Elastic scattering cross sections for 12C, 14N, and 16O recoils by 32S ion bombardment below 70 MeV at recoil angles of 20°, 25°, 30°, and 40° have been investigated. The experiments are performed by measuring the elastic scattering yields near the Coulomb barrier energies for the kinematically reversed 32S (12C, 12C) 32S, 32S(14N, 14N)32S and 32S(16O, 16O)32S reactions. At a threshold energy, above which the Rutherford model becomes invalid, the cross sections are found to fall off rapidly. No prominent resonancelike structures are observed in the present energy region. The non-Rutherford threshold energies, and the elastic recoil excitation functions are presented. Based on fits to the present heavy ion recoil data and earlier heavy ion scattering data from the literature, a classical semiempirical formula for predicting the projectile threshold energies for 12C, 14N, and 16O recoils is introduced. Above the threshold, the rapid decrease of the cross sections renders useful elastic recoil detection analysis impossible. These energies thus constitute a practical high energy limit for elastic recoil spectrometry.