A Novel Formula for Calculating the Dynamic Torque of an Engine Based on Its Geometric Parameters and Static Measurements

Torque is the fundamental working parameter of the internal combustion engine (ICE). In a spark ignition (SI) ICE, static torque is a function of rotational speed and throttle angle. However, ICE inertia, the distance between the throttle and cylinders, the time interval between subsequent intake strokes and increased oil viscosity in the warm-up phase limit the use of this characteristic in dynamic states. The novel and simple formula for calculating ICE torque in dynamic working states, presented in the article, includes all the mentioned factors. The new formula is based on ICE static tests where the torque, speed, throttle angle and airflow are measured. On the basis of the intake manifold geometry, the phenomena occurring in this component are described to determine the delay in the ICE response to throttle position changes. Moreover, the influence of ICE inertia is included. Finally, the formula includes the ICE warm-up period, which is characterized by high friction losses that decrease ICE torque. The proposed formula is validated by comparing model performance in dynamic working states with measurements. The results show a high level of accuracy: the delay in ICE response differs by less than 0.01 s, and the calculated torque differs by less than 5%.