[LM24 Race] Energy Use at Le Mans

[tomerswayler]

Hi, here are my simulations on how to best use the energy limits defined by the regulations for the 8MJ LMP1 petrol category. I tried to calculate the four different tyre normal loads Fn from weight and downforce distribution, lateral and longitudinal load transfer.

Main car specs
m=965,6kg(car+driver+half a tank)
cd=0,453 cl=4*cd
Pmax=413kW

Tyre contact patch force to decrease with rising normal load:
Ft = Fn*(1,5-0,5*(Fn/10000N)^2)

I defined a track with online maps and tried to capture the assumed racing line. From this track i calculated the corner radius for the different track segments and then tried to find the fastest possible speed for each segment of 1m length that the tyre contact force allows. Longitudinal forces to overcome drag and acceleration and braking, lateral forces to overcome the centrifugal forces.

First i set both the weight and downforce distribution to 49% front and 51% rear and varied the power distribution between FWD, AWD and RWD. I didn't care about the 138MJ/lap petrol limit here and also didn't use any electric boost. The results:




As expected, somewhere around 70% rear wheel drive, the fastest laptime is to be found as AWD enables better acceleration at low speeds. With 30f/70r the time is 204,7s and the fuel consumption is about 163MJ.

Next is a graph of the velocity for the 30f/70r configuration. Seems pretty smooth overall, some small errors are probably caused by a poor track definition where the corner radius changes to fast. It's easy to spot the braking zones at the Mulsanne straight and the slowest point at Arnage.

[Pandemonium]

Very nice.

[tomerswayler]

I then went on to also use lift and coast to reduce the fuel consumption to 138MJ per lap with the 30% front/70% rear power distribution. The graph shows that if before every braking zone the throttle is lifted and only the drag and rolling resistance slow the car down(i didn't consider the engine braking torque and no kinetic energy recovery, too), the laptime increases to 207,6s(from 204,7s) if lift and coast is applied down to ~258km/h to meet the 138MJ limit.



The next step was to also use the 8MJ of electric boost to regain the time lost and maybe even improve beyond the 204,7s. The best combination of boost and lift and coast i could find is shown below in comparison with the 204,7s base in blue. Red shows a electric boost of up to 900kW up to a speed of 240km/h, depending on the tyre forces. Lift and coast happens down to 282km/h. The green line shows the difference in time between these two variants, multiplied by ten for a better visualisation. Yellow is the speed difference.



Finally, i also calculated how high the recovery power has to be from kinetic energy to always have enough energy stored for the acceleration zones. 100kW and 200kW are not enough, the 300kW version ends up with 1MJ of energy at the end of the lap.



Thoughts, critics, errors spotted?

[Aysedasi]

Way beyond me - I just watch 'em......

[whitemr2]

Very impressive, but it is to complicated for me though. Can you give a short version explaining in 'childrens laguage' (sorry don't know the proper english word) in dutch it is called Jip en Janneke taal

[GT6]

Me to a simplified version would be good

[J Jay]

Thanks for the analysis. I'll be looking forward to that 3:18 lap in qualifying

I know it's not a flat maximum but up to 900kW of electrical energy seems a bit high, as does the upper speed limit (I know Nissan are looking at this as a goal but still...) Apart from that all the numbers seem sensible. Interesting point about the required harvesting capacity, it seems obvious when you present it so well but the balance has to be struck between harvesting enough energy and not leaving too much left "in the tank".

[Muppetdave901]

Originally Posted by Aysedasi

Way beyond me - I just watch 'em......

Yup, my thoughts exactly! Good work though (I think!)

Hope I don't get in trouble for saying this (and not in an unappreciative way either), but the guys at/on Mulsanne Corner would probably appreciate that.

[PascaLM]

I thought this was about the amount of energy we need to absorb at the Ten-Tenths meeting.

[Aysedasi]

That equation is beyond comprehension, Pascal!

[Samoan Attorney]

Very interesting work - the small bits that I understand that is - but in conversation with grown ups the biggest issues with the 8MJ route are heat and weight, more energy stored more of both and how that is dealt with in the confined dimensions of an LM P1 car, that also has to race.

The other issue that emerged at Le Mans is the efficiency of the storage systems over 24 hours as opposed to 6.

It was put to me that both Toyota and Porsche had to trim their energy recovery systems back to give them a chance of lasting the race distance.

Audi, already at a weight disadvantage with their diesel system ran the 2MJ route and were nearer their maximum potential performance.

I tried to explain this in terms that I could understand HERE

I hope that I am not insulting your calculations with my rather simplistic approach, but I am a scribbler not an engineer.

All of this could be a pointer as to why Nissan have apparently adopted a radical solution to these issues with the laws of physics. Fascinating stuff, even from my rather low level, so thank you.

It is this sort of post that attracts me to 10/10ths rather than some other forums where it is endless speculation and parroting of press releases.

[tomerswayler]

Sorry for the break, i'll write a bit more later on.

With the reveal of the new Nissan, i found an interesting quote in http://www.dailysportscar.com/2015/0...bowlby-qa.html .

"If you have an 8MJ system that fails during Le Mans, you’re going to lose over 7 seconds a lap."

For my simulations, the time loss for a malfunctioning 8MJ system would be 207,6s(no boost, lift and coast) -198,5s(900kW boost, lift and coast) = 9,1s. Not too far off.

[tomerswayler]

Originally Posted by PascaLM

I thought this was about the amount of energy we need to absorb at the Ten-Tenths meeting.

Well, half a liter of beer is about 1MJ. If one lap is 24h, that's (24*60min)/138bottles = 10,4min/bottle. You can add some bratwursts or croissants to use the additional 8MJ, if you don't mind. Using cognac as a reference, the energy content is five times higher than for beer.

[tomerswayler]

Somw wanted to know what exactly i have done in more detail, so i'll try to explain.

As stated, id defined an estimated racing line from online satelite maps. I always took the most likely apex and tried to create a smooth line into and out of the corners. I then calculated the radius r of a circle that passes through three consecutive points from this track. This gives me the corner radius for the complete track.

I defined a car with the main specs being:

m=965,6kg(car+driver+half a tank)
cd=0,453 cl=4*cd
Aref=1,7m² (area of the car seen from the front)
Pmax=413kW

To know how much force the tyres can produce parallel to the ground, you have to know the force that acts on each single tyre normal(vertical) to the ground. This normal force Fn changes with the weight distribution front/rear, the downforce distribution front/rear and load transfers front/rear and left/right because of the lateral and longitudinal accelerations. See http://en.wikipedia.org/wiki/Weight_transfer#Cause how the wheelbase(or track for lateral acceleration), center of gravity height change the normal loads.

I connected the normal and tyre forces by

Ft = Fn*(1,5-0,5*(Fn/10000N)^2)

where the part in the brackets is the tyre coefficient, which decreases with the normal load.

The code i wrote then simply checks for the whole track what the highest velocity for each point of the track is. The tyres have to provide
-lateral force during cornering: mass*velocity²/radius
-drag force: air_density/2*cd*Aref*velocity²
-inertia force: mass*acceleration

If the car can accelerate, i calculated the maximum forward acceleration either defined by the tyre traction limit or by the engine power limit. Before corners the velocity is reduced according to the drag, tyre force and eventually lift and coast is applied. The result is a table of velocities for every part of the track at 1m track distance to each other. This table let's me look up how much energy is spent at each 1m segment and how much kinetic energy(1/2*m*v²) can be recovered.

Better to understand now?

[tomerswayler]

I did some more calculations for the other petrol energy categories, 0MJ to 6MJ. According to the rules i adjusted the maximum fuel flow and fuel/lap limit.

The results compared:

version lift_and_coast fuel_energy laptime electric_energy
8MJ_____nolc___________163MJ_______204,7s__0MJ
8MJ_____lc258__________138MJ_______207,6s__0MJ
8MJ_____lc282__________138MJ_______198,5s__8MJ

6MJ_____lc278__________139,5MJ_____199,8s__6MJ

4MJ_____lc278__________143,3MJ_____200,6s__4MJ

2MJ_____lc278__________147MJ_______201,5s__2MJ

0MJ_____lc287__________157,2MJ_____199,9s__0MJ(LMP1 850kg)

The last version shows that my calculations probably overestimate the influence of the ICE as the laptime is less than the 2MJ LMP1-H. For the other categories, each 2MJ less cost between 1,3 and 0,9s according to the results.

Can i compare my results with some published information on how the electric boost should influence the real laptime for Le Mans?

[Aysedasi]

I don't see why not!

[tomerswayler]

So maestro, do you mind to link to the data?

[Aysedasi]

That should be OK, as long as it isn't to another forum or anything else which isn't permitted.... PM me beforehand, if you're in any doubt.

[silente]

Tomerswayler,

is your vehicle model a 4 wheel one, with load transfer and suspensions or are you using a point mass approach?

I would love to ask you some questions about your simulation, if you don't mind.

Thanks a lot!

[tomerswayler]

Thanks to the information provided in the Audi thread (http://tentenths.com/forum/showpost....postcount=9568), i could estimate the effect of the new fuel regulations for next year in the 8MJ petrol class. It should be similar for the other classes, but as the trend is to go for the higher energy classes, i chose this one. I kept the cd value the same for both variants, although usually with a lower engine power you use less drag(and downforce).
This means that the 2016 car can achieve about the same corner speed in the simulation but be slower than the 2015 car on the straights. In reality the lower cd(and cl) would raise the straight line speeds a bit and decrease the corner speeds a bit.

The input data are:
cd = 0.453 coefficient of drag
eff = 4 = cl/cd aerodynamic efficiency
cl = cd*eff coefficient of lift
A = 1.7m² frontal area
rho = 1.225kg/m³ density of air
crr = 0.015 coefficient of rolling resistance

P2015 = 416kW power ICE 2015
P2016 = 387kW (-7%) power ICE 2016

m2015 = 965.2kg mass with driver and half a tank
m2016 = 963.4kg

er = 1.06 rotational mass factor

weight and aero distribution is set to 49% front and 51% rear


And these are the results. P is the power if the ICE, Pel the electric power and vel the speed up to which the electric power is used when enough traction is available. LiftCoast indicates the speed above which lift and coast is used to save fuel.

The first two lines show the two cars without electric power support and without caring about the fuel allowance per lap. The difference in laptime is slightly below 3 seconds here, the top speed comes down by about 8km/h. But keep in mind that the cd is the same for both cars, so the "real" speed decline should be smaller.

The grey lines show the two cars limited to 300kW in electric power deployment, as demanded by the 2016 regulations at Le Mans. Again the difference is about 3 seconds. These speed traces and the gap between those two variants is shown in the graph.

For the last two lines, the electric power of the 2015 car was increased to 450kW, this only increases the gap by about 2 tenths.

What the simulation shows is that the amount of lift and coast stays about the same, top speeds are expected to be a bit lower.

I expect the real laptimes for 2016 to be pretty much on par with what we saw this year as!

[tomerswayler]

Originally Posted by silente

Tomerswayler,

is your vehicle model a 4 wheel one, with load transfer and suspensions or are you using a point mass approach?

I would love to ask you some questions about your simulation, if you don't mind.

Thanks a lot!

It's a rather simple model, suspension movement is not modelled, slip angles and ratios are not considered. It is far from perfect!

What does it look in general?

I defined an estimated racing line with Google Earth and converted the coordinates into cartesian coordinates. That way i could calculate the radius for the complete track.

I defined the basic car parameters, mass, track width, center of gravity location, cd and cl, aero distribution. I divided the track into 1m segments and first calculated the maximum speed that the car could do there when the longitudinal acceleration is zero. As the track radius is fixed the lateral acceleration is defined as v²/r, this causes a load transfer(change in normal load). With rising normal loads i modelled the coefficient of friction to decrease, where the tyre force is Ft=Fn*cof(Fn).

I(the simulation) increased the speed and checked if the tyres can provide enough force to overcome the drag and keep the car at the given radius. The lateral and longitudinal forces are connected through Ft²=Flat²+Flong² for every single tyre.

Then two steps follow, the first checks if the car is able to reach the next segment under the constraints given by the tyre force or if the speed at the next segment is too high. If the speed is to high, the maximum acceleration is calculated. This step accelerates the car out of corners.

The final step looks back if the previous segment can be reached and lowers the speed at the previous segment if necessary. This simulates the braking process.


I currently look into improving the simulation by not defining a racing line. I try to only define the track limits and let the code fine out the fastest way around the track. We'll see if this works in the future!

[tomerswayler]

Originally Posted by Artur

Hi tomerswayler, I checked the thread and I didn't understand this part:
my understanding is that the Tyre contact patch force increases with rising normal load. That's the whole point of downforce!
my understanding, again, is that the tractive force = Fn*CoF(coefficient of friction)

From the various samples of test rig data that I have seen, I would say it's quite hard to model the variation of CoF with load. Normally it decreases(but I have seen it rise a few times over a load range) but it does in varied ways

Best thing to do, imho, to have somewhat close values of the LMP1 Michelins' CoF would be to assume some aero values for a car(cl), then get the variation of CoF across the various loads/speeds through the lat accel graphic

For instance, I think Toyota(2014 Le Mans, iirc) was reaching ~3.2G sustained through one of the Porsche Curves, at speeds of ~230kmh.

I think they published their downforce for Le Mans config last year. IIRC, it was ~18000N at 280kmh. With this figure, you would have ~12140N at 230kmh. Add the car's ~9750N weight to that and the normal force would be ~21900N

With 3.2G, the cornering force of the car would be ~31200N, so, the CoF can be estimated to be 1.42, for a normal force of 21900N

If they reach, say, 1.6G through Arnage(don't know, have to look into the videos. Later I'll see if I can do that) at 80kmh, you have a CoF of 1.39 for a normal load of 11220N

If you do this appropriately, ie, with correct values taken from a video(not this likely incorrect values that I have used here), you can calculate the values of the CoF for several vertical loads(speeds) and then, built a graph sort of projecting the values all across.

If I wrote nonsense somewhere, please let me know. Hope I could help and looking forward to your results (the 10MJ fuel allocation reduction will result in a 7% decrease in power, I was told)

You are rigth about the formula you quoted, the tyre contact patch force still increases with rising normal loads. It is the coefficient of friction that decreases.

But the sum of the contact patch force for all four tyres decreases with the load transfer. For example we have four tyres at 1000N normal load each and a cof of 1 at 1000N. That would result in 4*1000N*1=4000N available force.
If load transfer changes the normal loads to 500N at one side of the car and 1500N at the other side with a cof of 1.1 at 500N and 0.85 at 1500N then the total tyre force is 2*500*1.1 +2*1500*0.85=3650N.


My simulations indicate a highest lateral acceleration of 2.7G, so i probably underestimated the cornering capabilities. Either the cof, the downforce or both is set too low.

The speed through Arnage is 20m/s or 72km/h in the simulation. Maybe the off season is a perfect time to tune my simulation...

[silente]

tomerswayler,

i can provide some more realistic data regarding how the "car" coefficient of friction (with the car defined as a point mass) decrease with loads, providing more realistic coefficients for your equation.

I work on "driver-in-the-loop" simulations and have worked on several lmp cars, including recently an lmp1 model based on Perrinn data (althoug the tire data i used don't come from him, his ones was not so reliable).

Is your code written in excel, or do you use something different (matlab?)?

It looks similar to what James Hakewill did many years ago. I tried to do something similar as well, but at a certain point i left the project because of lack of time.

Regarding track modeling, i suggest to base it on logged data, deriving corner radii (m per m) from speed and lateral acceleration. You can basically create a list of points, each with its own radius. Said radius will be very big for straights (so you can maybe set a switch in your simulation, identifying anything with a radius bigger than ... as a straight and anything with a radius smaller than ... as a corner) and then use your method.

I would love to discuss with you and maybe take a look to your code, if possible at all.

What i did to properly mode the effects of weight transfer and downforce still using a point mass approach (where weight transfer cannot be simulated) was to previously run some constant radius corner simulations to identify how lateral accelerations evolves at different speeds (because of downforce), deriving the curve of grip vs load (or alternatively vs speed, as the load depends on speed^2 because of downforce).
I then tried to identify the maximum cornering speed for every corner, basing on this preliminary study.

Are you also including an engine power curve and a gearbox in your simulation?

Would love to further discuss about it, maybe per pm?

Thanks!