The use of high-temperature superconductors in electric machines offers potentially large gains in performance compared to conventional conductors, but also comes with unique challenges. Here, the electromagnetic properties of superconducting electric machines with bulk HTS trapped-field magnets in the rotor and conventional copper coils in the stator are investigated. To this end, an analytical model of the electromagnetic field in radial air-gap synchronous electric machines is developed and validated, taking into account the specific difficulties that occur in the treatment of machines with bulk HTS. Using this model, the influence of pole pair number, stator winding thickness, rotor surface coverage, and air gap width on the machines Esson coefficient is calculated. In contrast to numerical simulations, the method presented here can provide results within minutes, making it particularly useful for work in early development and systems engineering, where large parameter spaces must be investigated quickly.