a semi-empirical mathematical model for predicting physical part of ignition delay period in the combustion of direct - injection diesel engines with swirl is developed . this model based on a single droplet evaporation model . the governing equations , namely , equations of droplet motion , heat and mass transfer were solved simultaneously using a rung-kutta step by step unmerical method . the computation excuted until somewhere in the vapor layer around the droplet a near stoichiometric mixture of the fuel vapour and air having at least the self-ignition temperature of the fuel formed. the predicted physical ignition delay time for particular d.i. diesel engine is in good agreement with engine standard data and existing data in the technical literature . also validity of the model examined with variation of the combustion chamber and fuel injection parameters . from the parametric studies it seems that physical delay period to be particularly effected by fuel initial temperature , ambient temperature , injection pressure , air/fuel ratio , swirl level and the engine speed . also from parametric studies an algebraic relation for predicting physical part of ignition delay derived.