Ever wonder just why a big four cylinder almost invariably has more punch down low, and less need to rev than a similar-sized six or V8? There’s a very simple but easily forgotten law of physics that explains it. Of course, details of their construction and tuning can affect or alter that somewhat too, but fundamentally, the law applies to all IC engines. To underscore the point, we’ll start by looking at three engines with similar features but vast differences in displacement per cylinder and corresponding torque and horsepower peaks.
These images represent three engines from the mid-’50s to the mid-’60s. Each of them was designed for maximum power output, with a hemi/pent roof combustion chamber, overhead cam(s), and large valves and ports, all the classic hallmarks of a high-output engine.
The one on the left generated 5.4 hp per cubic inch @21,500 rpm and 1.06 lb.ft. per cubic inch @17,000 rpm
The one on in the middle generated 1.48 hp per cubic inch @6500 rpm and 1.26 lb.ft. @5250 rpm
And the one on the right generated 0.27 hp per cubic inch @2000 rpm and 0.87 lb.ft. @ 1350 rpm
Now for the big difference: their displacement per cylinder. From left to right, in cubic inches: 1.5, 67, and 181.6
Like so many other things in nature, engines don’t scale without significant impacts.
Before we explain the physics, let’s take a quick look at these three engines, as they’re interesting in their own right.
First: 1966 Honda RC116 50 cc racing motorcycle (note: the cross section at the top is actually from a different Honda engine; close enough). This masterpiece was Honda’s last 50cc racing bike, the culmination of several generations of 50cc racing bikes going back to 1962.
Here’s how the tiny 49.8 cc (3.0 cubic inch) twin cylinder engine looked. From its 50cc (3.0 ci), it generated 16.5 hp @21,500 rpm, and 3.25 lb.ft. of torque @ 17,000 rpm. Each 25 cc cylinder was fed by a four-valve head.
And here’s the crankshaft, pistons and connecting rods.
Given its very narrow power band, it took a nine speed transmission to put that power to the ground. Max speed: 175 kmh, or 110 mph. Brakes? Calipers working on the rims, just like on a bicycle; lighter than drum brakes. Weight: 50 kg, or 110 lbs. Here’s a video of it in a bit of mild action:
Two: 1955 Meyer-Drake Offenhauser 270 racing engine:
The M-D Offy four cylinder racing engine is an American legend, dominating oval track racing from midgets to Indy 500, for decades. An evolution of Miller racing engines of the 1920s, which started out as an improved copy of the first DOHC Peugeot racing engine of 1913, the Offy 270 was one of the larger ones.
Its 4.374″ bore and 4.5″ stroke yielded 270 ci (4.4 L) from four cylinders. That made for phenomenal torque; 340 lb.ft. at a reasonably low 5250 rpm for a racing engine. That was key to its ability to accelerate out of corners at its torque peak without shifting, and then reach its top speed and full power peak of some 400 hp (depending on fuel, etc.) on the straights, also at a fairly modest 6500 rpm.
Its torque output of 1.26 lb.ft. per cubic inch is exceptional for a naturally aspirated engine, and one of the keys to its long career.
Its distinctive bark and roar were familiar sounds to the generations of Americans that watched it on tracks of all sizes and kinds.
Three: Hall-Scott 400:
The Hall-Scott 400 six cylinder gas engine was the culmination of a long line of legendary H-S engines designed to for maximum performance in trucks and buses, using the same basic principles (OHC hemi head) that Hall-Scott initially used in racing and aero engines. Since diesel engines inherently generate less torque than gas engines (unless boosted), it offered a way to cover more distance per day, if at the price of higher fuel costs.
With a bore of 5.75″ and a massive stroke of 7″, it displaced 1090 ci (17.9 L). Its torque curve was fairly flat, and peaked at 1350 rpm. And hp peaked at a very low 2000 rpm. But note that even though it was clearly designed for maximum torque, given its application, its torque output per cubic inch is the lowest of the three engines at 0.87 lb.ft. per ci. We’ll explain that shortly, as it’s all part of the same issue.
So on to the physics: Scaling up creates issues, all across nature. If you double (square) the dimensions of a sphere, cube or cylinder, the resulting volume is then 8x (cubed) larger. That creates two issues with engines that we’ll deal with here.
The first one has to do with mass, as the mass (weight) of an object also is 8x greater when its dimensions are doubled. If you were to scale up a mouse to the size of an elephant, it would collapse under its own weight. The elephant’s skeleton is much more than just proportionately stronger. That increases weight very disproportionately, hence the elephant needs very thick bones. And it’s forced to move relatively much more slowly compared the mouse.
This is of course also very much true in engines, in terms of the increased strength that would be required for the components of a larger engine to turn at the same speed as a smaller one. It’s obvious and intuitive: larger engines need to rotate at lower speeds than smaller ones, otherwise the huge masses of the reciprocating parts could never be contained; there’s just no materials strong enough, up to a point.
One could increase the bore and stroke of an engine by a factor of say x2, which would increase its displacement by x8, if we used super strong components. In fact, modern F1 engines (before 2014) did just that, and can rev as high as 20,000 rpm with a displacement per cylinder of 300 cc, or a bit more than x8 of the Honda’s tiny engine (190 cc). This is the result of huge progress in material strengths like titanium, as well as better breathing, but we’ll leave that aside for now, and also acknowledge that this was impossible back then. And that it would still be impossible to build an engine of the Hall-Scott 400’s size and have it be able to rev that high. Maybe someday.
For now, we can put aside these issues of mass and component strength, because there’s a more fundamental one yet: volumetric efficiency. Even if we had infinitely strong materials, this issue still governs the operating speed and power peaks of a naturally-aspirated gas engine.
Volumetric efficiency (“VE”) is the actual amount of air flowing (“breathing”) through an engine, compared to its theoretical maximum. Basically, it is a measure (percentage) of how full the cylinders are filled during the intake stroke. That is primarily dependent on airflow through the valves and ports. It was discovered quite early (as in this 1901 Truscott marine engine) in the engine’s development history that maximizing valve and port size by using canted valves in a hemispherical combustion chamber maximized VE, with a corresponding increase in torque and hp output. The hemi head was quickly adopted by racers starting in 1905, and became almost universally used where maximum VE was desired. Today essentially all gas IC engines use a variation of the hemi/pent head.
Here’s the big(ness) problem:
This is the formula for determining the volume of a cylinder. If its main dimensions (radius & height, corresponding to 1/2 of bore & stroke) are doubled (squared), the volume increases by x8 (cubed). In terms of volumetric efficiency, it’s easy to predict that in order to fill that cylinder as full as possible, the area of the valves and ports should also increase proportionately (x8).
But when the radius or diameter of a circle (valve) is doubled (x2), the area is only increased by x4, or at half the rate of increase as the cylinder volume.
As an example: let’s say we have a single cylinder engine with bore and stroke of 2″ each = 6.283 cubic inches
And there’s room for two 1″ diameter (0.5″ radius) valves in the head = 0.79 sq. in. of intake valve area.
Resulting in an intake valve area to displacement ratio of about 1:8.
Now we double the engine’s dimensions:
Bore and stroke of 4″ each = 50.265 cubic inches
The valves now have 2″ diameters (1″ radius) = 3.14 sq.in. of intake valve area.
Resulting in an intake valve area to displacement ratio of about 1:16
The problem is now very obvious. As displacement per cylinder increases, the valve area to displacement ratio becomes worse, thus limiting the engine’s volumetric efficiency, at least at higher speeds. Thus the rpm of max VE decreases, resulting in ever lower maximum engine speeds, as the engine is increasingly limited by its breathing ability the faster it tries to run.
This means that completely apart from the issues of reciprocating masses, the larger the engine, the lower it inherently revs, as its valves will become increasingly unable to adequately pass enough air/fuel. Correspondingly, its torque peak (at max. VE) will be at ever lower rpm, and thus as well its hp peak.
Meanwhile, a very small engine has such an abundance of valve area, that its max. VE (and torque peak) will tend to be very high, as well as its hp peak.
Of course there are many variables in engine design and tuning that will offset this basic principle to some degree or another, but the principle prevails.
The most obvious way to negate the issue of small valve area was to increase bore relative to stroke. The Ford Kent 1.0 L ohv four from 1959 was one of the first of very significantly oversquare (bore greater than stroke) engines, with a bore of 3.19″ and a stroke of 1.91″, resulting in a bore-stroke ratio of 1.67:1, one of the highest ever. This direction certainly improved volumetric efficiency, but also resulted in a relatively high-revving (6000 rpm) engine in an otherwise very mild state of tune. And it also meant a relatively higher torque peak than the typical British long-stroke engines of the time, which made it feel rather weak-chested.
The oversquare era did not last long, as it was found to be inherently “dirtier” in terms of smog-forming emissions, undoubtedly due to its shorter combustion cycle. The trend has been to longer strokes and more undersquare engines, but offset by ever-better breathing heads with four valves and improved valve timing due to variable valve timing technologies.
In the racing world, massively oversquare engines rule, as it of course allows for larger valves as well as reduced piston speeds and reciprocating masses through lighter and stronger components. This is a Ferrari from 2000; further advances have been made since then.
The downside to shortening stroke is that intake velocity is proportional to piston velocity. So the point of optimum volumetric efficiency, due to intake inertia, will occur at an ever higher rpm. That is why long stroke, long rod engines tend to produce peak torque at a lower rpm than short stroke, short rod engines. Peak engine torque will usually occur at the point of peak volumetric efficiency.
The basic principle, that increasing an engine’s displacement by making its dimensions ever larger would not increase its power proportionately, was understood quite early. William Maybach, the brilliant pioneer in the field, thus created the first two cylinder engine with Gottlieb Daimler in 1889. Increasing the number of cylinders was/is the most expedient way to increase power, for a given displacement. This one had 34 cubic inches and made all of 1.5 hp @700 rpm. By 1899, Maybach built the first four cylinder, and so it went, to six, eight, 12 and 16 cylinders.
Adding more cylinders increased power and of course smoothness, but depending on each cylinder’s displacement, the torque curve did not benefit. Which explains why small multi cylinder engines have all disappeared. 2.0 L sixes were once common, and Ferraris mostly had 2 to 3.0 L V12s. Good maximum hp output per displacement, but terrible torque curves.
We’ve seen rather extreme examples for illustration purposes. How about some common examples, from this period, comparing two engines with similar displacement overall, but different number of cylinders?
Here’s the stats and dyno charts of the Chevy 292 six (left) and 283 V8 (right):
170 gross hp @4000
153 net hp @3600
275 gross lb.ft @1600
255 net lb.ft @1600
185 gross hp @4600
150 net hp @4200
275 gross lb.ft. @2600
245 net lb.ft @2600
Similar displacement, similar head architecture, but different cylinder count. The 292 six had the same 3.875″ bore as the 283, but with its long 4.125″ stroke, it made its torque at a full 1000 rpm lower than the short stroke V8. One can debate minor differences in details, but fundamentally, these were quite similar except for the cylinder count, and a 1000 rpm difference in torque peak is very noticeable in their driving characteristics.
Truck operators strongly prefer a low rpm and flat torque curve, as it means that the engine can typically be run in the area of peak torque, which is also the area of peak volumetric efficiency and therefore the most fuel-efficient range.
I don’t have dyno charts, but here’s the ratings for 1969 Ford 300 six and 302 V8 (in gross numbers):
300 six: 170 hp @3600 rpm 283 lb.ft. @1400-2400 rpm
302 V8: 210 hp @4400 rpm, 295 lb.ft.@ 2600 rpm.
Note that the long stroke 300 six has a peak torque band that extends from 1400 to 2400 rpm. It doesn’t get better than that, and makes it a much more suitable engines for trucks than the higher-revving 302 V8.
This was a very real issue back when Henry Ford brought out his V8 in 1932. It was a well known fact that although it made 5 more peak hp than the Chevy six and had the same torque (130 lb.ft), but that torque peak arrived at a 50% higher rpm than the Chevy six, making it better choice for most normal driving, Bonnie and Clyde excepted.
The 1932 Ford Model B four had 200 cubic inches and made only 50 hp compared to 221 ci and 65 hp for the V8, but its torque peak was at a much lower engine speed, making it feel quite brisk at low speeds. I found this at a forum on the subject:
There was a real comparison in Rod&Custom Magazine in the ’70’s. Harrahs let them road test two ’32’s, a B roadster and a V8 Cabriolet, and they included some gentle acceleration tests and a drag race. The B came off the line best and then lost ground to the V8, and the B also showed a spurt forward gaining on the V8 at each shift, with the V8 then gaining at the higher revs in each gear.
That perfectly describes the different characteristics of two similar-sized engines with different displacement per cylinder.
One more data set, comparing the smaller 136 ci Ford flathead V8-60 and the 134 ci Willys Go-Devil flathead four:
60 hp @4000 rpm; 96 lb.ft. @ 2600 rpm
60 hp @3600 rpm; 105 lb.ft. @2000 rpm
The Ford V8-60 was universally panned in the US as being weak-chested. 2600 rpm was unusually high for a torque peak back then. The Willys four was known for its lusty power at low rpm.
There will likely be exceptions between two particular engines, but undoubtedly because of certain design factors, and the differences in displacement per cylinder not being very great. If you can find some, I’d be glad to hear of them. But generally speaking, this principle is readily experienced in the characteristics of engines with relatively greater or smaller displacement per cylinder.
I am not an engineer or knowledgeable in physics. There are undoubtedly other factors that can affect torque and hp peak. But this (reduction in VE rpm due to valve area reduction) is the most significant one. The way to offset it most effectively is with forced induction (super/turbocharging). That of course overcomes the limitations of the valve area, depending on the boost level. And that explains the great attraction to forced induction in modern engines, allowing them to generate much higher power without the corresponding increases in weight and friction losses.