Talking to a turbo expert

[olefud]

Maybe under some unstated parameters. But what about the example of the two engines sized for the same power rating, one power cycle with the conventional engine at 100% volumetric efficiency and the turbo at 150% VE? The larger displacement conventional engine will have greater volume for power stroke expansion thus utilizing more of the heat energy. The turbo will finish work expansion with higher residual cylinder pressure and waste a bit more with an earlier exhaust valve opening for blowdown to relieve the higher pressure prior to the exhaust stroke.
The energy reclaimed by the turbo is not useful energy. Turbocharging has advantages but thermo efficiency wouldn’t appear to be one of them. The whole purpose of compounding is to reclaim this wasted heat energy.

You should start thinking in energy balance to understand the advantages of specific configurations. The higher the thermal efficiency of an engine the more power it makes from the fuel. In that regard it primarily matters how much thermal and kinetic energy is dumped with the via the exhaust gas and the radiators. One aspect already covered by TC is the frictional aspect. Turbocharged engines run on lower revs and waste less power in friction than higher revving naturally aspired engines. You need to look at the basic physical aspects to determine where your efficiencies are generated. That means comparing the main loss drivers. One other aspect of turbo charged engines is the better suitability to direct injection spray guided combustion. This type of combustion delivers the best fuel/air ratios and combustion efficiencies. But it works best at lower revs because the known injection systems are too slow for rpms beyond 9,000 rpm. There is work under way to improve the speed of injection but it is a long way to reach the 15,000 rpm the regulations allow for the new engines. So there are several good reasons to focus on the lower hanging fruits of charged engines.

We’re using the same criteria but are having trouble with the many variables in a very complicated process. Think carefully about my example. Work is done on the power stroke. If there is high residual pressure in the cylinder, as there is when the exhaust valve opens in a turbocharged engine, the heat energy is dumped into the exhaust and wasted. On the other hand, a NA engine with its larger relative expansion volume utilizes more of the heat energy in work and has lower pressure when the exhaust valve opens, all other things being equal.

The turbocharged engine, having higher combustion pressure as it approaches BDC must also open the exhaust valve earlier to allow for blow down from the higher pressure. This blow down energy is not trivial. The Wright R-3350 Duplex Cyclone operated its compounding turbine solely on blow down energy to avoid back pressure on the exhaust stroke. Just the blow down normally wasted energy harvested increased efficiency on the order of 18%. Aircraft engines are a special case but do illustrate a point. As an indication of relative waste energy, I’ve never known of a compounded NA engine.

Again, set aside the preconceived, conventional knowledge and rethink this. It’s a bit different but not that complicated.

[WhiteBlue]

Olefud, I'm troubled to understand what you are trying to demonstrate. Our starting point was the comparison of brake thermal efficiencies of various F1 engine types.

Brake Thermal Efficiency is defined as break power of a heat engine as a function of the thermal input from the fuel. It is used to evaluate how well an engine converts the heat from a fuel to mechanical energy.

• Old NA V8 = 29% BTE
• turbocharged V6 DI = 33% BTE
• turbo compounded same engine = 36% BTE

were the estimates. If there are difficulties in understanding I'm referring to the percentage of power that is converted to mechanical drive power from the chemical energy that is entered with the fuel. I have posted the definition from engineering.com above for reference.

So on that basis I would appreciate an explanation which figures you find wrong in relation to each other and why. I'm aware that those figures are estimates. But I think that the relations between them are fairly accurate. Until now I have simply understood that you do not believe in the superior efficiency of turbocharged engines over comparable NA engines, but I may be wrong. So before going into finer details we might want to clarify the respective positions.

[olefud]

Olefud, I'm troubled to understand what you are trying to demonstrate. Our starting point was the comparison of brake thermal efficiencies of various F1 engine types.

Brake Thermal Efficiency is defined as break power of a heat engine as a function of the thermal input from the fuel. It is used to evaluate how well an engine converts the heat from a fuel to mechanical energy.

• Old NA V8 = 29% BTE
• turbocharged V6 DI = 33% BTE
• turbo compounded same engine = 36% BTE

were the estimates. If there are difficulties in understanding I'm referring to the percentage of power that is converted to mechanical drive power from the chemical energy that is entered with the fuel. I have posted the definition from engineering.com above for reference.

So on that basis I would appreciate an explanation which figures you find wrong in relation to each other and why. I'm aware that those figures are estimates. But I think that the relations between them are fairly accurate. Until now I have simply understood that you do not believe in the superior efficiency of turbocharged engines over comparable NA engines, but I may be wrong. So before going into finer details we might want to clarify the respective positions.

Yes, and recall that I didn’t question these figures but asked why the results were such in that the turbocharged engine is not intrinsically more thermo efficient than a NA engine. Since these results are apparently from modeling the several differing engines, I thought that perhaps the input parameters would explain the matter, i.e. a RPM differences at which the engines are modeled.

I don’t really care if I’m right or wrong. I just want to understand why the results were as posted.

[WhiteBlue]

Yes, and recall that I didn’t question these figures but asked why the results were such in that the turbocharged engine is not intrinsically more thermo efficient than a NA engine. Since these results are apparently from modeling the several differing engines, I thought that perhaps the input parameters would explain the matter, i.e. a RPM differences at which the engines are modeled. I don’t really care if I’m right or wrong. I just want to understand why the results were as posted.

The current V8 NA engine was studied in a thread together with Expensive and riff_raff. A long thread about engine friction was dedicated to effort of coming finally up with the 29% BTE figure. We mainly worked out the actual fuel consumption and compared it to the known engine power using an accepted figure for energy content in the fuel.

The turbo engine was an estimate that was based on several efficiency improvements that are going to feature.

• higher cylinder pressure and compression enabled by direct injection
• leaner combustion by spray guided technology
• reduced friction by lower rev level
• reduced friction from fewer cylinders and moving engine parts
• lower radiating losses from more compact engine, thermal losses smaller due to greater piston l/d ratio (according to riff_raff)
• lower tail pipe losses from reduced kinetic and thermal energy (influence of the turbo)

Those points were basically confirmed by the power and consumption figures that were published in the 2012 V6 thread.

a quick comparison of parameters

specific energy in fuel 46 MJ/kg (kJ/g)
V8 engine, 720 bhp (530 kW), fuel peak flow 39.6 g/s = 1.822 MW fuel flow enrgy--> BTE = 29.1 %
V6 turbo engine, 580 bhp (427 kW), fuel peak flow 27.8 g/s = 1.279 MW fuel flow energy --> BTE = 33.4%

The TurboCompound engine was calculated by Ringo in this thread. He made themodynamic design calculations for the compressor, the turbine and what residual power was available for electric transfer from MGU-H to MGU-K. That additional power will raise the BTE by more than 3% over the simple turbocharged engine. I have to re calculate this as I have already pointed out.

I now estimate the available electric power at peak performance at 100 kW from the MGU-K although 120 kW are allowed. 90 kW will come from the MGU-H and 10 kW from the battery and kinetic energy recovery.

V6 incl Turbocompound 527 kW, 1.279 MW fuel flow energy --> BTE = 41.2 %
You see the turbocompounded engine will make an even bigger jump than previously predicted if indeed the total power will be on par with the current engines.

[olefud]

the current V8 NA engine was studied in a thread together with Expensive and riff_raff. A long thread about engine friction was dedicated to effort of coming finally up with the 29% BTE figure. We mainly worked out the actual fuel consumption and compared it to the known engine power using an accepted figure for energy content in the fuel.

The turbo engine was an estimate that was based on several efficiency improvements that are going to feature.

• higher cylinder pressure and compression enabled by direct injection
• leaner combustion by spray guided technology
• reduced friction by lower rev level
• reduced friction from fewer cylinders and moving engine parts
• lower radiating losses from more compact engine, thermal losses smaller due to greater piston l/d ratio (according to riff_raff)
• lower tail pipe losses from reduced kinetic and thermal energy (influence of the turbo)

Those points were basically confirmed by the power and consumption figures that were published in the 2012 V6 thread.

a quick comparison of parameters

specific energy in fuel 46 MJ/kg (kJ/g)
V8 engine, 720 bhp (530 kW), fuel peak flow 39.6 g/s = 1.822 MW fuel flow enrgy--> BTE = 29.1 %
V6 turbo engine, 580 bhp (427 kW), fuel peak flow 27.8 g/s = 1.279 MW fuel flow energy --> BTE = 33.4%

The TurboCompound engine was calculated by Ringo in this thread. He made themodynamic design calculations for the compressor, the turbine and what residual power was available for electric transfer from MGU-H to MGU-K. That additional power will raise the BTE by more than 3% over the simple turbocharged engine. I have to re calculate this as I have already pointed out.

I now estimate the available electric power at peak performance at 100 kW from the MGU-K although 120 kW are allowed. 90 kW will come from the MGU-H and 10 kW from the battery and kinetic energy recovery.

V6 incl Turbocompound 527 kW, 1.279 MW fuel flow energy --> BTE = 41.2 %
You see the turbocompounded engine will make an even bigger jump than previously predicted if indeed the total power will be on par with the current engines.

Thanks. I’ve only followed this thread. Since I’m working on a more efficient NA engine concept, the thought that a noncompounded turbo engine is intrinsically more efficient is a concern. However, the data are for two rather differing engines and we can agree on the data while differing as to the ultimate efficiency of turbo vs. NA.

It would seem that the first three points, higher cylinder pressure, leaner combustion and lower RPM friction are also operating parameters available with a NA engine. The turbo would have a higher specific output relative to displacement thus lower friction. But I would think the big difference is in RPM since the V8 was designed to rules that featured power and the V6 rules bowed towards efficiency.

I question the lower radiation losses since, for a given power, if not radiated the energy would be rejected through the radiator. The turbo would have a hotter overall burn in a smaller volume. Neither engine would be adiabatic.

The turbo may have lower (specific?) exhaust energy but this would not be to the benefit of the engine power since the turbo energy use is parasitic.

The above is not intended to further the debate. Each of us has our “facts” on the relative efficiency of straight turbo vs. NA. My ethic when accessing the expertise of others is to also input my thinking, if any, for what its worth.

[WhiteBlue]

it's what engineers call higher brake thermal efficiency, which can also be called higher overall efficiency(not what engineers call thermal efficiency (aka indicated thermal efficiency), which has a different meaning)

Well, I was a bit sloppy I realized when I went back to check all the figures. I was talking of the brake thermal efficiency most of the time. The fact of the matter is that both TE and BTE are higher in an F1 turbo design than in an F1 NA engine. All things being equal the current 2.4L V8 has a piston design that is tweaked for high revs and high inertial forces giving it a very cubic aspect with a short stroke. The 1.6L turbo V6 will have a much larger piston l/d ratio. This will help to improve the internal thermal efficiency of the engine because the heat exchange area is reduced and less heat is transported to the radiators.

Regarding the BTE I have written enough in the previous posts. I hope this is clear now.

[WhiteBlue]

I’ve only followed this thread. Since I’m working on a more efficient NA engine concept, the thought that a noncompounded turbo engine is intrinsically more efficient is a concern. However, the data are for two rather differing engines and we can agree on the data while differing as to the ultimate efficiency of turbo vs. NA.

It would seem that the first three points, higher cylinder pressure, leaner combustion and lower RPM friction are also operating parameters available with a NA engine. The turbo would have a higher specific output relative to displacement thus lower friction. But I would think the big difference is in RPM since the V8 was designed to rules that featured power and the V6 rules bowed towards efficiency.

I question the lower radiation losses since, for a given power, if not radiated the energy would be rejected through the radiator. The turbo would have a hotter overall burn in a smaller volume. Neither engine would be adiabatic.

The turbo may have lower (specific?) exhaust energy but this would not be to the benefit of the engine power since the turbo energy use is parasitic.

The above is not intended to further the debate. Each of us has our “facts” on the relative efficiency of straight turbo vs. NA. My ethic when accessing the expertise of others is to also input my thinking, if any, for what its worth.

It is good that we could clear up some of the issues. It helps me to understand what you are trying to do. Nevertheless I'm convinced that your project is doomed compared to an alternative project that will use turbochargers for the same purpose. That actually holds true for racing as for road car engine if we make fuel efficiency the primary yard stick. Please have a look at my Porsche turbo research.

..looking at the Porsche Cayenne S and Turbo engines. Both are 4.8L V8 DFI with 120 bar fuel injection pressure, so they obviously have the same injection system and basic engine except for the turbo charging. Bore × stroke: 96.00 mm × 83.00 mm

S-version:
Power: 294 kW @ 6,500 rpm
Torque: 500 Nm
Compression: 12.5:1
Fuel: 10.5L/100km

Turbo-version:
Power: 368 kW @ 6,000 rpm
Torque: 700 Nm
Compression: 10.5:1
Fuel: 11.5L/100km

It gives a good idea what is possible with the V8 in both NA and turbo version. While the fuel consumption goes up by 9.5% the power increases by 25% and the torque goes up by 40% when the turbo is added.

This is a fairly modern road car example from 2010. Please take notice of the old fuel injection system at 120 bar. If a more modern 200 or 500 bar system was used the compression of the turbo could be higher and the engine would probably have an even higher efficiency from the improved knock resistance. As it stood at that time they had to reduce the compression which is a disadvantage for the BTE of the turbo.

Naturally we do not get figures for brake thermal efficiency because no peak power fuel consumption figures are ever published for such engines. But we can take some clues from the European consumption cycle figures that were given. If we compare fuel per power used we get:

35.6 L fuel/100 km and MW engine power for S
31.3 L fuel/100 km and MW engine power for the Turbo

It tells us that the same vehicle with a downsized turbo engine of the same peak power would get 13.7% better milage. That is not bad to have. Now imagine that you use other downsizing options like making it a V6 with smaller displacement but the same power and a faster injection system. The efficiency advantage would probably grow to 20% or more because you would be using less friction, better combustion and fewer internal thermal losses. The advantage of the turbo engine does not stop there. You also get a lighter and more compact engine which makes it more valuable for a road car. I think it is well worth considering for your project. The figures will not look much different if you are looking at a racing engine project. From all I have ever seen the turbo option is indeed inherently more fuel efficient compared to the NA.

From the opening page of the thread:

If you .. used turbo-charging to increase the low-end of the engine, you’ll actually see better drivability from a two-liter engine than a three liter (non-turboed) engine: more torque, more low-end response, higher top end and better fuel consumption. American OEMs need to realize you don’t use turbos for horsepower alone, but to enhance the total driving experience. You can make the engine 30 to 35 percent smaller, which takes all the weight away and you might use fewer cylinders and overall you have a lighter drive train.

[olefud]

It is good that we could clear up some of the issues. It helps me to understand what you are trying to do. Nevertheless I'm convinced that your project is doomed compared to an alternative project that will use turbochargers for the same purpose. That actually holds true for racing as for road car engine if we make fuel efficiency the primary yard stick. Please have a look at my Porsche turbo research.

..looking at the Porsche Cayenne S and Turbo engines. Both are 4.8L V8 DFI with 120 bar fuel injection pressure, so they obviously have the same injection system and basic engine except for the turbo charging. Bore × stroke: 96.00 mm × 83.00 mm

S-version:
Power: 294 kW @ 6,500 rpm
Torque: 500 Nm
Compression: 12.5:1
Fuel: 10.5L/100km

Turbo-version:
Power: 368 kW @ 6,000 rpm
Torque: 700 Nm
Compression: 10.5:1
Fuel: 11.5L/100km

It gives a good idea what is possible with the V8 in both NA and turbo version. While the fuel consumption goes up by 9.5% the power increases by 25% and the torque goes up by 40% when the turbo is added.

This is a fairly modern road car example from 2010. Please take notice of the old fuel injection system at 120 bar. If a more modern 200 or 500 bar system was used the compression of the turbo could be higher and the engine would probably have an even higher efficiency from the improved knock resistance. As it stood at that time they had to reduce the compression which is a disadvantage for the BTE of the turbo.

Naturally we do not get figures for brake thermal efficiency because no peak power fuel consumption figures are ever published for such engines. But we can take some clues from the European consumption cycle figures that were given. If we compare fuel per power used we get:

35.6 L fuel/100 km and MW engine power for S
31.3 L fuel/100 km and MW engine power for the Turbo

It tells us that the same vehicle with a downsized turbo engine of the same peak power would get 13.7% better milage. That is not bad to have. Now imagine that you use other downsizing options like making it a V6 with smaller displacement but the same power and a faster injection system. The efficiency advantage would probably grow to 20% or more because you would be using less friction, better combustion and fewer internal thermal losses. The advantage of the turbo engine does not stop there. You also get a lighter and more compact engine which makes it more valuable for a road car. I think it is well worth considering for your project. The figures will not look much different if you are looking at a racing engine project. From all I have ever seen the turbo option is indeed inherently more fuel efficient compared to the NA.

I think you’re correct as to the status quo. What I’m doing would improve both the turbo and NA efficiency, but from poorly controlled testing (dissimilar engines and rather agricultural data logging) the NA thermal efficiency would benefit more than the turbo.

I’m sorry that I can’t communicate more details but the patent situation is rather up in the air. I’ve had a bit of success with inventions and know that complex automotive technology is not the best place to do so –and I already have one such proven automotive patent that I’m shopping. Still there’s the siren song of something new.

Back to the issue -it’s difficult to have a discussion without nailing down the operating conditions. The F-1 engine has a near unity full power duty cycle. The Porsche engines have a near negligible full power duty cycle, though the rare full power capacity is important. The design considerations and operating conditions are very different for power vs. economy. Having done a bit of the former while in racing, I’m taking the same approach to optimize economy rather than power. But working in new areas primarily in theory with limited empirical confirmation of course means that I could well be wrong –I certainly have been on occasion in the past.

The input by you and others has been very helpful, both as to information and by challenging me to think deeper on the matter. I would like to offer more in return, but I think you have heard rather enough on why I think the turbo is inefficient relative to NA.

[WhiteBlue]

The input by you and others has been very helpful, both as to information and by challenging me to think deeper on the matter. I would like to offer more in return, but I think you have heard rather enough on why I think the turbo is inefficient relative to NA.

Thank you for the feed back. It is appreciated. I would be very keen to hear about your idea when you have nailed it in a patent application. It surely is a steep task to overcome the thermodynamic advantages of a turbo. I have actually studied thermodynamics many years ago and know a bit about drive systems from professional experience. That doesn't actually mean I have any particular knowledge in ICE design. I'm just an interested amateur to the art. Nevertheless I find such mechanical developments and particularly anything about energy transformation very fascinating. It certainly is much more fascinating than aerodynamics to me. I'm very much convinced that in some years time all ICEs from mid market level upwards will have turbo chargers or even turbo compounding. Due to its efficiency the turbo engine is the logical choice for hybrids, and hybrid systems will have the bigger growth than pure electrics.

[olefud]

The input by you and others has been very helpful, both as to information and by challenging me to think deeper on the matter. I would like to offer more in return, but I think you have heard rather enough on why I think the turbo is inefficient relative to NA.

Thank you for the feed back. It is appreciated. I would be very keen to hear about your idea when you have nailed it in a patent application. It surely is a steep task to overcome the thermodynamic advantages of a turbo. I have actually studied thermodynamics many years ago and know a bit about drive systems from professional experience. That doesn't actually mean I have any particular knowledge in ICE design. I'm just an interested amateur to the art. Nevertheless I find such mechanical developments and particularly anything about energy transformation very fascinating. It certainly is much more fascinating than aerodynamics to me. I'm very much convinced that in some years time all ICEs from mid market level upwards will have turbo chargers or even turbo compounding. Due to its efficiency the turbo engine is the logical choice for hybrids, and hybrid systems will have the bigger growth than pure electrics.

Having studied “innovation” as a process, I look for the basic or radical (in the sense off being prime) insights that might support a simple but effective improved result. If you’re interested I could provide an example that is so truly elegant that PhD experts in the field told me that the art was so fully developed, and has been for over 100 years, that my idea was, as it were, doomed to failure. Yet, if anything, it is too effective. There’s some interesting physics, but the insight process is the main feature.

If there’s interest, I can start a more appropriate thread and quit abusing this one.

[pgfpro]

I love this thread good stuff all the way around. =D>

I think the key to efficient engines of the future at the OEM level will be smaller engines with DI and new advance turbo charged engines.

I also think that F1 will help bring some new Hybrid technology to the table with the MGUH and MGUK units.

[Pierce89]

The MGU for KERS/HYBRID use in the powertrain 'is' the gearbox. one and the same unit an ESERU. (with a lighter geartrain, more compact, stronger and no direct engagement clutch but still with seven fixed stepped ratios).
Electricity generated by the turbo generator can be fed directly to it for primary motive power at the same time electricity from battery, flywheel or capacitor storage is also fed to it for the same purpose.
Under braking the (MGU)/ESERU harvests braking energy to storage as does the turbo generator. This is then fed back to the ESERU as primary motive power on acceleration. The ic engine augments this application of power up to the level demanded by the throttle pedal and control system.
There is no need for seperate or extra MGU's as all these functions are dealt with by the Electric Shift Energy Recovery Unit.
Control over turbine load and operation is far better than any mechanical flybrid system or other mechanical geared system, as is electric drive control over the intake compressor. For maximum power bursts, full intake pressure can be selected with minimum load on the exhaust turbine plus full electric apply from all available electrical storage.
At the other extreem, the ic engine can be turned off completely and primary drive from electrical storage only used. The ic engine could also be un-coupled from the powertrain (without using a clutch, there would be no conventional clutch)and run solely to generate electricity to storage to augment brake energy harvesting, useful when blowing a diffuser under braking, without wasting the energy used to provide the extra exhaust gas volume.
Non of this tries to rewrite the laws of physics, as all methods of energy harvesting from either braking or exhaust gas require a dual energy conversion at or around the quoted efficiency. However this nowhere near takes into account the many other improved control, and efficiency benefits that this system provides.

Have you built a working prototype?

[Pierce89]

But it works best at lower revs because the known injection systems are too slow for rpms beyond 9,000 rpm. There is work under way to improve the speed of injection but it is a long way to reach the 15,000 rpm the regulations allow for the new engines. So there are several good reasons to focus on the lower hanging fruits of charged engines.

Porshe used a direct injected 3.4l V8 at 10,800 rpm back in 2007

[WhiteBlue]

But it works best at lower revs because the known injection systems are too slow for rpms beyond 9,000 rpm. There is work under way to improve the speed of injection but it is a long way to reach the 15,000 rpm the regulations allow for the new engines. So there are several good reasons to focus on the lower hanging fruits of charged engines.

Porshe used a direct injected 3.4l V8 at 10,800 rpm back in 2007

Can you give us a reference for details? I suspect you have the LMP2 Spyder in mind. The rpm on that was 10,300 according to my sources and it wasn't a DI system either. It is being described as multi point which is a common name for intake port fuel injection.
There is no problem going to higher rpm with DI than the system can do in spray guided combustion. You simply loose the efficiency because you must inject earlier and more fuel. For general purposes it is not a big problem but for F1 2014 rules you have a problem. You are not generating as much power as you possibly can from the limited fuel flow.

[Edis]

But it works best at lower revs because the known injection systems are too slow for rpms beyond 9,000 rpm. There is work under way to improve the speed of injection but it is a long way to reach the 15,000 rpm the regulations allow for the new engines. So there are several good reasons to focus on the lower hanging fruits of charged engines.

Porshe used a direct injected 3.4l V8 at 10,800 rpm back in 2007

Can you give us a reference for details? I suspect you have the LMP2 Spyder in mind. The rpm on that was 10,300 according to my sources and it wasn't a DI system either. It is being described as multi point which is a common name for intake port fuel injection.
There is no problem going to higher rpm with DI than the system can do in spray guided combustion. You simply loose the efficiency because you must inject earlier and more fuel. For general purposes it is not a big problem but for F1 2014 rules you have a problem. You are not generating as much power as you possibly can from the limited fuel flow.

Spray guided injection is a means to achieve charge stratification at part load and low speed (other solutions to achieve charge stratification are air or wall guided injection), the purpose is of course to improve part load efficiency. But charge stratification can't and isn't used at high speed and load, which is why it isn't used for direct injected racing engines. Direct injected racing engines only operate with homogeneous mixtures, typically rich but under certain conditions also lean homogeneous mixtures. Passenger car engines can sometimes be limited to homogeneous charge modes (makes exhaust aftertreatment a lot easier), while others use all three modes; charge stratification at low loads and speeds up to perhaps 3000 rpm, lean homogeneous mixtures above that and rich mixtures at high loads and speeds.

When the Porsche MR6 (V8) engine was released it had a port injected fuel system, but was later modified for direct injection. This engine is not the highest reving direct injected racing engine, however. Mercedes-Ilmor ran direct injected Formula 1 engine in their test cells before the 100 bar fuel pressure limit. These engines ran to 16,500-17,000 rpm without power loss according to Mario Illien. At speeds higher than that there was some powerloss. The fuel pressure used for these engines was 150 bar and the reduction in fuel consumption was about 5%.