The unsteady lift response of an airfoil in a sinusoidal gust has in the past been modelled by two different transfer functions: the first-order Sears function and the second-order Atassi function. Previous studies have shown that the Sears function holds in experiments, but recently Cordes et al. (J. Fluid Mech., vol. 811, 2017) reported experimental data that corresponded to the Atassi function rather than the Sears function. In order to clarify the observed discrepancy, the specific differences between these models are isolated analytically. To this end, data and analysis are confined to unloaded airfoils. These differences are related to physical gust parameters, and gusts with these parameters are then produced in wind-tunnel experiments using an active-grid gust generator. Measurements of the unsteady gust loads on an airfoil in the wind tunnel at Reynolds numbers (
and reduced frequencies between
confirm that the Sears and Atassi functions differ only in convention: the additional gust component of the Atassi problem can be scaled so that the Atassi function collapses onto the Sears function. These experiments, complemented by numerical simulations of the set-up, validate both models across a range of gust parameters. Finally, the influence of boundary-layer turbulence and the turbulent wake of the gust generator on experimental convergence with model predictions is investigated. These results serve to clarify the conditions under which the Sears and Atassi functions can be applied, and demonstrate that the Sears function can effectively model unsteady forces even when significant fluctuations in the streamwise velocity are present.