Section 5 Humidity

You may have read something that goes like “...the air was heavy with moisture...”. The literary idea might be good, but the scientific fact is that at a given pressure and temperature moist air is less dense than dry air. The molecular weight of dry air is 61% greater than that of an H₂O molecule.

The maximum amount of water vapor in the air depends on the temperature and pressure. High temperature and low pressure make the percentage of water mass in the air increase, Remember, though, the standard atmosphere is perfectly dry, free of any water vapor. Because humidity is always present for model builders, this is another factor that changes atmospheric properties for us. Increasing humidity makes both density and R_e go down.

The biggest effect is that each molecule of water vapor displaces one molecule of dry air reducing the amount of oxygen available and reducing the density. The maximum power a model aircraft engine (without a pipe) can develop is limited by the amount of oxygen drawn in through the intake. The needle valve is opened enough to provide fuel for all the available oxygen, which is directly proportional to the density of the air with the water vapor removed.

Humidity is usually reported as relative humidity in percent. This is the percentage of the mass of water vapor in the air compared to the maximum. Wet bulb and dew point temperatures are also used to measure humidity. The wet bulb temperature is the temperature reached by evaporating water in the air sample until it becomes saturated. At any humidity lower than 100% the wet bulb temperature is always lower than the ambient. It is the lowest temperature one can get using a perfect ’swamp cooler’. The dew point temperature is lower than the wet bulb temperature and arrived at by cooling an air sample with a fixed amount of water vapor until it becomes saturated and ’dew’ begins to form in the container. With very dry air the dew point, or frost point, is much lower than any low temperature record set on earth, so it is not as intuitively useful a measure as the wet bulb temperature.

The maximum amount of water vapor that can be held by a given volume of air (saturated, or 100% humidity conditions) is a function of air temperature only. The graph below shows the percentage volume the water vapor takes up at sea level pressure. This volume displaces the oxygen the engine needs to generate power.

The standard atmosphere is defined to be dry, however humidity for model flying conditions is often quite high and seldom below 25% or so. As a consequence humidity corrections to dry atmosphere data can be important.

The volume of air being drawn in by an engine is limited by its displacement and induction system. The oxygen available to burn is proportional to the density times the volume of dry air drawn in. Variations in density were discussed earlier. When the air is humid some of the volume is taken up by water molecules as shown in the graph above.

For engine power corrections, then, both the density and humidity have to be taken into account and, because the maximum quantity of water vapor depends only on temperature, air at a given relative humidity will have a higher percentage of water mass when the temperature is high and the pressure low. In other words, the water displaces more dry air at these conditions, even though the relative humidity is the same.

As an extreme example, consider flying at standard sea level pressure (29.92 in Hg) but at 90 ^oF.

In this case the Density altitude for dry air is 1972 feet. At 100% humidity the density altitude is 2581 feet. The density is 93% of ’standard’, but because the water molecules displace the air molecules the mass of oxygen for a given volume of air is only 90% of sea level standard.

All the calculations above can be accomplished accurately with the program ATMO99.