Economic evaluation involves the assessment of the economic worth of a project in order to ensure the optimal use of scarce economic resources. It involves the quantification of economic benefits and costs, as opposed to financial income and expenditure. Benefits are compared with costs on a marginal basis, i.e. relative to the null alternative. A project is regarded as justified if the benefits exceed the costs, regardless of who pays and who benefits.

Benefits are normally derived from a reduction in road user and maintenance costs relative to those incurred on the null alternative. Road characteristics which lead to cost and quality optimised models can be described by user related costs on a road, the " Vehicle Operating Costs" ( VOC). Vehicle operating costs consist of cost components like petrol, tyre, maintenance and depreciation costs. 'VOC' are a function of the riding quality of the roads on which the user travels. While the normal differences in evenness of paved roads have only a slight or even negligible effect on individual vehicles, heavy traffic loads have a considerable influence on the total sum of vehicle operating costs, a situation which, however, is seldom encountered under Namibian traffic circumstances. The vehicle operating costs do, however, strongly increase on unpaved roads with bad riding qualities and high roughnesses, even for relatively small traffic numbers. It is therefore important to know the relationship between vehicle operating costs and riding quality of a road surface in order to establish a cost and quality optimised maintenance model. This relationship is changing from place to place, thus indicating its dependence on local conditions. To achieve meaningful results, an attempt will be made to acquire the essential 'VOC' data for Namibian conditions.

Vehicle operating costs on unpaved roads with a poor riding quality are considerable higher than on roads with good riding quality. This can be illustrated by the following example [35]. The reported findings indicate that operating busses on the poorest class of investigated unpaved roads entails the following additional costs over and above the cost on level, paved roads:

- Petrol: increases by 20%, depending on speed and topography;
- Tyres: increases by 100%, depending on the type of gravel;
- Maintenance: increases by 40%, depending on vehicle age;
- Total: increases by 40%.




Due to the fact that currently only little Namibian 'VOC' data exists, it will be required for any 'VOC' study to make use of the 1985-RSA model which, again, is based on the World Bank "Brazil model". The ' National Transportation and Road Research Institute' of the CSIR in South Africa is busy with a research project to develop a specific South African 'VOC' model which can also be applied to Namibian conditions which. At the present moment the Department of Transport of Namibia has not got the means to collect the required 'VOC' data and to implement any research project in this regard on its own. Thus it will not be possible that a comprehensive 'VOC' study can be done in the framework of this thesis. For the time being the South African model can be used with confidence as a preliminary model for Namibia. Where there is reason to believe that different 'VOC' results can be expected, the South African model can be accordingly adjusted. Considering the fact that any future Namibian ' VOC' model will be based on different international user cost studies it will be worthwhile to give a summary of the major 'VOC' models which have been established to date.

The impact of road performance on its users has been studied for considerable periods [36]. But it was until the 1970's when the World Bank started to examine seriously the impact of surface conditions like roughness and geometric variables on vehicle operating costs whereby the first studies concentrated on geometrics like gradeline and alignment only. The basis of these studies were the estimation and modelling of relationships between road construction and maintenance and vehicular use through the collection and analysis of a wide range of pavement performance and 'VOC' data bases. The major survey data of the four main 'VOC' models are described in table 21 [36]:




|                                     VEHICLE OPERATING COST STUDY |
| ITEM              |    KENYA     CARIBBEAN      INDIA     BRAZIL |
| Vehicle Classes   |     5           4           3           7    |
| Survey Sample     |                                              |
| (Vehicles)        |    289         68         939      1.675     |
| Survey Period     |                                              |
| (Years)           |      2          2           3           4    |
| Size of Routes    |                                              |
| monitored (km)    |  9.300       1.000     40.000      36.000    |
| Range of Design   |                                              |
| Variable          |  Min Max    Min Max    Min Max    Min Max    |
|                   |                                              |
| Roughness (IRI)   |  2,8 12,4    3,3 24,1   4,6 19,0   2,7 20,0  |
| Rise and Fall     |                                              |
| (m/km)            |    15 70        8 82      1 60      10 50    |
| Curvature         |                                              |
| (deg/km)          |    1 50       90 1.040   1 1.200      6 294  |
|                   |                                              |
| Largest Truck     |                                              |
| (GVM tons)        |    40           12          18         40    |
| Bus types         |     1           None          1         2    |

The objective yardstick for the riding quality ( roughness) of a road is the Quarter Car Index 'QI' and the International Roughness Index ' IRI'. Both were used in the " Brazil Study". QI has been derived from a single measuring wheel to establish the riding quality of a pavement. It is an " Average Rectified Slope" (ARS)-measure with arbitrary units of 'counts/km', and is based on an early reference simulation of a " Response Type Road Roughness Measuring System" (RTRRMS). QI was based on the readings taken from a particular piece of hardware as operated on paved roads in Brazil. QI can be considered as an earlier version of IRI. Although the original definitions of QI are difficult to apply with confidence in many cases, the data from the "Brazil Study" indicate that for all practical purposes, QI can be considered to be IRI with different units and an offset. IRI is equivalent to the ARS computed using a reference mathematical RTRRMS for a standard speed of 80 km/h. It is a mathematical property of the profile of a single wheel track [37]. The world wide tendency is going into the direction to use rather the IRI in place of the older QI or the PSI ( Present Serviceability Index)-values. The relationships between these three riding quality values are calculated as follows:

QI = (92,63 - 56,39 ln PSI)*0,0769
PSI = e(1,63-0,0173*QI) [52]
QI = 31,96*LDI+3,04 'LDI' = "Linear Displacement Integrator"
LDI (m/km) has to be calibrated for each specific vehicle.
Above calibration formula applies to thesis test vehicle
QI = IRI*14 - 10 [37]

'PSI' is a function of slope variance, rut depth, cracks and patching. These relations must be seen critically but due to lacking research results they have to be accepted for the time being.

Above roughness values are measured by means of the LDI-vehicle to identify specific problem roads, to establish maintenance standards for acceptance and rejection criteria and to determine which IRI level is acceptable. The Namibian " Maintenance Design System" ( MDS) based on the Brazil HDM3-system must be verified by LDI-readings. IRI resp. QI values are based on response-type-roughness. The movements between the LDI-vehicle axle and the vehicle chassis are integrated. Naturally the suspension of the LDI-vehicle plays a role. Calibration of the vehicle is, by means of rod and level, required. The LDI measures roughness as the cumulative vertical movement of the rear axle relative to the body of the vehicle and the results are therefore dependent on the vehicle type and the state of the suspension system. The instrument is mounted inside the vehicle and connected to the rear axle housing by a cable which extends vertically through the floor. Any car with a rigid rear axle can be used, although vehicles with a softer and coil suspension are preferred. In the instrument the cable passes over a grooved drum which translates the linear movements to a rotary motion. Sprag clutches between the drum and a shaft cause the shaft to rotate in one direction only, thus summing the movement between the axle and car body. A helical spring controls the return of the drum as the distance between the axle and body decreases. A disk with a circle of holes spaced at regular intervals is attached to the shaft. When these holes pass an infrared light sensor, a pulse is generated and transmitted to the control box.

There have been different versions of the " Highway Design and Maintenance Model" (HDM) which were developed by the World Bank, Washington D.C. The "Brazil Model" rests on the HDM3-model which gives prediction for 'VOC' dependent on roughness in terms of IRI values as well as influences like gradeline geometry and horizontal alignment. This model is at present under revision to incorporate also width effects and speed-volume capabilities to evaluate capacity problems. Table 22 gives as an example the vehicle operating costs for the Brazil HDM3 prediction model for a medium truck operating over a paved road in rolling terrain for 1.000 km [85]:




                     |    QUANTITY   |   UNITS    |     COSTS   |     %    |
| Fuel                        |    221,79     | litres     |     55,45   |   13,7   |
| Lubricants                  |      3,52     | litres     |      3,73   |    0,9   |
| Tyres                       |      0,13     | ENT 1)     |     35,91   |    8,9   |
| Crew time                   |      0,00     | hours      |     0,0     |    0,0   |
| Maintenance Parts           |      0,21     | PNVP 2)    |    94,75    |   23,5   |
| Maintenance Labour          |      9,86     | hours      |   112,40    |   27,8   |
| Depreciation                |      0,15     | PNVP       |    67,87    |   16,8   |
| Interest                    |      0,08     | PNVP       |    33,93    |    8,4   |
| Vehicle Speed               |     74,1      | km/h       |             |          |
|                             |               |            |             |          |
| TOTAL COST                  |               |            |   404,04    |  100,0   |
NOTA: Calculated: 'HDM3'-Program [85]: Medium Truck: MB W/2 axles
      1) = Equivalent new tyres 2) = Percent. of new vehicle prices
      Costs: In US $/1.000 vehicle km, calculated for the US $/Rand
             relation: December 1989 in Namibia (1 US $ = R 2,63)
      Model Inputs: Roughness: IRI=3,0; Positive Grade 1,00 %
                    Negative Grade 1,00 % Proportion uphill
                    travel 10%; Curvature 100 degrees/km
                    Altitude: 1200 m.

The calibration of 'VOC' studies can be based on both primary and secondary data sources [36]. Primary user cost data are those which can be directly linked to road performance characteristics while secondary data concentrate on economic conditions, the transport and road haulage industry and the overall characteristics of a road network for an entire region.

The HDM3 model has many advantages once it has been fully calibrated to be used as a management tool in order to evaluate alternative road maintenance strategies. The disadvantage of this ' VOC' model is the difficult calibration adaption which results in a weak transferability to different circumstances. The calibration work to Namibian conditions will have to concentrate on the adaption of fuel and at a later stage maintenance parts and labour costs. The development of user cost management systems can be characterised by the following components:

- Instrumented condition survey vehicles have to record geometrical values and road surface roughness values in order to relate these values to vehicle operating costs;
- Long term investigations of vehicle operators using roads with known design variables to establish the non-fuel components;
- In order to prepare, edit and store the analysis files electronic computers will have to be used and the necessary software like the World Bank computer program 'HDM3' has to be used;
- Mechanistic modelling of vehicle speed and fuel consumption;
- The collected survey data should be obtained from a wide range of transport companies operating over a wide range of different road characteristics.




The Namibian Pavement Management System 'MDS' for gravel roads used above mentioned relations, based on the HDM3 Brazil model, for the prediction of vehicle operating costs for the developing of economic procedures in order to prioritise road rehabilitation and maintenance. The ' PMS' system for paved roads is not based on ' VOC' due to the extreme low traffic numbers on Namibian roads. Due to these low traffic figures it will be proved later that 'VOC' have a negligible influence on any maintenance and rehabilitation strategy for paved roads. In the case of unpaved roads the picture is, however, different, but the question may be asked whether these relations are suitable for Namibian conditions in general. Due to the importance of 'VOC' in calculating benefits of road improvements in the case of unpaved roads, the South African National Transport and Road Research Institute of the CSIR decided to investigate the applicability of overseas 'VOC' relations to southern African conditions [38]. This study used a wide range of approaches, from experimental procedures to straight calibration attempts. The background of such a research project is the establishment of the components of road user costs. These road user costs consist of quantitative and qualitative elements. Quantifiable elements are vehicle operating costs, time and safety whose dependence from road performance factors are shown in table 23 [38]:




| Vehicle Operating        | Fuel Consumption             | Road Geometry        |
| Costs                    | Oil Consumption              | Congestion           |
|                          | Depreciation and             | Roughness (Riding    |
|                          | Interests                    | Quality)             |
|                          | Tyres                        | Road Width           |
|                          | Parts and Maintenance        | Type of Wearing      |
|                          |                              | Surface              |
| Time                     | Speed                        | Skid Resistance      |
| Safety                   | Accident Rates               |                      |

Diversity of opinion still exists in the evaluation of the value of speed as a function of time and its economic impact for drivers and passengers. Time as such has no intrinsic value because it cannot be stored and it is only of any economic significance when time savings result in the undertaking of other activities instead [38]. Therefore it is, for the purpose of this thesis, considered not to include speed, time and accident costs. As comparison, Namibian investigations for the Trans-Caprivi Highway revealed hourly time rates for cars: US $ 4,75 and for trucks: US $ 7,65 (50% in cars are workers; all workers are of the middle income group; 100% in trucks are workers; car occupancy: 2,3 people per vehicle; truck occupancy: 2,0 people per vehicle). An average cost of US $ 15.000,00 for an accident can be assumed for Namibian conditions. It is further assumed that a rate of 1,2 accidents per million vehicle kilometres can be assumed for an average two-lane, two-way paved road in Namibia (Highest accident rate on unpaved section of Trans-Caprivi Highway T.R. 8/4: Takwasa- Divundu: 8,5 accidents per million vehicle kilometres) [39].

Qualitative elements like physical and psychological comfort, convenience and impedance of uniform speed are difficult to quantify and are therefore not included into the South African and hence Namibian user cost analysis. In the next section an attempt will be made to relate the quantifiable elements of road user costs to different road surface conditions which are applicable to Namibian circumstances.




Since ' VOC' data in South Africa were so scarce it was decided by the ' NITRR' to use the cost data of a single bus company operating on a wide scale of different road surfaces during the initial phase of the South African 'VOC' study. The selected transport company operated a fleet of approximately 740 vehicles from eight depots, with a combined annual utilisation of about fifty million kilometres. These vehicles are mainly operating in Natal and Kwazulu, both in South Africa, over a wide spectrum of different road surfaces - from good paved roads to poorly maintained earth roads and veld tracks in difficult mountainous terrain. The cost data for the vehicle running costs and tyre consumption have been collected for each and every condition from the eight depots.

Representative surface conditions of different road networks allocated to the different depots were measured by road roughness determinations which then have been averaged by weighted means to get estimates of kilometre utilisations per roughness class [40]. These roughness figures then were related by regression analysis to maintenance and tyre costs. Fuel consumption as function of road roughness and surface texture which again are related to rolling resistance was investigated in a separate study. This study involved a passenger car, two medium-sized trucks as well as two passenger busses and resulted in a regression model where fuel consumption was related to road roughness. The other studies, except those for fuel consumption, used only passenger busses which can be regarded as a first step in formulating 'VOC' relations for southern African conditions. FUEL RELATIONSHIPS


 Fuel consumption is probably the easiest 'VOC' factor to be established and many investigations exist, although the earlier ones failed to relate them to road surface conditions. Later investigations used road roughness as an indicator of riding quality, but results differed widely as to the contribution of roughness to fuel consumption. The Brazilian HDM3 study was the most comprehensive one, using vehicles from different categories. This model was based on principles of kinematics and internal combustion engines with some assumptions of driver behaviour. Other studies used analyses of measured fuel consumption for different operational conditions. Fuel consumption figures have to be obtained from field data collected in experiments but it must be borne in mind that fuel consumption variations between different vehicle types and driving behaviours can be larger than the different effects of varying road conditions. The Brazil model resulted in a significant roughness effect on fuel consumption whereas the other studies were not able to achieve the same effect. In order to predict fuel consumption for steady state speeds two approaches can be used, the regression techniques method and a method employing basic principles of vehicle motion. The regression technique has due to its lacking transferability to different circumstances and different vehicle types a limited application value. However, due to the difficulties and costs involved using a mechanistic approach within the framework of this thesis it was decided to make use of the regression technique for the establishment of fuel consumption predictions for Namibian conditions which will be discussed in the next sections. The South African 'VOC' study decided to investigate the roughness effect on fuel consumption firstly and then, later on, to expand on speed-roughness and driver-behaviour relationships.


For the South African ' VOC' study a general formula for fuel consumption was developed based on the basic principle of motion and vehicle kinematics which is directly related to energy transformation due to road surface [38]:

F = P1 + P2/V + P3*V2 + P4*G

where: F = fuel consumption (ml/km)
V = velocity (m/s); G = gradient (m/m)
P1 = coefficient for rolling resistance
P2 = coefficient related to idling fuel consumption
P3 = coefficient for air resistance
P4 = coefficient for gradient resistance

The P values can be easily adjusted to provide for new technologies in tyres without having to repeat the whole experiment.

Two studies [41] [42] investigated the change in rolling resistance for different roughness conditions. The different results of these two investigations identified the need to perform an experiment with a range of vehicles and different road conditions including surface texture under local conditions [38]. During the South African experiments to establish the rolling resistance, air and tyre temperatures were recorded continuously under conditions where wind speeds were less than 4 m/s and cold tyre pressures were maintained at all times [40]. In order to calculate above mentioned coefficient P1 deceleration and speed squared were calculated. These experiments resulted in above equation for fuel consumption under southern African conditions.




                 |                 ROUGHNESS IRI (m/km)                        |
| PASSENGER CAR    | IRI = 1,80                | IRI = 6,50                      |
| 100 km/h         | GOOD PAVED                | POOR PAVED                      |
| TEXTURE DEPTH    |               |           |                  |              |
| (mm)             | 0,5           | 4,0       | 0,5              | 4,0          |
|      | 25 RRc    | 0,162         | 0,173     | 0,178            | 0,185        |
| TYRE |    FCc    | 7,23          | 7,33      | 7,43             | 7,52         |
| TEMP |-----------|---------------|-----------|------------------|--------------|
| (oC) | 45 RRc    | 0,139         | 0,153     | 0,168            | 0,182        |
|      |    FCc    | 6,96          | 7,12      | 7,31             | 7,48         |
| TRUCK AND BUS    | IRI = 2,00       | IRI = 6,50        | IRI = 15,00          |
| 80 km/h          | GOOD PAVED       | POOR PAVED        | POOR UNPAVED         |
| TYRE   |         |                  |                   |                      |
|PRESSURE| PREDICT |                  |                   |                      |
| (kPa)  |         |                  |                   |                      |
|        | RRh     |  0,110           |  0,129            |  0,168               |
| 540    | FCt     | 29,7             | 31,6              | 35,6                 |
|        | FCb     | 30,9             | 32,8              | 36,5                 |
|        | RRh     | 0,029            | 0,112             | 0,150                |
| 640    | FCt     | 27,9             | 29,8              | 33,6                 |
|        | FCb     | 29,1             | 31,0              | 34,8                 |
NOTA: RRc = Predicted Rolling Resistance (N/kg) for Cars
      RRh = Predicted Rolling Resistance (N/kg) for Trucks and Busses
      FCc = Predicted Fuel Consumption (l/100 km) for Cars
      FCt = Predicted Fuel Consumption (l/100 km) for a 12 t Truck
      FCb = Predicted Fuel Consumption (l/100 km) for a 12 t Bus

Table 24 [40] shows that the results from these experiments indicate that rolling resistance and hence fuel consumption are a function of the road surfacing texture, road roughness and tyre temperature as well as tyre pressure. It was, for instance, established that on a level road the influence of road surface texture is amounting to 7% fuel consumption difference for 100 km/h while road roughness and tyre pressure amounts to more than 20% respectively due to the heavy influence of these two components on rolling resistance. Further it was established that for heavier vehicles surface texture was not found to exercise a very heavy influence on fuel consumption due to high tyre pressures and different tyre types for these vehicles. The effects of road roughness on the fuel consumption and rolling resistance for different classes of vehicles on a level road are exhibited in table 24. It was not possible so far to establish the influence of loose material on gravel roads on fuel consumption due to a lack of data. Basically the South African ' VOC' study lays the basis to select surfacing types which could be fuel consumption optimised which has to be adapted to Namibian conditions.

The oil consumption was for the very small part lubrication oils represent in the total vehicle operating costs not investigated in the South African 'VOC' study. TYRE RELATIONSHIPS


Tyres represent between 8 and 14% of the total vehicle operating costs [40]. The tyre life is a function of safety considerations, driver behaviour, load conditions and speed as well as roughness of the road surface.

Tyre consumption can be determined by two methods namely the multiple regression technique and mechanistic approaches. Tyre consumption can be described as a function of the road roughness and vehicle dynamics. The multiple regression technique can include factors which are normally not easily covered during experiments like, for instance, sharp angular stones on gravel roads. With increasing road roughness on bad gravel roads the speed, however, will be reduced which again benefits tyre consumption [43]. Prediction formula which have been derived from experimental works are available and can even include factors like unusual conditions like oversize sharp stones on a gravel road surface.

The main component of tyre wear is the interaction between tyre and road surface. Survey techniques will only result in a limited quantification of this interaction [38]. While experimentation and mechanistic modelling would permit the individual identification of road condition effects, an interesting relation for tyre wear by considering the level of tractive force exerted by a vehicle and the tyre slip which occurs at the road surface-tyre interface was developed by the following formula [44]:

V = (D*FH2)/(FV*K*S)(units in the imperial system)

where: V = volume of tread rubber worn (inches3)
D = total distance travelled (miles)
FH = total force in the horizontal plane at the pavement-tyre interface (lb)
FV = vertical load (lb)
K = µ-slip coefficient (lb/lb)/(ft/ft)
µ friction number
S = empirically determined coefficient, termed slip-energy
volume wear coefficient (lb-miles)/inch3

The K and S values describe friction and roughness of the road surface which have to be developed experimentally to represent a specific tyre type, pavement type and roughness. The µ- slip coefficient K is obtained by determining the horizontal and vertical forces on an experimental tyre, and the different distances travelled by the tyre and the vehicle. The slip-energy volume wear coefficient S is determined by plotting the measured volume of tread rubber worn against the product of total distance slipped and the horizontal force. K values of 21 and 25 and S values of 95 and 250 respectively have been established for passenger vehicle tyres on smooth textured roads for the low values and harsh textured roads for the high ones. This prediction method must be seen as a valuable enhancement of the regression techniques and will be included into the South African ' VOC' study in the future [38].

From the data files extracted from the depot tyre records the following relationships for tyre wear as affected by road condition on the basis of an " Equivalent New Tyre Life" (ENTL) was derived [40] which has firstly been used in the Kenya study:

ENTL = TK /(1+NR/R)

where: ENTL = Equivalent new tyre life (103 km/tyre)
TK = Total distance per casing (103 km)
NR = Average number of retreads per casing
R = Ratio of new tyre price to retread price

Resulting from those tyre data a simple log-linear relationship was established with the resulting regression model [40]:

ENTL = 131,5 - 21,0 ln (14*IRI-10)
with R-squared = 0,81 and standard error = 5,42

The South African tyre prediction formula compares well with results from the Kenya and Caribbean models but not with those from the Indian and Brazil studies [40]. It is believed that the main reason for these differences lies in the different material types of gravel wearing courses used on unpaved roads between the two study groups. Consequently the South African 'VOC' study followed this assumption further up. Many gravel road users in Namibia know by experience that tyre life is not only influenced by road roughness but also by the quality of the gravel material. It is possible that even on relatively smooth gravel roads sharp angular stones in the gravel wearing course may result in tyre punctures due to penetrations or cuts. The South African 'VOC' consequently revealed that the bus depot with the largest fraction of rough gravel roads experienced a tyre failure rate of more than 50% due to penetrations caused by sharp, angular stones in the wearing course of unpaved roads. The number of penetration scrappings was thus included into the South African tyre prediction formula which emerged as follows [40]:

ENTL = 60,2 - 11,0 ln (14*IRI-10) - 6,4 ln PENS

with R-squared = 0,93 and standard error = 3,59
where: PENS = number of penetration scrappings per 1.000 km

The following three representative values for PENS-values were established [40]:

PENS = 0,06 for rough, angular wearing course material
     = 0,01 for average conditions
     = 0,005 for rounded aggregates, sandy or paved conditions

The lack of data still doesn't give conclusive evidence about the effects of materials properties on tyre life and the research must still continue. VEHICLE MAINTENANCE RELATIONSHIPS


Maintenance costs of vehicles include servicing, repair and part replacement costs. Due to the diversity of vehicles and their different operating conditions it was suggested [45] to treat maintenance costs in terms of labour costs (hours) and the costs of parts in terms of a percentage of the depreciable value of the vehicle. This variable of maintenance expenditure can be given [40] as P/VP where P is the cost of spares in US $ per 1.000 km and VP is the new vehicle price in 105 US $ (1987 prices in South African Rand 'R' have been recalculated via the consumer price index for Namibia for 31.12.1989 and transformed into US $: 1 US $=R 2,63). The objective of these investigations is to estimate the labour costs in terms of hours as a function of the predicted part costs. For instance, in the Brazil and Kenya studies it was established that labour costs increase at a declining rate as part costs increase. On the other hand the Kenya study revealed less labour input for given part costs for higher roughness levels. The Kenya and Caribbean studies developed relationships of parts consumption divided by the new vehicle price as a function of road roughness for different vehicle types [38]. Maintenance labour cost revealed to be 45% of the part costs. The results of the Brazil and India studies revealed that maintenance on vehicles operating under very rough conditions are more labour intensive than is the case for smoother roads [40]. All these different relationships have to be adopted to South African conditions which are very similar to Namibian circumstances and have to be coupled to specific local road conditions.

The cost of spare parts [40] in the South African ' VOC' study have been derived from above mentioned company records and plotted against different road roughnesses under consideration of vehicle ages. The results of these investigations showed a model with distinct cost increases together with those of increasing roughness and age. A surprising end result revealed that there was a drop in expenditure after reaching a specific vehicle age, as also experienced in the Brazil model. The South African spare part prediction formula has been established as follows:

ln (SP/VP) = -0,5254 + 0,6779 ln AGE + 0,3338 ln (14*IRI-10)

where: SP = Spare parts cost in US $ per 1.000 km
VP = New vehicle price in US $*105
AGE = Vehicle age in 103 km, AGE = AGE - 125 if AGE > 350
IRI = Road roughness in m/km

The South African model proved that the relationship between labour costs and road condition was difficult to establish. Due to a lack in more suitable data it was decided by the NITRR to use the Brazil labour model with some local adaptions with the following labour costs prediction formula [40]:

ln 0.52*LC = 1,29 + 0,517 ln 0.52*SP + 0,00548*(14*IRI-10)

where: LC = Labour costs in US $ per 1.000 km
SP = Spare part costs in US $ per 1.000 km
IRI = Road roughness in m/km

Due to a lack of compatibility between this prediction formula and real data as obtained from above mentioned bus company it has to be recommended to refine this formula by further research [40]. It is also strongly felt, although it cannot be realised at the present moment, that due to a lack of Namibian data, the preliminary South African maintenance models have to be adapted to Namibian conditions which as far as the spare part/labour relationships are concerned, are differing from South African conditions. VEHICLE DEPRECIATION RELATIONSHIPS


Depreciation and interest costs are important for both road management system effectiveness on the basis of resource costs and for the transport industry to decide whether to remanufacture or to buy a new vehicle. Furthermore it must be tried to establish a model based on local data which determines an inter-relationship between surface condition of a road and service life of a vehicle. Depreciation is a major component of vehicle operating costs and accounts approximately to one-third of the total ' VOC'[38]. The total depreciation of a vehicle during its lifetime should be its original purchase price minus the tyres with a negligible residual value at the end of this period (usually 10 to 15%).

Different studies resulted in different relationships between annual depreciations and utilisations as well as depreciation per unit distance and an estimation of the hours per year driven for predicted vehicle speeds on a specific route. The determination of depreciation per kilometre must be regarded as a rough estimate only. These studies are based on vehicle class value-age (VA) relationships established from large-scale surveys of used vehicle prices and compared to data obtained from user surveys. It can be differed between use-related depreciation where a vehicle has been used with maximum effect and time-related depreciation when a vehicle has been used with minimum effect, but nevertheless depreciates [38]. The problem arises how to establish a realistic split between these two depreciation models. A possible solution was proposed [43] but will not be further outlined. The 'VA' method is based on different assumptions to determine the average annual depreciation.

The one assumption is based on the varying vehicle life method [45] where a straight-line depreciation over a predetermined service life takes place which is assumed to decrease as speed increases, and a constant vehicle life method where the straight-line depreciation is assumed to be constant irrespective of vehicle speed and equal in magnitude to the user specified input for service life in years.

The 'VA' approach encounters, however, some shortcomings. Firstly the values obtained from this method cannot be related to the condition of road surfaces as well as to kilometre utilisation but only to age in years and secondly about the missing link between running costs and vehicle value [46]. The 'VA' method cannot cover important effects like these that improvements in road surfaces lead to lower running costs and consequently to longer service lives as well as higher age values for vehicles.

To overcome the shortcomings of the 'VA' model the optimal life method 'OL' was developed [47] where a way is provided to predict vehicle lives under the consideration of the new vehicle price, the discount rate and the increase of maintenance costs with time. The following equation shows this cost minimising model:


¶(m(s) - m(t))e-rtdt = VP (Integral(¶) was not found in HTM Language)


where: VP is the new vehicle price (US $)
m(t) represents the running costs flowing at the rate m(t)
t represents the age of a vehicle
s represents scrapping of the vehicle after s years
r = per time per cent period continuous discount rate

This equation is valid as long as utilisation does not vary with age [46]. Further it was maintained [46] that only these parts of vehicle depreciation which can be related to road conditions should be included into the road management system which is very difficult to quantify because the relevant information must be obtained from historic records which are lacking under Namibian circumstances. To use data from other studies like for instance the Brazil study is very difficult due to the poor transferability of such data to different conditions. The 'OL' model which is used in the South African ' VOC' study makes use of a comprehensive cost study of a single well organised bus company operating over a wide range of different road surface conditions which are measured by the ' LDI' instrument, as reported in previous sections. The surface conditions are represented by very good to extreme bad surfaces with different surface types like earth, gravel and paved roads. The 'OL' model shows that maintenance flow and the depreciation of the vehicle fleet can be directly linked to the condition of the road surface under consideration of remanufacturing of existing vehicles. Under southern African conditions vehicles are normally remanufactured after 10 years or 1 million kilometres (trucks and busses but not passenger cars and pickups) [40].

The actual results of the South African 'VOC' study [46] where three levels of road conditions have been considered, namely poor unpaved surfaces of IRI=11,5, good unpaved surfaces of IRI=5,0 and good paved surfaces of IRI=2,0. The average nominal vehicle prices at the time of the survey were related by a regression analysis to the independent variables of road roughness and vehicle age under consideration of the bus maintenance flow. The results predicted service lives of 9 year for the IRI=11,5, 11 years for the IRI=5,0 and 14 years for the IRI=2,0 road surface types. These predicted values compared well with real data as submitted by the transport company except the prediction for the IRI=2,0 road surface where the predicted value differed by one year life underestimation. The importance of the 'OL' model is self-evident taking into account the fact that other models failed so far to show a meaningful improvement in vehicle utilisation after major rehabilitation or better maintenance methods of road surfaces with the consequent reduction in surface roughness. Further research efforts are, however, required to include, for instance, truck data in order to further improve the efficiency of pavement management systems under southern African conditions which also apply to Namibian road circumstances.




The results of the South African ' VOC' study have been determined in the following three tables after having been recalculated and adapted to Namibian conditions for December 1989. They were verified for Namibian conditions by means of field testing for fuel consumption during 1989/91. The figures are vehicle operating costs figures for passenger busses, cars and trucks of those types which are normally used in the developing areas of southern Africa including Namibia. The fuel prediction formula in relation to road conditions and surface texture as well as tyre pressure can easily be adapted to Namibian conditions and can be regarded as a realistic 'VOC' model after having verified for Namibian conditions (fuel only). The effects of loose gravel surfaces, stoniness and the level of compaction on fuel consumption must, however, be further investigated. The same argument is valid for the relationships between speed and roughness before a final roughness-fuel model for Namibian circumstances can be formulated. The South African tyre life model as a function of road roughness can, with the same amount of confidence, be used in Namibia. More work, however, is needed to evaluate the influence of road wearing course material on tyre performance. Both road roughness and vehicle age have an effect on maintenance and labour costs of vehicles [40] which again are directly related to the level of road maintenance policies. The vehicle depreciation relationship to road condition will have to be further expanded to include more vehicle classes and to be verified for Namibian data. Furthermore, road geometrics will have to be included into the South African 'VOC' study, and it will have to be investigated whether road geometrics could affect roughness coefficients under southern African conditions. A ' VOC' study verified for Namibian conditions should also include the effect of dust and the consequent accident hazard as well as time factors on vehicle operating costs.




|ROUGHNESS| TEXTURE |----------------------------------------------|
|         |         |      |    LABOUR | INTEREST   |      |       |
|  1,50   |    P    |  2,8 |     7,0   |    9,4     | 14,6 |  33,8 |
|  2,00   |    P    |  3,1 |     7,8   |    9,7     | 15,3 |  35,9 |
|  3,00   |    P    |  3,5 |     9,1   |   10,5     | 15,4 |  38.5 |
|  3,50   |    P    |  3,9 |     9,8   |   10,9     | 15,5 |  40,1 |
|  4,25   |    P    |  4,3 |    10,5   |   11,4     | 15,6 |  41,8 |
|  5,00   |   UP    |  4,7 |    11,4   |   11,7     | 15,9 |  43,7 |
|  5,75   |   UP    |  5,1 |    12,1   |   12,2     | 16,0 |  45,4 |
|  6,50   |   UP    |  5,5 |    13,3   |   12,5     | 16,2 |  47,5 |
|  7,00   |   UP    |  5,9 |    14,1   |   12,9     | 16,4 |  49,3 |
|  7,50   |   UP    |  6,2 |    14,5   |   13,3     | 16,6 |  50,6 |
|  8,40   |   UP    |  6,7 |    16,0   |   13,7     | 16,7 |  53,1 |
|  9,00   |   UP    |  7,0 |    16,8   |   14,1     | 16,9 |  54,8 |
|  9,75   |   UP    |  7,8 |    17,2   |   14,5     | 17,0 |  56,5 |
| 10,50   |   UP    |  8,2 |    17,6   |   14,8     | 17,2 |   57,8|
NOTA: Tables 25 to 27: Data are recalculated and adapted to
Namibian road conditions for the price level of December 1989
(1 US $=R 2,63). P = Paved Roads; UP = Unpaved Roads. Original
data of the Natal/Kwazulu Study were established for the year 1986. Prices have been established without taxes and subsidies.




|ROUGHNESS| TEXTURE |----------------------------------------------|
|         |         |      |    LABOUR |  INTEREST  |      |       |
|   1,50  |    P    | 0,30 |    1,57   |     5,03   | 3,52 |  10,4 |
|   2,00  |    P    | 0,44 |    1,95   |     5,82   | 3,55 |  11,8 |
|   3,00  |    P    | 0,47 |    2,30   |     5,94   | 3,59 |  12,3 |
|   3,50  |    P    | 0,57 |    2,65   |     6,32   | 3,62 |  13,2 |
|   4,25  |    P    | 0,65 |    3,04   |     6,77   | 3,67 |  14,1 |
|   5,00  |   UP    | 0,68 |    3,41   |     7,22   | 3,71 |  15,0 |
|   5,75  |   UP    | 0,74 |    3,78   |     7,72   | 3,80 |  16,0 |
|   6,50  |   UP    | 0,82 |    4,12   |     8,23   | 3,87 |  17,0 |
|   7,00  |   UP    | 0,87 |    4,53   |     8,64   | 4,01 |  18,0 |
|   7,50  |   UP    | 0,96 |    4,97   |     9,16   | 4,03 |  19,1 |
|   8,40  |   UP    | 1,04 |    5,26   |    10,11   | 4,08 |  20,5 |
|   9,00  |   UP    | 1,10 |    5,65   |    10,79   | 4,18 |  21,7 |
|   9,75  |   UP    | 1,17 |    5,90   |    11,70   | 4,26 |  23,0 |
|  10,50  |   UP    | 1,21 |    6,30   |    12,57   | 4,29 |  24,4 |
|  11,00  |   UP    | 1,26 |    6,64   |    13,48   | 4,40 |  25,8 |




|ROUGHNESS| TEXTURE |----------------------------------------------|
|         |         |      |   LABOUR  |   INTEREST |      |       |
|   1,50  |     P   |  3,1 |    17,1   |    14,0    |  9,3 |  43,5 |
|   2,00  |     P   |  3,5 |    17,9   |    14,4    | 10,1 |  45,9 |
|   3,00  |     P   |  3,9 |    18,7   |    15,0    | 10,6 |  48,2 |
|   3,50  |     P   |  4,1 |    19,1   |    15,4    | 11,1 |  49,7 |
|   4,25  |     P   |  4,3 |    19,8   |    15,8    | 11,8 |  51,7 |
|   5,00  |    UP   |  4,7 |    20,3   |    16,1    | 12,2 |  53,3 |
|   5,75  |    UP   |  5,0 |    20,8   |    16,6    | 12,9 |  55,3 |
|   6,50  |    UP   |  5,3 |    21,4   |    17,1    | 13,6 |  57,4 |
|   7,00  |    UP   |  5,7 |    22,0   |    17,3    | 14,0 |  59,0 |
|   7,50  |    UP   |  6,1 |    22,9   |    18,0    | 14,7 |  61,7 |
|   8,40  |    UP   |  6,5 |    23,3   |    18,4    | 15,2 |  63,4 |
|   9,00  |    UP   |  6,8 |    23,9   |    18,8    | 15,8 |  65,3 |
|   9,75  |    UP   |  7,4 |    24,5   |    19,4    | 16,4 |  67,7 |
|  10,50  |    UP   |  7,8 |    25,2   |    20,0    | 17,0 |  70,0 |
|  11,00  |    UP   |  8,2 |    25,7   |    20,5    | 17,6 |  72,0 |

Table 25 [40] shows between the two extreme roughness relationships a maximum increase in total vehicle operating costs of 71% from a very smooth paved road with IRI=1,50 to a very rough unpaved road with IRI=10,50. The same relationships will be developed also for a passenger car in table 26 [40] (increase in total ' VOC' = 147% for a riding quality difference between IRI=1,50 and IRI=11,00) and for a medium truck in table 27 [40] (increase in total 'VOC' = 65% for a riding quality difference between IRI=1,50 and IRI=11,00) adapted to Namibian conditions (all for rolling terrain).




The results of the South African 'VOC' study have to be verified by Namibian field data. Road test sections with surface types commonly used on Namibian roads were identified, covering a variety of different roughnesses and surface textures as well as paved and unpaved sections. Each section had a uniform gradient over its length. The road roughness was measured in terms of LDI-values and recalculated to PSI or QI values, respective to IRI values. The LDI values were established by the Namibian Department of Transport between February 1984 and December 1989 for a wide variety of paved roads and the LDI values for the test runs on unpaved road sections simultaneously with the fuel measurements during November 1990/January 1991 (see: appendix tables 1 and 2 (appendices 9 and 10)). TEST VEHICLE


For the volumetrical measuring of the fuel consumption a "HESSAG-Kraftstoffverbrauchtester 1000 B" with an indicator device "HESSAG Anzeigegerät 400 B" was used. The test vehicle was a TOYOTA 2000 4x4 pick-up van. Before testing commenced, a distance of at least 10 km was travelled to allow the tyres to warm up to operating temperatures. Cold tyre pressures were kept in accordance with manufacturer's specifications and pressures were monitored before and after runs. Only the driver occupied the vehicle, windows were kept closed and fuel tanks were kept to at least three-quarters full to limit mass variations. Tests were conducted under windless conditions although occasional gusts of wind were encountered.

Serviceability criteria for the volumetrical measuring device were satisfactory for moderate temperatures below 30oC. Problems were, however, encountered for higher temperatures above 30oC where the petrol started to reach its boiling-point with resulting larger measuring variations. Normal 93 octane petrol used in Namibia reaches its boiling-point between 33o and 188oC. Measurements were, therefore, only taken in the cooler mornings. A temporary field solution was the cooling of the petrol pump by means of a wetted cloth which brought the petrol temperature down. ANALYSIS OF RESULTS


The fuel consumption and roughness data were reduced to an average squared fuel consumption and roughness trend curve. These values were then used in a linear least-squares analysis to solve for the intercept constant C1 and the coefficient C2 in the following equation calculating the fuel consumption 'FC':

FC = C1 + C2*IRI (ml/km) where: C1 = 110,4 and C2 = 2,4

The process is demonstrated in figure 2 from which the expected linear relationship between squared fuel consumption and roughness for paved roads is evident. A total of 75 mean observations (12x75=900 measurements) on 54 sections was used to develop the equation. The R-squared value is 0,006 and the standard error of Y estimate is 12,007. (See appendix table 1 for a description of all these paved sections). The relation can be explained as follows:

- An increase in road roughness, for a constant tyre temperature, increases fuel consumption;

The spread of the measured values can be attributed to effects like:

- An increase in tyre temperature, resulting in an increase in tyre pressure, reduces fuel consumption (on good paved roads);

- The effect of road roughness on fuel consumption increases with an increase in tyre temperature (higher temperature means higher pressure with resulting higher bumpiness (roughness) on bad unpaved roads);

- An increase in fuel temperature, resulting in air bubbles in measuring device, increases fuel consumption.

The trend curve for all the data gives an increase of 9,033% fuel consumption for the test vehicle between IRI=0 and 3,5. Extrapolating the data resulted in a fuel consumption increase of 28,4% between IRI=0 and 11,0 as compared with 28,9% for the South African 'VOC'-study (table 26) for passenger cars (29,1% for HDM3).

The Namibian fuel consumption model developed by linear regression techniques, indicates that for any road vehicle the road roughness IRI is significant in determining the fuel consumption 'FC'. The model appears to be well established for the roughness range IRI 1,5 to 3,5. The model proved almost identical with the South African 'VOC' fuel consumption model based on mechanistic principles. Few data for paved roads at higher roughness values were available, which renders the regression technique vulnerable within this range.

Further tests were undertaken on various sections of unpaved roads with IRI values of 2,2 (MR 59); 5,1 (MR 51); 7,0 (MR 46) and 11,1 (MR 47) to test the model further (description of the unpaved test sections: appendix table 2). The process is demonstrated in figure 3 from which the expected linear relationship between fuel consumption and roughness for unpaved roads is evident. A total of 8 mean observations (12x8=96 measurements) on 4 sections was used. The trend curve for all the data between 0 and 11 for unpaved roads gives an increase of 37,1% of fuel consumption for the test vehicle as compared with 28,4% for various Namibian paved roads and 28,9% for the South African ' VOC'-study for unpaved and paved road data (table 26) for passenger cars. The higher slope of the trend curve for unpaved roads against that of paved roads is caused by the higher rolling resistance ( loose gravel) and the effect of tyre temperature on roughness ( bumpiness) for unpaved roads. Tests on damp to very wet gravel pavements on the same road sections with similar riding qualities resulted in slightly higher fuel consumptions and a steeper slope of the trend curve against dry unpaved roads due to an increased rolling resistance caused by lower tyre temperatures and suction effects on wet unpaved roads as well as the volumetric change of fuel at different (cooler) temperatures (figure 3).

Under ideal conditions, i.e. a level road under windless circumstances, the effect of road surface properties over the tested range on fuel consumption could be expected to increase between 28% and 37% at 90 km/h. Higher fuel consumption can be expected under more severe conditions like heavier vehicles, higher loads, wind and positive grades. The small differences in slope and intercept between this model and those by the South African 'VOC'-study [48] can be attributed to the mechanistic approach used by above 'VOC'-study against the volumetric one used in the Namibian model. Thus, these results can be applied with confidence in circumstances where road surface types are similar to the experimental conditions.

The fuel consumption values for the Namibian ' VOC'-study compare well with those of the South African 'VOC'-study because the economic and technological environment in Namibia is very similar to that prevailing in South Africa at the times of the research. Therefore, it will be accepted that other 'VOC' -components likes tyres, maintenance and depreciation will follow similar trends. This assumption has to be verified by further Namibian 'VOC'-studies which exceed the framework of this thesis.


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The relationship between the South African/Namibian and the HDM3 ' VOC' studies is pictured in figure 4.

It has, however, to be observed that direct comparisons between the two models have to be judged with scepticism due to the different special conditions which ruled each specific study. The HDM3 study is, for instance, based on a complex mechanistic model which predicts inter alia vehicle speed. The special input which is necessary for that (for instance engine size, braking forces etc.) is in many cases not compatible with vehicles used in the southern African region including Namibia. Furthermore, it is important to remember that it is not the absolute but the relative values of the predictions which are relevant for any economical evaluations.

Figure 4 shows that, despite the differences in the slopes of the curves, the magnitude of vehicle operating costs as function of road roughness for the two studies are of a similar order. The predicted 'VOC' for passenger cars for the Brazil study are higher for very high riding qualities ( IRI<2) while the RSA/Namibian trend curve climbs steeper. The 'VOC' for medium trucks follow the opposite trend: the 'VOC' for the Brazil study are lower for low riding qualities (IRI<8) and it climbs steeper than the RSA/Namibian curve. The 'VOC' values for the Brazilian bus are generally higher than for the South African/Namibian one with a steeper slope for the latter. The average combined 'VOC' for 85% passenger cars, 5% busses and 10% trucks (combined to one vehicle) seem to follow the same tendencies. For an IRI=0 both have the same 'VOC' of US $ 120/1.000 km/vehicle while the RSA/Namibian curve is slightly steeper than the HDM3 one (RSA/Namibia: US $ 120/1.000 km/vehicle to US $ 320/1.000 km/vehicle from IRI=0 to IRI=12; HDM3: US $ 120/1.000 km/vehicle to US $ 250/1.000 km/vehicle from IRI=0 to IRI=12).

The differences seem not to be very meaningful and can be ascribed to different road materials and road construction/ maintenance methods as well as different vehicle running and maintenance cost relationships between Brazil and Namibia. It also has to be stated that it makes little sense to mix prediction equations from different studies since within each country wages, prices and other economic conditions were relatively constant, ensuring that each set of equations has a coherency which is threatened if mixing is taking place. The vehicle operating costs established to above discussed principles are important for road management decisions such as:

- The optimal grading frequency for a specific unpaved road and the best distribution of available grading effort for an unpaved road network;
- The determination of optimal gravelling frequencies and rehabilitation of an unpaved road network resp. specific roads;
- The determination of the optimal surfacing point of unpaved roads.
The figures cannot be shown due to the uncompatibilty of my old graphics program (Old Harvard Graphics:in the 1980s).




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