Defining Power & Torque

Torque is a force that tends to rotate or turn things. SI (metric) units of torque are Newton-meter; English units are pound-inches or pound-feet. Notice torque units contain a distance and a force. To calculate the torque, you just multiply the force by the length of the arm from the center of rotation to the point where the force acts. 

Engine torque is usually measured with a dynamometer (dyno) consisting of a rotor and stator. The engine is connected to the dyno by a drive shaft connecting the engine's crankshaft to the dyno rotor. If the direction of rotation of the engine crankshaft (and rotor) is clockwise, the stator will undergo a force equal to but opposite to the torque generated by the rotor through the engine crankshaft. The reaction torque on the stator will be anti-clockwise. Attaching an arm on the stator (and calibrating it properly) makes it possible to measure the torque the engine produces.

The torque exerted by the engine is: T = F . r 

Power is torque multiplied by engine speed to produce a measurement of the engine’s ability to do work over a given period of time. The story of its origin is well known, but worth repeating briefly. In the 17th century, steam engine inventor James Watt sought a way to equate the work his steam engine could perform to the number of horses required to perform the same task. Watt performed simple tests with a horse as it operated a gear driven mine pump by pulling a lever connected to the pump. He determined that the horse was capable of traveling 181 feet per minute with 180 pounds of pulling force. This multiplied to out to 32,580 pounds-feet per minute which Watt rounded off to 33,000 pounds-feet per minute or 44742 Nm/min. Divided by 60, this gives 550 lb.ft/sec or 735.7 Nm/s, which became the standard for one horsepower.

Thus horsepower is a measure of force in newtons/pounds against a distance in meters/feet for a time period of one second. The distance per second of a rotating engine would be the circumference of an arbitrary arm connected to the crankshaft (=2.p.r) multiplied by the number of revolutions in one minute divided by 60 (seconds in a minute). 

And thus horsepower equals to: F.r.2.p.RPM/60 = T.2.p.RPM/60 = 550 lb.ft/s or 745.7 Nm/s

Hence the formula in English units for power is: 

Power [HP] = T [ft.lb] . RPM / 5252

In SI units power is expressed in Watt = (T [Nm] . 2p . RPM/60)     (1kW= Watt/1000) 

Power [kW] = T [Nm] . RPM / 9549
Power [HP] = T [Nm] . RPM / 7121

kW x 1.341 = HP

Conclusion: 

Torque is the static measurement of the how much work an engine does while power is a measure of how fast the work is being done. Since horsepower is calculated from torque, what we are all seeking is really the greatest possible torque value over the broadest rpm range we can get. Different combinations of torque and rpm can yield the same horsepower. Therefore a slow revving engine (like the UL260i) needs a high torque to produce the same amount of horsepower as a fast revving engine (like Rotax). 

The strain gauge is a tiny electronic circuit which changes its' signal output according to the stretching or contracting movement of the surface on which it is attached.

The mechanical mechanism of earlier generation dynos to measure torque has been replaced by electronic sensors (load cells).

Computers register and transform signals coming from the dyno and engine into meaningful data which can be recorded for later analysis.

In many cases the dyno is similar to a water pump. Water is allowed to flow into the pump housing - the stator, and the rotating pump wheel - the rotor, drives the water out. Varying the amount of water flowing into the dyno increases the work load the engine must produce to drive the water out of the pump housing. In effect the pump is acting as a brake on the engine. So came the name Brake Horse Power, this is the power produced by an engine on a dyno.

Modern dynos no longer rely on a mechanical weighing mechanism to measure the force exerted by the engine on the arm attached to the stator. An electronic load cell is used instead.

Where as the arm of the stator acting on the older mechanical scales moved noticeably, the arm acting on the load cell does not seem to move at all. The load cell uses a strain gauge to measure the minute expansion or contraction it undergoes. Using information supplied by the strain gauge, the load cell sends electronic signals to a computer which registers and transforms the data into a meaningful display.

Although to the human eye the engine's crankshaft seems to be rotating smoothly, this is not the case when you analyse the motion of the crankshaft during two complete  revolutions of a 4 stroke engine (in the case of a single cylinder engine). When the power stroke starts on the first half of the first revolution, the piston imparts a sudden and sharp acceleration to the crankshaft. The remaining 1,5 revolutions the crankshaft is slowing down because the piston has to drive out the exhaust gases, induct a fresh fuel/air mixture and then compress it to the stage when the spark can ignite the mixture to supply the next torque impulse to the crankshaft. This results in sharp peaks in the torque at the beginning of the power stroke, and then diminishing torque values until the next power pulse.

Since load cells are able to register the torque value many times a second, they can actually register the peak of torque pulses caused by the individual explosions in the cylinders as well as the much lower values when none of the cylinders are firing and the crankshaft of the engine is actually slowing down. Engines with four cylinders have fairly high torque pulses. Six or eight cylinder engines have a much smoother torque output because more cylinders are firing in the same period of time so the torque registered by electronic means will probably be less fluctuating.

Because of the fluctuating torque values a load cell can measure (up to about 7% difference between the highest and lowest values), it could be tempting to publish peak figures only, but an honest engine manufacturer should take the average torque.

Measurement uncertainties

Another issue is the question of uncertainties in the values of measuring equipment used for calculating the power output. Presuming the dyno has been properly calibrated, there are always additional inaccuracies which need to be taken into consideration. The sensitivity of the various sensors registering and transmitting the signals, and the method of averaging out the registered values of RPM and torque are the most important. Since electronic sensors send their signals many times a second, the power shown on the monitor is the result of many calculations made using all these signals.

Most of us are familiar with digital read-outs which show constantly changing values. Unless the values are very similar, it is often difficult to make much sense of these constantly changing values. Therefore, the values recorded are often "averaged out" so that values of torque and RPM can be read easily on the display monitor. All these factors play a role in the degree of accuracy of the final power output figure. The uncertainties could cancel each other out, but equally possible is that they all add up in either the positive or negative direction. The total degree of uncertainty in the power output shown could easily be ±5%. This means that if a dyno displayed the engine's power as 100hp it could actually be producing anything in between 95hp and 105hp.

Although most dynos operate using the same basic principles, the test results obtained from testing exactly the same engine in exactly the same conditions on different dynos can vary significantly, even though the operators have taken care to calibrate the force acting on the rotor arm meticulously. It is not uncommon for test results performed on the same engine but on different dynos to vary by 5% to 10% ! This means that if you are comparing the power performance of engines of ±100hp, you should not place too much emphasis on differences of ±8hp.

The raw results from a dyno measurement give the actual power output of an engine in it's current operating condition. However, the (atmospheric) condition in which the engine is running greatly influences the power it can produce.

The air density is positively correlated to the power output. The denser the air, the more air the engine takes in for the same volume and if the fuel mixture is adapted accordingly, the more torque the engine produces. Air density is influenced by the air temperature, air pressure (influenced by barometric pressure and altitude) and relative humidity. 

The air T° (hotter air = less mass in the same volume) and air pressure (high altitude and low pressure yield a lower air density) have the greatest effect on power output. Humidity (water vapor displacing air mass) has only limited effect.

The following table gives an example of what power an engine could produced due to the different conditions it is operating in:

If the same engine can produce such a large variation in power just because atmospheric conditions it is being tested at are very different, it is obvious that engines cannot be compared with each other unless they are tested in identical conditions.

For aircraft engines, International Standard Atmosphere (ISA) conditions are used as a basis. These are: 

Always testing  engines in ISA conditions is not practical. Only a handful test facilities have the capability of fully controlling the atmospheric condition in the test room. Therefore in most cases, while an engine is being tested, the power output as well as the prevailing atmospheric conditions are recorded. The recorded values can then be corrected/converted afterwards to the ISA conditions. See "ISA conditions & conversion" for more details.

Converting power to ISA conditions is a theoretical calculation. As long as the testing conditions don't differ too much from the ideal conditions, the results will be accurate. The more the testing conditions deviate from the standard, the higher the chance the end result could be incorrect. Bear in mind that inaccuracies in the measurement of the various atmospheric parameters in which the engine is running, can also influence the end result when converting to the recorded values to the ISA standard. For example: a 3°C (5.4°F) difference in air temperature corresponds to a (theoretical) difference of ±1% power.

Engines using a carburetor to meter the fuel with the inducted air usually need to heat the resulting fuel/air mixture in a plenum chamber (which is in direct contact with the engine block or oil sump) to make sure that as much fuel as possible is in the form vapor and no longer existing as liquid. Even when the engine is operating at high power levels (and a lot of outside air is being drawn into the manifold) the fuel/air mixture which is actually drawn into the cylinders has been significantly heated above the point when it entered the air filter. A 40°C [104°F] increase is not uncommon. In the case where the outside air was 15°C [59°F], the fuel/air mix reaching the inlet valves could be 55°C [130°F]. If an engine manufacturer "corrected" the test results to ISA conditions, using the T° of the fuel/air mix close to the inlet valve instead of at the air filter, they would be able to publish a "gain" of 40°C/3°C = ±13%!!

Compairing Engines

Measuring inaccuracies, differences in testing facilities, and the need to correct/convert the recorded figures to a theoretical baseline, all mean that engine manufacturers have a certain liberty to publish power/torque figures which can be regarded as optimistic. Since many potential buyers of aircraft engines place a lot of emphasis on the power rating (as they do when they buy a car), for marketing purposes it is very tempting for the manufacturer to use these uncertainties to publish power ratings which are higher than the figures actually measured. It is highly unlikely that an aircraft owner would notice much difference in the performance of his/her aircraft if the engine had 5-10% less power. A significant performance difference would only be noticed from 15-20%.

Propeller manufactures who fabricate a propeller specially for the published power output of an engine for a particular aircraft can be the first to know if an engine manufacturer has published figures which are evidently too high. For example; when a propeller has been fabricated which will absorb 100 hp at 3.000 rpm for a given pitch, an engine rated with a maximum of 100 hp at 3.000 rpm will just be able to drive the propeller at this rotational speed. Providing the propeller manufacturer has also done their calculations correctly, their blades are fabricated precisely according to plan, and the actual flight testing conditions are also converted to ISA, the engine should be able to drive the propeller at a predetermined propeller rpm for a given thrust = absorbed power. If the engine can only manage a maximum of 2.750 rpm instead of 3.000 rpm at the reference pitch for example, then the engine manufacturer has published figures which are overly optimistic. It is a fine line between publishing "optimistic" figures and being dishonest..... 

If one would really like to compare different engine models, then he/she should test the engines on exactly the same dyno and in very similar weather conditions. This way, even though the dyno might give better or poorer figures than what the engine manufacturers claim, the same test rig, accessories and recording equipment is used to make the comparison. Providing identical warming up, testing periods, adequate cooling and strict adherence to the manufacturers operating instructions have been used for the comparison, and after adjusting the local testing conditions to ISA conditions in the same manner, any engine can be compared with another in a fair way

Using the same dyno set-up, engine model A developing 78 hp at 2.500 rpm is definitely more powerful than model B producing 72 hp at 2.500 rpm. Two or three identical runs with the same engine would give an average figure which couldn't be disputed. Ideally the tests should be repeated with two or three engines of the same type.... 

Engines convert the energy in fuel into power. Usually the power output is transmitted through a rotating shaft. The force of this rotation is the torque. Power is the product of the torque and the rotational speed of the shaft. 100 hp could be the result of a shaft turning very slowly but with a large rotational force, or conversely, a very low rotational force and a very high rotational speed - typical of turbine engines.