Originally issued in 1971, this report was prepared to assist in predicting the vertical motion of high altitude balloon systems. In anticipation of the increasing use of balloons as an energetically efficient mans of transporting instrumentation or commercial payloads, it seemed desirable to enlarge the report to include a calibrated model for predicting the vertical trajectory of zero-pressure balloons. A number of errors in the 1971 edition have been corrected in this revision. The additions in the revised report to the dynamic and thermodynamic analysis contained in the original edition provide the balloon engineer an efficient, calibrated computer program to predict balloon ascent rates, ceiling, and behavior at float.