The majority of very large vapour cloud explosions occur in such low wind speeds that vapour flow is gravity driven. The rate of stripping (or detrainment) of heavy gas by the wind is so low that almost all of the gas released remains in a gas "blanket", which typically slumps in all directions around the source. Such gravity driven flammable clouds may extend many hundreds of metres from the source in all directions without significant dilution: their development cannot be assessed with conventional windy dispersion models. Previous work on the basic problem of gravity-driven vapour transport on a flat open surface is reviewed. Existing methods suffer from a number of deficiencies including arbitrary specification of current height and velocity and the neglect of surface friction. A new method of analysis is presented. Close to the source the flow can be calculated from the initial conditions at the source by integration of momentum and continuity equations. Entrainment of fresh air and friction increase the stability of the flow (Richardson number) and the rate of dilution declines towards zero. When the Richardson number approaches unity the current becomes critical and further out from the source the flow is under downstream control. The new method is used to calculate the total dilution of a vapour cloud before entrainment of fresh air is completely suppressed. This determines whether clouds are flammable at long-range. The effects of surface roughness, bund height, vapour density etc. are described. Predictions are compared with data from incidents. Crown Copyright (C) 2017 Published by Elsevier Ltd.