The "rebound effect" occurs when reductions in energy consumption following energy efficiency increases are lower than engineering estimates. In cars this happens when drivers increase their distance travelled or average speed, as a behavioural response to cheaper travel. Rebound effects due to increased distance travelled have been extensively studied, but only one existing study attempts to quantify rebound effects due to increased average speed. This paper builds on that study, using a much larger empirical base and offering more generalised and more widely applicable mathematical modelling. It uses data from 30 Formula 1 Grand Prix time trial sessions of 10 vehicles doing 3 trials each, in 2014 and 2015. The heavily regulated Formula 1 regime, with its precisely measured data, provides a highly controlled framework for developing mathematics of average speed rebounds. The study thereby shows how speed and distance rebounds can be coherently combined in road vehicle travel to produce total rebound figures. It then shows how even small increases in average speed can nullify all the energy savings that are expected from energy efficiency increases. It also raises critical questions on the adequacy of proposed new road vehicle fuel efficiency testing procedures. (C) 2017 Elsevier Ltd. All rights reserved.