POWER CORRUPTS
Calculating, remembering and quoting the maximum power per litre of an engine is something that many people love to do. The last hundred years have seen a huge increase in the magnitude of this yardstick, but very little progress was made in the first 25 years of motoring history. At that time just about the only way to get more power from an engine was to increase the cubic capacity.
However, advances in our understanding of airflow, mechanical stresses and especially the development of new materials have seen major improvements since then.
For unsupercharged engines the 100 HP/litre barrier was crossed in the late ’50s by a racing 500 cm³ Norton Manx single, and about ten years later for a production engine by a 125 cm³ Honda Benly CB92. At present, production sports car engines are approaching 125 HP/litre and Formula One engines are developing close to 300 HP/litre. Supercharged engines can only be compared in the same way if they’re running at the same boost.
UNITS
Most countries, except the USA, have now accepted the kilowatt, an SI unit, as a measure of power. SI units are a lot easier to work with, but it does mean that the above numbers will sound less impressive when converted to kW/litre because one HP is only equal to 0,746 kW. For example, 100 HP/litre will become 74,6 kW/litre.
This change has given the various controlling organisations the chance to clean up the various ways that power output can be measured. In earlier days the situation was less clear, because there were a number of different test methods in circulation, so that the output you associated with the engine in your car depended on the country of manufacture as well as the test method employed.
The concepts of force, work and power are related by the fact that work is defined to be the force applied to an object multiplied by the distance moved as a result of the force, while power is the work done divided by the time taken. In short this means power = (force x distance)/ time. In terms of modern SI units one watt is equal to one joule per second. The practical formulae involved operator to calculate the power.
The output quoted by an engine manufacturer is measured on an engine dynamometer at full throttle while varying the engine speed by changing the load. In this case the engine is coupled to the dyno by means of a short shaft. This means that the output is what the engine delivers at the flywheel minus a small loss in the two universal joints that form part of the coupling shaft.
Power transferred to the road are shown in the separate panel, but they can be linked to the above definition.
MEASURING POWER
The power developed by an engine can only be measured by giving it work to do. An engine brake or dynamometer is used for this purpose. Most of these units use either paddles rotating in water inside a casing or an electric generator to absorb the engine’s output.
The dyno measures the torque and the revs per minute and this enables the is measured with a chassis dynamometer. These are usually installed below ground level so that the rear wheels of a car being tested can rotate a drum that is coupled to the dyno. Manufacturers use such dynos for endurance testing, and laboratories use them for fuel consumption and emissions testing.
The motor trade uses them to ensure engines are tuned correctly, but in a number of cases we’ve come across they’re being used to relieve clients of their money because it’s very easy to get false readings on such a machine. The output obtained in this way is also between 20 and 25 per cent lower than the measurement with an engine dyno because of frictional losses in the drivetrain as well as between the tyres and the dyno drum.
HISTORY
In the USA most organisations still use horsepower, the Imperial unit for power. This is usually written as brake horse power (BHP) to emphasize that it is measured on an engine brake and not calculated.
The idea comes from James Watt, one of the earlier pioneers of steam power. In 1782 Watt and his partner Matthew Boulton determined that a brewery horse could lift 32 400 foot.pounds per minute. They rounded this number off to 33 000 and called it one horsepower.
This means any combination of weight lifted multiplied by the distance of the lift and divided by the time taken in minutes that comes to 33 000 will be equivalent to one horsepower. Dividing this number by 60 will show that one horsepower is also equivalent to 550 ft.lbs per second.
The problem with HP measurement (and to some extent kW) is that some standards allow measurement procedures that do not give realistic numbers. For example, in earlier days most manufacturers quoted gross BHP which was obtained when all accessories were stripped off, and a special laboratory exhaust system was fitted. Even today we sometimes find that quoted outputs are so far from the truth that they can only be called advertising HP.
On the other hand, most modern manufacturers quote nett BHP, which is close to the output obtained when the engine carries all the accessories as mounted in the vehicle, including the standard exhaust system.
METRIC POWER
In the days when German manufacturers were reluctant to use the kilowatt, their DIN standards authority, roughly the equivalent of our SABS, invented a metric horsepower, called PS (Pferdestärke), by choosing a combination of kilogram-force and metres per second that was close to the Imperial unit. As a result one metric HP is equal to 75 kilogram-force metres per second. This differs by only 10 watts from the imperial HP because one HP is 746 watts but one PS is only 736 watts.
As can be expected, the French system is particularly complicated. Their cv (lower case) is equivalent to PS but CV (upper case) is a power measurement used to tax motorists (see panel). Most other European countries have horsepower units that agree with PS, but today the kilowatt is gaining the upper hand.
Britain adopted hp for tax purposes as long ago as 1910. It was only abolished in 1947 and was called the RAC hp because the Royal Automobile Club was asked to come up with a suitable formula to estimate the actual power developed by an engine (see panel).
This formula was heavily criticised over the years because it did not take the stroke length into account. This led to whole generations of British engines with long strokes and small bores, which meant that their maximum piston speeds were high. This kept their maximum cruising speeds low.
CALCULATING ACTUAL POWER
An engine’s power can be calculated in two different ways, depending on whether you’re interested in what is actually transferred to the top of the pistons or whether you want to know what is delivered to the flywheel.
At the piston tops the
formula is:
kW = (PLAN)/9 549
where P = average
pressure on top of the
pistons in N/m²
L= stroke length in metres
A = piston top area in m²
for one cylinder times the
number of cylinders
N = r/min
The answer will be correct for two-stroke engines, but should be halved for fourstroke engines because there are only half the number of power strokes in such engines.
The average pressure has to be calculated from a graph of the pressure variation as the piston moves. The power calculated this way is known as the indicated power.
At the flywheel the
formula is:
kW = (TN)/9 549
Where T = torque in
newton.metres
N = r/min
The torque has to be measured on an engine dynamometer and in this case the power is known as the brake power.
The indicated power will obviously be higher than the brake power, and the difference is due to frictional and accessory drive losses. There are similar formulas for HP, and the answers are known as IHP and BHP respectively.
CALCULATING TAXABLE POWER
British taxable hp is given by:
hp = (D²n)/2,5
Where D = the cylinder bore in inches
n = number of cylinders
This formula was based on three assumptions that were correct in 1910 but became more out of date as time went by. These were a mean effective pressure on the piston of 90 psi (620,5 kPa), a mechanical efficiency of 75 per cent and a mean piston speed of 1 000 ft/min (5,08 m/s).
This meant that for the average 1910 engine the RAC rating and the BHP would be about the same. However, by 1947 these values had changed so much that the average 10 hp Morris or Austin actually developed about three times as much.
The current French taxable CV is calculated as follows
CV = (P/40)1,6 + U/45
Where P = maximum power in kW
U = amount of CO² emitted in g/km
In earlier days there was an even more weird formula for taxable CV.
