# Elliptical shape of the Carolina Bays

The elliptical shape of the Carolina Bays with raised rims distinguishes the bays from structures created by wind and water processes. The width-to-length ratio and the eccentricity of the elliptical Carolina Bays have very consistent values for bays of different sizes. The width-to-length ratios of Carolina Bays average 0.58, and the eccentricity averages 0.81. The bays in Nebraska are indistinguishable from the bays in the East Coast on the basis of their geometrical characteristics.

Carolina Bays near Myrtle Beach, SC

The consistent width-to-length ratios of the elliptical Carolina Bays can be explained if the bays were originally conic sections formed by impacts that created oblique conical cavities. The width-to-length ratios of the bays are related to the angle of impact by the relationship: $$sin(\theta) = W / L$$. The angle of impact for Carolina Bays averages 35 degrees. Terrestrial processes by wind and water do not provide a mechanism for stopping when the correct width-to-length ratio is achieved.

The following table has the coordinates and sizes of 23 Carolina Bays. The bays have clearly defined borders that make it possible to measure the major and minor axes accurately using Google Earth with a LiDAR overlay. The eccentricity of an ellipse is given by: $$e = \sqrt{1 - (b^2 / a^2)}$$, where $$a$$ is the length of its semi-major axis and $$b$$ is the length of its semi-minor axis.

Geometrical Characteristics of the Carolina Bays
Tag Latitude Longitude Major axis
in meters (L)
Minor axis
in meters (W)
W/L Eccentricity arcsin(W/L)
degrees
az0001  34.372438  -79.955112 2875 1582 0.5503 0.8350 33.38
az0002 34.355453 -79.897354 1142 627 0.5490 0.8358 33.30
az0003 34.348281 -79.885369 829 509 0.6140 0.7893 37.88
az0004 34.351854 -79.839793 1193 756 0.6337 0.7736 39.32
az0005 34.341673 -79.805336 2773 1505 0.5427 0.8399 32.87
az0006 34.354419 -79.792716 1234 812 0.6580 0.7530 41.15
az0007 34.281692 -79.769796 2406 1362 0.5661 0.8243 34.48
az0008 34.457433 -79.914511 1438 752 0.5229 0.8524 31.53
az0009 34.437885 -79.876300 519 281 0.5414 0.8407 32.78
az0010 34.387512 -79.831597 1216 780 0.6414 0.7672 39.90
az0011 34.516371 -79.685701 2013 1208 0.6001 0.7999 36.88
az0012 34.388400 -79.582470 1550 890 0.5742 0.8187 35.04
az0013 34.384065 -79.524621 1478 867 0.5866 0.8099 35.92
az0014 34.526274 -79.531788 1302 777 0.5968 0.8024 36.64
az0015 34.527690 -79.485771 3125 1765 0.5648 0.8252 34.39
az0016 34.623532 -79.579738 1848 1107 0.5990 0.8007 36.80
az0017 34.644750 -79.637077 1422 871 0.6125 0.7905 37.77
az0018 40.516923 -98.031921 5282 2854 0.5403 0.8415 32.71
az0019 40.566439 -98.166159 3627 1940 0.5349 0.8449 32.34
az0020 40.436968 -97.976410 1490 990 0.6644 0.7474 41.64
az0021 40.518205 -99.135957 2496 1210 0.4848 0.8746 29.00
az0022 40.425091 -98.985710 2150 1200 0.5581 0.8297 33.93
az0023 40.763450 -97.927499 2660 1570 0.5902 0.8072 36.17
Average  0.5794 0.8132 35.847
Sample Standard Deviation  0.0452 0.0326 3.19

The Carolina Bays are characterized
by their elliptical shape and raised rims

The tags in the images correspond to the table above.

The following images show a USGS topograpic map and a LiDAR image of Big Bay, a Carolina Bay just north of Pinewood, SC. The center of the bay is located at approximately Lat. 33.78645, Lon. -80.46785, and the bay measures 4,920 by 3,100 meters. This gives it a width-to-length ratio of 0.63 and an eccentricity of 0.78.

The small bay adjacent to the north-east of Big Bay with a center located at Lat. 33.801219, Lon. -80.450795 measures 1710 meters by 1120 meters. This corresponds to a width-to-length ratio of 0.66 and an eccentricity of 0.76. Both Big Bay and its companion have values close to the average for Carolina Bays.

Big Bay, north of Pinewood, South Carolina
(Lat. 33.78645, Lon. -80.46785)

According to Brooks (2010), the Carolina Bays evolved as a result of processes active episodically over a long period of time. Based on 45 Optically Stimulated Luminescence (OSL) dates, active shorelines and associated eolian deposition occurred during Marine Isotope Stage (MIS) 2 to late MIS 3 (~12 to 50 ka), MIS 4 to very late MIS 5 (60-80 ka), and late MIS 6 (120–140 ka).

Brooks states that Big Bay formed from wind-driven sand sheets from the Wateree River, which is 10 kilometers to the west. The sand moved across Big Bay about 74,000 years ago and was resurfaced subsequently 33,000 to 29,000 years ago. The innermost sand rim at Big Bay was remodeled as recently as 2,200 years before the present.

The paper by Brooks does not mention the consistent width-to-length ratios of the Carolina Bays and does not propose a mechanism for how the wind and water processes could have given Big Bay the typical aspect ratio of the other bays.