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Thursday, September 23, 2021

Le Mans 2021: Simulated Performance Analysis

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The 89th running of the Le Mans 24 Hours will be a first of its kind, with the hypercar category adorning the grid for the first time. Following a hat-trick of Le Mans victories with its TS050 hybrid, Toyota Gazoo Racing competes with the new GR010 hybrid Hypercar for the first time at the Circuit de la Sarthe in 2021. It faces Hypercar competition from Scuderia Cameron Glickenhaus, which enters two 007C non-hybrid Hypercars, and Alpine, which participates with a grandfathered non-hybrid LMP1 car. 

Sebastien Buemi (SUI) / Kazuki Nakajima (JPN) / Brendon Hartley (NZL) #08 Toyota Racing, Toyota GR010, Hybrid.
18.07.2021. FIA World Endurance Championship, Rd 3, Monza, Italy. Photo: XPB Images

In addition to its quest for a fourth consecutive Le Mans win, the 2021 edition marks the 10th time Toyota has competed at La Sarthe with a hybrid-powered prototype. In the nine attempts so far, the team has won three times, earned five pole positions and finished on the podium a total of nine times. 

In the September 2021 issue of Racecar Engineering magazine, Andrea Quintarelli undertook an in-depth analysis using lap time simulation to quantify and understand how the Hypercars may perform at Le Mans. The tool employed for this investigation was coded by the author and is based on a quasi-static approach: each small section of a track is analysed assuming a constant acceleration and that the vehicle is in steady-state conditions. The four-wheel vehicle model incorporates full aero maps, suspension kinematics, corner and heave springs, bump stops for each axle and anti-roll bars.

Aeromaps comparison. Photo: Andrea Quintarelli

The powertrain model inputs include a torque curve, gearbox efficiency, gear ratios, the portion of driving torque applied to each axle and shift time. The tyre model is similar to a Pacejka one, but each effect is modelled separately, including load, slip, camber and vertical characteristics (stiffness and expansion with speed). Simulation output results include more than 100 channels covering all areas of the car. Despite the simplified approach, the correlation against the real world is good, and the author feels engineers can use it with confidence for predictive analysis and general studies. 

Power Curve. Photo: Andrea Quintarelli

For this study, a non-hybrid Le Mans Hypercar was considered. The main features of the simulated car are as follows: 

  • Mass without driver and fuel: 1030kg. Mass with driver and fuel in qualifying trim: 1130kg 
  • Wheelbase: 3000mm
  • Front track width: 1670mm
  • Rear track width: 1660mm
  • Four 31/71-18 tyres with the same dimensions and characteristics
  • Powertrain power curve as the upper limit provided by the rules (both 500kW and 520kW cases have been considered)
  • Aerodynamic efficiency is slightly above four, as an average of the complete aero map (regulations data about aerodynamics is not publicly available)
  • Downforce coefficient set at the lowest allowed value to emphasise top speed
  • LMP-like suspension design
  • Gearbox with seven forward gears, ratios optimised for each engine power individually

At the time of writing, data from the 2021 WEC season’s first few races was available and could be used to understand how close the predictions and assumptions are to Hypercar performance on track at Le Mans. Spa-Francorchamps is a primary reference, as historically, this race is run with a similar setup to Le Mans in preparation for the 24-hour race.

Mike Conway (GBR) / Kamui Kobayashi (JPN) / Jose Maria Lopez (ARG) #07 Toyota Gazoo Racing Toyota GR010 Hybrid.
01.05.2021. FIA World Endurance Championship, Rd 1, Spa Francorchamps, Belgium. Photo: XPB Images

At Spa-Francorchamps 2021, Toyota achieved pole position with a lap time of 2m00.747s. Toyota was allowed 1040kg total weight and 520kW of power for the Belgian race. Simulation runs were performed with the same vehicle model employed for Le Mans analysis, weighing 1130kg and without any set-up modification from Spa-Francorchamps, which produced lap times between 1m59.6s and 2m00.1s with 500kW, and between 1m58.9s and 1m59.4s with 520kW.

Franck Mailleux (FRA) / Romain Dumas (FRA) / Richard Westbrook (GBR) #709 Glickenhaus Racing, Glickenhaus 007 LMH.
17.07.2021. FIA World Endurance Championship, Rd 3, Monza, Italy. Photo: XPB Images

To put this into context, the LMP2 vehicle model used to calibrate Le Mans simulation runs, set up with sprint gear ratios and settings suited to Spa, produced lap times between 2m02.970s and 2m03.392s, closely matching race weekend qualifying performance (pole was obtained by United Autosport with a time of 2m02.404s, with G-Drive in the second position on 2m02.984s). Supposing the assumptions considered for the Hypercar vehicle model are correct, it seems like the Hypercar class has not yet exploited its full performance potential at any of the circuits WEC has visited in 2021 so far, and the Hypercar grid could show more potential at Le Mans with little development and optimisation.

Andre Negrao (BRA) / Nicolas Lapierre (FRA) / Mathieu Vaxiviere (FRA) #36 Alpine Elf Matmut, Alpine A480 – Gibson.
29.04.2021. FIA World Endurance Championship, Rd 1, Spa Francochamps, Belgium. Photo: XPB Images

With around 25,000 gear changes, 4,000km at full throttle and over 2million wheel rotations in a typical race, Le Mans is a true endurance test. But, as this performance analysis highlights, it is all still to play for at the Circuit de la Sarthe in 2021.  

For the FULL 2021 Le Mans Hypercar simulated performance analysis, be sure to pick up the September 2021 issue of Racecar Engineering magazine here.  

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