Application of chebyshev's theorem for estimating CO₂ emissions due to overloading of heavy duty diesel trucks

The number of heavy duty diesel trucks (HDDT) loaded beyond the authorized limits is high. This overload causes additional CO₂ emissions that significantly increase the amount of pollutants emitted into the atmosphere. Measuring these emissions is complicated because it is required to know the truck's operating conditions at all times. That is, it would be necessary to know truck's speed, acceleration, load, and road roughness and slope. Certainly, recording these data for all vehicles at all times is impractical. In this work, a methodology for estimating these emissions from circulating overloaded and/or speeding trucks, based on the application of Chebyshev's theorem, is presented. With it, only few experimental data are needed to validate a truck's model. Once the truck model is validated, it is possible to simulate several operating conditions; including overloading and speeding. Also, using theoretical models, fuel consumption and CO₂ emissions are estimated within a certain statistical confidence level. In order to illustrate the proposed methodology, the problem of overloaded and speeding HDDT in México is analyzed. Simplified models for calculating tractive force, fuel efficiency and CO₂ emissions are used. It is estimated, within a 90% confidence level, that due to overloading and speeding, in México 60% more CO₂ is emitted compared to that produced if trucks were to operate within authorized loading and speed conditions.