Fruitflies regulate flight speed by adjusting their body angle. To understand how low-level posture control serves an overall linear visual speed control strategy, we visually induced free-flight acceleration responses in a wind tunnel and measured the body kinematics using high-speed videography. Subsequently, we reverse engineered the transfer function mapping body pitch angle onto flight speed. A linear model is able to reproduce the behavioural data with good accuracy. Our results show that linearity in speed control is realized already at the level of body posture-mediated speed control and is therefore embodied at the level of the complex aerodynamic mechanisms of body and wings. Together with previous results, this study reveals the existence of a linear hierarchical control strategy, which can provide relevant control principles for biomimetic implementations, such as autonomous flying micro air vehicles.