Accessing hadronic form factors at large momentum transfers has traditionally presented a challenge for lattice QCD simulations. Here we demonstrate how a novel implementation of the Feynman-Hellmann method can be employed to calculate hadronic form factors in lattice QCD at momenta much higher than previously accessible. Our simulations are performed on a single set of gauge configurations with three flavours of degenerate mass quarks corresponding to $m_pi approx 470 text{ MeV}$. We are able to determine the electromagnetic form factors of the pion and nucleon up to approximately $6 text{ GeV}^2$, with results for $G_E/G_M$ in the proton agreeing well with experimental results.
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