In the last few weeks, in particular after the latest WEC race in Silverstone, a new topic has been raised regarding ACO’s (till now pretty unsuccessful) attempt to balance the very different performances of Toyota TS050 hybrid and the privateer LMP1 cars – The Rebellion Oreca R13, the SMP-Dallara BR1 (competing with both AER and Gibson engines) and the ByKolles CLM P1/01.

Privateers complained not only about the huge advantage given in traffic to Toyota by their hybrid system (besides their pure performance advantage also on the single lap, which in Silverstone could be quantified in about two seconds in qualifying) but also about issues with the tyres that all the LMP1 cars used, that have been originally developed for Toyota.

Let’s try to understand that issue.

As most fans probably know, the hybrid and non-hybrid LMP1 cars are very different animals, although belonging formally to the same class.

If we ignore the hybrid system for a moment, privateer cars are actually allowed more, in terms of design freedom. Non-hybrid LMP1 cars are allowed to weigh significantly less than the Toyotas and, in terms of aerodynamics, they have been given more freedom in certain areas, with the intention to compensate for the lower budget and human resources that private teams have at their disposal to design and develop their cars.

We had a confirmation about this when analyzing Le Mans race data: in some parts of the track, the privateers were very close or even faster than Toyota, despite being significantly slower on a full lap. We have seen how, in particular in the first sector of the track (a twisty and relatively slow section) and in the Porsche curves (some extremely fast corners), the best times were obtained by the privateers, with the Rebellion Oreca R13 being particularly brilliant.

The reason for this, besides maybe Toyota not deploying so much hybrid power in these track sections, probably lies on the lower weight and high downforce of the privateers compared to the Japanese cars.

The incredible acceleration rates that hybrid LMP1 cars can achieve and the agility in traffic that they have thanks to the hybrid power is something that completely kills any non-hybrid car aspiration to beat the Japanese crews on pure pace.

On top of this, Toyota cars can also rely on tyres that have been developed specifically for them during the last few years, keeping in mind the specific features that an LMP1 hybrid car has. We will come to this point in a minute.

Before we dig into these particular characteristics we have to keep in mind that LMP1 cars use tyres with the same dimensions at the front and at the rear axle. This is a trend that started some years ago, following a very simple logic: a bigger tyre, can normally produce more grip. This means that having tyres with the same dimensions at the front and at the rear axle (instead of having smaller tyres at the front as, for example, in Formula 1 or also in LMP2) should ensure to the car an overall grip advantage and, hence, higher performances in cornering and braking maneuvers.

This is effectively possible only if all four tyres work in their right “operating window”, a term that mainly identifies parameters like inflating pressure, tyre and ambient temperature and, more in general, something related to how the car stresses its tyres and to the conditions the teams encounter during the race: if the tyre finds itself out of this window (for example because its temperature or inflating pressure rises too much or, on the other hand, because the driver cannot keep tyre temperatures high enough to ensure proper grip), their performance will be suboptimal. This could lead to tyres producing lower grip, more degradation, debris pick up or even tyre damage (for example, what engineers call graining). In any case, being out of the right window means that the car will perform worse than its actual potential, because its interface with the road will not operate at its best.

As mentioned, the tyre operating in the right window depends, beside ambient condition, on how much energy the car injects into the tyres themselves: if the car doesn’t stress the tyre enough, it will not reach the right operating temperature and it will underperform; analogously, stressing the tyre too much could mean going over the ideal operating temperature and pressure and/or having a faster degradation.

How much energy the car injects into the tyres is strictly related to car design, on a higher level and on car setup, on a lower one. If a tyre is designed to enter its correct window under a certain stress level, both lower or higher energy being transmitted to it will push it out of said window and reduce its performance.

As I briefly said before, an LMP1 hybrid car is a very special vehicle, because of its architecture and peculiar features.

First of all, hybrid cars are heavier than non-hybrid ones. Toyota cars have, at least for some portions of a lap, power being transmitted by the electric motors to the front wheels, with the car operating in certain phases (for example corner exit) as an all-wheel-drive vehicle. During braking, the electric motors also operate as a generator recharging the batteries, although this is not important for our discussion.

Because of the higher overall weight and the motors driving the front wheels, we can suppose that the static weight distribution (which portion of the overall weight loads the front tyres in static condition and which the rear ones) will be more forward biased than a non-hybrid car: in other words, given car weight, a bigger part of it will act on the front wheels when the car doesn’t move, because of components seating very much forward inside the car.

On the other hand, LMP1 private cars are not only lighter, but we can suppose they also have a more rear biased static weight distribution. One reason for this is that they don’t have any motor seating more or less in the same longitudinal position of the front wheels, as the hybrid cars do.

Picture courtesy of Lawrence Butcher (Race Engine Technology): Toyota TS050 front MGU unit.

A second reason is that they have a shorter wheelbase than, say, an LMP2 car (on which they are based in some cases, see Rebellion and SMP); if the tub remained the same than the LMP2 car, the wheelbase reduction happened mainly because of a shorter rear end of the vehicle (engine, gearbox and rear suspension), this meaning that the rear wheels seat more forward compared to the TUB itself than in an LMP2. This causes the CG position to be closer to the rear axle or, in other terms, a more rearward static distribution.

The reason why the CG moves closer to the rear wheels if we move them forward and closer to the Tub is easy to understand, if we look at the previous picture: the movement of the rear wheels forward, makes the three arrows (identifying here respectively tub, engine and gearbox weight forces) to be in a more rearward position, compared to rear contact patches. In other terms, the arrows stay in the same position in space in the two cases, while the rear wheels move forward, hence having to react a bigger portion of the overall weight of the car.

Besides weight and weight distribution, privateers don’t have any power being transmitted through the front wheels. Their internal combustion engines, which are normally more powerful than the hybrid cars ones, are connected only to the rear wheels.

What are the consequences of these differences?

It is easy to understand that having the front wheel driven by an electric engine in some phases that a hybrid car will stress the front tyres much more (for example in corner exit) than a non-hybrid one.

As well as this, a hybrid car having more overall weight and more static weight acting on the front tyres means that, in a corner, they will produce higher cornering forces (particularly at the front) and hence, will be subject to a higher stress and higher slip.

The reason for this has been analyzed in one of our articles about racecars handling. To negotiate a constant radius corner (with R being the radius) in steady-state conditions (constant forward velocity V), a heavier car will have to produce higher overall centripetal forces at its contact patches, as stated by Newton’s second law.

This equation shows how, the bigger the mass of the car, the bigger the centripetal force Fy produced by the tyres must be, in order to maintain a forward speed V. Fy is the sum of all the lateral forces that each tyres exchange with the road. In our case:

Since the front static weight portion is higher, a bigger portion of the overall cornering force will have to be produced at the front tyres contact patches, in order for the car to be in equilibrium for both translation and rotation.

The two pictures show a car with the CG seating more or less in the middle of the wheelbase (same distance from the front and rear axle and, hence, about 50% front weight distribution) and one with its CG seating closer to the front wheels. In this second case, our parameter “a” (distance between the front axle and CG) will be smaller and “b” (distance between the rear axle and CG) larger.

Looking to the second equation (rotational equilibrium), we immediately recognize how “a” being smaller and given the sum of Fyf and Fyr doesn’t change (in other terms, the car moves in the same circular path with radius R at the same forward speed V), in the second case Fyf will have to be larger than in the first case (while Fyr will be smaller), because “a” is now smaller and “b” larger.

Also, under braking, having forward-biased weight distribution, should allow the application of higher braking torques on the front wheels before reaching a tyre lock. This also leads to potentially higher forces being exchanged between the road and front tyres under braking.

What does this all mean?

In order to work well and be also able to last long enough without being subject to a too strong degradation, Toyota’s front tyres will need to be able to withstand much higher loads than what a non-hybrid car will be able to ever produce.

This probably means that a front tyre developed specifically for Toyota will have a stronger structure and, possibly, a harder compound than what a tyre developed specifically for non-hybrid cars would need. This lead to the issues that the privateers have, not being able to keep front tyres in the right operation window (temperature, for example) because the tyre is “too strong” for their needs. Most likely, they could work much better with softer compounds at the front, just to name one possibility, because they stress them less than a hybrid car.

On the other hand, privateer cars will tend to stress the rear tyre more than a Toyota. Despite being lighter, a larger portion of the overall cornering force that the car produces will be delivered by the rear tyres because of the more rear biased static weight distribution (for the reasons we have seen already for the case with a more front-biased car).

Besides this, private LMP1 cars can accelerate out of the corner exchanging a longitudinal force with the ground only with the rear tyres. Their engines are also more powerful than a hybrid car, so the rear tyres will be more stressed than Toyota’s ones.

If the tyres are effectively the same for Privateers and Toyota, as it has been reported, this probably leads to both front and rear tyres of the non-hybrid LMP1 cars to work out of their ideal operating window, although for opposite reasons.