Highways and Highway Transportation - George R. Chatburn

Zone	Weight	Farm A		Farm B
Zone	Weight	Acres	Influence Front-Feet	Acres	Influence Front-Feet
1	50	320	2640	80	660
2	25	240	990	160	660
3	15	160	396	240	594
4	10	80	132	320	528
Total		800	4158	800	2442
Contact Feet			5280		1320

Procedure with Unequal Zones or Irregular Lots.

—Where the zones are not equal in area or the property lines do not intersect the roadway at right angles or the lots are irregular in shape, the method of procedure is not quite so simple, although the principle is the same. While it is customary to make the zones of uniform width this is not absolutely necessary. Likewise the ratio of weights vary with different states and cities. One city uses 33¹⁄₃, 20, 16²⁄₃, 10, 10, 10 for the weights in its six zones; another uses 33¹⁄₃, 25, 16²⁄₃, 15 and 10. Neither of these, as shown in the tables on [pages 315] and [316] varies materially from the theoretical ratio.

Using the latter of these ratios a small district has been worked out as shown in the figure and table on [page 320]. Incidentally this also shows a good method of recording lot assessments during the process of computations. The work is readily checked. The sum of the lot areas must equal the sum of the zone areas and that of the whole district. The sums of the weighted areas for the same divisions must balance. The sums of front-feet likewise. Also cross and vertical summations may be made to check.

Second Method of Apportioning Assessments.

—A second method based upon a different definition has something in its favor. If the front-foot is defined as a lot 1 foot wide measured in the direction of the street extending directly back through all the zones to the limit of the assessed area it will have a weighed area of W₁z₁ + W₂z₂ + W₃z₃ ... and so on, where W₁ represents the weight of the zone, whose width is z₁, and W₂ the weight of the zone, width z₂, etc. If z₁ = z₂ = z₃ ... etc., as is usually the case the weighted area of 1 front-foot is (W₁ + W₂ + W₃ ... ) z = Wz = 100z, since W is always = 100. The total number of front-feet in the district, or in any lot, will be the number of weighted feet in the district or in the lot, divided by 100z. In the district represented on p. 320, the number of front-feet is the total frontage, 1,936,000 divided by 4000 = 484; and for each lot the amount shown in the table. The results obtained by the two methods are directly proportional, so that either may be used for making assessments. In fact they are proportional to the weighted areas, so that the weighted areas may be used instead of the front-feet if desired.

Rule for Assessment.

—To get the assessment for any particular lot divide the total cost of the improvement by the total number of front-feet in the district and multiply the quotient by the number of front-feet in the lot.

ZONE	WT.		ZONES		LOT 1		LOT 2		LOT 3		LOT 4		LOT 5		LOT 6		LOT 7
ZONE	WT.		AREA	WTD. AREA	AREA	WTD. AREA	AREA	WTD. AREA	AREA	WTD. AREA	AREA	WTD. AREA	AREA	WTD. AREA	AREA	WTD. AREA	AREA	WTD. AREA
1	39	¹⁄₃	22,800	760,000	4800	160,000	3600	120,000	2400	80,000	3000	100,000	3000	100,000	6000	200,000
2	25		20,400	510,000	2400	60,000	3600	90,000	2400	60,000	3000	75,000	3000	75,000	6000	150,000
3	16	²⁄₃	18,000	300,000	300	5,000	3300	55,000	2400	40,000	3000	50,000	3000	50,000	3000	50,000	3000	50,000
4	15		15,600	234,000			1200	18,000	2400	36,000	3000	45,000	3000	45,000			6000	90,000
5	10		13,200	132,000					1200	12,000	3000	30,000	3000	30,000			6000	60,000
Total			90,000	1,936,000	7500	225,000	11700	283,000	10800	228,000	15000	300,000	15000	300,000	15000	400,000	15000	200,000
Front Feet 1st Method600						69.73		87.71		70.66		92.97		92.97		123.97		61.99
Front Feet 2nd Method484						56.25		70.75		57.00		75.00		75.00		100.00		50.00