The category of ultralight airplanes ranges from hang gliders to light versions of general-aviation airplanes. They fill a need for experimenters and for pilots who want to fly inexpensively and with little regulation. Ultralight airplanes evolved as did the early flying machines, by much cut-and-try and flight testing. Although these designs have been useful, indications are that many commercial ultralights are deficient in stability and control.

Human-powered airplanes are extreme ultralights, designed not for practicality but to push the engineering and human limits of aviation. Early efforts at human-powered flight were discouraging because of the poor performance and extreme fragility of the machines that were constructed before the first successful one, the Gossamer Condor.

13.1 Apparent Mass Effects

For very light airplanes, not much heavier than the air in which they fly, apparent mass effects must be considered. These effects were first noticed in 1836 by George Green, who found that pendulum masses in a fluid medium were apparently greater than in a vacuum. The apparent mass effect can be described as follows (Gracey, 1941):

The apparent increase in mass can be attributed to the additional energy required to establish the field of flow about the moving body. Inasmuch as the motion of the body may be defined by considering its mass as equal to the actual mass of the body plus a fictitious mass, the effect of the inertia forces of the fluid may be represented as an apparent additional mass; this additional mass, in turn, may be considered as the product of an imaginary volume and the density of the fluid. The effect of the surrounding fluid has accordingly been called the additional mass effect. The magnitude of this effect depends on the density of the fluid and the size and shape of the body normal to the direction of motion.

The primary motivation for Gracey’s work was to be able to correct airplane and wind – tunnel model moments of inertia measured by suspending the airplanes or models and swinging them aslarge pendulums. To the extent that the NACA wasinvolved with equations of motion for the airships of those days, this would have given Gracey yet another motivation to study apparent mass.

The 1941, the NACA apparent mass tests were made by swinging covered frameworks of various shapes as compound pendulums. The test specimens were swung both in air and in a vacuum tank. It is interesting that Gracey started out with balsa wood shapes, but found that their weights varied with air pressure and humidity. Gracey’s training in this exacting experimental work must have helped him to appear later on as NASA’s expert in airspeed and altitude measurement methods.

Interest in apparent mass effects returned with the advent of the plastic and fiber materials that could be used to build very light airplanes, such as the human-powered Gossamer Condor and the high-altitude, long-duration pilotless airplanes Pathfinder and Helios, all built by Aero Vironment, Inc., of Monrovia, California. Apparent mass effects are important as well for lighter-than-air and for underwater vehicles. Mathematical models of these craft for dynamic stability analysis include apparent mass terms, as a matter of course. In the series expansions for aerodynamic forces and moments originated by G. H. Bryan, apparent mass terms appear as derivatives with respect to linear and angular accelerations.

Lacking the vacuum swinging apparatus of Green and Gracey, one can approximate apparent mass terms in the equations of airplane motion by adding cylindrical air masses to the lifting surfaces, with diameter equal to the surface chord for motions normal to the chord and equal to the surface thickness for motions in the chord plane. This approximation yields the following astonishing results for the Gossamer Condor. The apparent masses in lateral and vertical motions are 21 and 170 percent of the actual airplane mass. The apparent moments of inertia in pitch and roll are 140 and 440 percent of the actual moments of inertia.

In addition to measurements on swinging models and the approximations mentioned above, panel computer codes can be used for apparent mass estimation. David A. Lednicer reports that the VSAERO code is used routinely for apparent mass calculations on underwater vehicles.