# Dynamometer inertia considerations and calibration

When purely inertial dyno is used, the calculated power on wheels is directly proportional to inertia value entered in the calculation:

Power = rotational speed * rotational acceleration * inertia

Inertia value has direct influence on measurement result. It’s worth mentioning, that inertia of all bodies accelerating during the run is required for accurate result. If these bodies are rotating at different speed than dyno roller shaft, their inertia should be multiplied by the speed ratio. This is especially important in case of chassis dyno, where vehicle drivetrain bodies rotate with dyno roller. If dyno inertia is calculated, it’s more important to think about typical inertia of vehicle wheels and shafts than to focus on roller bearings inertia.

In the Dyno2 software there are multiple places that contains information about inertia of rotating bodies.

• SETTINGS / Dyno / Frequency Input n / Connected inertia – here you must enter rotational inertia information about your dynamometer. Each of these is associated with particular rotational speed and acceleration from controller frequency input.
• SETTINGS / Dyno / Frequency Input 3 (Engine speed) / Connected inertia – input 3 is associated with speed of the engine. Inertia entered here is used only for engine power calculation and it is not included in power on wheels.
• PROJECT / Eng. inertia – this inertia have same meaning as inertia in Frequency Input 3 (Engine speed). Both inertia values are summed for calculation. This is preferred place for engine inertia, as it should be adjusted for every project. The value here should represent inertia of all engine rotating elements up to clutch, transferred to crankshaft. Typical engine inertia is roughly related to displacement and can be automatically filled in by right clicking the field in PROJECT DATA.
• PROJECT / DT inertia – this is value of inertia that is associated with car drivetrain – from clutch up to and including wheels. The inertia must be recalculated as inertia transferred to first roller rotational speed. Most important part here is played by wheels, which have the biggest diameter of all elements. The drivetrain inertia also plays important role in overall inertia dyno result.

Here is an example of dyno and inertia that play part in calculations:

Lets take example chassis dyno: 2WD, 30cm roller diameter.
The rotational inertia of this set is somewhere around 10kg*m². This value should be entered in SETTINGS / Dyno / Frequency Input 1
Now we put small car on this dyno: Toyota Yaris 1.0l, 175/65R14 wheels.
Engine inertia for 1.0l engine is somewhere around 0.15kg*m². This value transferred to roller with speed ratio 2.0, gives 0.3kg*m². It’s 3% of our dyno inertia.
Wheels inertia transferred to roller for this car is around 2.46 kg*m². It’s 24.6% of the rollers inertia!
If the car inertia from this example is omitted on our inertial dyno. The dyno would show only 78% of our car real power (we take friction losses out of the equation for simplicity).
Now you think: OK, lets put all this inertia into dyno inertia and forget about it. One of the problems with this thinking is that the engine inertia is disconnected from the dyno on loss calculation. This in 3% error in loss calculation. Another problem is the next car on our dyno: Ford F150 5.0l.
The rough estimate of the engine inertia would be 0.5kg*m². For the massive 265/70R17 wheel set it will be around 11kg*m². As you can already see our dyno roller inertia is now less important than the car wheels inertia

All this inertia information can make us very sad about measurement accuracy on our dyno. There are however some points to make things better:

• We only want to tune our car to have more power. The absolute value is not that important. We are OK, because with the same car on our dyno, horsepower measurement precision (not accuracy), will be fine, even with some unknown inertia values around.
• We want our rollers to have as much inertia as we can sanely put in our dyno. If we get huge 100kg*m² roller set, the Ford inertia effect will reduce from 100% to 10%.
• We can use inertia estimations available in Dyno2 software. These are only estimations and real values can be different, but it’s better to use these than to completely ignore the problem.
• If we can afford an absorption dyno that can hold our F150 on constant speed, the inertia problem in calculation of power on wheels disappears as the 0 acceleration in power equation results in 0 power from inertia. All the power is measured on absorber load cell. There is a catch however. Inertia information is required for loss power calculation to get engine power estimation.

## Inertia calibration methods

• Inertia calculation from physics experiment – we can roll our roller down the ramp and measure time it takes for it to get to the bottom 😉
• Performing inertia calibration experiment and using one of Dyno2 software tools.
• For amateur dyno, where precise dyno calibration is not required, the dyno can be calibrated by making measurement of power of a vehicle with known power. The vehicle power can be confirmed on other calibrated dyno and then the measurement on our dyno can be made. Our dyno inertia should be corrected using equation below: correct inertia = current inertia * real power / measured power

## Inertia effect on absorption dyno

When absorption dyno is used, engine power is calculated using brake torque measurement and torque calculation resulting from inertial body acceleration. In inertia in our setup changes often or there is no way to estimate it, accurate measurements can still be achieved by minimizing or completely eliminating dyno acceleration. If in the dyno equation

Power = rotational speed * rotational acceleration * inertia

the rotational acceleration will be 0, the power associated with inertia will not take part in the final result.

## Falling mass inertia calibration tool

The tool is available in SETTINGS / Dyno settings / Frequency input (1/2/3) / Calculate inertia from falling mass experiment

Dyno inertia can be measured without sophisticated equipment by conducting simple experiment.

• Before starting the procedure, roller diameters and load cell coefficients must be set up correctly.
• Tape a thin rope to one of the rollers. It should be taped in a non permanent way. When the rope would unwind to this spot, it should disconnect.
• Wind the rope on the roller and route it through a pulley located in a high spot.
• Hang an object of known mass at the end of the rope. The object mass should be significantly higher than mass of the rope.
• Start the measurement by clicking START button and release the object. It should accelerate the roller set. The rope should disengage from the roller before the object hits the floor.
• The roller set should freely slow down to a stop and the measurement should be stopped.
• Open the measurement with the calibration tool.
• If loss model is not calculated in the run, it should be calculated by right clicking on it and calculating it as described. Pay no attention to loss power values as this have no meaning until inertia is calculated.
• Enter the mass of object which was accelerating rollers and select part of measurement with constant acceleration.
• Calculated average inertia will be displayed in the lower part of the tool.
• The inertia can be loaded to the settings by clicking Load calculated value to settings button.

## Hard braking inertia calibration tool

The tool is available in SETTINGS / Dyno settings / Frequency input (1/2/4/5) / Calculate inertia from hard braking experiment

In case of absorption dyno, the inertia can be estimated by braking with full power of the brake while measuring braking torque and roller deceleration.

Rotational inertia = (absorber torque + friction torque) / roller deceleration

Absorber torque is known from absorber load cell.
Friction torque can be estimated from free roller deceleration with use of loss model calculator.

• Before starting the procedure, roller diameters and load cell coefficients must be set up correctly.
• Start the measurement by clicking START button.
• Accelerate the roller to high speed.
• Wait for the roller to stop freely.
• Accelerate the roller to high speed again.
• Set full brake power in manual mode.
• STOP the measurement.
• Open the measurement with the calibration tool.
• If loss model is not calculated in the run, it should be calculated by right clicking on it and calculating it as described.
• Select run section where brake was on full power.
• Calculated inertia is available below.

Keep in mind that if you are accelerating the rollers with vehicle, and the vehicle is still on the rollers during hard braking, the inertia shown is a sum of dynamometer inertia and vehicle inertia.