A "Barb"ed question

I have the impression that someone forgot to do the math about the size of the Barb ranch.

Alec Waggoman told his son Dave the Barb ranch was 100,000 acres twice in one scene.

100,000 acres equals 156.25 square miles, which is a large area. 156.25 square miles equals a square 12.5 by 12.5 miles, which is not as impressive.

Suppose that the Barb is circular. The area of a circle is Pi times the radius squared. If Pi is 3.14159, which should be close enough, 156.25 square miles divided by Pi is 49.735961. The square root of 49.735961 is 7.0523.

So if the Barb was circular, the radius would be 7.0523 miles and the diameter 14.1047 miles.

But Alec also said he owned all the land that one could ride though for three days in any direction and more. That can't be literally true - the rival ranch of Kate Canady should be a lot less than 3 day's away from Alec's ranch house, forming an enclave in Barb territory. If someone rode 5 to 10 hours per day at a speed of 2 to 4 miles per hour, or 10 to 40 miles per day, the radius of the Barb would be at least 30 to 120 miles, and it would cover at least 2,827.431 to 45,238.896 square miles, or at least 1,809,555.84 to 28,952,893.44 acres!

That is at least 18.09 to 289.52 times 100,000 acres. That is quite a difference in scale.

By comparison, the King Ranch, the largest ranch in Texas, has about 825,000 acres, 3,340 square kilometers, or 1,289 square miles. As the map shows, it is not a simple rectangle or circle, but a highly complex shape, with two of the four main divisions not even connected to other divisions.


So either Mr. Waggoman owned many contiguous ranches, of which the Barb, his main one, was only 100,000 acres, or else somebody failed to do the math.