Performance Measurements - Accuracy

What is repeatability? And what is accuracy? How do they correlate? The second part in the series of articles on performance measurements will answer these questions. It will also describe how measurement chains and tolerances will affect the accuracy of your test equipment.

Accuracy - Repeatability

Accuracy and repeatability are always present when it comes to measurements. In most cases only one of them are mentioned and they are often misunderstood. It is very common to hear that you don't need accuracy, only a good repeatability. This statement could mean it is OK to present false values as long as you do it all the time...

How can it be explained? Let's say you shoot 6 shots on a target. All of them hit the target but on the left side. They are fairly close to each other, which means the repeatability seems to be fairly good. Although the repeatability itself does not say anything about the absolute accuracy!

Accuracy - Repeatability

Let's shoot two more rounds. It turns out each round has a fairly good repeatability. All together it seems the absolute accuracy is within target every time. The question is: How big is the target? There is only one relation existing between accuracy and repeatability: If you have good accuracy, you are bound to have good repeatability.

Accuracy - Repeatability

All measurements are estimates! The true value is never exactly known. It is always measured ± tolerance. High accuracy means small tolerances and vice versa. In other words, to be sure to have good measurement you need to keep the tolerances to a minimum.

First step towards minimizing the tolerances is to have a direct measurement. This means that you measure the property directly, i.e. measureing the weight on a balance. An example of an indirect measurement would be if you set a weight on a hydraulic cylinder and measure the pressure of the fluid. The weight could then be calculated from the internal dimensions of the cylinder and the sensor value. However the total tolerances will include not only the size of the cylinder but also internal friction, temperature dependency etc, and also added the accuracy of the sensor itself.
Direct / Indirect measuring
Measuring the propert directly does not automatically make it a good and accurate measurement. A measurement chain describes the way the forces have to take from the actual object to the sensor. In this picture the weight is measured directly but the force has to travel from the lever through the gearbox and then via another lever before it reaches the actual balance. The ideal solution is to have the object (weight) as close as possible to the sensor (balance). For every link in the measurement chain there will be an added tolerance. Referring to dynos: High accuracy demands direct measurement of torque and speed and sensors close to the engine / car.

Measurement chain
Repeatability can be of different kinds:

  • Short term can be measurements made close in time.
  • Long term can be measurements made in the beginning of the racing season compared to the middle of the same season.
  • At different locations.

  • When it comes to the discussion about repeatability of dynos it is nearly always referring to the short-term situation described above. Mostly it consists of two measurements after one another on the same engine / car.

    The picture describes the pressure acting on the piston inside the cylinder. The spark is fired before the piston reaches TDC. The pressure acting on the piston before TDC is producing negative work whereas after TDC it is positive. Optimum timing will be when the sum of the contributions is highest.

    Cylinder pressure
    Measurements on a car with a modern four-valve engine cruising at 50 km/h show a big variaton in the combustion process. The picture shows 50 combustions in a row from the same cylinder. Ignition timing is the same all the time. This is a typical result from an engine running on petrol.

    Combustion chaos
    Here the same engine is running WOT at 2000 rpm. This is also a typical result. The combustions are quite unstable from cycle to cycle. Bottom line is that an engine is not the best object to use for testing of repeatability. The uncertainty is even worse if the tests are done at different occasions and/or locations. The only way to be sure of the measurements is to calibrate with a known source, i.e dead weights.

    Combustion chaos

    Test Conditions

    Another important area, which can have a big influence on the results, is "Test Conditions". This makes it important to include information about how the test was performed so it can be repeated later or compared to other results. The best is to have as close to normal conditions as possible.


  • Inlet air temperature
    • Measurement point
  • Atmospheric pressure
    • Weather / altitude
  • Relative humidity
    • Geographic location / Season

  • Fuel
    • Fuel type and quality
    • Octane number / energy contents
    • Fuel temperature
  • Drivetrain temperature
    • Engine cooling fluids
    • Gearbox oil
    • Rear axle oil

    No matter how hard you try you cannot achieve exactly the same conditions from time to time or even during a test series. A way of adjusting the numbers to normal conditions is to use "Power corrections". There are numerous corrections depending on engine type, fuel etc. This formula describes the correction for petrol engines. It is important to understand that general corrections are exactly that, general! All engines are individuals and respond slightly different from others. For this reason the total amount of correction should be small. The standard even sets a limit on the amount; it has to be less than 7%. The power corrections have always to be described in detail.

    Power corrections

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