In applying the zone method some difficulty is encountered in determining an equitable distribution on those parcels of land lying partly in one zone and partly in another, but the rate may be arrived at with reasonable accuracy by pro-rating in accordance with the exact conditions.

In. Fig. 1, let it be a.s.sumed that the a.s.sessment area is to be two miles wide, one mile on each side of the road and the various ownerships to be indicated by the parcels of land numbered 1 to 8, as shown. Each zone for the a.s.sessment of the 3-1/4 mile section is 1/4 mile wide and the rates for the several zones are 50, 25, 15 and 10 per cent respectively. Let it be a.s.sumed that the portion of the cost of the 3-1/4 miles of road to be a.s.sessed on the area shown is $20,000. The a.s.sessment would then be as follows:

------+-------+----------------------+------------+------------- | | Rate frontage on | Amount of | Parcel| Rate | improved road = | a.s.sessment | a.s.sessment | | a.s.sessment units | per unit[1]| 1 | 2 | 3 | 4 | 5 ------+-------+----------------------+------------+------------- 1 | a 50 | 50 2640 = 132,000 | $0.016655 | $1558.46 | b 75 | 75 1320 = 99,000 | | 1153.90 2 | 40 | 40 2640 = 105,600 | | 1230.77 3 | 10 | 10 2640 = 26,400 | | 307.69 4 | 25 | 25 1320 = 33,000 | | 384.66 5 | [2]85 | 85 5280 = 448,800 | | 5230.88 6 | 15 | 15 5280 = 79,200 | | 923.08 7 | [2]65 | 65 7920 = 514,800 | | 6000.00 8 | 35 | 35 7920 = 277,200 | | 3230.77 | | ------------------- | | ----------- | | 1,716,000 | | $20000.00 ------+-------+----------------------+------------+-------------

[1] The a.s.sessment per unit is obtained by dividing the total a.s.sessment by the total of column three.

[2] On these two parcels, it is decided that more than half of the zone rate should apply to the half of the zone toward the improved road, but some modification of the rates adopted might be justified.

[Ill.u.s.tration: Fig. 1]

The a.s.sessment of the cost of the east and west one-mile section of road is made up in like manner, and let it be a.s.sumed that the portion of the cost of this road that is to be a.s.sessed on the area shown is $5500. The a.s.sessment area will be one mile wide and each zone one-fourth mile in width and the rates for each zone the same as before.

------+-------+----------------------+------------+------------- | | Rate frontage on | Amount of | Parcel| Rate | improved road = | a.s.sessment | a.s.sessment | | a.s.sessment units | per unit | ------|-------+----------------------+------------+------------- 1 | a 75 | 75 x 1320 = 99,000 | $0.010417 | $1031.25 | b 15 | 15 x 2640 = 39,600 | | 412.49 2 | 75 | 75 x 2640 = 198,000 | | 2062.53 3 | 50 | 50 x 1320 = 66,000 | | 687.51 4 | a 25 | 25 x 1320 = 33,000 | | 756.25 | b 15 | 15 x 2640 = 39,600 | | 5 | 10 | 10 x 3300 = 33,000 | | 343.73 6 | 10 | 10 x 1980 = 19,800 | | 206.24 ------|-------| | |------------- | | 528,000 | | 5500.00 ------+-------+----------------------+------------+-------------

It will be noted that the combined a.s.sessment for the two sections of road is especially heavy on parcels 1, 2 and 3. In order to prevent unjust charges against such properties, laws usually limit the total a.s.sessment against any parcel of land to a fixed percentage of a fair market value or of the a.s.sessed value. The a.s.sessment on these parcels would be reduced as seemed expedient and the deficit would be distributed over the remainder of the area in the same manner as the original a.s.sessment was spread. In practice such re-distribution is ordinarily made by the arbitrary adjustment in accordance with what the authorized officials consider to be fair and equitable. The method outlined is merely a mechanical means of securing distribution and must not be considered as an infallible method of making the a.s.sessment. It is always necessary to review the results in the light of the actual benefits to be presumed for each parcel of land.

Nevertheless, the method outlined will prove equitable in a majority of cases.

=General Taxation.=--There is a general community benefit derived from the construction of good roads in that the actual cost of marketing farm products is lessened with a resulting lowering of the price to the consumer. The benefit also accrues from the greater facility with which all community business may be conducted. The introduction of better opportunities for social, religious and educational activities in the rural districts which results from improved highways is also a community benefit of no mean importance. A part of the cost of road improvement may therefore be equitably paid from funds obtained by general taxation.

A considerable portion of the current expense of maintaining the township and county highway work and at least a part of the cost of maintaining state highway activities is met from funds obtained by general taxation. Likewise, the funds required for the amortization of bond issues are often obtained from general taxation although vehicle license fees are sometimes used for that purpose.

General taxes are levied on all taxable property in a political unit under statutory provisions regulating the amount of the levy and the purpose for which the revenue is to be used. In the aggregate, the road taxes are large but in the township or county the rate is generally small compared to some other taxes, such as the school tax.

=Vehicle Taxes.=--The great direct benefit derived by those who actually operate vehicles over the roads justifies the policy of requiring a vehicle to pay a license fee in lieu of other taxes, the funds so obtained to be used for the construction and maintenance of public highways. In practice, this method has already been applied to motor vehicles in most states and has proven to be an important source of revenue. Its application to horse-drawn vehicles has not been attempted, due probably to the fact that such horse-drawn vehicles as use the public highways are also employed about the farm or in the towns and the determination of an equitable basis for taxation involves many difficulties.

The rate of the fee for motor vehicles should be based on their destructive effect on the road so far as that is possible. The scale of fees should therefore take account of weight and speed of vehicle and if the license is in lieu of all other taxes, it should also be graduated with the cost of the vehicle.

When funds are thus derived, every precaution should be taken to insure that the money is used judiciously for construction and especially for maintenance on those roads most useful to motor traffic.

=Highway Bonds.=--Bond issues for road improvement afford a means of constructing roads and paying for them while they are being used. A very large volume of such bonds are outstanding in the United States.

Road bonds should be issued only for durable types of improvement and the life of the bond should be well within the probable useful life of the road surface. It is customary and highly desirable that the general nature and extent of the improvement be established before the bonds are issued. It is desirable that bond issues be subject to approval by referendum before issue and that is provided in every instance.

Highway bonds are of three cla.s.ses known as Sinking Fund, Annuity and Serial Bonds, respectively. The earlier bonds issued were almost all of the sinking fund cla.s.s, but in recent years the serial bond has been widely employed and is probably the most satisfactory to administer.

=Sinking Fund Bonds.=[1]--When this type of bond is employed, the amount of the expenditure for road improvement is determined upon and the length of the period during which tax payments shall be made is settled. To employ a concrete example, it may be a.s.sumed that $100,000 is to be expended for road work and is to be paid at the end of ten years. The interest rate on the bonds will vary with the condition of the bond market and the stability of the political unit issuing the bonds, but is usually about 5 per cent. Knowing these factors, the amount to be added to the sinking fund each year is computed. In order to pay the interest on the bonds, a tax of suitable rate is levied, and in order to retire the bonds at the end of the period, a sum is set aside each year which is supposed to be invested and draw interest which will be added to the principle, and the principle and interest comprise the sinking fund. The principle of the sinking fund is obtained by tax levies, a sum being added to the principle of the sinking fund each year.

[1] For a more detailed discussion of highway bonds see Bulletin 136, U. S. Dept. of Agriculture, which is the basis of this discussion.

The success of this method of financing depends upon the proper administration of the sinking fund. It must be invested with fidelity and the fund be kept intact. Usually the sinking fund cannot be invested at as high a rate of interest as the bonds bear and there is some loss as a result. Road bonds bearing 5 per cent interest can usually be sold at par while the sinking fund will usually net about 3 or 3-1/2 per cent interest. The total cost of a bond issue will be greater by the sinking fund method than by either of the other methods described.

=Annuity Bonds.=--Annuity bonds are drawn in such a manner that the amount of the payment for principle and interest is the same each year during the life of the bond. When the amount of the issue and the rate of interest has been determined and the amount of the desired annual payment has been determined, the number of years the bonds must run is computed.

This method is convenient in that the amount of the tax to be levied each year remains constant.

=Serial Bonds.=--Serial bonds are drawn so that a uniform amount of the principle is retired each year after retirement starts and the total interest payments decrease each year after the first bonds are retired. The first bond may not be retired for a number of years after the issue of the bonds, but when it once starts retirement proceeds at a constant rate annually.

=Comparison of Methods of Issuing Bonds.=--The relative costs of financing by either of the three methods depends upon the rate of interest in each case and the net rate secured on the sinking fund provided for retiring sinking fund bonds.

For comparative purposes, some typical examples are given in Table 3.

These ill.u.s.trate the differences in total cost of securing $100,000 by each of the three methods at various interest rates.

TABLE 3

TOTAL COST OF A LOAN OF $100,000 FOR 20 YEARS, INTEREST COMPOUNDED ANNUALLY

---------+---------------------------------------+---------+--------- Annual | Sinking Fund Compounded | | Interest | Annually at | | on Bonds +----------+----------------+-----------+ Annuity | Serial |3 per cent| 3-1/2 per cent | 4 per cent| | ---------+----------+----------------+-----------+---------+--------- 4 | $154,431 | $150,722 | $147,163 |$147,163 | $142,000 4-1/2 | 164,431 | 160,722 | 157,163 | 153,752 | 147,250 5 | 174,431 | 170,722 | 167,163 | 160,485 | 152,500 5-1/2 | 184,431 | 180,722 | 177,163 | 167,359 | 157,750 6 | 194,431 | 190,722 | 187,163 | 174,369 | 163,000 ---------+----------+----------------+-----------+---------+---------

=Desirability of Road Bonds.=--In theory the bond method of financing enables the highway authorities to construct a large mileage of roads in a few years and spreads the cost over the period during which the public is being benefited. Better prices are obtained on contracts for a large mileage than for smaller jobs, and the community can receive the benefit more quickly than where construction proceeds piecemeal with current funds. The vital consideration is to insure that the term of the bonds is well within the useful life of the road, and that ample provision is made to maintain the roads during that period.

Under proper restrictions the bond method of financing is to be commended. The bonds are an attractive investment and readily marketable on satisfactory terms.

CHAPTER III

DRAINAGE OF ROADS

=The Necessity for Drainage.=--The importance of drainage for all roads subject to the effects of storm or underground water has always been recognized by road builders, but during recent years constantly increasing attention has been given to this phase of road construction. It is unfortunate that there has in the past been some tendency to consider elaborate drainage provisions less necessary where rigid types of surfaces were employed. It has become apparent, from the nature of the defects observed in all sorts of road surfaces, that to neglect or minimize the importance of drainage in connection with either earth roads or any cla.s.s of surfaced roads is to invite rapid deterioration of some sections of the roadway surface and to add to maintenance costs.

The degree to which lack of drainage provisions affect the serviceability of the road surface varies with the amount of precipitation in the locality and the manner in which it is distributed throughout the year. In the humid areas of the United States, which are, roughly, those portions east of a north and south line pa.s.sing through Omaha and Kansas City, together with the northern part of the Pacific slope, precipitation is generally in excess of 30 inches per year and fairly well distributed throughout the year, but with seasonal variations in rate. In these areas, the effect of the precipitation, both as regards its tendency to lower the stability of soils and as an eroding agent, must be carefully provided against in highway design.

Outside of the areas mentioned above, the precipitation is much less than 30 inches per year and its effect as an agent of erosion is of greatest significance, although in restricted areas there may be short periods when the soil is made unstable by ground water.

=Importance of Design.=--The drainage system for a proposed road improvement ought to be designed with as much care as any other element, and, to do so, a study must be made of all factors that have any bearing on the drainage requirements and the probable effectiveness of the proposed drainage system. The well established principles of land drainage should be followed so far as applicable.

The basic principle of road drainage is to minimize the effect of water to such an extent that there will always be a layer of comparatively dry soil of appreciable thickness under the traveled part of the road. This layer should probably never be less than two feet thick and for soils of a structure favorable to capillary action it should be at least three feet thick. The means employed to accomplish the requisite drainage will be as various as the conditions encountered.

=Surface Drainage.=--The drainage method which is by far the most nearly general in application is that which utilizes open ditches, and the system which employs these ditches is usually referred to as surface drainage. The full possibilities of this method of minimizing the effects of storm water are rarely fully utilized in road construction. Very frequently, deterioration of a road surface is directly attributable to failure to provide adequately for the removal of the storm water or water from the melting of snow that has fallen on the road, or water that flows to the road from land adjacent thereto. Surface water can usually most cheaply and expeditiously be carried away in open ditches, although special conditions are occasionally encountered which require supplementary tile drains. The cross section commonly adopted for roads lends itself naturally to the construction of drainage ditches at the sides of the traveled way, and these are usually the princ.i.p.al dependence for the disposal of storm water.

=Run-off.=--The capacity required of side ditches to insure satisfactory surface drainage will be affected by the amount and nature of the precipitation in the region where the road is built. The annual rainfall in a region may amount to several feet, but may be well distributed throughout the year with an absence of excessive rainfall for short periods, that is, flood conditions may rarely occur. In other areas, the annual rainfall may be comparatively small but the precipitation occurs at a very high rate, that is, flood conditions may be common, or it may be at a low rate extending over a considerable period. These peculiarities must be known before an adequate drainage system can be planned.

It is almost universally true in the United States that precipitation at a very high rate will be for a relatively short duration, and during these short periods, which usually do not exceed thirty minutes, a portion of the water that falls on the areas adjacent to the road and that drains to the road ditches will soak into the soil and therefore not reach the ditches along the road. The extent to which the water is taken up by the soil will vary with the porosity and slope of the land and the character of the growth thereon.

Cultivated land will absorb nearly all of the water from showers up to fifteen or twenty minutes duration; gra.s.s land a somewhat smaller percentage; and hard baked or other impervious soil will absorb a comparatively small amount. Rocky ground and steep slopes will absorb very little storm water.

The surface of the road is designed to turn water rapidly to the ditches, but when the material is the natural soil, there is always considerable absorption of storm water. Surfaces such as sandclay, gravel and macadam do not absorb to exceed 10 per cent of the precipitation during short showers. Bituminous surfaces, brick and concrete pavements, do not absorb an appreciable amount of storm water.

Generally it is best to a.s.sume that if a rain lasts for forty-five minutes or more, all of the water will run off, as the soil will reach a state of saturation in that time. This is not true of deep sand, but is for nearly all other soils.

The ditch capacity needed will therefore depend upon the area drained, the character of the soil, the slopes and the rainfall characteristics of the region, and upon the nature of the road surface.

For a required capacity, the cross section area of the ditch will vary inversely as the grade, because the velocity of flow increases with an increase in the grade of the ditch. If the surface water must be carried along the road for distances exceeding five or six hundred feet, the ditch must be constructed of increasing capacity toward the outlet in order to accommodate the acc.u.mulated volume of water.

The velocity of flow varies not only with the grade, but with the shape of the cross section, cleanness of the channel, the depth of the water in the channel, alignment of the channel and the kind of material in which the channel is formed. It is not necessary to go to great refinement in the design of the side ditches for the ordinary case where the water is carried along the road for only a few hundred feet. The ditches are made of ample capacity by using the commonly accepted cross section for a road, which will be discussed in a later paragraph. But where large areas must be drained by the road ditches, it is desirable carefully to design the side ditches. The basis for that design is too lengthy to be included herein, and reference should be made to a standard treatise on the subject.

=Ordinary Design of Ditches.=--For grades of one per cent or less on roads in the humid area, the bottom of the ditch should be at least three and one-half feet lower than the traveled surface of the road, except for very sandy soil. For grades greater than one per cent, this depth may be decreased one foot, and for grades of four per cent and upward, the depth may be still less. These general rules for depth are susceptible of variation but are believed to be the minimum except in arid or semi-arid climates. It is far better to be too liberal in ditch allowance than to be too conservative. In arid or semi-arid regions, the ditch design will be based on the necessity of providing for flood flow and preventing damage through erosion. Ordinary drainage requirements will be satisfactory with the ditch about one foot deep.