----------------------+-----------------------+-----------+---------- | | Tractive | Tractive | |Resistance |Resistance Type of Surface | Condition of Surface | in lbs. | in lbs.
| | per ton | per ton | | 10 miles |12.4 miles | | per hr. | per hr.
----------------------+-----------------------+-----------+---------- Asphalt | Good | 20.4 | Asphalt | Poor | 22.6 | 25.5 Wood block | Good | 24.2 | 25.3 Brick block | Good | 24.6 | 26.6 Granite block | Good | 40.3 | 45.75 Brick block | Slightly worn | 25.1 | 28.0 Granite block with | | | cement joints | Good | 25.5 | 30.2 Macadam, water bonded | Dry and hard | 23.3 | 25.8 Macadam, water bonded | Fair, heavily oiled | 35.9 | 38.7 Macadam, water bonded | Poor, damp, some holes| 36.3 | 41.6 Tar macadam | Good | 25.7 | 28.0 Tar macadam | Very soft | 36.8 | 38.7 Tar macadam | Many holes, soft, | | | extremely poor | 52.4 | 60.6 Cinder | Fair, hard | 27.5 | 30.6 Gravel | Fair, dusty | 30.4 | 33.0 ----------------------+-----------------------+-----------+----------
[Ill.u.s.tration: Fig. 8]
=Effect of Grades.=--Grades increase or decrease the resistance to translation due to the fact that there is a component of the weight of the vehicles parallel to the road surface and opposite in direction to the motion when the load is ascending the hill and in the same direction when the vehicle is descending. In Fig. 8 _W_ represents the weight of the vehicle, acting vertically downward, _w_ is the component of the weight perpendicular to the road surface and _W_{2}_ is the component parallel to the road surface.
_W_{2}_ = _W_ tan _THETA_.
tan _THETA_ = 0.01 per cent of grade.
_W_{2}_ = 0.01 _W_ per cent grade.
_W_{2}_ = 0.01 2000 per cent of grade, for each ton of weight of vehicle.
Hence _W_{2}_ = 20 lbs. per ton of load for each one per cent of grade.
The gravity force acting upon a vehicle parallel to the surface on a grade is therefore 20 lbs. per ton for each one per cent of grade and this force tends either to r.e.t.a.r.d or to accelerate the movement of the vehicle.
Let _F_ = the sum of all forces opposing the translation of a vehicle.
_F = f_{r} + f_{i} + f_{p} + f_{a} + f_{g}_ (1)
where
_f_{r}_ = rolling resistance of road surface.
_f_{i}_ = resistance due to internal friction in the vehicle.
_f_{p}_ = resistance due to impact of the road surface.
_f_{a}_ = resistance due to air.
_f_{g}_ = resistance due to grade, which is positive when ascending and negative when descending.
All of the above in pounds per ton of 2000 lbs.
Let _T_ = the tractive effort applied to the vehicle by any means.
_T_ >= must be greater than _F_ in order to move the vehicle.
By an inspection of (1), it will be seen that for a given vehicle and any type of road surface, all terms are constant except _f_{a}_ and _f_{g}_. _f_{a}_ varies as the speed of the vehicle and the driver can materially decrease _f_{a}_ by reducing speed. _f_{g}_ varies with the rate of grade. For any vehicle loaded for satisfactory operation on a level road with the power available, the limiting condition is the factor _f_{g}_. If the load is such as barely to permit motion on a level road, any hill will stall the vehicle. Therefore, in practice the load is always so adjusted that there is an excess of power on a level road. If draft animals are employed the load is usually about one fourth of that which the animals could actually move by their maximum effort for a short period. With motor vehicles, the excess power is provided for by gearing.
If it be a.s.sured a load of convenient size is being moved on a level road by draft animals, there is a limit to the rate of grade up which the load can be drawn by the maximum effort of the animals.
Tests indicate that the horse can pull at a speed of 2-1/2 miles per hour, an amount equal to 1/8 to 1/10 of its weight, and for short intervals can pull 3/4 of its weight. The maximum effort possible is therefore six times the average pull, but this is possible for only short intervals. A very short steep hill would afford a condition where such effort would be utilized. But for hills of any length, that is, one hundred feet or more but not to exceed five hundred feet, it is safe to count on the draft animal pulling three times his normal pulling power for sustained effort.
The limiting grade for the horse drawn vehicle is therefore one requiring, to overcome the effect of grade, or _f_{g}_, a pull in excess of three times that exerted on the level.
A team of draft animals weighing 1800 lbs. each could exert a continuous pull of about 1/10 of their weight or 360 lbs. If it be a.s.sumed that the character of the vehicle and the road surface is such that _f_{r}_ + _f_{i}_ + _f_{p}_ + _f_{a}_ = 100 lbs. per gross ton on a level section of road, then the gross load for the team would be 3.6 tons. The same team could for a short time exert an additional pull of three times 360 lbs. or 1080 lbs. For each 1 per cent of grade a pull of 20 lbs. per ton would be required or _f_{g}_ for the 3.6 tons load would be 72 lbs. for each per cent of grade. At that rate, the limiting grade for the team would be fifteen per cent.
If, however, the character of the vehicle and the road surface were such that _f_{r}_ + _f_{i}_ + _f_{p}_ + _f_{a}_ = 60 lbs. per gross ton on a level section of road, the gross load for the team on the level would be 6 tons, and the limiting grade 9 per cent.
The above discussion serves to ill.u.s.trate the desirability of adopting a low ruling or limiting grade for roads to be surfaced with a material having low tractive resistance and the poor economy of adopting a low ruling grade for earth roads or roads to be surfaced with material of high tractive resistance.
It may be questioned whether horse drawn traffic should be the limiting consideration for main trunk line highways, but it is certain that for a number of years horse drawn traffic will be a factor on secondary roads.
In the case of motor vehicles, excess power is provided by means of gears and no difficulty is encountered in moving vehicles over grades up to 12 or 15 per cent, so that any grade that would ordinarily be tolerated on a main highway will present no obstacle to motor vehicles, but the economy of such design is yet to be investigated.
=Energy Loss on Account of Grades.=--Whether a vehicle is horse drawn or motor driven, energy has been expended in moving it up a hill. A part of this energy has been required to overcome the various resistances other than grade, and that has been dissipated, but the energy required to translate the vehicle against the resistance due to grade has been transformed into potential energy and can be partially or wholly recovered when the vehicle descends a grade, provided the physical conditions permit its utilization. If the grade is so steep as to cause the vehicle to accelerate rapidly, the brakes must be applied and loss of energy results. The coasting grade is dependent upon the character of the surface and the nature of the vehicle. In the cases discussed in the preceding paragraph, the coasting grades would be five per cent and three per cent respectively. For horse drawn vehicles then the economical grades would be three and five per cent, which again emphasizes the necessity of lower grades on roads that are surfaced than on roads with no wearing surface other than the natural soil.
The theory of grades is somewhat different when motor vehicles are considered, since it is allowable to permit considerably higher speed than with horse drawn vehicles before applying the brakes and the effect of grade can be utilized not only in translating the vehicle down the grade, but also in overcoming resistances due to mechanical friction and the air. On long grades, a speed might be attained that would require the use of the brake or the same condition might apply on very steep short grades. There is at present insufficient data on the tractive resistance and air resistance with motor vehicles to permit the establishing of rules relative to grade, but experience indicates a few general principles that may be accepted.
If a hill is of such rate of grade and of such length that it is not necessary to use the brake it may be a.s.sumed that no energy loss results so far as motor vehicles are concerned. Where there is no turn at the bottom of the hill and the physical condition of the road permits speeds up to thirty-five or forty miles per hour grades of five per cent are permissible if the length does not exceed five hundred feet and grades of three per cent one thousand feet long are allowable. It is a rather settled conviction among highway engineers that on trunk line highways the maximum grade should be six per cent, unless a very large amount of grading is necessary to reach that grade.
=Undulating Roads.=--Many hills exist upon highways, the grade of which is much below the maximum permissible. If there are grades ranging from 0 to 4 per cent, with a few hills upon which it is impracticable to reach a grade of less than six per cent, it is questionable economy to reduce the grades that are already lower than the allowable maximum. It is especially unjustifiable to incur expense in reducing a grade from two per cent to one and one-half per cent on a road upon which there are also grades in excess of that amount. The undulating road is not uneconomical unless the grades are above the allowable maximum or are exceptionally long or the alignment follows short radius curves.
=Safety Considerations.=--On hills it is especially desirable to provide for safety and curves on hills are always more dangerous than on level sections of road. Therefore, it is desirable to provide as flat grades as possible at the curves and to cut away the berm at the side of the road so as to give a view ahead for about three hundred feet. Whether a road be level or on a hill, safety should always be considered and the most important safety precaution is to provide a clear view ahead for a sufficient distance to enable motor vehicle drivers to avoid accidents.
[Ill.u.s.tration: Fig. 9.--Types of Guard Rails]
=Guard Railing.=--When a section of road is on an embankment, guard rails are provided at the top of the side slope to serve as warnings of danger, and to prevent vehicles from actually going over the embankment in case of skidding, or if for any reason the driver loses control. These are usually strongly built, but would hardly restrain a vehicle which struck at high speed. But they are adequate for the protection of a driver who uses reasonable care. A typical guard rail is shown in Fig. 9, but many other designs of similar nature are employed. At very dangerous turns a solid plank wall six or eight feet high is sometimes built of such substantial construction as to withstand the severest shock without being displaced.
Trees, shrubs and the berms at the side of the road in cuts are particularly likely to obstruct the view and should be cleared or cut back so far as is necessary to provide the proper sight distance.
=Width of Roadway.=--For roads carrying mixed traffic, 9 feet of width is needed for a single line of vehicles and 18 feet for 2 lines of vehicles. In accordance with the above, secondary roads, carrying perhaps 25 to 50 vehicles per day, may have an available traveled way 18 feet wide. Those more heavily traveled may require room for three vehicles to pa.s.s at any place and therefore have an available traveled way 30 feet wide. Greater width is seldom required on rural highways, and 20 feet is the prevailing width for main highways.
=Cross Section.=--The cross section of the road is designed to give the required width of traveled way, and, in addition, provide the drainage channels that may be needed. In regions of small rainfall the side ditches will be of small capacity or may be entirely omitted, but usually some ditch is provided. The transition from the traveled way to ditch should be a gradual slope so as to avoid the danger incident to abrupt change in the shape of the cross section. The depth of ditch may be varied without changing to width or slope of the traveled part of the road as shown in Fig. 10.
[Ill.u.s.tration: Fig. 10]
=Control of Erosion.=--The construction of a highway may be utilized to control general erosion to some extent, particularly when public highways exist every mile or two and are laid out on a gridiron system, as is the case in many of the prairie states. The streams cross the highways at frequent intervals and the culverts can be placed so as effectually to prevent an increase in depth of the stream. This will to some extent limit the erosion above the culvert and if such culverts are built every mile or two along the stream, considerable effect is produced.
Where small streams have their origin a short distance from a culvert under which they pa.s.s, it is sometimes advisable to provide tile for carrying the water under the road, instead of the culvert, and, by continuing the tile into the drainage area of the culvert, eliminate the flow of surface water and reclaim considerable areas of land.
Erosion in the ditches along a highway can be prevented by constructing weirs across the ditch at frequent intervals, thus effectually preventing an increase in the depth of the ditch.
Wherever water flows at a velocity sufficient to produce erosion or where the drainage channel changes abruptly from a higher to a lower level, paved gutters, tile or pipe channels should be employed to prevent erosion.
=Private Entrances.=--Entrance to private property along the highway is by means of driveways leading off the main road. These should always be provided for in the design so as to insure easy and convenient access to the property. The driveways will usually cross the side ditch along the road and culverts will be required to carry the water under the driveway. Driveways that cross a gutter by means of a pavement in the gutter are usually unsatisfactory, and to cross the gutter without providing a pavement is to insure stoppage of the flow at the crossing. The culvert at a driveway entrance must be large enough to take the ditch water readily or it will divert the water to the roadway itself. Generally end walls on such culverts are not required as in the case of culverts across a highway.
=Aesthetics.=--Much of the traffic on the public highways is for pleasure and relaxation and anything that tends to increase the attractiveness of the highways is to be encouraged. Usually the roadside is a ma.s.s of bloom in the fall, goldenrod, asters and other hardy annuals being especially beautiful. In some states wild roses and other low bushes are planted to serve the two-fold purpose of a.s.sisting to prevent erosion and to beautify the roadside. In humid areas trees of any considerable size shade the road surface and are a distinct disadvantage to roads surfaced with the less durable materials such as sand-clay or gravel. It is doubtful if the same is true of paved surfaces, but the trees should be far enough back from the traveled way to afford a clear view ahead. Shrubs are not objectionable from any view-point and are to be encouraged for their beauty, so long as they do not obstruct the view at turns.
CHAPTER V
EARTH ROADS
Highways constructed without the addition of surfacing material to the natural soil of the right-of-way are usually called earth roads. But if the natural soil exhibits peculiar characteristics or is of a distinct type, the road may be referred to by some distinctive name indicating that fact. Hence, roads are referred to as clay, gumbo, sandy or caliche roads as local custom may elect. In each case, however, the wearing surface consists of the natural soil, which may have been shaped and smoothed for traffic or may be in its natural state except for a trackway formed by the vehicles that have used it.