Thermodynamic Analysis of Mercedes-Benz PU106C Hybrid Power Unit

Summary:

This report is going to analyze the modern Formula One power unit from a thermodynamic standpoint.  It will be using the Mercedes-Benz PU106C Hybrid Unit as a reference for this analysis.  This will be done due to the fact that there is enough information about this unit in order for it to be properly analyzed and because Mercedes-Benz have been leading the field when it comes to power unit performance, reliability, and efficiency.  It will start with a short history on power units in Formula One and why the governing body decided to implement the 1.6L Hybrid V6 units.  The individual components will then be discussed and the power unit will be modeled using an excel spreadsheet that has been setup specifically for this project using thermodynamic laws.  There will also be an ending discussion that talks about the future of both these power units.

Background

Formula One has always been about pushing the boundaries of both the car and the driver.  Over the years it has established itself as the bleeding edge when it comes to any type of automotive engineering.  The internal combustion engine has played a massive role in this development over the years and it has remained one of the main engineering focuses of the sport.  Formula One cars pioneered large turbocharged engines in the 1970’s and have introduced all sorts of advanced technology into the automotive industry including mainstays such as stability/traction control and anti-lock brakes.  The roar of a Formula One engine flying by at twenty thousand RPM became a clear part of the DNA of the sport.  One of the draws for big automotive companies to invest the massive amount of money required for Formula One development and research is that they will gain valuable information and technology that can be applied to their road car divisions along with the massive global viewership numbers for advertising purposes.

As mentioned the Formula One engine has always been the beating heart of the sport.  These engines were incredibly powerful but also relatively inefficient and unreliable.  Back in the 1970’s it wasn’t uncommon to use an engine for a few laps at a time.  When the governing body of Formula One, the FIA, where looking to redesign the cars going into the 2014 season, it was clear that they wanted to push Formula One into the future of automotive technology.  This goal was accomplished by switching from a naturally 2.3L V8 engine to a brand new 1.6L V6 hybrid unit.  They also restricted the amount of engines to four per season.  This change put the focus on efficiency and reliability in a way that had never been seen in the sport before.  Now that these power units have been in service for multiple years, it’s clear to see the impact that they have had on the technological development, and it’s very impressive.  Mercedes-Benz announced during the 2018 season that they achieved over fifty percent thermal efficiency for their power unit.  This change to a V6 hybrid unit meant that the engines were making the same amount of power as the V10 naturally aspirated engines used in 2005 while using half the amount of fuel.  Going into the power unit structure and systems used to achieve such a remarkable improvement in efficiency will be the next section of this report.

The modern power unit can be broken down into five key elements.  These are the internal combustion engine (ICE), turbo, energy store (battery), MGU-K, MGU-H, and the control electronics.  These components are all working together constantly in order to maximize both the performance and efficiency of the Formula One car as it completes its laps around the circuit.  

In order to keep the teams in line with each other the FIA has an extremely strict set of rules for each season that dictate how the teams can build and operate their cars.  These rules determine the dimensions of the cars, the maximum RPM of the engine, and thousands of other elements regarding the car.  These rules give the engineers very little room to operate, but also forces them to be creative with both their resources and designs.  This engineering creativity is what drives Formula One teams to devise such brilliant solutions to complex problems.

For the 2014 power units the main restrictions established by the FIA were fuel flow rate (100kg/hr maximum), a maximum ICE RPM of 15,000, and a maximum 100kg on fuel on board.  This meant that teams were going to have to leverage the hybrid elements of the drivetrain in order to achieve similar power levels compared to the naturally aspirated V10’s and V8’s the preceded the hybrid V6’s.  

The main components of the hybrid system are the MGU-K and the MGU-H.  Both of these are electric motors that also function as generators depending on current running scenario.  The MGU-K is a larger electric motor that is built into the gearbox under the ICE. This motor can supply 120kw of power and works together with the ICE to directly power the rear wheels through the transmission.  During braking this motor functions as a generator and can harvest 2MJ maximum per lap.  Additionally it is allowed to deploy 4MJ to lap.  This is a pretty standard “hybrid” setup that is employed by many road going hybrid automobiles.  

The MGU-H is an electric motor that is connected to the turbocharger.  Mercedes employs a split turbocharger that has the compressor and turbine on either side of the internal combustion unit.  The MGU-H is connected to the shaft in between both.  This allows the turbo to run more efficiently as instead of wasting energy with a wastegate that dumps directly into the exhaust, the generator can harvest that exhaust energy and save it for both MGU-K and MGU-H deployment.  So effectively the electric motor is controlling the inlet pressure of the engine by taking a specified amount of energy out of the exhaust flow.  This gives the engineers far more control over the turbocharger compared to non-electrified units.  Additionally the split turbo nature of the Mercedes power unit allows for other benefits, mainly due to the high temperature exhaust turbine being isolated from the compressor.  This lowers the intake temperature of the engine and increases power production.  It also means that there is significantly less plumbing required due to the location of the compressor being next to the inlet and the turbine being in the path of the exhaust.  This means the engine is more responsive and that a smaller intercooler can be used which helps with the overall aerodynamic packaging, another important performance aspect due to the complex packaging requirements of the power unit.  The isolated turbine and exhaust plumbing also means greater reliability from other components due to the greater control of temperatures across heat sensitive components.  The split turbocharger with MGU-H integrated in between proved to be a great decision that led to many substantially gains both in terms of performance and reliability.

The MGU-H is also used during acceleration as the compressor turbine takes time to spool up coming out of a corner.  Instead of waiting for the gas to spin the turbine, the MGU-H will be used to spin the turbine and eliminate that lag.  This “turbo lag” is a common phrase used to described the feeling of driving an automobile with a turbocharged engine.  This MGU-H gives the driver a much more linear power band which also makes the car easier to drive.  

The MGU-H is an important part of the engine formula due to the overall lack of restrictions put on it by the FIA.  There is no power limit or harvesting limit put on the MGU-H so teams are allowed to use the MGU-H however much or little they desire.  Part of the technical analysis using the excel model in the next section will be investigating the amount of power that the MGU-H could theoretically achieve using thermodynamic analysis of the ICE and the conditions of the exhaust flow.  According to Mercedes the MGU-H provides sixty percent of the electric power that is used by the entire hybrid system.  This shows how important both the turbocharger and MGU-H are to to the performance of these power units.

The energy store is effectively just a large lithium-ion battery that acts as a power reservoir for the harvested electrical energy from the exhaust flow (MGU-H) and kinetic energy of the car during braking (MGU-K).  However the only restriction on this battery is the weight of 20kg.  This means that teams are able to push the boundaries of battery technology in order to achieve the maximum amount of performance and energy density.  These battery packs have to be build to withstand extreme temperatures and packaging, along with the high performance output requirements that a Formula One power unit demand.  Keeping these cells cool is important to their performance, so the pack is liquid cooled and uses its own radiator.  During an average race these battery packs are fully charged and discharged up to seventy times.  These units are very relevant to road going cars due to the use of similar battery packs in both hybrid and full electric road going vehicles.  Battery energy density is a vital performance metric that applies to many areas of modern life, so any developments that are pushed in this area can have many applications beyond motorsport.  Mercedes-Benz used a modified version of their early Formula One battery unit in a road going electric prototype that has laid the groundwork for many Mercedes-Bens hybrid road cars and their fleet of upcoming fully electric vehicles.  It is clear that this will continue to be a massive area of research and development for all the teams going forward.

Practical PU Component Use Analysis

To explain how these components work in the actual car, it could be useful to analyze the car going through a specific turn at a race track.  While the car is accelerating towards the turn the engineers will want to maximize the amount of power being produced by all the components.  This means that the ICE will be running at a maximum fuel flow rate of 100kg/hr and the turbo will be running at the maximum pressure allowed by the ICE.  The left over energy will be actively recovered by the MGU-H during this time because the turbine is already spinning at its maximum RPM and doesn’t require any power from the MGU-H.  The MGU-K however will be operating as a motor and supplying the additional 120kW at it’s disposal.  

When the driver reaches the braking point they disengage the throttle and hit the brake pedal.  This signals the system to shift into another stage of operating. The MGU-K acts as a generator during this time, effectively acting as the rear brakes to the car.  The control systems will be keeping the harvesting within the maximum allowed amount per lap (2MJ).  The MGU-H will continue harvesting whatever exhaust flow is still occurring during this off throttle section.  The energy store will be received this power and storing it in the form of potential electrical energy in the battery.  

As the driver hits the apex of the turn they will start accelerating out of the turn.  This is when the MGU-H uses its power and spins the compressor up.  This would actually happen before the driver even hits the throttle.  The car does this automatically due to the control systems having very accurate information on where the car is on the track and this allows it to anticipate the drivers inputs before they even act.  It does this using both practice data and lots of telemetry, including GPS and transponders.  This means that when the driver does hit the throttle that the turbine of the compressor will already be compressing the air going into the engine and the driver will be able to have maximum power without any delay.  The MGU-K also provides its power to the transmission during this time.  

This analysis of a single turn is a simple overview of how the components are used, but in reality it becomes far more complicated to manage during a real race.  The engineers need to develop complex engine modes that adapt to all sorts of conditions.  Each track will have its own “program” developed around the drivers.  These programs effectively function to set the parameters of all these components depends on the demands and preferences of the drivers.  For example one driver might want more MGU-K power earlier in the lap while another might prefer to have more later on.  The culmination of all of this is an extremely complicated control unit that has an interface on the steering wheel.  The drivers are constantly adjusting the amount of harvesting and the power levels during the race depending on both ambient and internal conditions.  An example of just how small the margins are with such a system can be shown with an example situation that occurred during the 2018 season.  A driver was noticing power loss during a lap.  The team wasn’t sure what the issue was as everything looked appropriate with the telemetry being sent from the car.  It turns out the driver was driving so well that he was slightly ahead of the control unit program for where the power and braking points would occur.  This meant that the driver was asking for throttle before the MGU-H had gotten the input from the control electronics to spin the compressor, leading to the turbo lag that the driver noticed.  The team adjusted the programming and the performance issues were resolved.  Another example would be a driver having rear brakes that were overheating.  By increasing the MGU-K recovery under braking the MGU-K is able to take more of the braking load off of the rear brakes, lowering their temperature.

The main variables that determine theses system parameters are fuel level, temperatures (and other environmental parameters such as elevation and humidity), reliability, and ultimate performance required.  It becomes a delicate balance of maintaining whatever performance is necessary while avoiding unnecessary stress on the engine and components.  If a driver is leading the race by a large margin the engine will be tuned down to produce less power in order to maintain its reliability both in that race and upcoming races.  The FIA enforces strict penalties for engine replacements so reliability is a massive focus for these teams.  If a driver is trying to overtake another one the team will allow them to run an aggressive mode that produces the maximum amount of power and uses all the energy stored in the battery over a short period.  However due to the strain this puts on the car and the amount of fuel it consumes, the driver will have to compensate for this by switching to a lower output mode afterwards.  Even before that driver switches into that “attack” mode, they will use a “harvest” mode that ensures that the MGU-H and MGU-K charge the battery to the maximum level.  All these variables due to the complexity of the hybrid system allows for an element of strategy to come into play.  Mercedes-Benz engineers have done a great job of understanding how to achieve the maximum performance not just out of every individual component, but all the the components acting together as one.  This fact is illustrated nicely by the fourteen trillion individual calculations that are done by the control unit over the average race distance.

Technical Analysis

Due to the secretive nature of Formula One and the scale of the investment that goes specifically into the power unit, finding technical running data can be difficult.  However using the information given be Mercedes and the FIA, it is possible to model this engine using the fundamental laws of thermodynamics.  This section will use an excel spreadsheet that has been setup to model the Otto cycle internal combustion engine by applying these laws and the operation conditions that are known within the cycle. 

Mercedes-Benz PU106C Hybrid Specifications: 

Displacement (L): 1.6

Cylinders: 6

Compression Ratio: 18

Bore (mm): 80

Stroke (mm):  53

Maximum RPM: 15000 

Fuel Rate: 100 kg/hr

Single Turbocharger

Additionally the inlet temperature is set by the FIA as being at least ten degrees Celsius over the ambient air temperature.  This allowed for the inlet temperature and pressure to be set as inputs for the model.  Combined with the compression ratio, maximum revolution per minute, and engine displacement the process table of the entire cycle can be derived.  This also allows for the turbocharger to be modeled using the output parameters of the exhaust flow.  This allows for the analysis of the power the MGU-H is able to harvest when the maximum P1 pressure is reached by the turbocharger compressor (this is the point where instead of using a wastegate, the turbocharger uses the MGU-H to prevent an overboost scenario; a wastegate is still used in case of an MGU-H failure).  These numbers are acquired with a compressor pressure of 3.5 bar which seems to be a standard maximum boost level for these engines (due to the maximum fuel flow rate), but is not a disclosed metric.  The efficiency was stated by Mercedes-Benz at being 47% so that was what was used in the calculations.

Discussion

The calculated results seem to match up well with the rumored power levels and efficiency of these engines in real life.  When you add the MGU-K power of one hundred sixty horsepower, you get a total calculated power output of around one thousand horsepower, which is similar to what these engines produce when set to the maximum power settings.  This shows that thermodynamic analysis can be applied to even advanced engines such as those used in Formula One.

The MGU-H calculations show a maximum power of one hundred twenty six horsepower being generated from the turbine.  Unfortunately there isn’t much discussion about MGU-H power levels that have been disclosed to the public, but these numbers do seem reasonable considering the amount of reliance of this component as a generator for the entire electrical assist system.  Without the MGU-H this energy would be lost to the environment through the exhaust flow and be wasted.  Mercedes advertises an efficiency of over ninety percent for all their electrical components so the MGU-H calculations were made with the assumption of ninety percent efficiency when operating as a generator.  

Using some real world data from a race track that this engine would race at can provide some insight into the energy that the MGU-H would be harvesting.  The Shanghai International Circuit is one of the most demanding tracks in terms of using the maximum potential of the power unit due to the fact that the drivers are at full throttle for fifty four percent of the lap.  The full lap usually takes around one minute and thirty seconds.  So that is around 49 seconds at full throttle.  Using the MGU-H data from the model (and making the assumption that the engine is at fifteen thousand revolutions per minute during this time), this would mean the MGU-H could be harvesting about five thousand kilo-joules per lap at that specific circuit.  These numbers back up teams stating that the MGU-H provides most of the electrical power for the electric assist systems on the car.  It is clearly one of the most important components of the new engine formula due to its usefulness of control the turbocharger parameters with precision while also eliminating turbo lag and providing electricity for the rest of the systems.  The FIA decisions to leave the MGU-H and energy store open to technical development by not locking them down with regulations was a great way to push all of this technology to the forefront.  

Conclusion

The switch to a hybrid powertrain was met with lots of criticism from both the Formula One teams and the fans, but it clearly evident now just how much they have pushed the sport forward into a new age of technological advancement.  The fact that these engines are producing just as much power as the older naturally aspirated units while using half the fuel is quite an accomplishment.  By adding components like the MGU-K and MGU-H the teams now have far more creativity and development opportunity as compared to the older combustion engines.  Not only does that increase the performance levels in Formula One, but these technologies are very applicable to both road going automobiles and other sectors.  By leaving the battery capacity open and only restricting the weight the FIA has opened up increases in battery power density.  This real world relevance increases the willingness for these engine manufactures to spent the money on engine development as they know it will benefit the entire brand, not just its racing team.  Mercedes-Benz now spends overs two hundred million dollars a year for their Formula One engine development division.  In the future this might mean that new engine manufactures are willing to join the sport, simply because of how much they can benefit from such an extreme environment like Formula One.

These changes also made the racing more strategic in terms of the use of all these systems.  The strategic management of these systems means that teams have more variables to contend with during the race.  This means that there is a great chance of teams being on different strategies or a team making a mistake under pressure, elements that can make racing more exciting.

As Formula One looks to the future it is clear that the current engine configuration is only the beginning of electrified system integration.  The teams never stop developing and pushing the engineering envelope and it’s undeniable that there will be significant improvements ahead.  These power units will become even more powerful and efficient, maintaining their status as the peak of internal combustion hybrid engine design.  As easy as it is to miss the screaming sounds of the naturally aspirated engines of old, there is something very impressive about knowing that the new engines are so quiet because they are simply converting all of that exhaust energy to power.   The sport needed to answer the changing times of environmental and efficiency concerns and these engines have clearly accomplished that goal.  It is an exciting time in power unit development and it will be interesting to see how teams manage to push these amazing designs even further in upcoming seasons.