I thought that you are maybe interested in seeing how easy is, in principle, to extract a graph of a car’s speed vs time just from engine sound.
First of all, what we need an audio track of engine sound, it would be perfect to have a microphone attached to the car. Bernie is so kind to give it to everybody having a tv
. Unfortunately Italian tv commentators have the bad habit to always talk during on boards, Suisse tv commentators more often let you hear the engine sound and thanks to that I was able to extract a few good “clear” segments. The best one is roughly 23-24 second long, and it’s the Renault engine sound from Fisichella on board with 16 laps to go (I did choose it also because there was the rev counter on tv so if you taped the race you can compare the reliability of my program for rpm extraction with the tv rev counter). Presumably GF was already taking care of the engine at that point using reduced revs, but I don’t care about that, it’s only the method I care about here.
Once we have the audio data, we need to extract rpm. That’s not particularly difficult, although obviously requires a bit of knowledge of signal analysis, of what Fast Fourier Transform is and an even rough filtering of the signal.
Here the result from the analysis of that Fisichella onboard (end of the segment is roughly at the braking point for the last corner, where the speedtrap is) :
[IMG:152:129]http://img103.imageshack.us/img103/1452 ... 8pv.th.jpg[/img]
As you can see the signal is quite clear (although there are a few disturbs on the signals causing unwanted spikes) and it’s quite easy to distinguish upshifts due to the sudden revs loss. More difficult to distinguish the downshifts because they happen in rapid succession meaning that the time resolution isn’t good enough to catch them perfectly and with engine already losing rpm.
Rpm vs time is already, in principle, car speed vs time. You need only to know the gear ratios and to extract them isn’t difficult.
First of all it’s necessary to identify which gear the driver was using at a given point and for that we measure and compare the slope of the curve in the different parts. For example, assuming that between 18” and 24” it was in 7th gear (minimum slope), the slope of the part right before downshift (between 4” and 8”) is higher, hence you can see that the driver was in a shorter gear. Using these two info as starting point we can assign the right gear to each segment as I did in the figure. At that point it’s possible to compare the slopes of the different parts to verify that the assignment is correct (BTW, the slope on each part isn’t exactly constant).
Then from the figure we can easily extract the ratio between two successive gear ratios, and that comes from engine rpm drop during the upshift.
Example, passing from 6th to 7th gear the engine rpm drops from 19000 to 17050 meaning that the 6th gear ratio is 1.11 times the 7th gear ratio.
We can repeat it for each upshift and we have then each gear ratio in proportion to the following one, and consequently in proportion to the 7th.
At the end to know the 7th we just need to know the car speed at a given point.
In this case we know from the video that the speed trap was close to the end of that segment. I don’t have precise data about speed trap at the moment (and certainly not about that particular lap), so let’s just make an assumption, let’s assume it’s 295 km/h because that’s the roughly the speed level commentators mentioned during the race.
Rpm there is 18500 = 1937 rad/s. Wheel rotational speed is (radius =0.33, from rules) 295 / (3.6 *0.33) = 248 rad/s => the gear ratio is 7.81. Consequently we can calculate the others :
3rd = 1.52 = 11.87
4th = 1.35 = 10.54
5th = 1.23 = 9.6
6th = 1.11 = 8.67
7th = 1 = 7.81
Now, last step. Applying to each part the right gear ratio, we can extract the speed vs time for the whole segment. For example, if engine rpm is 18k and the gear is 4th, then the speed is 18000 / 10.54 * (2 pi / 60 * 0.33 * 3.6 ) = 212.5 km/h, repeat the same for every point and you have the curve car speed vs time for Fisichella’s Renault.
Only problem is obviously the downshifting part, because in that part the rpm isn’t directly related with car speed so we have an hole, hole that anyway it will be possible to fill with a later estimate of deceleration.
I also didn’t eliminate the disturbs on the signal causing a few spikes because I wanted to show the result without tweaking, but it would be easy to fix it substituting to the clearly wrong points an estimate of speed from the adjacent ones :
[IMG:152:124]http://img93.imageshack.us/img93/4264/m ... 0tb.th.jpg[/img]
Obviously this is just a first order approximation made in few minutes, with elementary instruments, lack of precise data (for example about speed trap) and without application of “cosmetics” to improve the quality of results, but I hope it was enough to show the principle of the method.