What is the Relation Between Power and Torque in Engine?

We’ve seen in the previous article how torque and power are defined and calculated – now let’s look more closely at how they relate to engine design. The concept of an engine’s torque output seems to be confusing to many people judging by newsgroup threads but it needs to be clearly understood if one is to design the best ways to improve power output.

Torque can be thought of as the instantaneous turning force generated at the crankshaft. As such it is a measure of the amount of energy being developed in the engine during each operating cycle – in other words a function of the amount of air/fuel mixture being burned per cycle.

Power can be thought of as a measure of the amount of energy being developed in the engine per minute – in other words a function of the amount of air/fuel mixture being burned per cycle multiplied by the number of cycles per minute. So power is torque times speed as we have already seen.

To increase torque we need to either process more air/fuel mixture per cycle or extract more energy from the air/fuel that is processed. We can do the latter in a variety of ways including:
1) Improving mechanical efficiency with attention to design of such things as bearings, piston rings etc.
2) Increasing compression ratio which extracts more energy from the mixture being burned.
3) Optimising fuelling and ignition timing.
We’ll look at the above another time – for now lets concentrate on getting more air/fuel mixture into the engine.

We can simplify even further by leaving out the fuel part of “air/fuel” mixture as this is really a calibration issue and falls under 3) above. It is increasing the air consumption that is the real problem and in fact it is not a bad idea to think of an engine as an air pump. The better we can make this pump work the more torque and power we can generate. Our problem of increasing torque output has now ended up as a problem of getting more air into the engine each cycle. There are only 2 ways to do this:

1) To increase the engine size. This is not always an option or at least not always a cost effective option. We may be running in a racing class where the engine size is limited or we may own an engine where parts such as longer stroke crankshafts or bigger pistons are expensive. As a general rule though, a bigger cylinder will process more air per cycle than a smaller one unless limited by other factors.

2) To increase the filling efficiency of the cylinders – i.e. to increase “Volumetric Efficiency“. If a cylinder is 500cc in volume but processes only 400cc of air each cycle we can say that the volumetric efficiency is 80%. In fact to be absolutely correct it is normal to express VE in terms of mass of air not volume but that is getting more complicated than is needed for now. To get into the cylinder, the air has to pass through the carb or injection system, the inlet manifold and finally through the port and valve.

The more restrictive to flow each of these components is, the harder it is for the air to get through them. By testing each of these items on a flow bench and modifying them to increase their flow capacity we can allow the air an easier passage into the cylinder and this will increase not only VE and therefore torque but also allow the engine to run at higher speeds and increase peak horsepower.

In fact the ultimate horsepower potential of any engine is really a function of the flow capacity of the induction system. By just increasing engine size, say with a longer stroke crank, we will increase torque at low rpm but not necessarily increase peak horsepower by much at all. The flow capacity of the induction system imposes the ultimate limit on the amount of air that the engine can process per minute and whether we have a small engine running at high speed or a big engine running at low speed, it is total airflow per minute that matters. The only real difference between a 3 litre car engine producing 200 bhp and a 3 litre Formula 1 engine producing 800 bhp is the flow capacity of the cylinder head.

We can also increase airflow per cycle by opening the valves for longer or to a higher lift. This has its downside though because long duration camshafts don’t work well at low engine speeds and while this might be ok for a race engine it is not what we want for a road engine. Increasing the airflow capacity of the induction system has very little downside although there can still be minor adverse effects on low speed performance. As a general rule it is much better to have a high flow induction system and be able to use a short duration camshaft to achieve the desired horsepower than vice versa.

The most restrictive part of the induction system and therefore the part that often shows the greatest benefits from being improved is the cylinder head. In fact the flow efficiency of the cylinder head is the key to good engine design and is the reason why modern engines are increasingly being designed with 4 or more valves per cylinder rather than 2. More valves mean more valve area and it is valve area that limits flow. Cylinder head design merits its own section and we’ll discuss it in detail in other articles.

To conclude our look at torque and power let’s see what sort of figures engines actually produce. The charts below show the manufacturers quoted outputs for a variety of road engines.

Although the average figures for both power and torque per litre are almost the same there is a much bigger spread for the power figures. The highest power output is 66% greater than the lowest whereas the torque per litre figures only vary by 18%. We ought to have expected this because while it is possible to tune an engine to deliver more power at high speed, there is only so much air you can get into a cylinder per cycle which determines torque. Let’s see if the same story applies to 4 valve engines.

Although both power and torque per litre are higher than for 2 valve engines we see a similar story with a much greater spread of power outputs than torque outputs. In fact only the BMW stands out for its high torque output (perhaps even a tad suspiciously so) although there is a 52% spread of power per litre figures. We ought by now to be realising that increasing torque per litre is much harder to do than increasing power.

In fact torque per litre figures can be used as a very good guide to the truth or otherwise of quoted power claims. It is hard to get even a race 2 valve engine to produce much more than 75 to 78 ft lbs per litre and for a 4 valve engine more than 85 to 88 ft lbs per litre. For modified road engines though, especially those retaining standard type carbs or fuel injection systems, the limits above are a good target.

For big budget engines where a lot of time and money has been spent on dyno testing of inlet and exhaust manifold lengths and diameters then of course it is possible to push the limits higher. With well developed cylinder heads, good inductions systems (i.e. side draft carbs or even better, multi butterfly throttle body systems) and efficient camshafts it is possible to push highly modified road engines to around 80 ft lbs per litre for 2 valve designs and low 90s ft lbs per litre for 4 valve engines.

It is possible to increase peak torque even further by selecting the intake and exhaust lengths to “pulse tune” the engine most efficiently at peak torque rpm. This will reduce peak power though and as maximising power is the primary goal for a competition engine this strategy is not normally of any use. Occasionally there are race series where the engines have to abide by an rpm limit which is lower than that at which they could otherwise produce best power. In such cases the engines will be tuned to maximize output at the limited rpm which can lead to torque/litre figures approaching 100 ft/lbs per litre.

The reduction in peak power this creates is of no consequence if the engine is not allowed to rev that high. Such torque figures should not be used as a guide to what is possible from conventional best tuning on a non rev limited engine though. I have still to come across reliable data for any engine producing more than about 93 to 94 ft/lbs per litre where ultimate power was the aim – except of course for unreliable estimated “flywheel” power and torque figures derived from rolling road wheel bhp measurements in which case the sky is the limit.

I once saw a rolling road power curve where peak torque was supposedly 120 ft/lbs per litre from a 4 valve engine of fairly uninspiring design. Even the operator finally admitted something didn’t look right when we went through the maths together. The conclusion was that there had been massive wheelspin during that power run and none of the figures generated were of any use at all.

When you see power claims that look suspicious, calculate the torque values using the formulae in the previous article. If you see peak torque values higher than those suggested above then I suggest you start to get, if not suspicious, then at least very analytical. Modern motorbike engines are quite similar to custom race car engines in terms of them being short stroke, 4 valve etc and although I have no data to hand I think it would be interesting to see the sort of torque per litre figures being claimed for them given that they achieve well over 100 bhp per litre. If anyone wants to summarize some power specs for me I would be grateful.

You might think that it is only possible to get 100% Volumetric Efficiency from an engine – after all when a cylinder is full of air at atmospheric pressure surely that is the end of the story. What this fails to take into account though is what is called “Pulse Tuning” which is taking advantage of the pressure waves which exist in the induction and exhaust system. These pressure pulses can actually ram air into the cylinder to achieve up to 130% VE although it takes very carefully designed pipe lengths and diameters to achieve this and the effect only works over fairly narrow rpm bands – usually with a corresponding adverse effect somewhere else in the rpm range.

We can see by now that there is a close relationship between VE and torque per litre and it might be reasonable to ask if it is possible to calculate one from the other. Well the full answer is no because the torque achieved also depends on burn efficiency, mechanical efficiency and other things. A rough guide though is that if you multiply the torque per litre by 1.4 you get a close approximation of the VE as a percentage. So the 4 valve engines running at 72 ft lbs per litre are perhaps achieving about 100% VE in road tune. 130% VE would equate to 93 ft lbs per litre which also ties together the maximum figures I have seen from different sources for both of these measures quite nicely.

Below is a summary of the power and torque figures for multi valve 4 cylinder sports bike engines. I am trusting that all these data are flywheel power figures rather than test results from rear wheel rolling road sessions – the CBR250 torque does look a bit on the low side.

The power per litre from these very over square bike engines is far higher than any car engine but the torque per litre is in line with the suggested maxima above. Hopefully this proves beyond doubt that although power per litre can vary enormously dependent on engine design, the torque output of an engine is still primarily a function of engine capacity. This makes it one of the best measures for evaluating whether dyno claims are accurate. Remember though that the measure we are after is PEAK torque per litre – the torque of an engine at peak power rpm will be some 10% lower than the torque at peak torque rpm.