Highways and Highway Transportation

by George R. Chatburn

Other Methods of Estimating Amount of Traffic.

—The amount of road traffic may be roughly estimated from the area served by the highway. Upon a map is outlined the tributary territory and its area measured by any one of several means. The area may be divided into small squares of known size and the number of squares counted; it may be divided into strips and the length of the strips measured with a scale and thence the area computed, or a planimeter may be used. Having found the area the unit tonnage is estimated from a knowledge of the character of the crops raised and the industries in the territory from which the haulage is calculated. The average haul may be determined, if desired, by finding approximately the center of gravity of the area and measuring its distance from the market. If the market place is at the center of a circle surrounding it and the products are uniformly distributed over the circle the mean distance is two-thirds the radius of the circle.

The tonnage, arising from farms, which is transported over the roads varies with the kind of crop, the fertility of the soil, the amount of stock fed, or kept for dairying, and numerous other local conditions. Studies made by various authorities[179] indicate that the marketable products vary from ¹⁄₁₀ to ¹⁄₂ ton per acre. If a circular area with market place at the center is served by six uniformly distributing radial roads a mathematical analysis will show that the tonnage upon each one of these roads, one-sixth that from the whole circle, will be

T = 335.12qr²

where	T	=	total tons per year,
	q	=	yield of marketed crops in tons per acre,
	r	=	maximum haul-radius of the circle.

Dividing T by the number of working days per year (usually taken as 300) gives the average daily haul into the market. The average length of haul may be taken as ²⁄₃ r. The haul over any zone whose edges are concentric with the circle is considered to be all that originating in the area outside the zone plus that originating within the zone times the mean distance from the inner edge of the zone. The result of the analysis gives this equation, for the haul over any zone having an outer radius a, and an inner radius b,

H = T_r - T_a + 2a² - ab - b² 3(a + b) (T_a - T_b),

where T_r, T_a and T_b represent the tonnage originating on the sectors of radius r, a and b respectively.

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
			Over 1st Mile	Over 8th Mile		Over 1st Mile	Over 8th Mile		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]

Graphic representation of distribution of traffic on roads located along section lines.

His analysis assumes the lay of the country makes all roads equally traversable and that the traffic seeks the nearest highway thence to the main traveled road east and west or north and south through the market center. This analysis shows that 4.8 per cent of the total mileage carry 39.3 per cent of the traffic; that 9.5 per cent of the roads carry 71 per cent of the traffic. In his opinion this analysis corroborates the observation of engineers to the effect that 20 per cent of the roads carry 80 per cent of the traffic. Of course the most important roads, measured in traffic, are the ones nearest the market, 15-22, 15-16, 16-21, 21-22. Following these naming only one of the four symmetrical roads, in the order of importance are 14-23, 14-13, 13-24, 13-x, 14-15, 11-12, 12-x, 12-13, 1-x, 11-14, and 1-12.

Road between Sections			Relative Importance
15	-	22	100
14	-	23	60
14	-	13	25
13	-	24	20
13	-	x	15
14	-	15	13
11	-	12	7
12	-	x	7
12	-	13	2
1	-	x	2
11	-	14	1
1	-	12	1

The same objections to this method hold as to the preceding. Local conditions always affect the travel on roads; hills, valleys, soil, drainage, nearness to other cities, railways, streams, and location of farmhouses, schoolhouses, churches, and factories, all enter into the estimate. A reconnaissance and the good judgment of the observer must supplement any method of formal procedure.