A primary input to any study of automobile fuel economy is the tractive energy required by vehicles to negotiate prescribed driving schedules. This energy depends on both the particular characteristics of a vehicle and the detailed velocity profile of the particular schedule. Two schedules of special interest are the EPA Urban and Highway used in government fuel-economy regulation. In making comprehensive studies of the influence of various vehicle parameters on fuel economy, an ability to readily and accurately predict the tractive and braking energy requirements of vehicles can be very valuable.The author published such a capability in 1981. (Numbers in brackets denote References at the end of the paper.) Since that time he has used it for addressing several different fuel-economy related issues (2,3,4). Over these same years the physical basis for the near linearity of solutions of the equations for tractive and braking energy has become clearer. This provides additional validation for the resultant linear energy equations that fit those solutions nearly exactly ! However, some of this information has not been made available to the technical community at large. This is one purpose of the present publication. In addition, It is hoped that a somewhat different execution of the analysis will facilitate the comprehension of its true nature, and lead to increased appreciation for the significance and value of its results.