Hi

This formula is used to calculate lap time improvements using the 6th root principle. Do you guys think there is merit in the formula? What are the pitfalls of this formula? (Thanks to Larry Ouzman for passing the formula and the explanation to me).

I quote: "Herewith a practical example of two cars, one with 234 hp and the other with 325 hp. In this example we are assuming a lap time of 71.5 secs.

Lap times are supposed to vary by the 6th root of your cars power.ie "x" multiplied by itself 6 times will give you 234 or 325.

Enter 234 on your calculator, press LN (natural logs) button, divide this by 6 and then press the e to the x button. (small e with the x raised above and alongside the e). Store this number,2.4824, as it is your 6th root of 234.

Repeat the process with 325 to get 2.6221. Divide 2.4824 by 2.6221 to get .9467.

Your present lap time is 71.5 seconds. Multiply this by .9467 or 94.67% to get 67.31 seconds or 1.07.31 and this is your new expected lap time.....without nitrous!!!

If you don't have LN and e to the x functions can use log and 10 to the x instead. Same answer.

Teach a man to fish........."

Johan
Almost broke racing
www.almost.co.za

 

Johan, just off the top of my head, I do not see how that formula could be accurate to any degree. Lap times are determined by many more factors than acceleration, and depending on the track layout, acceleration may have a differing influence. For example, on a track with sweeping turns, and average length straights, the effect of HP on acceleration diminishes due to the higher exit speeds, and so it will be less of a factor than on a track with tighter corners and longer straights. On that track HP will have a greater factor because you are accelerating from a lower speed over a longer time.

 

Larry H

Thanks, I thought as much but it is always wise to test the feedback. For what it is worth this formula gave quite an accurate estimate on ONE particular circuit we run on. It may just be that the formula suits the circuit (or does the circuit suit the formula?). I have not yet tested in on other circuits.

Johan

 

Johan,

From a purely mathematical standpoint, it should be possible to calculate the improvement in lap time from increases in HP. However, the formula would become increasingly complex as you try to account for all of the relevant variables. Assuming that you held all variables constant apart from HP (e.g., same driver, same car, same track, etc . . . ), you might be able to guess pretty well, although the forumla would likely still be much more complex than the one you listed. In the end, I can't see how the work would be worth it. Interesting nonetheless.

TD

 

In the end lap times will improve as talent increases and a significantly greater rate that lap times will improve as hp increases.

Talent is just too large a variable. In come cases keeping talent constant and increasing the hp may have no effect on lap times.

What is the purpose of this exercise?

 

George, I think that is the understatement of the year. I firmly believe, and my 2 years with the GT3 have proven to me that as the HP goes up, the talent must go up with it. There are so many more variables to control as the power increases that many drivers run out of talent. My own personal experience has shown me that if you take 4 drivers who run together in 200 hp cars, and put them into 400 hp cars, one of them will be faster than the others. This also expains why there were a number of drivers who could run with Michael Schumaker in carts and lower formula cars, but he was obviously superior when he jumped to F1. Just my opinions on this subject.

 

The fundemental problem is that the formula does not take into account weight or handling dynamics, so it's not very useful to compare across car types. If you are just trying to get a directional idea of what +50hp means in to the exact same car, it may at least give a ballpark guess.

 

I think this is very interesting and can see some practical uses for it, such as cost-benefit analyses. For example if somebody says "I have a mod that will get you 15 hp for $2000" you can use this "6th power rule of thumb" to determine that you would gain 0.8 sec on a 90-sec lap in a 280 hp car. So is 0.8 sec worth $2000?

That said, I don't believe it. I just don't think 15hp would gain me 0.8 sec.

As a side note, I find the use of ln and exp rather odd. To get the 6th root of x, just take x^(1/6) and you'll get the same answer.

 

Too many variables...

1) HP only helps where accelleration is important... it does not improve cornering or braking performance, so the impact depends on the track config as Larrry points out

2) Power band is as important as max HP... in a road course, torque rules... a 300 hp car with a very peaky power band probably gets beat by a 270hp car with a very broad power band

3) Driving style... all other things equal, for large deltas in power, car set-up and driving style will change to take advantage of the power...so there are trade-offs....typically, as power increases, you will reduce entry speed and take a slightly later apex to maximize accelleration out of turns... so it is not totally linear...

4) Aero... more power means more speed means more drag... means power and speed are not linear...

etc...

 

You guys have cars with 234 or 325 hp? sigh...




Interesting formula but as was said there are many variables. It would be cool to do this with same car same driver same conditions and see what the ramp is and what the change is track to track. Perhaps you could setup a formula and than have a multiplier for each track. Summit point could be a .95 and WG a .88 but SC is a 1.20 or whatever.
I could think of a track that this would not work well on. SC at Summit point. There are many corners that the power you have is not the limiting factor and having a larger motor and I ***-u-me more weight motor in the car would be counter productive.

Good idea and please keep us up of any data you get

 

Ah, wise words. Just spent some time this morning talking to a local racer [Grand Am Rolex GT] who has traded his 2005 Cup for a new 997 Cup. He was quick to point out that the new car had more ultimate performance, but it took a lot more skill and driver effort to extract that performance. A much more demanding situation. Any given driver may hit his personal limits long before hitting the car's limits.

 

Too many variables is right. A big enough HP increase (assuming no weight changes) can allow you to do things differently.

Holding the lines taken and driving style constant. I would think that a formula would be able to at least identify the outer limits of lap time improvement. But you have to know how much of a lap could actually benefit with more HP ($$$) in the car.

Lets say you have 2 lights on your dash to record on video Brakes on and Wide Open Throttle. If you look at how much time is spent WOT, that is probably the amount of time that is subject to lap time improvement. OK. It is possible to measure time on full throttle.

So if you have WOT time identified, the outer limits of improvement would be mathematically calculated. Possible to reach the outer limit without changing driving style? Probably not. You would have to brake sooner and may have to manage the gas more carefully when shooting apexes. At least you have a theoretical outer limit. Any increases that you can chalk up beyond that should stroke egos rather nicely, but you know that would be due to changes in lines and driving style that accomplish this.

Am I setting the hurdle too low? I certainly need SOMETHING to feel good about.

 

It would be interesting to know how the formula was derived. Tons of professional race team data where best fit line (formula) was fitted? On what tracks, with what HP ranges included in the samples? I can see the data being good if we are looking at an oval track where restrictor plates are being tested (no suspension mods). Doubt the data came from such a clean scenario.

Sometimes empirical data analysis can be better than nothing?

 

The other problem with this formula is that it only uses peak HP to calculate estimated improvement. Other factors in the torque curve need to be considered besides just peak (e.g. area under the torque curve in the operating rpm range).

Oops, nevermind. JCP already mentioned this earlier..

 

It would be an extraordinarily complex formula, but it absolutely could be done. There is no such thing as too many variables I can imagine that you would start with a finite-element type analysis of the track, where you split up the track into minute elements so that you could sum the changes in each element over the entire course. You could have separate variables for every relevant detail (e.g., driver skill, chassis type, tires, torque, hp, etc. . . .), but to develop the formula, you would have to do extensive testing to verify and model, and, in the end, it just wouldn't be worth it. It would be interesting for someone to try, but I am far too lazy.