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The increasing importance of aviation activities in modern life coincides with a steady warming climate. However, the effect of climate warming on maximum aircraft carrying capacity or payload has been unclear. Here we clarify this issue using primary atmospheric parameters from 27 fully coupled climate models from the Coupled Model Inter-comparison Project 5 (CMIP5) archive, utilizing the direct proportionality of near-surface air density (NSAD) to maximum take-off total weight (MTOW). Historical (twentieth century) runs of these climate models showed high credibility in reproducing the reanalysis period (1950-2015) of NSAD. In particular, the model simulated trends in NSAD are highly aligned with the reanalysis values. This reduction in NSAD is a first order global signal, just as is the warming itself, that continues into the future. To examine the statistical significance of the density reduction, a t-test was performed for two 20-year periods 75years apart (2080-2100 vs. 2005-2025), using the Representative Concentration Pathways (RCP) 8.5 emission scenario of the Intergovernmental Panel on Climate Change (IPCC). Most continental areas easily passed the test at a P-value of 0.05. These future changes of NSAD will likely have significant economic impacts on the aviation industry. For these two 20-year periods that we examined, the most extreme changes are in the Northern hemisphere in high latitudes, i.e., a 5% decrease in MTOW, or 8.5-19% (aircraft-dependent) reduction in payload. The global average change is about 1%. For the busy North Atlantic Corridor (NAC), the reduction in MTOW is generally greater than 1% and that of payload several times larger.