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(And why Specific Power sucks)

Naturally aspirated engines present an interesting challenge for automotive engineers. Unlike their force fed counterparts, atmospheric engines are subject to finite limits on how much torque and power they can make, dictated by little more than their basic geometry. For this reason, naturally aspirated engines have for a long time been compared using a measure known as Specific Power, the amount of horsepower produced per litre of capacity. Generally speaking, 100bhp/litre is considered the benchmark for road cars, anything over is 'highly tuned' and anything under is considered, at best, 'average'.

There is one small issue with using Specific Power as a means to compare engines though, highlighted by the fact I need to state 'for road cars' in the previous sentence. The problem stems from the fact that power is dependent on RPM and because higher RPM always nets higher power, Specific Power is only really of any use when comparing engines that operate at a similar speed.

"Consider if you will, the Yamaha R1 superbike.
Does its impressive specific output of 197bhp/litre infer that it is more highly tuned than say, the S2000 with only 120bhp/litre? 
I would argue not..."

Let's think back to 2013, the last season of the naturally aspirated F1 engines. Back then the 2.4 litre V8s were producing around 800bhp from 2.4 litres, giving 333bhp/litre. A truly incredible figure no doubt, especially compared to the very best road going cars, hovering around 125bhp/litre.

Now let's imagine we handicapped that F1 engine to 50% of its maximum revs, so that it produced 'only' 400bhp. This handicapped engine would still be making 167bhp/litre, which on the face of it might still be considered to be more highly tuned than say, the S2000. But we know that this engine is capable of so much more...

Consider if you will, the Yamaha R1 superbike. Does its impressive specific output of 197bhp/litre infer that it is more highly tuned than say, the S2000 with only 120bhp/litre? Based on the above, I would argue not. What if it was capable of more?

"For this Top Ten list, we're going to use something different, a little something I've derived myself. I've called it the 'Performance Index.'"

It doesn't take much to come to the conclusion that using Specific Power as a means to compare engines is flawed, because it inherently favours the highest revving engines over everything else. For this Top Ten list, I'm going to use something different, a little something I've derived myself. I've called it the Performance Index.

What is the Performance Index?

"Rated out of 1000, the Performance Index can be used to compare the state of tune of absolutely any four stroke gasoline engine, be it a single cylinder go-kart, a screaming Japanese four cylinder motorcyle or a thumping NASCAR V8."

The maths is explained in more detail at the end of the article, but quite simply, the Performance Index is the rated power output of an engine, divided by the calculated maximum that particular engine is capable of producing. The closer an engine is to its absolute limit, the higher its Performance Index.

Rated out of 1000, the Performance Index can be used to compare the state of tune of absolutely any four stroke gasoline engine, be it a single cylinder go-kart, a screaming Japanese four cylinder motorcyle or a thumping NASCAR V8.

If this has you asking the question "How do you calculate the maximum power an engine can produce?" you can skip to the last page, where I cover the maths in a bit more detail, but if you're not too fussed about that kind of thing, let's just say that it's based on a maximum 'mean piston speed' of 25m/s and a maximum specific torque of 90lbf/litre. With that, let's jump straight into the Top Ten!

As a quick note before we start, we're only looking at production road cars here, and to avoid any one engine dominating the leader board only the most highly tuned incarnation of each engine has been included!

Hit the next page button to check out number 10 on the list...

10. Honda Integra Type R - B18C - 110bhp/litre

No Top 10 NASP engines list would be complete without at least one Honda, so its no surprise to see the Honda Integra Type R here. As is probably to be expected, its rev hungy B18C leaves nothing on the table in terms of engine speed, MPS is at the top end of the spectrum with its 87.2mm crank moving the pistons at 25m/s at its 8600rpm redline.

Also, somewhat predictably, torque is on the low side. With 138lbft from its 1795cc engine, specific torque stands at 77lbft litre. Although not particularly strong figure given the competition in this instance, that's still a good figure in the grand scheme of things!

With 197bhp out of a potential 254bhp, the Integra Type R scores a PI of 774, earning it 10th place on the leaderboard. A stellar performance considering the B Series engine design is almost 30 years old now!

Notable relations
  • Civic Type R (EK9) - PI 715

    9. Audi RS4 - 4.2 FSI V8 - 107bhp litre

    Despite its relatively lowly position on the leaderboard, the 2014 Audi RS4 actually tops the list for piston speed. With a relatively long 92.8mm stroke, the pistons are buzzing at a ballistic 25.5m/s at its 8250rpm redline.

    Although the engine is at the ragged edge in terms of speed, the torque figure does leave some room for improvement. With 317lbft from 4.2 litres, it manages a specific torque figure 76lbft/litre . Entirely respectable, but the lowest on our top 10 list! (Yep, the Honda makes more torque. Ouch)

    With 444bhp out of a theoretical maximum of 554bhp, the Audi RS4 ranks 9th with a PI of 802. (Specific Power - 107bhp/litre)

    8. BMW M3 CSL - S54

    The E46 M3 CSL contains the ultimate evolution of BMW's legendary S54 straight 6 engine, a motor already widly acknowledged as one of the worlds greatest engines. 

    Piston speed is down slightly from the RS4 at 24.9m/s thanks to a slightly short stroke, but it more than makes up for it with 273lbft from 3246cc, for a specific torque figure of 84lbft/litre.

    With 355bhp out of a theoretical maximum of 440bhp, the M3 CSL ranks 8th with a PI of 806. (Specific Power - 109bhp/litre).

    Notable relations
    • E46 M3 - PI 768

      7. Pagani Zonda R

      Despite having the highest redline on the leaderboard so far, the Zonda R's AMG V12 actually ranks with the lowest piston speed out of all the entries at 23.3m/s, owing to its short 80.2mm stroke.

      Mercedes more than make up for this though with what they do best, thumping torque. With 523lbft from 6.0 litres, it ranks with the second highest specific torque figure at 87lbft/litre. 

      Despite producing an already impressive 750bhp, the Zonda R is theoretically capable of 921bhp, meaning it ranks 7th with an NA PI of 814. (Specific Power - 125bhp/litre)

      6. Honda S2000 - F20C

      Now, I know we all like to rip Honda's for their lack of torque, and with 153lbft from 2 litres the S2000 does admittedly have one of the lowest specific torque figures to make the leaderboard at 77lbft, but all joking aside that is still a very impressive figure, especially given the age of the engine now.

      Like the B18C fitted to the Integra we just looked at, the piston speed is up there with the best, its 84mm crank firing the pistons up and down the bores at 25.2m/s at the 9000rpm redline.

      With 240bhp out of a theoretical maximum of 287, the S2000 comes in at number 6 with an NA PI of 818. (Specific Power - 120bhp/litre)

      5. Porsche 911 GT3 RS

      Porsche's GT3 RS models are well renowned for their screaming NA flat six engines and the latest incarnation of the GT3 RS pushes the boundaries even further.

      With 339lbft from its 4.0 litre capacity, Specific Torque is 85lbft/litre and with an 81.7mm stroke the 8800rpm redline means an MPS of 24m/s.

      With 500bhp out of a theoretical maximum of 605, the 991 GT3 RS comes in at number 5 with an NA PI of 826. (Specific Power - 125bhp/litre)

      Notable relations
      • 997 GT3 RS 4.0 - PI 812
      • 991 GT3 - PI 785
      • 997 GT3 RS - PI 724
      • 996 GT3 RS - PI 645

        4. Porsche 918 Spyder

        Porsche might be well known for the screaming N/A flat 6 engines in their 911 GT3 models, but its easy to overlook the NASP V8 fitted to the 918 because of the muddy waters of hybrid powertrains.

        When you shed the engine of its electrical assistance it does turn out to be quite an impressive piece of engineering. With 398lbft from 4.6 litres the Specific Torque is 87lbft, the second highest on this list, and with a 9150rpm redline and 81mm stroke, MPS is 24.7m/s.

        With 608bhp out of a theoretical maximum of 700, the Porsche 918 Spyder nudges ahead of the 991 GT3 RS, ranking 5th with an NA PI of 869.

        3. Ferrari 458 Speciale

        For a company renowned for making world class NASP engines, Ferrari only manage to get one engine in this top ten list, but what an engine it is! With 398lbft from 4499cc, the F136 V8 is a world record holder with the highest specific torque for any road going production engine at 88lbft/litre. 

        With an 81mm crank the pistons are moving at 24.3m/s at its 9000rpm redline.

        With 597bhp out of a theoretical maximum of 685 the Ferrari 458 Speciale ranks 4th with an NA PI of 869. (Specific Power 125bhp/litre)

        2. Lamborghini Huracan Performante

        Lamborghini have been setting a number of records with their incredible Huracan Performante, and that is due in no small part to its frankly incredible engine. Had we not have elected to only feature each engine once, the 5.2 litre Audi V10 would have found its way onto this leaderboard at least four times what with it powering various versions of the Huracan, Gallardo, and R8.

        Although a slightly lower redline of 8000rpm gives a small drop in piston speed to 24.7m/s, the torque is up from 413lbft to 443lbft for a specific torque of 84lbft/litre which more than compensates.

        With 631bhp out of a possible 692bhp, the Huracan Performante lands in 2nd position with an NA PI of 914.

        Next up is the grand finale, the most highly tuned NASP engine ever fitted to a production car. Can you guess what it is yet?

        With the other contenders in the list you might be forgiven for assuming it would be yet another large capacity European supercar, yet the engine to actually claim the top spot may come as a surprise, for it is in fact none other than a plucky 4 cylinder Brit...

        1. Caterham R500

        Although probably not what you'd class as a traditional supercar, there is no doubting that the bonkers R500 has supercar slaying potential and that DNA runs right down to the core of its powertrain. 

        Co-developed with Minster Racing Engines, Caterham took the venerable 1.8 litre Rover K Series into the laboratory and tortured it on the test bed, pushing it to the limits until it committed fiery suicide. Once they knew the absolute limit, they cranked it down half a notch so that it didn't quite explode, and fitted it in the 500kg 7 chassis to create the R500.

        Producing and incredible 230bhp out of a theoretical maximum of 248bhp, this incarnation of the K Series is nothing short of a pure race engine running on the absolute ragged edge of performance.

        Surprisingly, despite the astonishing headline figure, neither of our two core parameters are maxed out. With 155lbft from 1.8 litres the specific torque is 'only' 85lbft/litre and with 24.4m/s at its 9200rpm redline it actually ranks 8th for piston speed. 

        With an NA PI of 927 the Rover K Series takes the crown as the most highly tuned NASP engine ever fitted to a production car. A record that is, sadly, unlikely to ever be broken as natural aspiration enters its twilight years. #sadface

        Want to figure out how you engine ranks?

        Of course you do. You can read up the maths used to calculate the PI and check your own engine's PI here.

        Want to check out a longer list?

        We've listed 90 in a detailed table here.

        Think we've missed one, or want to add yours?

        Just email us the details and we'll get them added to the list! They don't have to be top performers, it'll be a bit of a laugh to check out some of the very worst too!

         

        Like the line artwork?

        That's actually what we do for a living. How do you fancy one of those personalised to match your car, laser engraved along with a full technical specification on an aluminium plaque?

        Sound interesting? Check out the catalogue here and grab 15% off any order over £200 with discount code NASP15!

         

        How was this all calculated?

        Want to know a bit more about how these engines were rated?

        Naturally aspirated engines have two major limitations. The first is how much torque they can make, the second is how fast they can spin.

        Specific Torque

        The first limitation is known as specific torque, the amount of torque produced per litre of capacity. A largely irrelevant figure in forced induction engines (because increasing the boost pressure has the effect of increasing the size of the engine), this figure is of interest in NASP engines because it conveniently describes how efficiently the engine can fill its cylinders with air fuel mixture, and how effectively it can convert that mixture into mechanical force.

        As NASP engines are only ever capable of producing a few percent over 100% volumetric efficiency, the absolute ceiling is about 90lbft/litre, with most performance engines sitting between 75 and 85lbft/litre.

        Mean Piston Speed

        The second limitation is one which affects both turbocharged and naturally aspirated engines alike, and that is the speed at which they can run. Whilst the maximum RPM of engines differs wildly, there is another, lesser known measure of engine speed, which paints a very different picture. its called Mean Piston Speed.

        Mean Piston Speed (MPS for short) describes the average speed at which the pistons are travelling in the bores, for any given RPM, the speed at which the pistons move will vary depending on the stroke length. The longer the stroke, the faster the pistons have to travel every RPM, so an engine with an 80mm stroke spinning at 8000rpm would have the same MPS (21.3m/s) as an engine with a 40mm stroke, spinning at 16,000rpm. 

        While there is theoretically no limit on the RPM an engine can run at, the maximum sustainable MPS for a four stroke gasoline engine engine is a little over 25m/s. Beyond this speed component stresses get so high as to start impacting engine service life, but more importantly we start to get into the realm of the piston starting to outrun the flame front on the power stroke, resulting in a dramatic drop in torque. With a fixed limit on the piston speed, we can compare an engine's actual MPS with the maximum of 25m/s as a method with which normalise the speed of all engines regardless of their operating RPM.

        The equation to calculate the maximum RPM of an engine from its stroke length is as follows: $$RPMmax = 30,000 \cdot \bigg({MPS \over Stroke}\bigg)$$

        Where bore is in millimeters.

        Torque and speed make...

        So, we know that the maximum torque an engine can make is limited to 90lbft per litre, and that the maximum RPM be caculated from the stroke length and a piston speed of 25m/s. Combining torque and RPM make power, so from this we can calculate a maximum power output for pretty much any engine, based on nothing more than its basic geometry!

        An engine's absolute maximum power output can be calculated as follows: $$ Pmax = 9.694 \times 10^{-3} \cdot Bore^2 \cdot Cylinders$$

        Where bore is in millimeters.

        For those of you that are interested, there is a full article explaining how that equation was derived here:

        Performance Index

        The Performance Index figure used in this article is simply the rated output of any particular engine, divided by its calculated maximum output, multiplied by a 1000. $$ Performance Index = {Pactual \over Pmax} \cdot 1000 $$ The PI is scored out of 1000 and this figure can be used to directly compare absolutely any naturally aspirated four stroke gasoline engine, because unlike BHP/litre it is normalised for engine speed.

        Find out your engine's Performance Index here

        Read this page first? Head back to page 1!

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        Comments

        Andy:

        True, if the stroke (=diamater of rod journal centerline rotation), then the piston will travel a total distance of 2*stroke per crankshaft rotation, hence avg piston speed is 2 * stroke * rpm.

        However, the maximum force exerted on the piston will vary greatly with different rod:stroke ratios, and it’s at this point of where the piston undergoes maximum acceleration that the engine will likely self-destruct.

        You’ll notice that usually whenever most manufacturers increase the stroke (appreciably), they also increase the deck height to allow room for a longer rod. They need to do this to maintain a certain safety cushion, and to ensure longevity. Conversely, if they don’t increase the deck height, they almost always reduce the redline for a stroked engine.

        In any case, I think it’s pretty safe to assume that as since most of the cars you’ve listed here are production vehicles, their respective manufacturers are pretty smart people and have designed the engines with a safe rod:stroke ratio, so using avg piston speed is probably a pretty reasonable metric.

        Oct 02, 2017

        Daniel Kozakewycz:

        Thanks for the comment Andy.

        I see where you are coming from, while I agree the acceleration and maximum piston speed will be different, if the stroke is 100mm and it spins at 1 rev per second, then the piston will travel 200mm in that 1 second regardless of the rod length?

        Oct 02, 2017

        Andy Somogyi:

        Very interesting and insightful article.

        Howrver, you’re neglecting rod length, and rod to stroke ratio. With a very long rod, piston speed approaches 1/2 * stroke * cos (\omega), where \omega is the angular velocity.

        However, with a short rod, max piston speed tends to infinity.

        I’d need to integrate over a crank rotation to see how mean piston speed is affected by rod:stroke ratio.

        Oct 02, 2017

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