Using the Magic Formula to describe the traction/slip relationships of tyres in soft soils

摘要

The tractive force/slip relationships of tractive elements are required as inputs to vehicle performance prediction models such as the NATO Reference Mobility Model. They also enable the tractive efficiency and work output of vehicles such as farm tractors to be estimated. This is important when the vehicles are performing tillage and similar high drawbar pull operations. The effects of altering tyre size, tyre pressure and ballast can be predicted. The so-called Magic Formula is widely used for describing the force/slip relationships of pneumatic tyres on hard road surfaces. The coefficients in the Magic Formula are usually derived from experimental measurements using mobile testers or laboratory flat bed or drum machines. Relationships are then developed to describe the coefficients as functions of normal load on the tyre. The paper describes how the Magic Formula can be adapted to describe the tractive force/slip relationships of pneumatic tyres in soft soils. The relationships for describing the coefficients in the Magic Formula are made functions of Mobility Number instead of normal load on the tyre. These relationships are based on the results of tests with a range of tyres in soft cohesive soils. This enables the tractive force/slip relationships to be predicted for a range of tyre sizes and soil strengths. The method could be extended to cover other soil types, lateral force/slip angle relationships and even combined longitudinal and lateral force conditions.