The accurate prediction of tyre forces requires an understanding of the friction characteristics between the tyre and the ground surface. A friction master curve represents the dependency of rubber friction on sliding velocity and temperature, typically obtained using a bespoke friction test rig. To circumvent specialised friction testing, this paper presents a methodology for extracting friction characteristics from pure longitudinal tyre force measurements obtained on a flat-track test machine. The methodology is demonstrated for two tyre types - a radial-ply road tyre and a cross-ply racing tyre. The identified friction characteristics are validated against directly measured friction master curves. Results demonstrate that the friction characteristics can be successfully and accurately extracted from flat-track data in a repeatable manner. For the studied passenger car tyre, only two pure traction slip curves (one at approx. 13% and one at approx. 105% of the rated tyre load) were required to obtain the available information on the rubber-surface sliding friction coefficient.