dash is not changed, but the display is fixed in a “clever” way in front of the original dash (this is one of those moments we like to call - "go to dig out the potatoes" ). DL1+DASH2, Kaloyanovo, braking mistake recovery It took me awhile to find the exact data from the logger, but thanks to GPS time and video file time, somehow succeeded. Loaded the data in i2Pro, some magic to overlay the screenshots from MoTeC and Sonic Visualiser (the open source software I used for the acoustic analysis). It is still not 100% matched, but with little imagination you can see that we have a match. Only the second throttle blip, when downshifting from 3 → 2 seems a little off... I don't know why, as well the little peaks on the straight. Here is what happened after the overlay: The red line is the data logger, the black is from the audio. To ease the reader – the left number is what I measured from the audio, the right one is the maximum from the data logger. I think this proves the theory with real data. Of course withing the limits of an acceptable error, as well the presence of good audio source. Here is a video from Sonic Visualiser, when I click Play. I find it easier to watch and listen, than to just watch static graphs Acoustic analysis of my driving at Kaloyanovo There is one another application that I think this will be useful. Synchronizing the data from the logger with Video. I think I read somewhere that MoTeC used markers in the audio recorded by normal Video Camera to sync it with the data. P.S. I thik that I read somewhere that Ferrari sponsored the original research (described in one of the SAE papers). The image of the CIA monkey came to my mind from one article about the same topic: Acoustic Spy The strange language on some of the images and video is Bulgarian. But it basically shows where I downshift, brake, where the redline is. The RPM values that I calculated from the audio can be read by anyone, I think. The reason for watching the FFT lecture in the first post was the need for more details about analysis and synthesis of the audio signal. I am thinking of a project in the future, that will help remove the manual process from determining the correct RPM from the audio and filter the noise. But am too far from understanding Gabor expansions....yet This has already be done, I have the patent papers and few articles, but now am trying to understand how to implement it myself.

[Andor]

very good info on this thread. spent a while reading everything and pleased to take some good things from this

[lz2lps]

Andor, the race monkey thanks you for the banana (feedback)