trinidefender
I will try to lay down my case as systematically as possible.
1. Purpose of the study: to find the HP difference between different engine manufactures in F1. I should specifically emphasize that I am not trying to pinpoint the exact HP of their PU’s. I assume that this is impossible even for them (to know the competitor’s exact HP).
2. Approach. There are two ways to make a model of the real PU’s differences: detailization and generalization. The first one is to put as many as possible parameters and thus to find the closest to the reality output. Of course, this is going away from our “Purpose of the study”, but most importantly, if you don’t have real world data for each of these many parameters, you will increase the error margin, and basically you will create a model of non-linear chaotic system which is sensitive on initial conditions. This is something that I would like to avoid. The second way, generalization, is to reduce the parameters to as less as possible. In this case your probability output range will be wider but the error margin will fall into this range. This is OK with our “Purpose of the study”, because the same error margin and the same probability range will be relevant for each PU and we can work with the centered value of the range: let say 860 (+/- 20) HP for Mercedes. The same (+/-20) will apply to MH, RedBull and Ferrari. In this way we can reasonably talk about the difference between them, not about their actual power. Very important initial condition: we should try to model only the speed trap real world data in qualifications, because only then the teams all are running with lowest fuel just above the minimum car weight, and all drivers are trying to put the whole available power on the speed trap straight. If you try to make the same exercise with speed traps from the race, you will compare apples with oranges.
3. Data Sources. I will outline each of them separately. Note that for some of them I am talking as “hard proven data”, not as “hard proven math” (as you tried to put wrongly in my mouth).
3(a). Straight Length, Corner Speed Exit, Speed Trap: go to FIA site and you will find a map describing the values for each corner and speed trap points:
http://www.fia.com/events/fia-formula-1 ... uit-data-8
Then you can go to Google Earth and trace the length of the Speed Trap Straight. The Speed Trap for Qualification you will find at the same place on FIA site. These are the “hard proven data”.
3(b). Car Frontal Area (CFA). There are many speculations about F1 CFA but most are centered around 1.3 m2. The most accurate attempt to pinpoint this value I found here:
http://www.roadandtrack.com/new-cars/ca ... passing-1/
this guy talks about CDA, too. Note that 0.01 in CFA gives you about 0.62 km/h difference on Hungaroring straight, but because of the F1 regulations the CFA of all cars are very close to each other. You can use CFA for very fine-tuning of the modeled output, which I think, is not necessary in our case.
3(c). Drag Coefficient (CDA). Many sources are talking about this but we can use the wiki article as good reference point:
https://en.wikipedia.org/wiki/Automobil ... oefficient
You can guess that on circuits like Monza or Canada you should go with the lowest values of 0.7-1.1 range. For Monaco and Hungaroring values above or around 1.0 should be applied. Note that 0.01 in CDA gives you about 0.8 km/h difference on Hungaroring. In other words, the calculator is quite sensitive to CDA.
3(d). Drive Train Loss (DTL). Actually this is the most interesting and controversial parameter that can absorb much of the generalization of the whole model. Speaking about the DTL in its classical terms, you will find on the net that for sport cars this is pointed to be about 15%. Many people assume that specifically for F1 this value should be as low as 5%. On the same time, the classic sport cars don’t have such problems with the engine mappings like the current F1. So, we can factor the engine mapping losses into DTL. Taking this, we can assume that the cars of engine manufactures (Mercedes and Ferrari) or those that have special relations with them (McLaren, RedBull), have DTL about 7%. The client teams have higher DTL about 9% exactly because they have problems to synchronize the PU with the clutch, gearbox and wheels (because they don’t have firsthand data for PU regimes). Note that a 1 % difference in DTL will give you about 7-8.5 hp difference in power. Interestingly, I found that if we stick to some numbers for DTL throughout all races the modeled output values are more close to the reality, because the differences are better explained with the CDA and CFA rather with DTL. Yes, here we have a lot of assumptions and generalizations but they work for the “Purpose of the study”.
4. Processing and Results. I ran the calculator for five race in 2014 and five races in 2015. Because they are different circuits with different CDA, and CDF and DTL are almost constant (or very close), you can get the center point of the power probability range for each car. Based on this I got that in 2014 Mercedes had 790 HP, Ferrari – 740 HP, RedBull – 760 HP. In 2015 Mercedes has 860 HP, Ferrari – 850 HP, RedBull - 790-800 HP, McLaren – 780 HP. The fine-tuning for each race can give you very interesting insights about the possible strategies of each team on different circuits. At, example, all client teams are running with lower CDA to compensate the DTL and this often gives them the best speed traps but they are sinking in the corners. In Monaco McLaren had tried to emulate this strategy but they ended behind the Mercedes clients because they lack their speed on straights. When the qualification speed trap of Hungaroring became available in Saturday, I found that this time McLaren were running with higher CDA than the client teams and that there are good chances in the race they to leapfrog them. Which happened on the next day: despite all dramas with punctures and penalties, McLaren had equal tempo with the 6th car throughout the whole race, and in any case this would guaranteed to them at least 9th and 10th places.
Now, a final note about how important is to know the exact numbers of all these parameters and many more. If you have these exact numbers, you can run very detailed models and work with them not as chaotic system but as deterministic equitation of functions. In this way you can make very reasonable strategies for each race, and in this way to fight your competitors. That’s why I don’t buy any media statements about power differences. We should realize that the teams are fighting not only on the track but also in media. You must try to trick your competitor on every occasion. Again, this is not my “Purpose of the study”. I only want to find a reasonable guess what the difference between the powers of each PU is.
P.S. 0.3 sec loss on the straight is loss in the lap, too. Neither had I, neither Button talked that this is the only loss through the whole lap.