PLAN 2, Torque and Power

Introduction

In my first book I wrote generally about engines, particularly High Speed engines producing High Specific Power Output, and in that case the “specific” was the power output from a given capacity of engine or, “Horsepower per Litre of capacity”. In this narrative on the topic of torque and power I look further into the dynamics of the 4 strokes of the typical normally aspirated engine.

Capacity in this topic is the swept volume of the cylinders making up the engine and these account for A, the area of the piston and L, the length of stroke which, for now, we can consider to be fixed. That leaves P and N as the other two variables for further discussion which I now deal with. The matter of the connecting rod length in proportion to the crank radius can be dealt with separately. It is not directly associated with the recognised formula for calculating horsepower but it does have some influence on the power output from an engine.

PLAN refers to the formula for calculating Horsepower where P represents the Effective (average) Pressure in a cylinder during the working stroke. L and A are the Length of stroke and Area of the piston. N is the speed of the engine in revolutions per minute (or second in some formulae) and the values of these 4 variables are multiplied together. In my first narrative I explained that the style of writing was such as to give insight into highly complex matters for those with sincere general interest but of limited technical/mathematical learning whilst at the same time to venture into highly technical matters with sophisticated technical boffins wherever I was equipped to do so. The overall objective was to bring together the understanding and discussion for those from widely different backgrounds and I continue with that approach in mind.

When I was studying I was reminded that some of us are Jack-of-All-Trades as well as some being Specialists. My contemporaries referred to the former as those who knew very little about many things and the latter as those who knew most things about virtually nothing. At the end of the day it is about teamwork and the Jack-of-All-Trades could be the catalyst who can do the lateral thinking for the Specialists to home in and drill down upon. None of us can be all things to all technical matters but just as with an engine we can tune our knowledge to peak where needed whilst at the same time maintaining a wide power curve or perspective to encompass a whole range of matters. In this brief narrative I wish to explore the matter of Torque and Power. Torque is directly related to P and Torque multiplied by rotational speed is a way to calculate Power or work done. In using PLAN then the work done is calculated from the force (Pressure X Area) multiplied by the distance over which that force acts (L, length of stroke) multiplied by the rate at which this happens, N.

The power of an engine is derived from the energy contained in the fuel that it consumes. The energy in the fuel is burned to generate heat and the engine converts that heat into mechanical energy in as efficient a manner as it can achieve. Efficiency is lost when some of the heat escapes via the exhaust pipe and some is lost by the need to cool the engine. There are considerable frictional losses, mainly those caused by the side thrust of the piston rubbing against the cylinder wall but also elsewhere. For instance, if the engine’s valves are operated using coil springs, then the very act of compressing the spring will induce heating of the spring material itself and the contact between cam and cam follower will generate heat.

If that part of the mechanical power from the burning of the fuel which is “lost” due to friction between piston and cylinder wall is 10% then the mechanical efficiency of the engine cannot exceed 90%. In 1963 this would have been about 55 HP loss in a 3 Litre V12. For a V8 it would be about 52. I do not doubt that in the intervening half century the matter of friction has been well researched and that materials in current use, both physical components and also lubricants, have reduced the coefficient of friction considerably. This “loss” of mechanical power arises because some of the heat energy remains as heat energy, energy which we cannot usefully work with but which we have to throw away in cooling systems, thereby heating the atmosphere around us. Energy cannot be destroyed, it exists constantly in one form or another (every action has an equal and opposite reaction). Generally speaking, fuel at 95 or 100 Octane contains the same amount of energy. In simple terms the octane rating concerns the ability to suppress pre ignition so as to increase the efficiency of an engine.

I reconfirm what I said in PLAN, “At a given mechanical efficiency, the faster an engine can consume fuel then the greater the power output”. This was the driving objective which created the design of the narrow angle 4 valve technology in 1963. This design of combustion chamber superseded the hemispherical head as the design of choice for engines for the following half century.

But mechanical efficiency is also variable not only in different engine designs and speeds but also at different engine settings and so I go on (as a jack-of-several-trades and an aspiring specialist in a few subjects of interest to me) to discuss some of the things which contribute to Torque and Power.

Torque and Power

Contrary to common belief, the torque generated in an engine is not constant throughout the 360 degrees of one revolution, nor is it constant over 720 degrees of the 4 strokes.

Likewise the power generated over the cycle of 4 strokes is not constant. It may be the same amount for each succeeding group of 4 strokes whilst the engine is at constant throttle and speed but the forum members were talking about acceleration derived from torque and power. And the specialists seemed to differ from the generalists (Jacks-of-all-trades).

Torque (or mechanical effort) is gained from the explosive force generated in the cylinder via the geometry of the crank and connecting rod. The power producing effort applied to the crank is generally applied, neither in line with the cylinder nor at right angles to the angle of the crank. These situations occur only at TDC and BDC, and on the two occasions when the connecting rod makes a right angle with the crank. These two positions where the crank and connecting rod are at right angles are not when the crank is at 90 degrees nor when the piston is halfway down its stroke, but modified due to the geometry of the Connecting rod length and the Throw of the crank.

In my work designing the Shell Twin in 1963 (before electronic calculators and way before computers) I calculated the forces acting within a cylinder at various positions around the 720 degrees and plotted these on graph paper so that measurements could be taken from positions on the curves between each of the positions which had been measured and calculated.

In working with these forces it is necessary to recognise that horsepower (mechanical power) is calculated from the pressure or load applied on the piston multiplied by the distance travelled. Thus the X Scale used is piston travel. It is also necessary to have the X Scale showing the relative crank angle to determine big end loadings as vectors.

The two separate forces acting upon the piston/connecting rod group, gas pressure and inertia, can be plotted in the same terms. I chose equivalent gas pressure thus the inertia forces, measured in lbs of effort (mass times acceleration) were converted to gas pressure by dividing by the area of the piston. Working pressure and inertial forces were then drawn on the same graph, X scale in inches, Y scale in pounds per square inch.

Since the curves are in the same measurement, the forces can then be summed together to show the resultant force acting along the line of the cylinder. From there, using the geometry of the connecting rod angle, the forces acting on the crank and their direction can be displayed on a polar diagram.

Graphical Representation

Firstly I have included three crudely drawn chartlets, A, B and C which show:
A – The inertia forces which are the same on all 4 strokes although in two different directions

B – The gas pressure on strokes 2 and 3. Strokes 1 and 4 are virtually nil in comparison.

C – The resultant 4 strokes when Inertia and Gas pressure are summed together.

The indicative curves above are intended to help interpretation of the actual graph 1A.

Side Thrust

The side thrust is now calculated from the above graph using the forces applied to the geometry to give the following chart.

Using these scales, the work/power loss is the area under the curves, this being pressure (load) multiplied by distance moved and multiplied by the coefficient of friction.
As speed increases, so the inertia forces, and therefore frictional losses, increase by difference between the square of the speeds.

Polar Diagram, Big end loading

In my example which follows, the polar diagram has 24 positions of the crank, each progressing 30 degrees to complete the 720 degrees of the 4 stroke cycle. 6 positions for a downward stroke and so on.
The following diagram shows the 24 positions of the crankshaft used when constructing the polar diagram of forces acting on the big end journal.

The effective pressure load drawn on the polar diagram is taken from the Y scale on the graph using the crank angle shown on the X scale. This force is plotted at the angle of the force applied to the crank through the connecting rod from the piston position, also seen on the graph. It can be seen from points 1 to 3 that the piston moves slowly at first but is past halfway down the bore before the crank reaches 90 degrees.

The following polar diagram shows the actual angle at which the force is applied by the big end of the connecting rod to the crank at each of the 24 crank angles having taken note of both the downward force from the piston and the side thrust from the sidewall of the cylinder.

I had no need to convert these forces into torque. In this design stage the objective was to determine bearing and component loads, and this could be done using the information shown in the preceding material.

The next step in design is to apply the data to all of the journals in the engine and to calculate the main bearing loads. Thus, in a similar manner, all of the load/torque inducing forces could be summed together. This exercise would demonstrate that torque produced is a very erratic and variable amount over the 720 degrees of one cycle. What matters is the torque measured at output to the flywheel, at a dynamometer or to the wheels.

The engine for which the above material was design data was a 3 Litre V 12, the cylinders being upsized by 6% from the Shell Twin and the stroke increased by approximately 18% to make 250 cc per cylinder.

A few points to note

1).Whilst the stresses/loads are at maximum there is no work done without motion at TDC, point 24, this is merely an instantaneous measurement. Work is relative to load and motion. A force in line with the cylinder produces no torque although it does just before and just after.

2).The direction of the loads is the line between the centre and the reference point.

3).The value of the loads is the measure of the distance from the centre to the reference point, the scale being the circular scales of 2500 and 5000 lbs.

4).The reference vector direction and the crank angle are not necessarily the same angle, the reference point being one of the 24 depicted above and the vector of the same number being at the angle shown.

5). The curve between points 11 and 13, including points 12a and 12b reflects the considerable change in pressure as the charge compresses and ignites. The curve (line) between 12a and 12b will produce no mechanical power unless the geometry of the connecting rod and crank permit this. Later combustion will cause points 12a and 12b to move to the right of centre and will affect their values. At the same time pressure continuing after TDC will produce increasing torque as the crank angle increases. This curve will change in shape considerably as the engine speed changes.

6). Pressures in the Shell Twin during initial testing were measured with the following key data:

• 1660 psi at 11 degrees ATDC at 9,500 rpm
• 1360 psi at 15 degrees ATDC at 10,000 rpm
• 927 psi at 20 degrees ATDC at 11,200 rpm
• 820 psi at 30 degrees ATDC at 11,400 rpm

7). BMEP is Effective, Brake, which means “Pressure after accounting for losses”, friction, heat etc.
I cannot here provide fuller mapping of data similar to that tabled above with which to work, it gets complicated due to other variables like ignition timing, inlet and exhaust tuning etc. The project on which I worked was done using very early monitoring equipment, nothing like that which is available today, but I do have horsepower data which is that essential bit of information needed for this discussion.

To put the dynamics in time context, at 15,000 rpm or 250 per second, half a stroke of the piston takes merely one thousandths of a second, the margin of time measurement in a Grand Prix. I would also add that this Jack-of some-trades who knows nothing about hall effect sensors considers that dynamic measurement of torque at the flywheel as proposed by riff raff would be a job for specialists, the dynamometer, or Brake as in BMEP, seems much more laid back and appropriate to me.

It can be seen from the polar diagram that the mechanical power is collected between points 13 and 17 and point 15 is probably where the torque will be at maximum during the 720 degrees. Optimised combustion will lead to higher BMEP, improved mechanical efficiency and less power from the fuel being pumped out of the exhaust pipes. In the following graph there is 25% increase in speed from 10 to 12.5 thousand revs, 56% dynamic increase, with 6% corresponding drop in BMEP showing the potential to produce increased power at yet higher revs if and when exotic materials could be introduced.

Torque/BMEP, rpm and Power

The BMEP and Power curves for the Shell Twin in May 1965 were as shown here:

This shows the engine output after a period developing a flat torque/BMEP curve as distinct from peak power.
This particular graph can be used to develop your arguments about torque and acceleration especially since the BMEP/torque recorded shows minor peaks at 7 and 10 thousand rpm and corresponding horsepower of 35 and 50. The growth of power between 9 and 10 thousand rpm may be useful for powering a car out of a corner whilst the continuing power increase towards 13 thousand rpm would help to accelerate the car into the increasing air resistance and greater tyre grip.

This engine developed 160 HP per Litre in May 1965, just a year and a half after starting the project from a clean sheet. It was designed to 15,000 rpm but temporarily limited to an absolute maximum of 13,000 because the pistons were cast alloy, forgings were over the horizon at that time, and cast pistons were in danger of separating the material above the top ring due to the 7940 g stressing at TDC.

Any suggestions to “beef up” the strength of this section of material would cause associated increases in strength requirements throughout the reciprocating parts leading to general degradation of potential.