Aeroplane Construction and Operation

by John B. Rathbun

Air is considered as a fluid since it is capable of flowing like water, but unlike water, it is highly compressible. Owing to the difference between air and water in regard to compressibility, they do not follow exactly the same laws, but at ordinary flight speeds and in the open air, the variations in the pressure are so slight as to cause little difference in the density. Hence for flight alone, air may be considered as incompressible. It should be noted that a compressible fluid is changed in density by variations in the pressure, that is, by applying pressure the weight of a cubic foot of a compressible fluid is greater than the same fluid under a lighter pressure. This is an important consideration since the density of the air greatly affects the forces that set it in motion, and for this reason the density (weight per cubic foot) is always specified in a test.

Every existing fluid resists the motion of a body, the opposition to the motion being commonly known as "resistance." This is due to the cohesion between the fluid particles and the resistance is the actual force required to break them apart and make room for the moving body. Fluids exhibiting resistance are said to have "viscosity." In early aerodynamic researches, and in the study of hydrodynamics, the mathematical theory is based on a "perfect fluid," that is, on a theoretical fluid possessing no viscosity, and while this conception is an aid in studying the reactions, the actual laboratory results are far from the computed values. Such theory would assume that a body could move in a fluid without encountering resistance, which in practice is, of course, impossible.

In regard to viscosity, it may be noted that air is highly viscuous—relatively much higher than water. Density for density, the viscosity of air is about 14 times that of water, and consequently the effects of viscosity in air are of the utmost importance in the calculation of resistance of moving parts.

Atmospheric air at sea level is about 1/800 of the density of water. Its density varies with the altitude and with various atmospheric conditions, and for this reason the density is usually specified "at sea level" as this altitude gives a constant base of measurement for all parts of the world. As the density is also affected by changes in temperature, a standard temperature is also specified. Experimental results, whatever the pressure and temperature at which they were made, are reduced to the corresponding values at standard temperature and at the normal sea level pressure, in order that these results may be readily comparable with other data. The normal (average) pressure at sea level is 14.7 pounds per square inch, or 2,119 pounds per square foot at a temperature of 60° Fahrenheit. At this temperature 1 pound of air occupies a volume of 13.141 cubic feet, while at 0° F. the volume shrinks to 11.58 cubic feet, the corresponding densities being 0.07610 and 0.08633 pounds per cubic foot, respectively. This refers to dry air only as the presence of water vapor makes a change in the density. With a reduction in temperature the pressure increases with the density increase so that the effect of heat is twofold in its effect.

With a constant temperature, the pressure and density both decrease as the altitude increases, a density at sea level of 0.07610 pounds per cubic foot is reduced to 0.0357 pounds per cubic foot at an altitude of 20,000 feet. During this increase in altitude, the pressure drops from 14.7 pounds per square inch to 6.87 pounds per square inch. This variation, of course, greatly affects the performance of aeroplanes flying at different altitudes, and still more affects the performance of the motor, since the latter cannot take in as much fuel per stroke at high altitudes as at low, and as a result the power is diminished as we gain in altitude. The following table gives the power variations at different heights above sea level.

This air table also gives the properties of air through the usual range of flight altitudes. The pressures corresponding to the altitudes are given both in pounds per square inch and in inches of mercury so that barometer and pressure readings can be compared. In the fourth column is the percentage of the horsepower available at different altitudes, the horsepower at sea level being taken as unity. For example, if an engine develops 100 horsepower at sea level, it will develop 100 × 0.66=66 horsepower at an altitude of 10,000 feet above sea level. The barometric pressure in pounds per square inch can be obtained by multiplying the pressure in inches of mercury by the factor 0.4905, this being the weight of a mercury column 1 inch high.

NOTE.-Densities marked * are interpolated from a graph, but are close enough for all ordinary purposes.

In aerodynamic laboratory reports, the standard density of air is 0.07608 pounds per cubic foot at sea level, the temperature being 15 degrees Centigrade (59 degrees Fahrenheit). This standard density will be assumed throughout the book, and hence for any other altitude or density the corresponding corrections must be made. Owing to the fact that the temperature decreases as we gain altitude, further corrections must be made in the tabular values, but as the changes are rather difficult to make and are relatively small we will not take the matter up at this point.