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ºAY 24'56
THE INCREMENTAL METHOD
OF DETERMINING
MOTOR VEHICLE TAx RESPONSIBILITY
An Analysis Developed
For The
Montana Fact Finding Committee
On
Highways, Streets and Bridges
By
Ralph D. Johnson
T-
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Research Engineer
Montana Highway Department
Revised: April, 1956
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The Reason.
One of the main problems faced by any legislature is the equitable allot-
ment of taxes amongst the recipients of benefits provided by the government.
In the matter of distributing the costs of highway construction and maintenance,
this problem is most difficult to solve because of the complex use of the
facilities. Motor-vehicle users not only employ the highways for different
purposes, but also impose different conditions upon its structure, requiring
the improvement of standards in some cases, and contributing to the decline
of existing facilities in others. Because of the complexity of the problem,
the road tax structures in most States, while based on reasonable presumption
and experience, fall far short of the desired goal of equity.
In recent years, highway tax studies throughout the States have sought
to establish a firm basis, or measuring stick, for a reasonable and fair
apportionment of highway costs amongst the users of highways. Different methods
of , analysis have been applied. The most common is probably the gross ton mile
method, which would assign relative responsibility between motor vehicle groups
according to the product of gross weight transported by vehicle miles travelled.
This has the appearance of an equitable solution, since it takes into consideration
the two major factors known to influence road costs ; weight and relative use.
However, the gross-ton mile theory ſailſ, to account for the actual relationship
between weight and road costs and, in fact, is predicated on the assumption that
such a weight cost relationship cannot be accurately determined. It, therefore,
disregards known factors, and ignores the road in the assignment of tax responsi-
bility. Another method of analysis which has been applied is the cost function
method. This approach to the problem groups the different elements of con-
struction and maintenance cost, according to the benefits provided to different
classes of highway-user. Thus, there are "standby" costs which are apportioned
to all vehicles equally; "non-weight-use" costs which are apportioned by relative
use or vehicles miles; and "weight-use" costs which are apportioned to heavy
vehicles by ton-miles. This is certainly a scientific approach to the problem.
However, each detail of road construction does not easily fit a category where its
benefits to one or another class of vehicle are clearcut. Considerable argument
must result from application of the method. Other methods of analysis are like-
wise complicated, and often ignore the effect of the vehicle on the roadway.
Of all the methods applied, one stands out as both scientific and reasonable.
This involves the engineering or incremental approach, and is sometimes called
the method of differential costs. The following general description of the
incremental method is taken from a memorandum to members of the Committee
on Highway Taxation and Finance, Sub-committee No. 1B, of the Highway Research
Board, dated December 1952.
"The salient characteristic of the incremental method, sometimes known
as the method of differential costs, is that it purports to assign motor
vehicle tax responsibility in proportion to the highway costs occasioned by
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vehicles of different types and sizes. The use of the term "incremental"
arises from the fact that most highway costs that are variable with size
of vehicles may be considered as built up from a basic cost in which all
vehicles share, and to which successive increments are added to accommodate
the requirements of vehicles in ascending order of size."
For example: A flexible pavement structure composed of two inches of
plant-mix asphalt, four inches of crushed rock cushion, and twelve inches of
select, compacted sub-base material, would easily support considerable traffic
of loaded two-axle vehicles weighing five tons. State practice may determine
that three inches of plant-mix asphalt with the same supporting structure
is necessary to accommodate the same traffic of eight ton two-axle vehicles.
In making an incremental assignment, the first truck would only pay its
share of the cost of the two-inch mat, since the additional thickness re-
quired for the larger vehicle is of no benefit to it. The second vehicle would
pay its share of the two-inch mat, plus an additional share of the three-inch mat.
Vehicles still larger would be assigned shares of the first two "increments"
plus share of any additional thickness required for their accommodation.
Mr. D. F. Pancoast, in a report titled, "Allocation of Highway Costs in
Ohio by the Incremental Method," makes the following pertinent remark: "It
is important to note that the incremental method is used only for allocating
the motor-vehicle share of highway costs. What that share should be, as
compared to the share to be borne by abutting property, the general govern-
ment, or other beneficiaries of highways, must first be determined by other
means."
The Method
The incremental solution to the problem of allocating responsibility to
motor-vehicle users for the cost of highway facilities is still in the develop-
ment stage throughout the United States. Alt'hough certain concepts have been
fairly well established, there is a wide range of possibilities in applying these
concepts. Certain problems peculiar to each State warrant individual analysis.
The purpose of this report is to describe the basis of a scheme of distribution
of incremental costs which will relate to practical highway building in Montana.
In order to compare this proposition with the most recent developments in
application of the incremental method, a general description of studies per-
formed by other States and agencies follows:
The most advanced thinking to date on the problems involved in making
an incremental analysis is presented in a series of memoranda to members of
the Committee on Highway Taxation and Finance of the Highway Research
Board. Since the Fall of 1951, this Committee has been engaged in developing
a framework for the incremental solution. Mr. D. F. Pancost, a contributing
member to this study, has used much the same framework in developing an
allocation of Highway Costs for the State of Ohio.
The essential method rests on the premise that the structure of a "basic"
roadway can be determined for a given volume range of traffic, that will
accommodate repetitions of axle loading by a defined "basic" vehicle. Four
or five volume classes of highways have usually been chosen. The highest class,
Type A, is the only one assumed to accommodate vehicles imposing repetitions of
the maximum legal axle load. (The use of axle loads as a criterion determining
the need for thicker and more costly pavement develops from recent road tests
which have proven this fundamental axle-load, thickness, relationship for both
flexible and rigid pavement.) Within this volume class, increments of cost
are distributed to intervals of axle loads between the maximum legal and the
"basic" - in Mr. Pancoast's study, 4 kips - as the thickness of pavement
structure, width of surface, width of shoulder, cost of shoulder treatment, etc.
is assumed to decrease as necessary to accommodate load intervals of smaller
magnitude. The engineer using the approach is faced with this problem in
consideration of facilities not actually constructed: What thickness of pave-
ment and type of related structure would be required in this volume class if
traffic were composed of passenger car; only; or, to designate the next highest
standard, if traffic were composed of vehicles imposing no more than 6K axle
load; and so on.
The contributing members to the Highwāy Rºşeārch Board have demonstrated that
their individual judgment, or the judgment of the agency they represent, differs
considerably in answering the problem. Considering passenger cars only, some
engineers are, undoubtedly, influenced by the standards to which high-volume
parkways are constructed. Others are influenced by the standard of construction
which must be applied to combat the effect of the elements. No criticism of the
framework which poses these problems is intended. A rigorous analysis, not sub-
ject to argument and debate at some point, has not yet been devised. However,
a uniform assessment of responsibility to different weight groups of vehicles
will not necessarily follow general adoption of the framework under consideration
by the Highway Research Board. For every difference in judgment as to what
constitutes a "basic" facility for a volume group, a different scale of relative
responsibility will result.
The next highest volume class of facility, designated as Type B, under the
framework of the above analysis, is not considered to accommodate sufficient
repetitions of the maximum legal axle load so that it has an effect on the re-
quired highway structure. Although maximum legal axle loads are considered, they
are charged with the same relative responsibility as the next lowest axle-load
interval. Distribution of cost is made in the same way as for the Type A facility.
Type C facilities are handled in the same mánner. In this case, axle
loads greater than those for which the facility is primarily designed are
charged with the same weight-effect as loads for which the facility is designed.
This progressive reduction of weight charge, as volume accommodation provided
by the structure becomes less, produces a triangular pattern of analysis. A
rectangular pattern, where the full weight-effect of the vehicle is considered
on all facilities, is also possible. However, this does not take into account
the number of repetitions of axle load which is of considerable significance in
design. A structure built to accommodate innumerable repetitions of a ten kip
axle load will also accommodate some limited number of repetitions of an eighteen
kip axle load. The amount of use that a heavy vehicle makes of a low-volume
facility will probably not produce sufficient repetitions of its axle load to fail
the structure before it deteriorates from other cause. Therefore, the full
weight-effect of the vehicle will not influence the structural design of this
facility. At the same time, since design is largely a matter of engineering
judgment, allowance is undoubtedly made for the greater weight-effect of the heavy
vehicle. Since it is impossible to determine, with any degree of exactness, the ex-
tent to which this weight-effect influences structural requirements, the triangular
distribution is more fair than the rectangular, but is definitely lenient towards
heavy trucks. The triangular pattern will be discerned in the Montana analysis.
The distribution which has been described is for pavement cost alone. One
of the essential considerations in this approach is the width of surface required
by a given vehicle type. The defined "basic" vehicle is thought to require
less width of travelling way. The assignment of grading and drainage cost in the
Ohio analysis is based on the ratio of graded structure required to accommodate the
"basic" vehicle to that required to accommodate trucks wider than the "basic"
vehicle. A progressive assignment of these costs by weight is not made. A certain
percent of cost is attributed to the "basic" vehicle; the remainder is shared
alike by all other vehicles.
The Ohio analysis does not treat Type D facilities incrementally. These are
non-surfaced roadways and weight is considered to have no effect in their structural
requirements.
The framework of the Highway Research Board and Ohio solution may be simply
illustrated as follows:
Standards are determined
by construction practices.
Type C Type B Type A
Axle Load 500-1000 WPD 1000-2000 WPD Over 2000 WPD
2", 22' 2' '... 22' º -,6' 22' |
0 - 6K Actual con- / (1)
struction
facility
6' 24' -6'
6K - 10K Actual con- ^ (2)
struction Q *.
facility *\\ §
ºr * s3' 10' 24' -10 ! W!
10K - 14K Actual con- $. (3)
struction Si
/ facility R
Statndards an: « determined |
by engineering judgment: . º
14K - 18K (4)
Actual cor-
stru Et ion
fat-i i ty
Figure 1.
Taking Type A as an example: The basic pavement (1) is charged to axle loads
between 0 K and 18 K; the increment of cost between (1) and (2) is charged to
axle loads between 6 K and 18 K, the increment between (2) and (3), 10 K and
18 K between (3) and (4), 14 K and 18 K. Eighty (80) percent of grading and
drainage costs are charged to 0 - 6 K; 20 percent charged equally to all vehicles
larger than those imposing 6 K. Maintenance is partially distributed by weight
as determined by a multiple corelation and regression analysis; partially to all
vehicles alike. Structures are treated incrementally by matching to above
facilities, and distributing incremental costs in the same manner. Type D high-
ways are not treated incrementally.
When dealing with Type B highways, the upper axle load interval, instead of
reading "10K to 14K", should read "over 10K". By means of the illustration and
example given, it is intended only to show the fundamental framework of analysis
used in Ohio and considered by the Highway Research Board Committees.







Although the above approach to the incremental solution is entirely
scientific, it is not proposed to abide entirely by its framework in the
Montana analysis. One of the reasons a departure is contemplated is the amount
of engineering judgment required to determine basic factors. In addition, the
wide surface width designated for low-volume roadways in this State precludes
consideration of width increment, since this geometric standard is chosen to
accommodate the high speed of passenger cars. It is thought that the controversial
definition of a "basic" vehicle, or "basic" facility can be avoided, and the
solution which will be proposed avoids these definitions. In the Montana proposal,
it is not so necessary to separate and individually describe the benefits of
certain elements of construction cost.
So that the point of view of commercial users of the highways will not be
overlooked in the Montana solution, consideration and study has been given to
a recent report made by the Virginia Highway Users' Association, which in-
corporated both a cost function and incremental analysis designed to test tax
equity in that State. (1)
It is noteworthy that the fundamental approach to the incremental analysis
contained in that report is that of consideration of the actual facilities con-
structed in that State, rather than "mythical" facilities deemed necessary to
meet needs when conditions other than reality exist. A similar "practical" approach
in the Montana solution should prevent contention that an individual engineer's
judgment has resulted in unfair tax allocation to the disadvantage of the
commercial user.
An extensive breakdown of current construction and maintenance costs provides
the basis for the Virginia Highway Users' solution. Elements of construction and
maintenance cost are assigned separately, either as weight functions or general
use functions. Axle loading is used as the weight criterion. Increments for
width, pavement thickness, gradient, structures, and related maintenance, are
assigned to weight-responsible vehicle groups. It is interesting to note that
the potential of a vehicle to impose a given axle load is used in the pavement
thickness assignment.
No special effort is made to relate a class of roadway to a vehicle-group
accommodation, except that the State Class I highways are described as the
predominate truck routes, and Class 2 highways as "mixed traffic" high-volume
routes with a smaller proportion of truck traffic. Much the same standard of
facility is provided for these two classes except for surface which is two feet
wider on Class I, and gradient requirements which are more demanding on Class I.
These differences are attributed to the larger proportion of trucks on Class I,
and comparison of these two facilities produces, first, an increment of width
(1) Testing the equity of Virginia's Motor Vehicle Tax Structure - a Report to
the Commission Established by Senate Joint Resolution Number 48. Sub-
mitted by the Virginia Highway Users' Association, June 1953.
for both surfaces and total graded structure, and, second, an increment of
gradient for construction of the total graded structure. These increments are
exclusively assigned to trucks, and essentially distributed by proportionate
vehicle miles. Differences in surface width between Class II and Class III,
and between Class III and Class IV routes of the Primary System are not considered
attributable to weight or size. These are progressively lower volume routes.
All remaining pavement construction cost and related maintenance cost, for
the Primary System, is distributed by weight-apportioned increments. About 60
percent of the maintenance of pavement on the Secondary System is distributed in
the same way. However, construction cost of pavement on the Secondary System is
not at all attributed to weight or size, presumably because this system is com-
posed chiefly of local rural county roads.
Structures on all systems, primary and secondary, are essentially treated
by weight criteria. The cost of all "basic" facilities, primary and secondary, and
administrative expense is distributed by relative use, or vehicle miles.
At first glance the solution appears to be entirely equitable, in fact to work
adversely for the heavy vehicle. Actually, it is "weighted" in favor of the
heavy vehicle. The authors make much of the distribution of one or another cost
factor entirely to trucks, when the accommodation provided would suggest a more
equitable distribution. Actually, the proportion of costs unfairly distributed
to the heavy vehicle, to the overall construction and maintenance cost. is small.
On the other hand, a "weighting" of the solution in favor of trucks is inherent
in the handling of pavement thickness.
Different types of pavement construction on the several facilities are not
recognized, and pavement cost is made proportional to thickness entirely.
This results in a very high relative standard for "basic" vehicle or passenger car
accommodation. Analysis of non-partisan solutions in other States indicated
the assignment to passenger cars may be as much as ten percent too high. The
lack of consideration of weight effect on the underlying structure tends to
destroy the argument of equitability. Also, although considerable passenger car
mileage must have been travelled on the 40,000 miles of Secondary System by
definition, this mileage is not subtracted when apportioning the cost of the "basic"
facility in the relatively high-cost Primary System.
Class I and II highways only are compared for width increment, when, in
fact, design standards cited call for less surface width on Class III and Class
IV. Partly because of the high relative "basic" pavement on the Primary System,
heavy vehicles are not considered responsible for any element of construction on
the Secondary System, although one-third of that system is hard-surfaced.
A cost function analysis is presented along with the incremental analysis.
The fundamental concepts applied to each are, to a degree, contradictory. In
the cost-function analysis, engineering and administrative costs are defined
as "standby" costs, and argument is presented that these costs should not be
distributed by relative use or vehicle mile criteria. They are apportioned
by registration. In the incremental analysis, all of these costs are apportioned
by relative use. Since the proportions by travel are different than the pro-
portions by registration, (trucks generally travel more miles per vehicle), the
cost function approach favors heavy vehicles in this respect.
There is no reason to divorce concepts applied to the incremental method from
those applied to the cost-function method. An incremental analysis, to consider
all aspects fairly, must incorporate the cost function approach. Some costs
are fairly separated from relative-use or weight criteria, and should be charged
on the basis of vehicle registration. The cost of collecting registration fees
is an example. Payments to related departments and agencies, legal fees, grounds
and buildings, some aspects of planning surveys, etc. bear little relationship
to the relative use of facilities. Beautification and 1andscaping should probably
be charged to passenger cars only.
However, engineering and administrative costs directly related to construction
or maintenance are not different in character from pavement or grading item costs.
If it entails more engineering and administrative expense to construct or maintain
thick pavement than it does to construct and maintain thin pavement, a certain
proportion of these costs may actually be weight functions. The administrative
and engineering expense of constructing and maintaining the "basic" facility is
reasonably distributed by relative use.
In the Montana analysis an approximate distribution of administrative
expense by function will be undertaken. This will be accomplished by a process
of elimination. First, administrative expense in no way related to the relative
use of highways will be separated. Since there are not many costs in this category,
this will not be too difficult a task. Second, "direct" engineering cost of con-
struction and maintenance will be separated. (These costs are generally a fairly
constant proportion of contract or force account construction and maintenance
costs). These costs will be added to other costs of the facility considered,
which will automatically cause them to be distributed incremental 1y. Remaining
administrative costs will be apportioned along with the cost of the "basic"
facility by relative use, or vehicle miles.
Before proceeding with the description of the Montana method, earlier
investigations should be mentioned, which are notable for their contribution
to present-day thinking on the incremental problem. They are as follows:
1. Report of the Interim Committee appointed by His
Excellency, Charles H. Martin, Governor of the
State of Oregon, for a study of the Motor Trans-
portation Act and the fees and taxes paid by the
Road Users for the Highway Facilities provided
by the State of Oregon - January 1, 1937.
2. Public Aids to Transportation, Volume IV, Public
Aids to Motor Vehicle Transportation - Federal
Coordinator of Transportation, 1940. (Often
referred to as The Eastman Report).
Although other analyses have been made by the incremental method, both in
the United States and in Canada, contributing to detail and structure, these
have not been studied in detail since the fundamentals applicable to present
studies have been "sifted" from the respective reports by Mr. Pancoast, Mr.
St. Clair and others.
The Montana Solution
The Montana solution is being prepared under the auspices of the Montana
Fact Finding Committee on Highways, Streets, and Bridges, in cooperation with
the State Highway Department. The method of analysis is essentially designed
to reflect present construction practice and engineering viewpoint in the State.
As has already been stated, certain problems of highway construction and
finance are peculiar to each State. An incremental analysis designed to fit
the needs of the heavily populated eastern states would not, in all probability,
result in a reasonable allotment of highway cost if applied in Montana.
Montana's peculiar problems arise from its topography which embraces extremes
of very flat to very mountainous terrain; from its lack of densely populated
centers which results in few high-volume traffic arteries; from its many
attractions for tourists which results in a relatively large number of out-of-state
vehicles on its highways; from the predominance of two major industries, farming
and mining, which results in greater load applications on low-volume highways;
from its situation with respect to other States and the mountain barrier. High-
way costs, especially high in mountainous terrain, must be distributed among
relatively few domestic highway users.
What, then, is desired, is a reasonable allotment of highway costs that
will bear a scientific relationship to the use of highways by different
vehicles imposing different conditions on the highway structure. It has been
amply demonstrated that no method of analysis can rigidly fix responsibility
for all elements of highway cost.
The basic premise of the Montana method of incremental allotment of highway
costs is that each standard of facility constructed on a homogeneous highway (1)
system is a "stage" in the construction of the next highest standard of
facility. This premise is supported from a historical point of view by con-
sideration of the manner in which highway systems have developed. Essentially, it
has been a process of improving existing facilities to accommodate a more demanding
traffic picture.
(1) Each homogeneous highway system will be treated separately under the
headings: Federal Interstate, Primary, and Secondary, without regard for
administrative jurisdiction. Local rural roads and city streets are ex-
cluded from the determinations which follow. These systems will be studied
separately. See the end of this text for further discussion.
- 9-
As population centers have grown and as the efficiency of motor vehicles
has been improved, it has been necessary to build connecting roadways to
ever increasing geometric standards to accommodate more vehicles at
higher speeds. As the use of highways for the transportation of freight
has increased, it has been necessary to devise stronger structures to
accommodate the heavy vehicle. New facilities may or may not have been
built on top of existing roadbeds, but, regardless, they constitute
improvement of existing facilities. The process still continues.
It is desirable to relate this process to the present program of
highway construction which is expected to provide adequate highway
facilities in this Staue within the next 20 years. Relative responsibility
between motor vehicle users will be developed for a total highway product
that will fit their needs. Although construction costs applied will be
those estimated for the 20-year program, the relative responsibility so
developed can be applied to a shorter range objective. The validity of
the solution should last until a totally different pattern of highway
needs becomes apparent.
Instead of defining a "basic" vehicle, or a "basic" facility as such,
a base mean standard will be chosen, as actually constructed in the State,
which will be relatcd, by engineering judgment, to the accommodation of a
specific upper limit of axle loading.
Consider the applicability of the basic premise to structural re-
quirements. Except on special purpose roads such as parkways, it is
usual to employ the highest structural standards on highways where there
is sufficient composite traffic to produce considerable repetitions of
the maximum legal axle load; and to relate, in design theory, the
thickness of pavement to the magnitude of this load.
It is usual to employ lower structural standards for less traffic,
because, where fewer repetitions occur, this same load is not considered
to have the same significance. It does, perhaps, have the significance
of loads of lesser magnitude which are produced in sufficient numbers
to govern the reduced structural requirements.
Lower standards are employed for still smaller volumes of traffic.
These standards may be similarly dictated by related axle loads which are
produced in numbers by including not only loads of the related magnitude
alone, but also all loads of larger magnitude operating, because of
fewer repetitions, with less weight effect.
This is the usual concept applied to the incremental solution, and
it is not unrelated to fact. It is obvious that a paved road designed
to withstand innumerable repetitions of a 6,000 pound axle load will
withstand some limited number of repetitions of the maximum legal load
of 18,000 pounds (which will not influence its design as a load of that
magnitude).
- 10 -
It is also a concept that can be applied to the increments of an
integrated road structure. It is not difficult to visualize each
increment as being related to a portion of the maximum load using the structure,
and, in addition, , as being related to loads of such a magnitude as to
require the thickness of increment, were it a separate road structure.
Thus each increment would be a charge against that 1oad and against that
portion of the maximum 10ad.
The basic premise of the Montana solution combines the two applications
of the concept by stating, in effect, that a given standard of roadway,
whose structure is determined by a related load, may exist by itself, or
as part of a roadway built to higher standards.
It is possible to derive an empirical relationship between traffic
volume and the magnitude of the repeated axle load. In answer to a
questionnaire circulated by Mr. G. P. St. Clair, Chairman of the
Committee on the Incremental Solution of the Highway Research Board, engineers
from several eastern States contributed to this determination. An approximation
of the results of their combined judgment is provided by the formula
L = .3WV, where L is the maximum repeated load in thousands of pounds, and
V is the traffic volume in vehicles per day.
Applying this formula to the several volume classes of roadway
designated by the Automotive Safety Foundation for the construction of rural
highways in Montana (1), the following relationships are established.
Maximum Traffic Maximum Axle k
Volume .3 VVT Load
(VPd) (Kips)
400 6 6
1000 9.5 10
2000 13. 4 14
4000 kºk 19. O 18
* The last column is rounded for practical purposes.
** Considered a reasonable upper limit of two lane volume accommodation.
At traffic volumes which are less than 200 to 400 vehicles per day,
there is a distinctive change in the type of surfacing recommended by the
Automotive Safety Foundation. For this volume of traffic, and for larger
volumes, weight dependent bituminous or portland cement concrete surfaces of
intermediate or high type will usually be employed; for smaller volumes, low
cost bituminous surfaces are contemplated. Although axle load is still an
important factor in incurred cost on this surface type, it does not operate
with the same uniformity of effect. It is for this reas on that load-volume
(1) See Table III.
- 11-
relationships are not listed for accommodations 1ess than 200-400 vehicles
per day.
A reasonable conclusion develops from the foregoing considerations:
that each volume of composite traffic will produce repetitions of a determinato
axle load in sufficient numbers to dictate structural requirements. The
analysis which follows will demonstrate that the geometric standards
required by each traffic condition are also reasonably related to the same
order of axle loads, if axle load is assumed to be a fair measure of a
vehicle's size and weight.
For this purpose, consider two two-1ane highways, each built to
geometric standards that will allow an average operating speed of 50-55
mphºk to be maintained at all times, but each accommodating a different
type of traffic. One carries vehicles of the general type of passenger cars,
pickups, panel and stake trucks, whose gross weights will not exceed 5
tons, and whose widths are not more than 7 feet. The operating characteristics
of these vehicles are assumed to be the same as those of passenger cars.
The other carries the usual composite traffic found on Montana's rural
highways, with 12 percent commercial vehicles whose maximum widths are 8
feet. The standard of gradient, a maximum of 3 percent, is indicated by the
high operating speed. For the determination of relative geometric standards
that are influenced by average conditions, a thirty percent restricted
passing sight distance is assumed typical of the general terrain encountered
in this State. !
Using data from the Highway Capacity Manual, it is found that the
practical capacity of the light vehicle facility is 522 vehicles per hour,
i.e. , 600 vehicles per hour reduced by the sight distance factor. On the
other hand, the practical capacity of the heavy vehicle facility is only
324 vehicles per hour, since each commercial vehicle is equivalent to 6
passenger cars on a 3 percent grade with 30 percent restricted sight distance,
(284 # . 14 x 284 x 6 = 522). It is obvious that each facility does not
provide equivalent accommodation for its respective traffic. However,
if sight distance is further restricted on the roadway with 1 ight vehicles,
so that the resulting factor is 324 + 600, parity is reached. Thus 75
percent restricted sight distance on the facility accommodating light
vehicles with a 3 percent grade is equivalent to 30 percent restricted
sight distance on the facility accommodating heavy trucks with a 3 percent
grade.
Now consider limiting geometric standards that must be introduced for
economic reasons on sections of the two roadways. Where desirable grades
cannot be constructed, operating speeds will be compromised. Engineers will
increase gradient to a limiting condition where the maximum possible capacity
of a facility is realized. As grades are steepened, operating speed is re-
duced, and capacity is increased, until the optimum capacity of any two-lane
highway is achieved at 30 mph. Both lanes are full and a11 traffic is pro-
ceeding at that speed. Grades on the roadway carrying the 5-ton vehicles may
be increased to 6 percent for optimum capacity since these trucks are capable
of sustaining 30 mph on such a grade (1). However, although capacity can be
* Considered desirable in Montana.
(1) Highway Capacity Manual, Fig. 20.
- 12-
increased on the facility carrying the heaviest trucks, optimum capacity
can never be realized since these vehicles cannot sustain 30 mph even on
3 percent grades. (1) Because reduction in grade for parity in this
consideration would cause a disproportionate practical capacity, and because
the cost of obtaining better sight distance and that of obtaining better
gradient, which are the two variables, are in the same order of magnitude,
it is sufficient to assume equivalence between the 6 percent and 3 percent
grades on the two facilities with their respective traffic.
Let us extend the comparison to other geometrics. Adequate shoulders render
a service capacity-wise and safety-wise by providing a place to park disabled
vehicles out of the traffic stream. It is apparent that the two facilities
being examined must provide similar accommodation for the largest vehicles they
carry, if the same relative effect on capacity and safety is to result.
Because lighter vehicles are able to park closer to the lip of a fill slope,
6-foot shoulders will provide almost the same accommodation for 7-foot wide
stake trucks that 10-foot shoulders will provide for 8-foot wide combinations.
The following diagram will illustrate.
K— 7'—ºk 3'---- "— l'H'- —- l'Hº- 8"—-i- 3'---- 8' —-
E O- O F $E? F
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ow Rºss-e SS 2-ze ---
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—J
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O
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6' 12" —- -w | 2' -I-
Thus, when capacity is used as a criterion, the following geometric differences
occur between the accommodation provided for vehicles of 5 tons gross vehicle
weight, and those provided for the heaviest trucks.
Vehicles of 5 -Tons GVW Heaviest Vehicles
Passing Sight Distance 25% 70%
Gradient 6% 3%
Shoulders 6' 10'
(1) Climbing Lane Theory and Road Test Results by T. S. Huff and F. H. Scrivner,
of the Texas Highway Department. Vehicle Climbing Lanes, Highway Research
Board Bulletin 104, 1955, p. 10, Fig. 18.
"Any traffic variable or any roadway condition that prevents vehicles
from moving safely at a speed of 30 miles per hour lowers a roadway's
capacity." - Highway Capacity Manual.

- 13-
In addition to the geometric standards already considered, there are
those that are not so easily analyzed for proportionate weight assignments.
Stopping sight distance, for example, is influenced by many factors.
Relative speed is a 1arge consideration in this respect. In flat terrain,
on good alignment, the law imposes a speed differential between passenger
cars and trucks by limiting the latter to 45 mph, whereas cars may be ex-
pected to travel at speeds near to 70 mph.
In mountainous terrain, the opposite extreme, gradient and relatively
poor alignment impose their own restrictions. Trucks are forced to proceed
slowly and passenger car speeds are considerably reduced on ascending grades.
Both types of vehicle tend to travel at the same speed on descending grades.
For reasonable economy, design speed tends to approach this average operating
speed. Shorter stopping sight distances are employed. It is in this terrain
that the highest order of cost is incurred by sight distance requirements,
and it is with this terrain that we shall begin an analysis.
Since minimum sight distance requirements will apply to the downgrades,
and since all vehicles travel downgrade at approximately the same speed,
standards are largely influenced by the braking performance of different
types of vehicles. At a typical speed of 40 mph, passenger cars and "very
light vehicles," as defined in a recent publication by the Bureau of Public
Roads, will be able to stop in 198 feet (1), (driver stopping distance), plus
a downgrade factor. The heaviest 5 and 6 axle combinations will be able to
stop in 335 feet, plus a downgrade factor. If this factor is 50 feet on a
typical 6 percent grade, designers would be able to employ a 248-foot
stopping sight distance for light vehicles, and a 385-foot stopping sight
distance for heavy vehicles. Without consideration of the height of line of
sight, this produces an assignment of 35.6 percent of the cost of providing
stopping sight distance to trucks over 5 tons gross vehicle weight. However,
the height of a driver's eyes purchases sight distance on vertical curves
(but not to a large extent on horizontal curves). Therefore, the above per-
centage of weight assignment should be reduced. Although vertical control is
likely to be imposed more often, each horizontal control is likely to
incur more relative cost in steep sidehill cuts and fills. For this reason
a 30 percent weight assignment is considered reasonable.
There is little justification for charging heavy vehicles with any
of the costs incurred to provide adequate stopping sight distance in level
terrain. Passenger cars at 70 mph require the same braking distance that
heavy trucks require at 50 mph. Since sight distance is much less costly
in this case, a 20 percent overall average weight assignment is reasonable.
This might be considered applicable to the in-between topographic condition
described as rolling terrain.
There is little use trying to derive the exact order of costs that are
assignable to heavy vehicles considering curvature as a separate geometric
standard. Justification for a difference of a degree or so in their presence is
found in superelevation practices. Where maximum super rates cannot be used on
(1) Braking Performance of Motor Vehicles. - Published by the Bureau of
Public Roads, Washington, D. C. 1954, p. 108.
-14-
grades where heavy vehicles might slide to the inside shoulder, curvature is
restricted and additional cost incurred. The tracking width of heavy vehicles
requires the widening of some curves of 7 degrees and over. For these
reasons, and because curvature is closely allicd to the provision of sight
distances, the ordcr of weight-assignable costs is assumed to follow that
of other geometric standards.
Now let the order of geometric differences that have been attributed
to vehicles heavier than 5 tons be examined:
Vehicles of 5 Tons GVW Heaviest Vehicles
Passing Sight Distance 25% 70%
Gradient 6% 3%
Shoulders 6' 10'
Non-Passing Sight Distance & .80 (525) = 420' 5.25"
* Approximate assignment in rolling terrain.
From Table III, Design Standards of Rural State Highways, it is apparent
that the order of geometric difference listed above is the same order of
geometric difference that has been recommended between two-1ane facilities
carrying 200-400 vehicles per day and those carrying 2000-4000 vehicles per
day. The latter is related structurally to 18,000-pound axle loads;
geometrically to vehicles which will impose an 18,000-pound axle load. The
former is related structurally to 6,000-pound axle loads; geometrically to
vehicles which will impose a maximum 6,000-pound axle load. Therefore,
geometric differences may be equitably assigned along with structural
differences as each relates to a traffic condition and as each, in turn,
relates to the same range of axle loads.
Thus, there is logically established a "base mean standard" for this
analysis, which is that facility designated by the Automotive Safety
Foundation to provide adequate accommodation for 200-400 vehicles per
day. Its structure and geometrics are related to innumerable repetitions
of a 6-K axle load which are created not only by loads of that magnitude
alone, but by all loads of greated magnitude using the structure. It may
exist as a structure by itself, or as part of a structure accommodating more
weight and more traffic volume.
Before proceeding further, it is well to review and consider those
elements of roadway structure whose cost will be wholly or partially
assigned by weight in this incremental analysis. This is best accomplished
by considering what differences occur between the base mean standard and
highest type two-lane highway. There will be differences in: pavement
structure; type of pavement; thickness and type of base; and width and
treatment of shoulders. It will be noted that there is no difference in
roadway surface width.
The Automotive Safety Fouridation and engineers of the State Highway
Department have been influenced, in choosing geometric standards for this
State, by certain characteristics of motor vehicle operation peculiar to
Montana. Although there are night-time speed limits, and zones of limited
- 15-
:
speed, there are no further restrictions on the speed of passenger
cars in this State. Trucks are limited to 45 mph. As a result, average
operating speeds are 5-10 mph higher than the national average. To provide
safety and comfort at high expected speeds, a twenty-four foot width
of travelling surface is the absolute minimum to be constructed on any highway.
The people of Montana desire this accommodation. Engineers feel entirely
justified in giving it to them as a result of the savings in maintenance
and replacement cost that will be realized. The edges of plant-mix
pavement, not subjected to heavy loads, will not ravel as they have done
in the past, and Montana's highway engineers have found certain decided
advantages to the exclusive use of plant-mix rather than road-mix or
penetration-type pavement. Although the weight factor provides justification,
State highway men are insistent that the 24-foot width of travelling
surface on low-volume facilities is an accommodation which is essentially
provided for passenger vehicles.
The differences in pavement structure; type of pavement; and thickness
and type of base are obviously weight-determinable elements. It has been
demonstrated that a four to six ratio of shoulder width is a legitimate
weight assignment. However, the structural soundness of highway shoulders
needs further consideration. In this respect, the results of the WASHO
road test are significant. By effecting containment of materials in the
whole underlying road structure, structural 1y sound, well-consolidated
shoulders add considerable stability to the paved travelling surface
itself. Some engineers in the Highway Research Board have recommended extending
full thickness of pavement to the shoulder for this purpose. It is
obvious that heavy vehicles parking on the shoulder will require a stronger
shoulder structure. It is for these reasons that the treatment of shoulders
contemplated on large volume facilities is legitimately considered a size
and weight requirement.
At this point it may be mentioned that it is only those geometrics
that have a proven relationship to weight that will be charged along
with related structural costs. The costs of obtaining and marking
right-of-way; other costs of controlling access; the beautification and
provision of recreational facilities, etc. will be subtracted from the
weight apportionment.
Other geometrics and differences in structural cost are related by
volume accommodation to their respective axle loads as follows:
Axle Load Interval Volume Accommodated
(Kips) (VPD)
– 6 200 - 400
6 - 10 400 - 1000
10 - 14 1000 - 2000
14 - 18 2000 - 4000
—16-
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According to the basic premise, the 200-400 roadway is included in all
higher volume roadways as a "stage" in their construction. Therefore, the total
mileage of the 200-400 VPD facility considered in the analysis is the mileage
of all two-lane facilities accommodating 200 WPD upwards in any homogeneous highway
system. (1) The total mileage of the 400-1000 facility is the mileage of all two-
lane facilities in the system accommodating more than 400 WPD, and so on. The
estimated cost per mile of constructing each standard will be determined from Auto-
motive Safety Foundation and State Highway Department cost determinations. The
differences in cost per mile between standards will be incrementally assigned to
vehicles in accordance with the axle loads they impose. The total cost of the
weight-assigned structure in a system will be later determined by multiplying
vehicular responsibility per mile of any standard by the number of miles of that
standard figured as above. The details of this distribution and reintegration will
become apparent as the discussion continues.
Vehicles will be grouped under different types by Gross Vehicle Weight
classification. The maximum potential axle loading of each Gross Vehicle Weight
class will be determined. Each axle load will be first applied to its own interval
and related roadway increment according to its potential. It will then be applied
to each increment below its own requirement, assuming the proportions of the maximum
axle load in the interval related to that increment. The load on each axle, as
applied in each interval, (or related increment), will be multiplied by the vehicle
miles that the related Gross Vehicle Weight class travels on the facility in the
system which includes that increment. This establishes a relative measure of use
of the interval. Mileage projected to mid-point of the program period will be used.
Table I illustrates the distribution. The increment of cost per mile of construction
that is required to accommodate each increasing axle load interval is developed
as follows:
DEVELOPMENT OF INCREMENTAL COSTS
Volume Class Construction Cost Increment of Axle Load
(V. P. D.) Per Mile Cost Per Mile Accommodated
($) ($) (Kips)
200 - 400 30,000
400 - 1000 45,000 15,000 6 - 10
1000 - 2000 56,000 11,000 10 - 14
2000 - 4000 66,000 10,000 14 - 18
/
a ‘f tºſ d # !
This cost will then be apportioned by kip-axle-miles to axles using the
increment. All of the figures are for illustrative purposes only.
(1) See footnote, page 9.
- 17-
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The use of kip-axle-miles as described on the following page
is now modified. Investigation of the traffic actually transported
by facilities in this State has disclosed that the number of total
axle miles of travel determines the magnitude of repeated axle
load as it relates to traffic volume accommodated. The relationship
is a smooth logarithmic curve and A = a log L # b, where A is the
number of axle miles and L is the repeated load. Thus the efficiency
of a load is defined, dependent on the number of axle miles that
loads of that magnitude travel on a roadway. The axle miles travel
by each load will be multiplied by a factor equal to N
a log L # b
where N is the number of axle miles travelled by a11 loads of the same
magnitude. This has the effect of assuring that load and axle miles
have the same effect on cost. We are indebted to Mr. D. F. Pancoast
of Ohio for suggesting that some such determination should be made.
APPORTIONMENT OF INCREMENTAL COSTS
Increment Cost
Volume Group Annual Increment of per Thousand
Accommodating Kip-Axle Miles Cost Required Kip-Axle-Mile *
Axle Load Interval (x 1000) * ($) (Cents)
200 - 400 50, 500,000 Developed by Different Process
400 - 1000 4,800,000 15,000 . 31250
1000 - 2000 1,500,000 11,000 . 73333
2000 - 4000 900,000 10,000 1. 11111
* From Table I.
The use of kip-axle-miles, or thousand-pound axle miles, is a new concept
in this analysis. It has the effect of distributing the responsibility within
each interval by weight, so that vehicles near the borderline of decreased
responsibility are not pennlized in favor of vehicles near the borderline of
increased responsibility. The use of potential axle loads, to be determined
from a vehicle's registered weight, is considered a better criterion of its
responsibility in the requirement of higher-standard roadways than the use of
axle loads actually imposed which might be derived from loadometer data. The
public cannot be expected to underwrite uneconomic operation.
It will be noted that to this point only the weight responsibility of
vehicles imposing more than 6 K axle load may be determined. The argument
supporting the use of kip-axle-miles stated that this criterion avoided
penalty near the borderline of weight responsibility. To extend this argument
further, the weight-charge against each larger axle load should increase on
a fairly uniform curve. This is both desirable and reasonable for tax
allocation. And it is practical to develop a uniform curve of increasing
weight responsibility by the following procedure. Having determined the relative
responsibility per kip-axle-mile for axle load intervals with divisions at the
upper limits of 10 K, 14 K, and 18 K, it is possible to plot the responsibility
so determined on axes representing these loads. The curve so developed, may
be mathematically extended to cut the 6 K axis and establish a weight-cost
at that point. This cost will be the charge per kip-axle mile for some un-
defined increment of construction accommodating axle loads between 2 K and 6 K.
It will be applied to this interval in Table I. Although the foregoing
responsibility is not rigidly defined, it is a reasonable development, avoiding
penalty to vehicles on the borderline of responsibility, and in keeping with
the trend of increasing weight responsibility.
It is not necessary or practical, to define weight responsibility for
vehicles with 2 K or less axle load. Gross Vehicle Weight classification does
not apply below 6000 pounds. Vehicles with axle loads of 2 K or less travel
75 percent of all mileage on our highways. By neglecting weight-responsibility
- 18-
© 2 ） _ \ __| |_| |_| |_| |_| |_| \___| |_| \_ — _* !_!
L_| ，_| |_| \__ \__ \_
in this bracket, the effect, by the method of elimination developed in this analysis,
will be to transfer any weight-cost chargeable to this group to the cost of the
undefined basic highway required by all axle loads, which will be distributed in
the ratio of their annual travel by vehicle-miles. (Non-weight-use costs.)
Vehicles with axle loads to and including 2 K will bear the largest share of the
cost of the basic highway: ergos they will bear the largest share of weight-cost
so transferred.
Multi-lane facilities, assumed to be necessary to properly accommodate any
volume in excess of 4,000 VPD, will be handled as follows. Each additional two
lanes will be considered, structurally, as equivalent mileage of the highest-type
two-lane facility. This mileage will be multiplied by the unit responsibility of
each Gross Vehicle Weight class for this standard, as developed from Table I. The
sum of these charges is then the "weight-charged" portion of the total cost of the
multi-lane highway. The remaining portion, the cost of medians, right-of-way,
control of access, etc. will automatically fall in the cost of the residual, or
basic, highway which will be charged to all groups by vehicle miles.
Where an additional climbing lane is provided, because operating speeds are
reduced by the presence of slow trucks, its cost will be deterinined and distributed
separately. State Highway engineers have pointed out that these additional lanes,
although required where heavy vehicles are present, are not exclusively provided
for their accommodation. If passenger cars and lighter trucks were willing to
slow down, their provision would not be necessary. The accommodation is largely
to maintain the operating speeds desired by operators of the lighter vehicles.
The ideal solution to the problem of distributing the cost of these climbing
lanes would be a solution in which the effect of the slow-moving vehicle on
decelerating traffic would create a "weighted" assignment of cost against them.
Fortunately, such a solution is easily derived from a practical and provable
standpoint, and as easily applied.
Highway capacity studies have derived the equivalence of trucks in terms of
passenger cars on various grades. As an example: if, on a 7 percent grade, of a
given length, it is found that one truck, of a given type and weight, has the
same effect on decelerating traffic as 10 passenger cars; and if it is found
that the same truck on level grade is equivalent to 2 passenger cars, it has five
times the effect in decelerating traffic than it is already paying for in the
incremental, distribution. This truck and passenger car will then be charged
with the additional cost of the climbing lane at a ratio of 5 to 1.
Having determined to this point the unit responsibility of each Gross Vehicle
Weight class for each weight-apportioned increment of roadway in a system, it is
now possible to sum all of these costs to obtain the part of the total cost
assigned by weight. For example: Commercial trucks in the 34,000 to 36,000
Gross Vehicle Weight class have axles which travel 140,000 thousand kip-axle-
miles on the standard accommodating 14 to 18 kips at 1.11111 cents per mile of this
standard constructed; 260,000 thousand kip-axle-miles on 10 - 14 K at 0.73333 cents
per mile of construction; 400,000 on 6 - 10 K at 0.31250 cents; 600,000 on 2 - 6 K
- 19 -
*
©_ &_| \___| ，_| ，__ (_| |_| |_| \__， |_| |_| |_| |_| |_| |_| |_ _ _| ，_|
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at 0.07321 cents. There are 400 miles of 14 - 18 K, which includes equivalent
mileage of four-lane facilities; 1500 miles of 10 - 14 K, which includes the
400 miles that this standard is a "stage" of the 14-18 K accommodation; 2500
miles of 6 - 10 K which includes the 1500 miles of higher standard; and 4,000
miles of 2 - 6 K, which includes the 2,500 miles of all higher-type facilities.
Then, the weight charge assigned to this vehicle group is (1400 x 1.11111) 400 #
(2600 x 0.73333) 1500 # (4000 x 0.31250) 2500 # (6000 x 0.01321) 4000 Or
$8,364,250. The sum of weight charges assigned to each vehicle group is the
total weight-cost of the constructed system. All figures used in the above
example are illustrative only.
To the weight-cost, determined as above, will be added the cost of additional
climbing lanes which will be separately assigned; of beautification, landscaping,
waysides, picnic sites, historical markers, and other recreational facilities
with appropriate signs, which will be separately assigned to passenger cars. The
result will be subtracted from the total cost of all construction on the system to
leave a residual which must be on the cost of the basic element of construction
which is required and used by all vehicle groups alike. The cost of the basic
highway will then be distributed to tie vehicle groups in proportion to their use
of the highway system, or, in other words, be vehicle miles.
This residual, which is the cost of the basic system structure since the
analysis is performed separately by systems, will include the cost of sections
of unsurfaced highway in the Secondary System. The resulting assignment of some
cost to heavy vehicles for roads which they may not actually use is supported
by the following considerations. First, it must be remembered that the Secondary
System does not include local rural roads which represent 75 percent of all rural
mileage. The Secondary System is designed to "feed" the Primary and Interstate
Systems. Although heavy vehicles do not make use of unsurfaced feeder routes
at this time, they may do so in the future, and are reasonably considered
responsible for this "stage" in the construction process. From a point of view
of economics, all State roads generate the product which is carried by heavy
commercial vehicles on primary highways. To the extent that this is true, most,
if not all, classes of highway user derive benefits from all roads, and should be
charged with some proportion of their cost. Therefore, allocation of the cost of
the basic structure in the main feeder system by relative use of the system as a
whole is fair and just, even though the basic structure includes some roads which
heavy commercial vehicles do not use.
Maintenance Cost.
The method of elimination developed in the handling of construction costs may
be extended, practically, to the allotment of maintenance costs, so that it will not
be necessary to consider each element of cost and the resulting benefits to one or
another vehicle group. Each facility considered as a "stage" in the incremental
solution has its prototype on the present highway system. Essentially, the process
- 20-
| | | _ |_| ，__ (_） |_| |_| |_| |_| |_|| []） ） ） _ __） (_） ） ） ）
will involve comparison of prototypes of the different standards for average
annual maintenance cost. Each set of standards so compared will be similarly
situated, so far as possible, with respect to topography, weather, and type of
soil, The average annual cost of maintaining each prototype over a period of
years will be computed, All costs which do not at all relate to the use of
facilities will be subtracted in the derivation of this figure. These will
include :osts of landscaping, beautification of campsites, historical markers
sidewalks and foot paths, etc. Costs not arising from the normal usage of
highways such as the costs of major slide removal and washout repair, channel
changes, riprap, etc., will be subtracted. The remaining average annual cost
of maintaining each standard of facility will be multiplied by a factor so that
the total cost of maintaining all standards will equal a sum estimated to meet
maintenance expenditures on the system for the program period. This latter
figure will be exclusive of costs of landscaping, beautification of campsites,
historical marker 3, etc. which will be developed for the same period and
separately charged to passenger cars. The total maintenance cost of each standard
for the program period will then be added to the construction costs developed
for cach ståndard, before increments of cost are calculated for distribution
to the several weight groups. Increments of maintenance cost chargeable by weight
may or may not develop. The "residual" will automatically become the cost of
maintaining the basic facility, and will be distributed by relative use.
Cost of Highway Structures
The cost of constructing major highway appurtenances, such as bridges over
20 feet in length and underpasses, will be allotted by the same method as the
cost of constructing the roadway itself is allotted, although a separate
incremental distribution will be necessary. For simplicity, underpasses will
be considered as bridges on the upper highway. The average cost per foot of
length of constructing a bridge that will "match" each standard of roadway
will be determined. For example: H-20 loading is considered for the design
of bridges accommodating over 2000 vehicles per day; H-15 loading for volumes
between 200 and 2000 WPD; H-10 loading for less than 200 VPD. Here the
weight relationship between different volume accomm oiation is apparent in the
way it influences designers to select these different standards. Differences in
width will result because of differences in shoulder width. Since the shoulder
requirement is attributable to weight and the effect of heavy vehicles on traffic,
so must the differing bridge widths be considered.
After costs are determined for each standard of facility, differences or
increments of cost per foot of length will be computed. These increments will
be distributed to each Gross Vehicle Weight class of vehicles of different types,
using the same kip-axle-mile figures employed in the roadway analysis, substituting
unit costs per foot of structure for unit costs per mile of roadway.
A unit cost figure for the 2 - 6 K axle load interval will be developed in the
same way. The unit vehicular responsibility in each axle load interval will be
multiplied by the length of related structure in the system. A total weight-
-21 -
distributed cost will be developed, and when this is subtracted from the total
cost of structures in the system, the residual will be the cost of the "basic"
structure, which will be distributed by relative use.
Tunnels are the only major structures which remain to be considered. The
increments of cost in their construction will not be in the same ratio as
average increments developed for bridges and underpasses. Because of the small
number of these facilities that may be built, a separate incremental distribution
of their cost will not be worthwhile. As an end result of the analysis, a chart
will be set up showing the total of all charges against each Gross Vehicle Weight
class of vehicle under the different type headings. By multiplying each cost by
the same index, the cost of tunnels and miscellaneous costs not otherwise con-
sidered will be covered. In other words, the relative scalo will not be in-
fluenced by their inclusion or exclusion, but a figure will be secured for the
program period.
Administrative Costs
The proposed method of handling administrative costs has already been
described. A minimum of selection is anticipated, and the usual method of
elimination will be used. Those costs which can be directly related to the
construction of various standards of facilities, e.g., a fixed proportion of
construction cost for engineering, will be added to other construction costs
before the incremental distribution is made. Thus, some of these costs will be
apportioned by weight. Costs definitely not related to highway use, such as the
costs of motor vehicle registration, legal costs, payments to related departments
and agencies, etc. etc. etc., will be separated and charged in proportion to the
number of vehicles registered. The remaining administrative costs, considered as
Contributing to construction and maintenance, will be distributed by relative
use or vehicle miles.
The Secondary System
The argument and analysis which has been presented is based primarily on
ständards devised for the State Primary System. However, it can be shown that the
same relative difference in accommodation is provided between corresponding volume
classes on the Secondary System. Economy dictates that the geometrics of
secondary highways be somewhat lower than the geometrics of primary highways,
c1a : sification for classification. Structural standards are also slightly lower,
because heavy vehicles do not make as much use of secondary facilities. The
200-400 VPD a cºommodation is still the "basic mean standard" and relates to
repetitions of a 6k axle load. The 400-1000 VPD accommodation is the highest volume
class of roadway to be constructed on this system. and relates to innumerable
repº titions of a 10 K axle load. Axle loads larger than 10 K will be charged
with the same responsibility, since vehicles imposing these loads do not use the
syste a to the extent they use the Primary, and facilities are not specifically
designed for their accommodation. Again, this produces the triangular distribution,
lenient towards the heavy vehicle. Weight responsibility will be extended down-
wºx dº to 2 K by the mathematics developed for the Primary System. Residual
cost will be developed and distributed in the same way.
- 22-
Structures, maintenance, and administration will be handled similarly. Table IV
shows the design standards that the Automotive Safety Foundation have developed
for the State Secondary System.
Federal Interstate System
Table II shows the design standards designated by the Automotive Safety
Foundation for the Rural Interstate System. It will be noted that volume
classifications are not used. However, the essential equivalence between
standards selected for this system and those designated for roadways carrying
more than 2000 VPD in the Primary System will be realized from comparison of
Table II and Table III. Therefore, increments of weight cost developed for the
Primary System will be employed in the distribution of cost of Interstate high-
ways. The System will be handled separately, and separate mileage figures of
vehicular use will be derived. Residual costs, structures, maintenance, and
administration will be apportioned in the same manner as on the Primary System.
Local Rural Roads and City Streets
In a State where the motor-vehicle share of the cost of providing adequate
highway facilities must be spread over relatively few domestic users, it is of
paramount importance that the cost burden of local rural roads be distributed
in a fair and equitable manner. The Montana Fact Finding Committee on Highways,
Streets and Bridges is cooperatively engaged with the Montana Agricultural
Experiment Station in a study to determine the relative benefits derived from
highway development by users and other beneficiaries of highways. Together with
this incremental analysis, the user portion of the cost of local rural roads will
be allocated.
Although commercial vehicles use this system very little, these roads,
nevertheless, generate the product that the commercial vehicle carries on Primary
highways. However, the farmer, who is the main user, does realize a particular
benefit from these facilities. There is a tie, in this repsect, with the concept
that the local rural road provides a large service to adjacent property. If the
agencies studying the problem do find and recommend that the services rendered
property is a substantial consideration in the apportionment of local rural road
costs, and that property should be taxed accordingly, then the farmer may be
considered to have been charged with his especial responsibility. The remaining
cost of local rural roads would be reasonably apportioned equally to all vehicles
registered in the State.
City streets will be studied separately. Some consideration will be given
to zoning ordinances, and the type of enterprise a given street is intended to
serve. This will affect the method used to distribute the motor vehicle uger's
share of the cost of these facilities. For example: In industrial zones where
the street is built to service heavy vehicles, an incremental, (weight |
distribution), of cost would be in order. In commercial zones, an incremental
distribution might be made to include the weight of axles of the heaviest vehicles
23
that commonly use the related streets. It does not appear that the incremental
method should be applied to residential streets. A study is under way by the
State Planning Survey, under the auspices of your Committee to develop the
proportionate use of different classes of city streets. Where the incremental
analysis is used, it is intended to apply the concepts and method developed
in this report with appropriate modification.
General
The advantages of the proposed method of incremental analysis, compared with
other methods, may be enumerated as follows:
(l) The number of considerations and assumptions is reduced to
a minimum. The load-structure relationships on which the
analysis is based are easily visualized, being related to
actual construction.
(2) No controversial definition of a basic vehicle or basic
facility is necessary.
(3) Once the premises are accepted as reasonable and just, it is
impossible to prejudice the solution against any class of
highway user.
(4) The solution is valid until the whole pattern of highway needs
is changed.
(5) The proportionate responsibility developed is validly fitted to
a program of "stage construction."
(6) Structures may be "matched" to the facility they serve, and the
same method of incremental distribution applied to them.
(7) Maintenance costs may be related to facilities which will actually
be constructed, and to prototypes which are now being maintained
on the present highway system. A minimum of definition of benefits
is involved, and no prejudice possible.
(8) Some administrative cost may be distributed incrementally.
A pictorial outline of the methology of the Montana solution is presented
in Figure II. Although the problem is complex, and copious argument must be
produced to describe and support the allotment of each element of cost to the
motor vehicle user, it can be seen that the distribution itself is relatively
simple. Once the premises of the solution are accepted as reasonable, little
is left to an individual engineer's judgment. The analysis is completely
without prejudice to any class of user on the highways. Careful consideration
of the details discloses that where one of the premises apparently works to the
disadvantage of a particular vehicle type, an offsetting advantage is produced
24
by another consideration. Equitability is achieved where exactness can not
be determined. It is on this basis that support of the solution is solicited
from all interested groups. Constructive criticism will be appreciated. No
figures have, as yet, been applied to the method so that it is impossible to say
what relative costs will result. All data necessary for the solution, however,
has been secured by your Fact Finding Committee. {
One additional problem remains to be considered as it relates to the incremental
solution. This concerns the allotment of Federal-aid funds to the highway
construction program. The form of analysis herein described takes no account of
this source of revenue, in developing the scale of relative responsibility by
which vehicles should be taxed. This is entirely as it should be. The relative
responsibility of any vehicle group is not affected by the source of income
which builds the highways. When the cost responsibility of the vehicle groups
for a system is developed, and if moneys to build the system come from sources
other than the motor-vehicle user, the whole curve of relative costs for that
system should be adjusted accordingly. This may be accomplished by subtracting
the "outside" income from the cost of the "basic" roadway structure in the system,
which is apportioned to all vehicle groups on the same basis. Thus, the weight-
responsibility curve is not destroyed. If the Federal Tax Structure obviously
recovers moneys from given weight groups out of proportion to the defined
responsibility, an adjustment can be made by subtracting the moneys so recovered
from the amount this State would collect from the same weight groups, and
"crediting" the lesser amount of Federal-aid to the cost of the "basic" structure.
This report is still in a preliminary stage. It is addressed to members of
the Montana Fact Finding Committee on Highways, Streets, and Bridges; to members
of the Incremental Advisory Committee; to the people of this State; and to
all interested groups. Written comments should be addressed to Mr. Wm. L. Hall,
Executive Director of the Montana Fact Finding Committee. The following are
members of the Incremental Advisory Committee : Mr. Scott P. Hart, State Highway
Engineer; Mr. Mort Flint, District Engineer, Bureau of Public Roads; and Dr.
E. R. Dodge, Dean of Civil Engineering, Montana State College. The analysis
has been prepared by Ralph D. Johnson, Research Engineer, Montana Highway Department,
under advisement of the Incremental Advisory Committee.
25
MONTANA FACT FIND ING COMMITTEE FIGURE II
ON
HIGHWAYS, STREETS, AND BRIDGES
|NCREMENTAL SOLUTION
DISTRIBUTION OF HIGHWAY COSTS TO MOTOR VEHICLE USERS
ON
PRIMARY AND INTERSTATE HIGHWAY SYSTEMS
ALL VEHICLES ..º.
# Example MiLEAGE of vehicle IMPostNG
14-18 K AXLE LOAD FOR DISTRIBUTING COST OF
INCREMENT NUMBER ( i) EQUALS MILES TRAVELLED
ON ROADWAY BUILT TO HIGHEST STANDARD. FOR
DISTRIBUTING INCREMENT NUMBER (2) ADD MILES
TRAVELLED ON ROADWAY OF STANDARD WHICH i NCLUDES
|OOO – 2000 VPD, 4 K INCREMENT NUMBER (2). FOR INCREMENT NUMBER
(3) ADD Mt LES ON ROADWAY whl CH IN CLUDES
INCREMENT, FOR INCREMENT NUMBER (4) ADD
2OOO VPD PLUS, 18K MILES ON ROADWAY WHICH INCLUDES INCREMENT.
For BASIC structure, ALL MILEAGE ON SYSTEM.
(l) |NC PROVIDES FOR 4 OOO VPD 8, 8K -— CHARGED TO || 4– 18 KIP AXLES # WEIGHT COSTS —
PROPORTIONED BY
(2) INCREMENT PROVIDES FOR 2 OOO VPD 8, 14 K - C HARGED TO |O– 18 KIP AXLES
5 T ON S GVW º : THOUSAND-POUND
-— CHARGED TO 6- 18 K P A XLES
(3) Increment, PRovides For | OOO VPD 8, O K | PS 6- 18 K AXLE MILES OF
ŽSXSºS2XYYXZWº%2S2NZX2S2S2S2S2$%s - i. 2. ^ - TE: f {} e---> 7, ſº T - PART LY CHARGED TO 2 – 18 K|P
(4) PAVED STRUCTURE PROVIDES FOR 200-400 VPD a 6 KIPs . . TAXLEs, REMAINDER TO RESIDUAL USE
-----, T-I I PR A –– ! R BASIC COSTS-
! Basic Roadway structure, OVIDES B sc --~~~~ 5 § | CHARGED TO ALL
6K 4 K | | - ! ,----- t C U VEHICLES BY
--~~- : Accommodation FOR ALL MOTOR VEHICLES - 4 L VEHICLE MILES
f i |
ACCOMMO DATION
~º. 2OO–40O VPD, 6K
400-IOOO VPD, IO K
-— HALF FOUR LANE
H|GHWAY


MONTANA FACT FIND ING COMMITTEE
O N
HIGHWAYS, STREETS, AND BRIDGES
AUTOMOTIVE SAFETY FOUNDATION, CONSULTANTS
DESIGN STANDARDS FOR RURAL INTERSTATE SYSTEM ROUTES
Toble II
Multi- Lone 2 - Lone
Terroin Closs F | 0 | Rolling Mountd in F| Of Rolling Mountd in
Design Speed — M.PH 7 O 6 O 50 7O 6 O 5 O
Operating Speed — M.PH 50-55 45-50 4 O-45 5O-55 45-50 4O-45
Sur foce Type Type I – High
Lone Width - Feet | 2
Shoulder Width - Feet | O 8 – O (D 4 | O 8-| O (D 4
Shoulder Type Full Width - Bifurninous Sedl and Cover
Maximum Curvature – Degree 3 5 7 3 5 7
* * ſ
Moximum Grodient – Percent 3 4 (2) 5 3 4 (2) 5
Stopping Sight Distance — Feet 7OO 525 4OO 7OO 525 4OO
(3) Min "/. Possing Sight 15O O' - | O |O sº
Distonce Avoilable Per Mile | 800' Nof Applicable - - | O
*Maximurn | Percent of |OO % 6OO 9 OO 8 OO
@º OHV Applicable 8O %, | OOO | 200 |3CO 55 O 8 OO 68 O
.. . Pistance F-355. Per Per Per 495 69 O 52 O
ossenger | Avoilable ©
Vehicles) 4O % Lone Lone Lone 42O 58 O 275
Minimum Medion Width — Feet (5) 20 4. Nof Applicable
* * º 4. º 2OO' Without Fronto qe Roods |50' Without Fronto qe Roods
Minimum Right of Woy Width — Ft. 3OO' With Frontoge *šoj: 25 O' Wº. #Jnº. %.
- Re d 1956 DHV Exceeds 30 O Portici Control of
Control of Access Required Ağ'Érº. Whº: 1956 DHV is Less #. 3OO.
Looding H 2.0 – S | 6 ( )
- Brid |OO Ff t- Len q th - Full A h Rood Width (Including Usobie Shoulders
(7) Bridges | Cleoronce Width — Feet É Over ibó'F. fºLºgif"ººh ãºt º tº' 3 Fº §§ º B or rier ºrbs
Vertico; Cledronce – Feet i 6
p º º o All Moin Line Crossings With 2 or More Tracks All Single
Railroad Separations All Railroad Crossings Track Moln Line Crossings with 1956 DHV Over 200.
Highwoy Sepdrations All Cross Rodds and Ploces of Access (9)
(D Wherever Feosible 8' Shoulders Should Be Provided in Mountainous Areas
Grodients in Rugged Terrain of 6 Percent, And in Unusual Conditions of 7 Percent, Moy Be Provided.
(3) Passing Sight Distance in Mountainous and Heavy Rolling Topography Shall Be The Highest Obtainoble With Reasonoble Economy
Determine Need For Truck Climbing Lones
(3) Equivotent Passenger Cor Copacities To Be Adjusted For Percent of Commercial Vehicles ond Grodes.
(5) Medion Width of 40 Feet Desirable
(6) For Portial Control of Access, Intersections of Grade (Public Roods ond Private Drives) Shall Not Exceed Two Per Side Per Mile, 1956 ADT Shall Not Exceed
50, and Access Rights Between Such lintersections Are Acquired.
(7) Sfondards Apply to Interstate Highway Bridges, Over passes, and Under posses. Stondords For Crossroad Overpasses ond Underpasses Sholl Be Those for the
Appropriate Protective Devices Sholl Be Provided at all Railroad Grade Crossings
(9) All Cross Rodds and Places of Access Where Full Control of Access is Required All Intersections With 1956 ADT of 50 or More on Sections Where Portiol
Control of Access is To Be Provided
* Crossrood.
Copacity And lysis Will


MONTANA FACT FIND ING COMMITTEE
O N
HIGHWAYS, STREETS, AND BR DGES Toble III
AUTOMOTIVE SAFETY FOUNDATION, CONSULTANTS
DESIGN STANDARDS FOR RURAL STATE HIGHWAYS
(OTHER THAN INTERSTATE SYSTEM ROUTES)
Multi – Lone 2 - Lone
1976 ADT GD (D Over 2000 | OOO to 2000 4 OO to |OOO 2OO ! O 4OO Under 20 O .
Terro in Closs Flot |Rolling | Mtn. Flot |Rolling| Mtn. Flat Rolling| Mtn. Flat Rolling | Mtn. | Flat Rolling| Mtn. Flot |Rolling | Mtn.
Design Speed — M.PH 7O 6 O 5 O 7 O 6 O 5 O 7 O 6O 5 O 7 O 6 O 5 O 6 O 5 O 4 O 6 O 5 O 4 O
Operoting Speed – MPH 50–55 |45–50 |4O-45 |50–55 45–50 |40–45 45-50 45-50 || 4 O-45 45-50 45-50 || 4 O-45 45–50 4O-45 |35–40 45-50 | 40-45 || 35-40
Surface Type Type I – High Type 2 – Inter mediate Type 3- Low —-
Lone Width – Feef | 2
Shoulder Width — Feet I O | 8-10 (2) 4 | O 8-10 (2) 4 8 8 | 4 8 | 8 4 6 6 4 4 4 4
Shoulder Type Bituminous Seol Ond Cover Grove
Maximum Curvofure – Degree 3 5 7 3 5 7 3 5 7 4 6 9 6 9 | 2 6 9 | 2
(3) Maximum Grodient – Percent 3 4 6 3 4 6 3 4 6 4 5 7 5 6 7 5 7 7
(3) Stopping Sight Distance–Ft. 700 525 | 400 || 700 || 525 | 400 600 475 350 | 600 475 350 475 350 275 475 350 275
§º . # 1000 | 1200 || 300 H.H.H.
Nof Applicable
(Equivolent Sight Distance Per Per Per
Possenger | Avdiloble 99 || Lone | Lone | Lane | *** | *ē9 || 939
Vehicles) 4 O 42 O 58O 275
s : - -- (5) 200' Without Frontoge
Min Right of Woy width-Feet | 4: 3OO' With Frontoge Rds. | 5 O | OO
Loc ding H-2O — S- || 6 H H-15 — S-12
Bridges | Ciecrance width — Feet (6) F- 3O + 28
Verf icol Cie or once – Feef | 6 -- | 4
: - - - - - - On Moin Line Crossings With 6 or More Troins Per Doy or Exposure -
(?) Railroad Separations All Main Line Crossings Foctor of IO,OOO or More Not Required
(D Multi-Lone Highway Required Where o Two-Lane Highway Will Not Provide Copacity for 1976 ADT
(2) Wherever Feasible 8' Shoulders Should Be Provided in Mountoinous Areos on Highways Carrying Troffic in Excess of 2000 ADT.
(3) Grodient and Sight Distance Standards for Volumes of Over 2000 ADT in Mountainous or Heavy Rolling Topography Sho || Be the Highest Obtoinoble with Reason-
able Economy. Capacity Analysis Will Determine Need For Truck Climbing Lone on Two-Lane Roods.
Equivalent Possenger Cor Capocities To Be Adjusted for Percent of Trucks on d Grodes. -
Portiol Control of Access Required for All Multi-Lone Construction on New Locofion. Minimum Medion Widih of 20 Feet in Flat and Rolling Terrain and 4
Feet in Mountainous Terroin. Wider Medion Widths Should Be Provided Wher ever Fe Osible.
Under 80 Feef in Length Full Approach Roodwoy Width. Over 80 Feet in Length Approach Povement Width Plus 3 Foot Offset from Borrier Curbs.
Appropriate Protective Devices Shall Be Provided of All Railrood Grode Crossings Where Exposure Foctor (Troins Per Day X ADT) 3000.
§
3.

MONTANA FACT FINDING COMMITTEE
O N
HIGHWAYS, STREETS, AND BRIDGES
AUTOMOTIVE SAFETY FOUNDATION, CONSULTANTS To ble IV
DESIGN STANDARDS FOR SECONDARY HIGHWAYS
|976 A D T 400 to IOOO (D 2O O to 4 O O | O O to 2 O O 5 O to |OO 25 to 5 O Under 25
Terro in Clo SS Flo i | Rolling | Mts Flat Rolling| Mts Flot Rolling| M is Fict Rolling | Mts Flo f | Rolling| Mts Flot Rolling M is
Design Speed – MPH 6O 5 O 45 5 O 45 4 O 45 4 O 35 4 O 3 O 25 4 O 3 O 25 4 O 3O 25
Sur foce Type * Low "ºne. LO w "ºne. sº Course sº Course || Grove -*"…..
Sur foce W d th — Fee f 24 24 24 24 24 22 24 24 22 24 24 22 22 22 2O 2 O 2O 2 O
Roodwo y Width — Feet 32 32 28 3 O 3O 26 28 28 26 24 24 22 22 22 2O 2O 2 O 2 O
Maximum Cur voture – Degree 5 7 |O 7 |O | 2 | O | 2 | 7 |2 22 4 O |2 22 4 O | 2 22 4 O
Moximum Grodient- Per Cent 5 6 7 5 6 7 5 6 7 5 7 S 5 7 9 5 7 |O
Stopping Sight Distance — Feet: 475 35 O 315 35 O || 3 |5 275 315 275 24 O || 2 75 2 OO || |65 || 275 || 2 OO |65 || 275 2O O 65
Maximum Right of Way Width-Fi |2O |OO |OO 66 66 66
Lodding H2O – S 6 H|5 – S 12 H|5 H 15 H |O H|O
Bridges Cle or Width — Feet 28 26 26 26 24 24 24 22 22 22 2 O 2O
Verticol Cledronce-Ft. | 4 | 4 |4 | 4 | 4 |4
Rollrood crossing Protection | ######"...:"siº'Aſſº"; º'bī‘‘’” “”
3.
Use Design St and ords for Ruro | S to te Highways When 1976 ADT Exceeds IOOO
in Built - up Suburb on A red s Use Munic pol Street St on dords
ill
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