A simple model of the world air market is used to test the function that liquid hydrogen (LH2) aviation might turn in reducing carbon dioxide (CO₂) emissions from this sector of the economy. Assuming that LH2 aircraft can penetrate up to 70% of the market and will do so along a logistic diffusion curve with Δt = 40 yrs. Using two scenarios - high and low demand - we find that although LH2 aircraft and the LH2 supply system can be configured to release zero CO₂, the remaining conventional aircraft in the market place continue to play a large role in the total sector CO₂ emissions. The model is very sensitive to the balance between the LH2 substitution effect, market growth, and efficiency growth. Liquid hydrogen aircraft can help reduce CO₂ emissions, but reducing CO₂ emissions below recent levels will also require controls on growth in the entire air market. Recognizing that the cost benefit analysis is an appropriate methodology to guide investments effectively to develop and produce sustainable types of alternative fuels for aircraft.