The Mathematically Boring Engine

Ted

The pilot formerly known as Twin Engine Ted
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This is more for the car guys/gearheads on here (aren't most of my threads these days?).

Back in the 90s (also known as "ancient history" to some of you kids), most new design automotive engines you saw followed the formula of 500 cc/cylinder. 2.0L 4-cylinders, 3.0L 6-cylinders, 4.0L V8s. The theory was that, through a bunch of engineering mathematical wizardry, it was determined that above and below the 500 cc/cylinder mark, an engine inherently was going to be less efficient, coming down to some balance of rotating assembly mass, square inches of combustion area for the combustion chamber at the top. Smaller cylinders would produce a revvier but less efficient engine, and larger would produce a torquier but also less efficient engine.

In the late 90s and through the 2000s we tended to see cylinders move to larger displacements (which as I understood it came about because of some shift in the optimization curve between fuel economy/efficiency and emissions), but we've been seeing this formula return in the past several years, often with some complex turbocharger setups to boost horsepower numbers as needed.

It didn't occur to me until recently, but I've driven (and owned) a number of engines that have fit this mathematically perfect equation. And none of them have been my favorites to drive. Even with varying significant levels of tweaking (my 3000GT VR-4 being a 3.0L V6 that I very heavily worked on), they all remained... boring. Even the 4.0L supercharged V8 in our XKR isn't a particularly exciting engine to me.

Here's my theory: This mathematically perfect engine also creates a mathematically boring engine, because it is too balanced. Not in terms of physical balance, but in terms of performance. These engines are decent at everything, but not great at anything. Start to diverge in either direction - bigger or smaller displacement per cylinder - the engine will get to be more enjoyable to drive.

Smaller: You get an engine that's revvier and will happily rev to higher RPMs. This is fun for winding it up and getting some serious revs.

Larger: You get an engine with bigger torque pulses that create a stronger visceral sensation of torque and performance.

Just like the idea of 500 cc/cylinder being mathematically perfect, diverging from it is an over simplification and there's a lot more to it. Undersquare vs. oversquare, cam profile, cylinder head and combustion chamber design, compression ratio, forced induction, engine calibration (fuel and ignition). If you look at the Cobra build, it's a Ford 351 (so 5.8L or figure 725 cc/cyl, and oversquare on dimensions at 4.0" bore and 3.5" stroke). I'm doing everything I can to make it really responsive and revvy. In some ways I do think the engine may not be ideally suited for it as far as size/weight/displacement go, but it will be an interesting engine.

There are other similar theories about number of cylinders as well, and all of these things come together. I think for motorcycles the equation changes some for various reasons. But for cars, I think this is true.

So don't be boring - buy a car with a displacement that's not 500 cc/cylinder. :)
 
Ted wants a Sentra. Secretly. He's too embarrassed to say it though.

If you give me your Sentra, the results will end up on YouTube.

That's all I'm going to say about that.
 
So don't be boring - buy a car with a displacement that's not 500 cc/cylinder. :)
A few counterexamples:
Alfa Romeo 3.0L V6
Lamborghini 6.0L V12
Aston Martin 6.0L V12
Jaguar 6.0L V12
 
Well, my first Firebird was a Formula with a 6.6 L (or 400 cu. in. ) engine-V8. It was a lot more fun to drive than my Special Edition Trans Am with a 4.9 L (302 cu. in. ) V8. Could also be manual transmission vs. automatic.
 
A few counterexamples:
Alfa Romeo 3.0L V6
Lamborghini 6.0L V12
Aston Martin 6.0L V12
Jaguar 6.0L V12

I knew that was coming. :)

Like I said, it would be incorrect and an oversimplification to say that's the only input to the function that is engine personality. The McLaren F1 BMW V12 is also 6.0L. However, my point is that the mathematical "perfection" also contributes to it being more boring.

I've driven two of those engines - the Alfa 3.0L V6 and the Jaguar 6.0L V12. I've also drive the Alfa 2.5L V6 and the Jaguar 5.3L V12s. In the case of the Jaguars I've driven probably 50 different Jaguar V12s total, with most being 5.3s but at least half a dozen 6.0Ls in there (we had a lot of them come in when I was a Jag mechanic). In both cases, I would argue that the smaller displacement (not 500cc/cylinder) versions are more interesting. Let's focus on the Jaguar since I know the most about those.

The Jaguar 6.0L V12 was essentially just a new crankshaft, and then I think they also moved the wrist pin up on the pistons to make up for it. The bore stayed the same at 90mm, the stroke went up from 70mm to, I believe, 78.5mm. The cylinder heads, intakes, camshafts, everything else stayed the same.

Now, the 6.0L had more torque and did make more horsepower. It also moved the RPM further down, which was a "better" fit for the XJ12s. While both were smooth engines, the 5.3s were smoother, owing to the short stroke, and they really enjoyed the revs. A V12 in an automotive application isn't generally designed as a torquey stump puller, though. The 6.0s didn't rev as freely.

And there's the point. It's not that the 6.0 was instantly given "boring" status. It's just that the 5.3 was more interesting from a driving perspective.
 
My ‘04 Escape has a 4-cylinder, 2.0l engine, and its been VERY interesting. Well, not so much the engine as the manual transmission...and not so much the manual transmission as teaching my daughter to drive it. ;)
 
I was leaving transmissions out of the discussion entirely. Everyone knows where I stand on what transmission is most fun. ;)

Haha I just mentioned it because you could be outside the formula and the transmission chosen could just make it awful.

Example: 5.7L Titan V8 in Ford trucks of an older vintage with Ford’s boring four speed slush box.

(Worst Ford V8 ever, matched to an incredibly boring Trans.)

Makes nice roaring noises in the wrong part of the torque band while “accelerating”.

Geared wrong. Doesn’t drive in any way exciting or good. Yawn. Can barely get out of its own way.
 
Haha I just mentioned it because you could be outside the formula and the transmission chosen could just make it awful.

Example: 5.7L Titan V8 in Ford trucks of an older vintage with Ford’s boring four speed slush box.

(Worst Ford V8 ever, matched to an incredibly boring Trans.)

Makes nice roaring noises in the wrong part of the torque band while “accelerating”.

Geared wrong. Doesn’t drive in any way exciting or good. Yawn. Can barely get out of its own way.

Exactly. Enjoyment of a vehicle is about the sum of the parts, and what that sum produces, rather than any one individual piece of it.

That's where some of these things get hard to discern - you usually have a total system you're evaluating, and so it's hard to identify which components of that system produce more interest vs. boring. So, maybe I should put together what would be the most boring car combination. :)
 
I've driven two of those engines - the Alfa 3.0L V6 and the Jaguar 6.0L V12. I've also drive the Alfa 2.5L V6 and the Jaguar 5.3L V12s. In the case of the Jaguars I've driven probably 50 different Jaguar V12s total, with most being 5.3s but at least half a dozen 6.0Ls in there (we had a lot of them come in when I was a Jag mechanic). In both cases, I would argue that the smaller displacement (not 500cc/cylinder) versions are more interesting
I suppose it's a matter of degree. In the case of the two Alfa engines, if the 2.5L is more enjoyable than the 3.0L in the same chassis then the difference is not very noticeable.
 
Haha I just mentioned it because you could be outside the formula and the transmission chosen could just make it awful.

Example: 5.7L Titan V8 in Ford trucks of an older vintage with Ford’s boring four speed slush box.

(Worst Ford V8 ever, matched to an incredibly boring Trans.)

Makes nice roaring noises in the wrong part of the torque band while “accelerating”.

Geared wrong. Doesn’t drive in any way exciting or good. Yawn. Can barely get out of its own way.

You talking about the 5.4L Triton?
 
I never found the 3.0L twin-turbo V6 (VG30DETT) in Nissan's 300ZX to be boring, but it's hard to compare it to something else in that same platform. The mathematically optimal engine size may have been constructed without forced induction or other tech (direct injection) in mind, which may change the theory a bit. Nissan/Infiniti's new variable compression engines may change that as well from an efficiency standpoint.
 
In my experience, having a mathematically optimal engine means nothing when it comes to practical application. Put the wrong air system on an engine that is an “engineering masterpiece” and it will turn into a turd. Same thing for the rest of the car and driveline, it all needs to be matched well.

Ive owned a lot of cars and motorcycles in my life (I’ve lost count of the total at this point) and there are some that stand out as being more enjoyable than others. The most enjoyable on the street weren’t the best track car, and the opposite is also true.
 
I suppose it's a matter of degree. In the case of the two Alfa engines, if the 2.5L is more enjoyable than the 3.0L in the same chassis then the difference is not very noticeable.

I've only driven one Alfa V6, in a 156 in Switzerland. I forget the displacement. It was definitely the best V6 I've ever driven.

I never found the 3.0L twin-turbo V6 (VG30DETT) in Nissan's 300ZX to be boring, but it's hard to compare it to something else in that same platform. The mathematically optimal engine size may have been constructed without forced induction or other tech (direct injection) in mind, which may change the theory a bit. Nissan/Infiniti's new variable compression engines may change that as well from an efficiency standpoint.

I think the idea behind that perfect engine displacement was more or less independent of forced induction being present or not. Mercedes has moved in that direction with 4.0L twin-turbo V8s in place of the naturally aspirated or supercharged V8s they had before.

In my experience, having a mathematically optimal engine means nothing when it comes to practical application. Put the wrong air system on an engine that is an “engineering masterpiece” and it will turn into a turd. Same thing for the rest of the car and driveline, it all needs to be matched well.

Agreed, it's all a system and it needs to work together. But at a certain point you make basic design decisions. The engine will have x cylinders, y displacement, a bore and b stroke. Things like that. And all of those individual decisions play into the result. And they need to be properly matched to the vehicle to make a enjoyable all around experience. Transmissions and axle ratios play a big role in it too. That's been part of the fun (and challenge) with building the Cobra, is matching it all together so that it does what I want it to. And I think I've more or less got it, but we'll see once I start driving it.
 
You talking about the 5.4L Triton?
4.6 Triton would be correct. Super high rear, ridiculous overdrive 4th gear, couldn't get out of its way.
2wd auto got me 22mpg - economy driving, in a 250k truck.

All of its power came on late, it sounded like it was going to fly apart before it started pulling.
 
4.6 Triton would be correct. Super high rear, ridiculous overdrive 4th gear, couldn't get out of its way.
2wd auto got me 22mpg - economy driving, in a 250k truck.

All of its power came on late, it sounded like it was going to fly apart before it started pulling.
I could see that. @denverpilot said 5.7L Titan . . . which is not a Ford engine size or name I'm familiar with, lol. The 4.6L was gutless in a truck, but pretty much bulletproof otherwise. They actually had a 4.2L V6 as well that was even worse in a 6K lbs truck. I had the 5.4L Triton 3V and had no issues with it being anything but reliable, no different in function than the 5.3L in my GMC. I had the 3.55LS rear in my F-150, which made for okay fuel mileage on the highway, but if I could have changed anything about that truck it would have been to get the 3.73 or a 4.10 rear in it to make acceleration/towing a lot better.
 
I could see that. @denverpilot said 5.7L Titan . . . which is not a Ford engine size or name I'm familiar with, lol. The 4.6L was gutless in a truck, but pretty much bulletproof otherwise. They actually had a 4.2L V6 as well that was even worse in a 6K lbs truck. I had the 5.4L Triton 3V and had no issues with it being anything but reliable, no different in function than the 5.3L in my GMC. I had the 3.55LS rear in my F-150, which made for okay fuel mileage on the highway, but if I could have changed anything about that truck it would have been to get the 3.73 or a 4.10 rear in it to make acceleration/towing a lot better.

Sorry meant the 5.4L Triton.

Bulletproof it was definitely not. Class Action lawsuit over the two piece dissimilar metal spark plugs, and there should have been one over the three valve version’s cam phasers.

Those items put the Lincoln LT the Mrs drives $4000 or so in maintenance over the same time period as our boring old Chevy 350 derivative in the Yukon.

Mechanics hate them.

Car Wizard:

Deboss Garage:

They’re the crappiest engine Ford has built that sold way too many of. The three valve being particularly crappy. Ha

Made a lot of people a lot of money helicoiling those engines after the spark plugs blew out, then they did the two piece dissimilar metal plugs, then they FINALLY had an actual engineer actually worked on it.

The joke is “How did an engine company over 100 years old not know how to do spark plugs?” LOL. I think one of the mechanics above mentions it amongst other things.

Deboss mentions his engine rebuilder won’t even rebuild the ones that have valve issues. Too many problems getting oil to the phasers.
 
The Ford mod motors were definitely an interesting engineering exercise.

"Let's replace three completely separate engine lines [302, 351, 460] with a single line that has a whole lot of parts in common!"

The idea itself wasn't inherently a bad one. As it was, the 302 and 351W shared a lot of parts, or at least could share a lot. Ford did some interesting gymnastics to make the mod engine series work, including the splayed crankshaft on the V10 to maintain even cylinder firing with a 90 degree V10.

I've owned three mod motors - a 4.6 in my '92 Town Car, and two of the 6.8 V10s, both in Excursions. Reliability wise, they did fine although my Town Car did try to blow out spark plugs once. It didn't, but it tried. The first V10 succeeded in doing it to the previous owner, probably why I got it so cheap, but I never had that issue.

As far as driving them went? Well, Town Cars are supposed to be boring, so I'll allow it. The V10 did the job pretty well, but I'd prefer a 460.
 
The 2V Triton (mainly 5.4L and 6.8L) were the plug spitters. The 3V was the 2-pc spark plug. However, the 2pc spark plug was pretty easily remedied by a TSB that included putting high temp nickel anti-sieze on the spark plug sheath which kept carbon deposits from adhering to the plug. Problem solved. The cam phasers were a bad design, but I never had a problem in 160K miles.

Never had to put a dime into repairs aside from a broken exhaust manifold stud (which all Tritons are notorious for).

I do have to add 2 qts of oil between every 5K-mile oil change on my 5.3L GMC thanks to that awesome AFM design. Nothing like buying an extra 40 extra quarts of synthetic oil over the course of 100K miles because it's considered "within normal tolerances" by GM.

Sent from my SM-N976U using Tapatalk
 
So don't be boring - buy a car with a displacement that's not 500 cc/cylinder. :)

I remember years ago reading I believe a Popular Mechanics magazine and they wanted to find the 'perfect' car, one basically what you're talking about. To make a long story short, the winner was the Ford Fairlane. The perfectly boring car.
 
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I remember years ago reading I believe a Popular Mechanics magazine and they wanted to find the 'perfect' car, one basically what you're talking about. To make a long story short, the winner was the Ford Fairlane. The perfectly boring car.

So a 182 is that perfectly boring Fairlawn of the skies, a Skylane.
 
Interesting concept... My two V8s adhere to your principles - one small and revvy (F355’s 3.5L 5 valve) and one big and torquey (V8 Vantage’s 4.7L). My 6 cyls kind of... one old school air cooled 3.6L flat 6 and one modern, torquey but mathematically average turbo 3L flat 6...

Another aspect for me is that I don’t really like the super common configs (3L turbo V6 and 2L turbo 4) - although ironically, I technically also have a few of those - but I don’t usually drive them...
 
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However, the 2pc spark plug was pretty easily remedied by a TSB that included putting high temp nickel anti-sieze on the spark plug sheath which kept carbon deposits from adhering to the plug. Problem solved. The cam phasers were a bad design, but I never had a problem in 160K miles.

The cam phasers, the timing chain guides, and tensioners, and pretty much everything related to the timing chain area. LOL. Once the phasers go the timing chain is usually banging on something.

You got super lucky if you haven’t had to replace all of that yet. Ours went around 120K I think. I’d have to look in her truck records. She doesn’t tow, she doesn’t haul heavy, she doesn’t really use it as a truck. If it can’t hold itself together better in “tall car light duty service”...

Both mechanics I posted say that the anti seize never worked right. Dumb fix that pretty much guaranteed misfires.

Any whoo... once you completely replace everything Ford screwed up on that engine... then it’s pretty solid. Hahaha.

And still mated to one of the worst shifting automatics and awful gear ratios I’ve ever driven. LOL.

I knew better than to buy the third F-150... but she still likes it.

Oh I completely forgot the calipers. A little corrosion and bang, the tech will snap off the bleeder valve. Ford will happily sell you a new one when they do that. That was a dealer tech, too.

First repair on that truck. Took it in for new brakes all the way around after buying it used at 40K miles and the tech busts the caliper. Service manager didn’t even care. Wouldn’t budge on saying the design wasn’t flawed.

It was, like the other two F-150s I’ve owned, just the first of many a repair on it.
 
The theory was that, through a bunch of engineering mathematical wizardry, it was determined that above and below the 500 cc/cylinder mark, an engine inherently was going to be less efficient, coming down to some balance of rotating assembly mass, square inches of combustion area for the combustion chamber at the top. Smaller cylinders would produce a revvier but less efficient engine, and larger would produce a torquier but also less efficient engine.

I heard that theory too, coming from some German University group IIRC. It's quite easy to show it is bunk. Look at the chart at the bottom of this web page:

https://en.wikipedia.org/wiki/Brake-specific_fuel_consumption

The Saturn I4 with 475 cc/cylinder, the Rotax 914 with 303cc/cylinder, the Lycoming O-720 with 1475cc/cylinder, and the Wright R3350 at 3048cc/cylinder all have fairly similar efficiencies.

Do you actually have the math behind the theory?
 
Ted, you ride a Harley that utilizes inferior pushrod technology. I don't care what you think about cars. Not even one little bit.
 
Interesting concept... My two V8s adhere to your principles - one small and revvy (F355’s 3.5L 5 valve) and one big and torquey (V8 Vantage’s 4.7L). My 6 cyls kind of... one old school air cooled 3.6L flat 6 and one modern, torquey but mathematically average turbo 3L flat 6...

Another aspect for me is that I don’t really like the super common configs (3L turbo V6 and 2L turbo 4) - although ironically, I technically also have a few of those - but I don’t usually drive them...

I certainly have a general dislike for anything hugely common (which should come as no surprise to anyone on here), so certainly the commonality does play a role for me. :)

Comparing your F355's 3.5L V8 vs. your old school Porsche 3.6L flat 6 I think provides an interesting exercise that illustrates the point well, though. In those two cars you have engines that are both in the 10-20% deviation range from the "optimal" displacement per cylinder. Both are sporty engines, but I bet they are both interesting and have different visceral characteristics - the Ferrari being something that loves to rev and the Porsche also still liking revs (maybe not quite as high) but also having a strong visceral feel from the torque pulses. They may make similar horsepower and torque (I actually don't know, having not looked up), but they "feel" different in how they do it, and both satisfying but just in different ways.

I heard that theory too, coming from some German University group IIRC. It's quite easy to show it is bunk. Look at the chart at the bottom of this web page:

https://en.wikipedia.org/wiki/Brake-specific_fuel_consumption

The Saturn I4 with 475 cc/cylinder, the Rotax 914 with 303cc/cylinder, the Lycoming O-720 with 1475cc/cylinder, and the Wright R3350 at 3048cc/cylinder all have fairly similar efficiencies.

Do you actually have the math behind the theory?

I don't have the math behind the theory, more just making my own theory based on the logic behind the theory posed by the Germans. However, I'd point out that BSFC by itself is sort of fickle and highly variable. I spent a few thousand hours running engines that looked a lot like 720s (360s, 540s, 580s, and probably one or two 390s). Of course we all know that BSFC will change with mixture setting, that part is easy. But assuming an optimal mixture setting, you'll get different BSFCs at different RPMs, and especially at part throttle.

The real concept behind the theory, which makes sense to me, is that for an automotive gasoline engine (emphasis on automotive, as horsepower requirements become much different for other forms of transport) that 500cc/cylinder produces a generally optimally balanced engine. Comparing to an aircraft engine isn't hugely realistic. Aircraft engines are running at high horsepower ranges all the time (note that if you compare to big medium/heavy duty diesel trucks that are doing similar, the equation changes dramatically and looks more like aircraft engines) whereas automotive engines are generally dealing with acceleration and transients for stop-and-go traffic, run at a lower percent power vs. their maximum horsepower, and these days are also heavily controlled as to their air/fuel ratios due to emissions regulations.
 
I’m not well versed in all things engine, but have owned outside of that band. I did have a Sentra, 1.6L with stick and no excessive fun to be found. A pair of VQ35s in a G35 and FX35 and both made the drive better for it. In reflection, nothing under 2.0L really was good though the majority of those were 90s or earlier.
 
I don't know a thing about engines and certainly nothing about the math behind it but I know what's important, and that is the sound of the engine.
The lower the full power rpm, the better.
The louder the thump of escaping exhaust, the better.
The more one can discern the sound of each Otto cycle, the better.
Screaming two-strokes suck.
Large, slow moving radials are heaven.
 
I’m not well versed in all things engine, but have owned outside of that band. I did have a Sentra, 1.6L with stick and no excessive fun to be found. A pair of VQ35s in a G35 and FX35 and both made the drive better for it. In reflection, nothing under 2.0L really was good though the majority of those were 90s or earlier.

The VQ35/37 I tend to think are the most satisfying V6s out of Japan, and second only to the Alfa V6, at least among cars I’ve driven. The Ferrari Dino V6 is one I would love to experience but that’s not likely in this lifetime.

I don't know a thing about engines and certainly nothing about the math behind it but I know what's important, and that is the sound of the engine.
The lower the full power rpm, the better.
The louder the thump of escaping exhaust, the better.
The more one can discern the sound of each Otto cycle, the better.
Screaming two-strokes suck.
Large, slow moving radials are heaven.

There are a lot of different engine sounds I can appreciate. I love the sound of a big diesel, a high revving I6, V8, or V12. I also love the sound of a big lumpy V8. 4-cylinders and V6s usually don’t do as much for me, but there are exceptions. 3 cylinders are also interesting, especially the 14k RPM 3-cylinder in my wife’s Triumph. I didn’t used to think much of them, but have come to appreciate them more lately. V-twins are also a lot of fun. I love the sound of my straight piped Moto Guzzi.

The science of engine sound is really quite fascinating, there’s a lot that goes into it.
 
The VQ35/37 I tend to think are the most satisfying V6s out of Japan, and second only to the Alfa V6, at least among cars I’ve driven. The Ferrari Dino V6 is one I would love to experience but that’s not likely in this lifetime.



There are a lot of different engine sounds I can appreciate. I love the sound of a big diesel, a high revving I6, V8, or V12. I also love the sound of a big lumpy V8. 4-cylinders and V6s usually don’t do as much for me, but there are exceptions. 3 cylinders are also interesting, especially the 14k RPM 3-cylinder in my wife’s Triumph. I didn’t used to think much of them, but have come to appreciate them more lately. V-twins are also a lot of fun. I love the sound of my straight piped Moto Guzzi.

The science of engine sound is really quite fascinating, there’s a lot that goes into it.

I understand

While it was not the best performing engine the one that I loved driving a lot was the 302 in my mustang. That thing just sounded amazing and the driving experience was visceral.
 
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I understand

While it was not the best performing engine the one that I loved driving a lot was the 302 in my mustang. That thing just sounded amazing and the driving experience was visceral.

Agreed. I've driven a few Mustangs, and the 302-powered ones were always my favorites. Certainly the 4.6 and now Coyote-powered ones are faster and better all around cars (especially in the handling department), but the sound and visceral qualities of the 302 beat the others any day.

Really, I don't think the Coyotes sound all that great for a V8. They still have that Ford V8 sound, but you can tell they're overhead cams. I do enjoy the sound of a good DOHC 32-valve V8, but I think that American pushrod V8s tend to sound better than their overhead cam counterparts.
 
In reflection, nothing under 2.0L really was good though the majority of those were 90s or earlier.

Additional thought - when you get under 2.0L for most cars, especially talking the 90s when they were all naturally aspirated, you generally aren't going to get an engine that'll be well matched because it will just be underpowered. So, looking at that level starts to get harder - you're basically looking at motorcycle engines.

Once you get to motorcycles, though, the design needs change significantly. You don't have to have a very efficient engine to still get good fuel economy since you've got such a small frontal area and engine in general, plus so light weight. That's a whole other discussion. My Harley gets laughably awful gas mileage for a motorcycle now with the big bore kit and the tune, something around 33 MPG (used to be 40-45). But that's still burning half the fuel (or less) of any of the cars I own and I am happy with how it runs now.
 
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