The Estimation of the Effective Centre of Mass Energy in $q\overline{q} \gamma$ Events from DELPHI

The photon radiation in the initial state lowers the energy available for the e$^+$e$^-$ collisions; this effect is particularly important at LEP2 energies (above the mass of the Z boson). Being aligned to the beam direction, such initial state radiation is mostly undetected. This article describes the procedure used by the DELPHI experiment at LEP to estimate the effective centre-of-mass energy in hadronic events collected at energies above the Z peak. Typical resolutions ranging from 2 to 3 GeV on the effective center-of-mass energy are achieved, depending on the event topology.