Highways and Highway Transportation - George R. Chatburn

For the first mile,

a = 1, b = 0.

H = T_r - ¹⁄₃T_a.

For the eighth mile,

a = 8, b = 7.

H = T_r - T₈ + ²³⁄₄₅(T₈ - T₇)

Theoretical Average Tonnage of Six Uniformly Distributed Market Roads[180]

Maxi- mum Haul	Aver- age Haul	Uniform Yield per Acre of
		One-tenth Ton			One-fourth Ton			One-half Ton
		Total Tons per Year	Tons Hauled per day		Total Tons per Year	Tons Hauled per day		Total Tons per Year	Tons Hauled per day
		Total Tons per Year	Over 1st Mile	Over 8th Mile	Total Tons per Year	Over 1st Mile	Over 8th Mile	Total Tons per Year	Over 1st Mile	Over 8th Mile
1	0.67	33	0.07		84	0.17		168	0.34
2	1.33	134	0.40		335	1.00		670	2.01
3	2.00	302	0.96		754	2.40		1,508	4.80
4	2.67	536	1.74		1,340	4.36		2,681	8.71
5	3.33	838	2.75		2,094	6.87		4,189	13.74
6	4.00	1206	3.98		3,016	9.95		6,031	19.90
7	4.67	1642	5.43		4,106	13.58		8,211	27.15
8	5.33	2145	7.11	0.85	5,362	17.76	2.13	10,724	35.52	4.25
9	6.00	2714	9.00	2.75	6,786	22.51	6.88	13,572	45.02	13.75
10	6.67	3351	4.13	4.87	8,378	27.82	12.18	16,756	55.63	24.35
11	7.33	4056	13.47	7.22	10,138	33.68	18.05	20,279	67.35	36.10
12	8.00	4826	16.04	9.79	12,064	40.10	24.48	24,128	80.20	48.95
13	8.67	5663	18.83	12.58	14,158	47.08	31.45	28,316	94.15	62.90
14	9.33	6568	21.85	15.59	16,420	54.63	38.98	32,840	109.25	77.95
15	10.00	7540	25.09	18.83	18,850	62.73	47.08	37,700	125.45	94.15

The table shows the theoretical average tonnage on each of six uniformly distributed radial roads. It is taken from Bulletin 136, U. S. Department of Agriculture. Since roads do not run in practice in this manner the results can only be used for comparison in confirming estimates.

Mr. E. W. James, of the Bureau of Public Roads, U. S. Dept. of Agriculture, makes an analysis of the distribution of traffic over the roads of a township located along the section lines of the United States land survey. The market place is taken at the center of the township.[181]