Global historical series spanning the last two centuries recently became available for primary energy consumption (PEC) and gross domestic product (GDP). Based on a thorough analysis of the data, we propose a new, simple macroeconomic model whereby physical power is fueling economic power. From 1820 to 1920, the linearity between global PEC and world GDP justifies basic equations where, importantly, PEC incorporates unskilled human labor that consumes and converts energy from food. In a consistent model, both physical capital and human capital are fed by PEC and represent a form of stored energy. In the following century, from 1920 to 2016, GDP grows quicker than PEC. Periods of quasi-linearity of the two variables are separated by distinct jumps, which can be interpreted as radical technology shifts. The GDP to PEC ratio accumulates game-changing innovation, at an average growth rate proportional to PEC. These results seed alternative strategies for modeling and for political management of the climate crisis and the energy transition.