 # Dynamometer math description

Dynamometer (Dyno) is a device used to measure power and torque of a connected engine. Power can be calculated from acceleration of fixed inertial mass load (inertia dyno), or from measurement of dyno absorption unit braking torque (absorption dyno, brake dyno). When using brake dyno, inertial mass load can also be accounted for.

For Frequency Input 1 – 3 following parameters are calculated:

• Rotational speed – Frequency input n rotational speed
• Rotational acceleration – Frequency input n rotational acceleration
• Torque resulting from acceleration and inertial mass load of dyno
• Roller n inertial torque = Frequency input n rotational acceleration * Inertia n
• Torque resulting from acceleration of engine
• Engine inertial torque = Engine rotational acceleration * Project Engine Inertia
• Power resulting from acceleration of engine
• Engine inertial power = Engine inertial torque * Engine speed
• Power resulting from acceleration of drivetrain
• Drivetrain inertial power = Frequency input 1 rotational speed * Frequency input 1 rotational acceleration * Project DT inertia
If Frequency input 1 has no signal, but other inputs have signals, Drivetrain inertial power is calculated assuming constant linear speed relation between rollers connected to frequency input 1 and other inputs.

For Load cell 1-4 inputs, torque values are calculated:

• Torque [Nm]: Load cell n value = input voltage * coefficient a + coefficient b

Load cell inputs 1 and 2 are for rotating set 1 (Roller 1). Load cell inputs 3 and 4 are for rotating set 2 (Roller 2).

Total brake torque per roller is calculated:

• Roller 1 brakes torque = Load cell 1 value + Load cell 2 value
• Roller 2 brakes torque = Load cell 3 value + Load cell 4 value

For each rotating set, received power resulting from acceleration and brake torque is calculated:

• Roller n received power = Frequency input n rotational speed * ( Roller n brakes torque + Roller n inertial torque)

Power received by rotating inertia sets and torque absorbers is called WHP – Wheel Horse Power.

• Power on wheels = Internal dyno loss + Roller 1 received power + Roller 2 received power + Roller 3 received power + Roller 4 received power

Engine rotational speed is required to calculate its torque based on measured power. The software can use 3 different sources of engine rotational speed. The speed source is selected with Engine speed source setting:

• calculated from frequency inputs and ratio – engine speed is calculated by multiplying rotational speed measured on frequency input 1 by constant ratio:
• Engine speed = Frequency input 1 rotational speed * Engine speed ratio
With chassis dyno, if only the second roller is accelerated, engine speed is calculated in the following way:
• Engine speed = Frequency input 2 rotational speed * Chassis dyno roller 2 diameter / Chassis dyno roller 1 diameter * Engine speed ratio
• engine clamp – engine speed is calculated from signal connected to Engine speed input and Frequency input 3 configuration. The signal can be sourced from inductive clamp placed on ignition wire, engine control unit signal, engine trigger wheel signal.
• OBD – engine speed is sourced from the car OBD interface.

On chassis dyno, the engine is connected to the dyno through drivetrain and tires. Both the drivetrain and tire – roller connection generate some losses in power.
Part of their losses is related to the dyno speed. It can be measured during the coast down phase of the run.

• Loss power from speed = f(Dyno road speed)

Another part of losses depend on load. It’s a result of drivetrain efficiency and additional tire deformation and slip resulting from power transfer. Drivetrain loss factor is entered in project settings. Vehicle to dyno loss factor is entered in SETTINGS / Dyno / General.

The losses displayed in results are a sum of the following factors.

• Loss power total = Drivetrain inertial power loss + Engine inertial power loss + Loss power from speed + Loss power from load

The engine power is calculated with the following equation.

• Engine power = Power on wheels + Loss power total

By measuring rotating inertia set deceleration with engine disengaged, it is possible to estimate power loss related to dyno speed.

To calculate Loss power from speed during loss stage, we disengage the clutch. This results in Engine power = 0 and Engine inertial power = 0 from the dyno point of view. The following equation in only valid with clutch disengaged. Because most of the losses will take place on the tire – roller contact patch, and the power transfer is near 0, we drop the load loss factors from the calculation.

• Loss power from speed = – Power on wheelsDrivetrain inertial power loss

When engine speed is acquired, it is possible to calculate the torque:

• Engine torque = Engine power / Engine speed

By using formulas provided with appropriate standards, we calculate engine power correction.

• Ambient correction factor = f(temperature, pressure, humidity, fuel type, boost type)
• Engine corrected power = Engine power * Ambient correction factor
• Engine corrected torque = Engine torque * Ambient correction factor