W.F. Prouty - Ellipticity of the Carolina Bays

William Frederick Prouty, a geologist and university teacher, was the author of numerous articles appearing in scientific journals, including a work on the "Carolina Bays and Their Origin," published posthumously in 1952 in the Bulletin of the Geological Society of America. Prouty proposed a modified meteoritic (air-shock wave) theory for the origin of the bays and pointed out several major characteristics that are not adequately explained by the terrestrial processes of bay origin, such as the overlap patterns of multiple bays.

Meteoritic theories for the origin of the Carolina Bays were refuted when stringent criteria for the identification of extraterrestrial impacts were introduced by Eugene M. Shoemaker in the 1960s. The new criteria require finding evidence of petrographic shock metamorphism, such as planar deformation features in quartz grains made by a hyperspeed impact, and enrichment of the impact site by siderophile elements, such as iridium, which are more common in extraterrestrial objects than in the Earth. The Carolina Bays do not have this type of evidence.

Although extraterrestrial impacts have been ruled out as the origin of the Carolina Bays, it is still possible to consider secondary ballistic impacts. Prouty's extensive research into the mechanism of formation and statistical analysis of the Carolina Bays still remains relevant today, even though his meteoritic theory has been invalidated.

One important aspect of Prouty's research was his study of ellipticity, which he defined as the difference between the major axis and minor axis divided by the major axis:

ellipticity = (major_axis - minor_axis) / major_axis

Since the major axis corresponds to the length (L) and the minor axis corresponds to the width (W) of an elliptical bay, we can rewrite the equation as e = (L-W)/L or e = 1 - W/L. The width-to-length ratio of a bay is then 1 - e. The width-to-length ratios of the bays are related to the angle of inclination θ of a conic section by the relationship: sin(θ) = W/L.  A circle has an ellipticity of zero, and the ellipticity increases toward one as an ellipse becomes more elongated. The width-to-length ratio is the opposite. It has a value of one for a circle and it decreases toward zero as the width of the ellipse becomes smaller relative to its length.

Prouty's 1952 paper reports the measurements of ellipticity of 130 Carolina Bays. Some of the measurements were conducted by Melton and Schriever (1933) and others by Prouty, as follows:

Melton and Schriever (1933)
Horry County, SC
41 bays, size: 500 ft to nearly 6000 ft (152 to 1828 meters)
Ellipticity min: 0.170, max: 0.495, ave: 0.340
W/L = 1-e = 0.660 corresponds to a conic section inclined at 41.3 degrees

Prouty (1952)
63 bays, size: 500 ft to 3700 ft (152 to 1128 meters)
Ellipticity min: 0.270, max: 0.457, ave: 0.363
W/L = 1-e = 0.637 corresponds to a conic section inclined at 39.6 degrees

Prouty (1952)
Marion and Darlington Counties, SC
26 bays, size: 550 ft to 7000 ft (168 to 2133 meters)
Ellipticity min: 0.245, max: 0.495, ave: 0.420
W/L = 1-e = 0.580 corresponds to a conic section inclined at 35.5 degrees

Prouty noted that, on average, small bays have smaller ellipticity than large bays, as illustrated in Figure 12 from his paper, below. That is, smaller bays are rounder or less elongated than the larger bays. Rounder bays correspond to a more vertical angle of impact.

If we consider that the projectiles that made the bays were in sub-orbital spaceflight ballistic trajectories, the rounder bays for the smaller projectiles could be attributed to: 1) a greater launch angle, or 2) the effect of air resistance as the projectiles re-entered the atmosphere. A large projectile with a greater mass would tend to keep its angle of impact, whereas a small projectile would slow down and the angle of its trajectory would be changed toward a more vertical approach.

Melosh (1989) discusses the atmospheric interactions of a meteoroid.  When a projectile penetrates and travels through the atmosphere, friction causes ablation, which is the loss of surface material by melting or evaporation, and the projectile loses mass during transit. The combined forces of atmospheric drag and gravity in the presence of ablation interact to slow down a constantly shrinking projectile thereby making its angle of impact more perpendicular to the surface. The following equation describes the change in speed that is due to drag and gravitational acceleration g, which must be considered as a function of altitude Z in deep atmospheres. CD is the drag coefficient, A is the cross-sectional area, ρg is the atmospheric density at any altitude, and m is the meteoroid mass.

The change in speed is inversely proportional to the mass of the projectile, so a large projectile is harder to slow down than a smaller projectile with a similar trajectory. Consequently, for projectiles initially traveling at the same angle and speed, the larger projectiles would create conic sections with greater ellipticity than the smaller projectiles. Melosh illustrates this with the trajectory of a meteoroid as it encounters resistance from the atmosphere (Fig. 11.1, below). He explains: "The minimum velocity that the meteoroid can attain occurs when all of its initial momentum has been spent by drag and it falls vertically toward the surface."  A vertical impact would produce a circular crater.

It is necessary to consider that if the Carolina Bays were produced by a saturation bombardment of glacier ice projectiles, the close proximity of the projectiles as they re-entered the atmosphere could have decreased the aerodynamic drag for the projectiles that traveled behind others. Drafting or slipstreaming occurs when moving objects align in a close group thereby reducing the overall effect of drag by exploiting the lead object's slipstream.