How are engine displacement and power/torque related?

I got involved in a discussion elsewhere on this topic, and wanted to share my response here as well.  This is meant to be a solid explanation in layman’s terms, for those who don’t want to dive down a big physics and thermodynamics rabbit hole!

While I’m an automotive engineer I’m ashamed to say that I still don’t really understand the relationship between displacement and power/torque produced. While I assume that the difference between the 1000+hp – 8l engine in the Veyron and the 645hp – 8.4l engine in the Viper is mostly determined by turbos I would prefer a more detailed explanation.

Leaving out for a moment questions of efficiency, turbocharging, and a lot of other smaller factors:

  • Torque is most proportional to displacement. This is mostly a matter of how much fuel you can burn per cycle of the engine. Torque is a force, and applies to questions like, “how heavy a car can I push up this slope?”
  • Horsepower is proportional to the product of torque and engine rpm. There’s a constant in the equation, but otherwise it’s a direct relationship. Power applies to the question, “How fast can I push this 4000lb car up this slope?”

Everything else is just a factor that modifies those two variables. Let’s take the steady-state example of a truck climbing a steady grade at a steady speed – it’s actually simpler to understand than everyone’s favorite “drag race” example. Want to increase the amount of load you can carry up the hill at a given speed (increase the power)? Here are the ways you can do it:

  • Make the engine bigger. If everything is proportional so that your efficiency is the same, your torque will go up proportionally as well, because you’re ingesting more oxygen and burning more fuel. This means your power will also increase proportionally. More torque at the same speed (more power) means you can pull a heavier load up the hill.
  • Spin the engine faster for the same road speed (RPM). You’re still making roughly the same torque at the engine, but to maintain the same road speed, you will have had to change the axle/transmission gearing. This gives your same engine torque more “leverage” on the road. This example both shows the difference between torque and power, and shows you why it’s power that matters for climbing hills. Looking directly at the power really tells you what your engine can do at a given road speed once you’ve factored in all the gearing – it simplifies everything (better tool for analyzing that type of job).
  • “Fake” making the engine bigger. You can do this with turbocharging, supercharging, nitrous oxide … your choice. Either way, you’re using an external component to force additional oxygen and fuel into your engine, faking the behavior of larger displacement. The result is more power. This solution will almost always be more efficient for some operating conditions and less efficient for others, so you get to pick where you gain and lose economy, too. You have to do more work “stuffing” in the extra air, which reduces efficiency, but it can let you tune for better efficiency when you don’t need full power. Ford Ecoboost is a good example of this idea.
  • Improve overall efficiency. You can do this by increasing compression, tweaking your spark timing, mechanical/frictional tweaks, anything that gets more of the energy from your fuel to your tires instead of going out the tailpipe and radiator. You tend to be pretty limited by your fuel quality here compared to the first three options.
  • Improve efficiency at the engine speed you’re operating. Change your valve timing. Here, you’ll trade better efficiency at the RPM you care about for worse efficiency elsewhere. Your limit here is that you still have a “peak” torque value proportional to displacement, which you can move around with valve timing but not really increase. Assuming you don’t change your gearing (RPM) at the same time, once you get to the point where your peak torque is at the RPM you’re climbing the hill, you’ve gained all you can with this option.

In short, power is everything. Torque only really matters in that you’d like most of it to be “well distributed” across engine RPM, instead of very concentrated in a narrow band – this just makes your engine more versatile and nicer to drive. However, for pulling a hill, etc, the question of “not enough torque” is always solved by “more gear”, because the power is the same either way; that power is really just a matter of how much oxygen you can stuff in, and how much heat you lose from there to the tires.

For a good comparative example, consider the difference between the 110ci engine in a Miata and the 300ci engine in a mid-90’s Ford. I have both. Both make roughly the same HP, plus or minus a few – around 140.

The Miata has high compression, good mechanical efficiency, and all of its variables (valve timing, etc) are tuned to maximize the available torque and power from 5,000 to 7,000 RPM. It’s torque curve is very peaky, maxes out at about 115 lb-ft, and below 3,000 it’s essentially worthless. This is okay for acceleration, because everything is lightweight, and the car has very steep axle gearing (4.56:1) to try to keep it where it makes some power. However, you’d never want to tow anything with this engine, because the high RPM and compression really limit reliability if you needed to make the full 140 horsepower long enough to, say, climb a 10 mile hill, something you’d never need in a 2500lb car even at full speed. You need five (efficient, manual) gears at a minimum to keep this little engine where it will get out of its own way, and you’re shifting constantly in hilly terrain and traffic.

In contrast, the 300 is in a 90’s van with a three speed automatic, probably the most reliable but inefficient transmission Ford ever produced. Because of the massive energy-suck of the transmission, considerably less of this engine’s power gets to the road than the Miata’s. It’s in a vehicle that weighs double what the Miata does, and which will happily tow its own weight – so this engine is happy moving four times the load of the Miata. Why? Rather than focusing on a narrow “happy” spot, the design focused on distributing it’s torque out well. It doesn’t have overwhelming “go” anywhere, with only 260 ft-lb of peak torque limited largely by very low compression compared to the Miata; at the same time, what “go” it has is available everywhere (over 200 for almost the entire operating range). It makes its maximum power at only 3500 RPM, which it will happily do all day long, on crappy fuel, in lousy, hot, humid weather. Because the torque curve is so flat, you almost never find yourself shifting for any hill but the most extreme. It’ll never get anywhere as fast as the Miata, but it will go everywhere with extreme reliability doing four times the actual work, strolling along like a big, dopey draft horse.

You can dive down the rabbit hole all day with the hundreds of smaller variables that affect torque and power, but sometimes the basics are better summed up with no math and a little example or two. If nothing else, hopefully this version was entertaining.

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