in terms of the axial load w for long milled tooth bits with intersecting teeth on different cones the total axial load is distributed over approximately one bit radius however the maximum force on a tooth occurs when that tooth row bears all the load thus the average maximum force per width of tooth pushing into the rock f is given by where k is a dimensionless number associated with the number of tooth rows k is expected to take a value between 1 and 4 for wedge shaped indentors penetrating plastically deforming materials the force required to penetrate is approximately proportional to the cross sectional area of the tooth in contact with the deforming material see fig2 for a blunt wedge that is loaded on the wedge flat and one face where f is the average tooth flat shown schematically in fig1 u03b8 is the semi tooth angle typically 20 u00b0 and u03c3 is a constant of proportionality related to the rock strength note that when the tooth flat f is greater than zero a threshold force of u03c3 f is required before indentation can begin using equation a 5 and a 6 equ4 if the function u03c3 f is defined as follows then equ5 u03c3 f is the apparent strength of the rock as it appears to a blunt bit with average tooth flat f at a weight on bit of w clearly u03c3 f is never smaller than u03c3 and u03c3 0 equals u03c3 the dependency of u03c3 f on w is such that the rock appears harder at low weight on bit than it does at high weight on bit see fig2 using equation a 9 to eliminate x in equations a 3 and a 2 respectively.