Dragutin Picman1 and Tibor Pentek1
1 Faculty of Forestry, University of Zagreb, Svetoimunska 25, P.O.B. 175, 10000 Zagreb, Croatia.
The problem of building forest roads in low-lying forests relates to the distance between the forest roads and their building and maintenance costs.
The optimal density of a forest road network in low-lying stands was calculated on the terrain according to known models. The model of minimum total costs (according to Sabadi) applied to the management unit iljakovacka Dubrava II; the classification of the forest roads was done on the terrain; the existing conditions for the opening-up of forests through a forest road network were recorded; an analysis of costs was made according to the type of roads, building method and maintenance financing in the public enterprise Hrvatske ume, forest management authority of Velika Gorica; optimum road density for the opening-up of forests in this management unit was calculated; and advantages and disadvantages of optimization of opening this forest area were critically analysed according to the above-mentioned theoretical model.
The results of the classification of forest roads in the area under research on the basis of frequency of their use indicated that there are:
· 6.0 km of public roads which open this forest area and for which the forest management authority does not bear any expenses;
· 7.5 km of primary forest roads; and
· 30.5 km of secondary forest roads.
This means that the total road length is 44.0 km with a density of 10.36 m/ha.
The research applied the theoretical model of forest road density; calculated the total expenses incurred with the existing roads as well as timber extraction costs; compared the results with the results of previous research on the suitability of this management unit with the theoretical model as well as by classifying total costs according to the business policy of the public enterprise Hrvatske ume and to the conditions in the forest management authority Velika Gorica. The following results were obtained:
· the optimum mutual distance between roads in the management unit is 680 m;
· a total of 62.5 km of forest roads is necessary to achieve optimum density of 14.71 m/ha;
· additional 18.5 km of secondary forest roads should be built in the management unit;
· the average extraction distance would decrease to 170 m;
· the average extraction length would be 187 m
The theoretical model for the optimization of the forest roads density in the low-lying forests of the management unit iljakovacka Dubrava II is based on minimum total costs and is recommended for this management unit. Concrete sketch designs for each road were also elaborated.
The opening of forests is a concept which means to make it possible to have access to a particular area in order to benefit from it. In most cases we think of exploiting forests to get the main forest product - timber species which give an immediate economic profit. We can extract them in various ways: by draught animals, slides, groundwater streams, railway, tractors, forwarders, skidders, cable railways, helicopters, etc.
Opening up with a forest roads network includes building of roads for mechanized transport of forest products, primarily of timber species. However, forest roads have wider application, both in forestry and for the needs of the social community. By their use the following is possible: easier and correct interventions on forest cultivation; wide application of mechanization in all forestry works; transport of workers and delivery of material to distant sites; better and easier organization of work; protection from fire and diseases; and easier measurement, management and supervision of the forest. Forest roads are also used in other economic sectors: agriculture, mining, tourism, health services, etc.
Therefore, if we look at forest roads in the entire environment, there is a manifold justification for their building although it should not be forgotten that opening-up by a forest roads network is the most expensive part of investment in forestry.
Problems of research
There are many different models for establishing the optimum density of a forest roads network for the transport of timber species through a combined use of tractor and truck. Most of them are based on the calculation of common timber transport costs and costs for forest roads.
Forest products are scattered over a large area. Extraction by tractors to auxiliary warehouses is slow; every shift only a small number of pieces is extracted and so costs are rather high. Transport by trucks is much quicker; a big quantity of products is transported at the same time, so this method of transport is cheaper. Today transport costs by trucks are 10 to 20 times lower than extraction costs by tractors over the same distance (according to Jelicic transport by truck is 20 to 30 times cheaper). Due to above-mentioned reasons, an effort is being made to reduce the extraction distance, thus enabling the trucks to get closer to the felled timber volume and this is achieved by building forest roads.
Therefore, the denser the forest roads network, the higher are the costs incurred for the roads. This is the reason why the optimum density of forest roads is determined by the distance between roads, when the sum of transport costs and costs for forest roads is lowest.
The following facts should be emphasized:
· The theoretical model for determining the optimum density of a forest roads network assumes a uniformly distributed timber volume on a certain area, as well as the design and construction of forest roads at equal distances between each other. As these conditions are never fulfilled on the terrain, mathematical formulae give approximate data for the optimum density of a forest roads network.
· As the prices of road construction and maintenance, as well as transport prices, are subject to fluctuations, the calculations optimum results only for a certain period
· Since transport systems, means of transportation and technology for timber extraction develop faster than the technology for building roads, extraction and transport costs tend to decrease. If such a trend continues, a lower density of forest roads will be needed in the future.
· The optimization of forest roads density from the point of view of the lowest costs for timber exploitation cannot be ideal, as other uses of a forest become increasingly important. Therefore, the opening-up of forests is not only and exclusively oriented towards the extraction and carting out of felled timber.
The density of a forest roads network represents the relationship between the length of the roads and the forest area that gravitates towards them (Sabadi 1992) and is expressed in number of metres per hectare.
y = density of a forest roads network (m/ha)
l = road length (km)
F = gravitational area (ha)
The theoretical model for determining the optimum density for the opening-up of forests assumes:
=> a uniform distribution of timber products over the whole area
=> a distribution of roads at equal distances between them
=> a parallel pulling in a direction vertical to a road
=> "a two-way" pulling in a low-lying area (Figure 1)
Figure 1. Diagram to calculate the density of a forest roads network
e = distance between forest roads
l = length of one road
ds = mean distance of pulling
At road distance e, the area gravitates towards each of its parts of length l:
For e and l expressed in metres, the area in hectares is:
If we substitute the above expression in formula (1), we will obtain an expression for the density of a forest roads network dependent on the distance between roads:
Figure 2. Relationship between the density of a forest roads network (y) and the distance between roads (e)
The research area
Research was carried out in the area of Zagreb, in the forest management authority Velika Gorica in the management unit iljakovacka Dubrava II.
The forests of this management unit cover a total area of 4 248 ha and are located in a Sava plain. Above sea level height ranges from 103 m to 119 m. The land is low-lying, mildly undulated with small depressions.
Orographic and hydrographic conditions
The land of this management unit is even with small depressions, that are often hardly visible at naked eye, with a height difference of 16 m. Groundwater streams that cross this management unit flow in north direction and empty into the Odra and then into the Sava.
The lowest parts are exposed to occasional floods when streams burst their banks, but the flooded water soon backs out either by itself or by artificially dug channels that surround certain parts.
Geological parent material
Geological parent material is made of diluvian and alluvial washes formed by sedimentation of material from the neighbouring hills into the Pannonian Sea. The upper surface layers are alluvial washes formed by interaction of the river Sava and its tributaries, and contain clays, loams, sands, crushed stones, sand silts and humus.
The most important kinds of soil in the area of this management unit are:
· alluvial soils - pseudogley and hypogley;
· low-lying pseudogley and hypogley;
· district brown soil - low-lying pseudogley and semigley.
According to Koppen this area belongs to a zone of warm - moderate rainy climate, classified under the sign Cfwbx. The least precipitation is in the months of February and March. Martonne's index of dryness "I" is higher than 40 on all climate stations of this area, which means that there is sometimes too much humidity. According to Thornthwaite's classification this area belongs to a humid climate.
In this management unit, the most frequent are the following forest communities:
· bay oak and ordinary hornbeam (Carpino betuli - Quercetum roboris typicum):
· bay oak with a big broom (Genisto elatae - Quercetum roboris);
· bay oak and ordinary hornbeam with beech-tree (Carpino betuli - Quercetum roboris fagetosum);
· sticky alder (Alnetum glutinosae).
Conditions of forest fund
According to their origin, the forests of this management unit are spermatophyte (92%) or coppice (8%). These are grown in a natural way. while conifers and ash-trees and a smaller part of oaks were artificially grown.
The average timber supply is 251 m3/ha; the current volume increment determined a drilling method is 5.5 m3/ha while the average increment percentage is 2.2 percent.
The opening of forests
In the management unit under consideration all communications are effected by different categories of roads. Their total length is 44 km, of which 38 km are forest roads with a density of 10.36 m/ha.
Objectives of the research
From a brief description of the area under research it can be noted that the terrain conditions for building a forest roads network are quite favourable, as it is a low-lying relief with no sudden height differences, which can be divided into even, straight-lined parts to enable the location of routes at approximately the same distance. The terrain characteristics present conditions very close to the assumptions made for the use of the theoretical model for determining the optimum forest roads density. Therefore, this model can be applied in this area with a fair degree of certainty.
Results of the research
Calculation of costs for a forest roads network
The forest management authority Velika Gorica provides its own financing for building forest roads. The rate of interest is calculated at 3 percent and the amortization time for a forest road is 33 years.
According to the frequency of use, and therefore the need for maintenance, the forest roads in the area under consideration can be divided into:
· primary - they are in constant use, require permanent annual maintenance;
· secondary - used occasionally, according to the need, require periodical maintenance.
The costs incurred in relation to the existing forest roads in this area can be divided into:
· amortization (T1);
· current maintenance (T2);
· periodic maintenance (T3);
· loss of revenue due to unproductivity of the area that is converted into a forest road (T4).
The amortization of a forest road is calculated as an average annual expense of the present value of the project, during the life period of a forest road.
The average price for building one kilometre of forest road in the Republic of Croatia, according to the regulations/instructions of the Administration public enterprise Hrvatske ume is DM 54 000. Due to numerous favourable circumstances (favourable terrain conditions, already existing rides, etc.), the price of one kilometre of forest road in the management unit iljakovaèka Dubrava II is DM 40 000.
The construction of both primary and secondary roads is carried out according to the same standards (the price of building one kilometre is equal as well as the lifetime), so the amortization cost for both types of roads is equal, and it can be calculated as:
a = instalment
C = present cash value
r = interest factor
p = annual rate of interest
n = number of years for repayment
For an amortization period n = 33 and an annual interest rate p = 3%, the annual cost (annuity) of amortization of one kilometre of forest road is:
2. Current maintenance
In our case, current maintenance of forest roads refers only to primary forest roads. In the management unit iljakovacka Dubrava II, only road number (1) has the characteristic of primary forest road as it is used constantly, is connected to public asphalt roads, more or less passes through the middle of the management unit, and has also been used by local people.
The current maintenance of the upper surface is done by the system of "gritting" and 100 m3 of gravel is needed per kilometre of road every year.
The forest management authority Velika Gorica has its own gravel pit, so it does not pay for the gravel, but only for the handling charges:
· cost of gravel loading by a loader - DM 1.25 per m3;
· cost of transport of the gravel to a distance of 20-25 km (distance of the gravel pit from the management unit) - DM 7.63 per m3.
These prices were obtained through bidding.
The transport price increases by 40 percent if it is transported by rail; so in this management unit it can be assumed that approximately 2.5 km are transported by rail. As these 2.5 km are within a tariff limit of 20-25 km, the price of gravel transport is:
Building-in of the gravel is not calculated as a separate item, as it is gritted during the drive of a lorry itself by regulating the tipping body through the backside of a tipper. It is considered that this is included in the transport price obtained through bidding.
The total handling charge 1 m3 of gravel is:
while the annual cost of "gritting" 1 km of a primary forest road is:
T2 = 100 · 10.7 = 1007.00 (DM/km)
3. Periodic maintenance
Periodic maintenance consists of:
· reconstruction of the upper surface of secondary forest roads every five years;
· maintenance (cleaning) of the drainage of primary and secondary roads every five years.
3.1 Reconstruction of the upper surface of secondary forest roads
It is carried out by a system of "gritting" with 100 m3 of gravel per kilometre of road every five years. This means that for forest roads whose lifetime is 33 years such an operation should be carried out six times at a cost of DM 1 007 per km.
The total value of individual periodical repairs that have to be done during the lifetime of a road is reduced to a present value by a model of discounted rent:
Co = present value of individual costs (DM)
C = value of individual periodic costs (DM)
As costs are periodic, the annual interest factor should be changed into an adjusted interest factor (r*):
r* = r5 = 1.35 = 1.159274
The present value of periodic repairs is:
and from this the annual cost (annuity) during an amortization period is:
3.2 Maintenance of drainage of primary and secondary forest roads
It is carried out every five years, and it includes clearing of plants that cover ditches (done by seasonal hired workers), as well as desliming of drainage (mechanical). The average cost of these works is DM 2 per linear metre.
The present value of these works for a road lifetime of 33 years and at an annual interest rate of 3 percent equals:
and the annual cost is:
4. Loss of revenue due to unproductivity of areas converted into forest roads
Assuming that the existing structural elements of a stand are constant during the whole rotation period, calculating the average exploitability of timber volume of the main and previous revenue at present average market prices of timber, and deducting cultural costs and costs for forest protection, our management unit gives an average annual net income "on stump" of about DM 200 per ha.
Therefore, building 1 km of an 8 m forest road, which corresponds to the average width of a trunk (Figure 3.), 0.8 ha of forest is converted into unproductive area and, therefore, the following revenue is lost per year:
T4 = 0.8 · 200 = 160.00 (DM/km)
Figure 3. Normal transverse profile of a forest road in the management unit iljakovacka Dubrava II
Table 1. Recapitulation of costs incurred for the construction of forest roads in our management unit
5. Traffic load and costs of forest roads in the management unit under consideration
Two roads of public traffic of a total length of 7.7 km pass through the management unit. Out of this, 3.4 km have a forest only on one side, so when expressing the size of the opened-up area, 50 percent of the length of this section is taken into account.
Therefore, 6 km of public roads belong to this management unit, which results in an opening of 1.41 m/ha. As the forest management authority has not built these roads, nor do they maintain them, they are not considered when calculating the costs related to the opening-up of the forests.
The forest road of the primary type was built as a connection between two public roads, and the network of secondary roads developed from it.
The stage of building roads as well as the progress of costs can be shown in the following way:
· there are no costs up to 6 km of roads, as these are public roads;
· building 7.5 km of primary forest roads, we obtain:· a total road length 1 = 13.5 km
· opening of the management unit y = 3.18 m ha
· total costs of primary roads Tc = DM 225 866.08 per year
· we assume that out of 13.5 km of roads in the area of the management unit, only secondary forest roads will be built at an annual cost of DM 2620.84 per km.
We can conclude that beyond a total road length of 13.5t km, the annual cost of the road network would develop according to the following model:
Tc = total cost for the forest roads network (DM/year)
l = total road length in the management unit (km)
Figure 4. Progress in opening the management unit iljakovacka Dubrava II depending on total road length
Figure 5. Annual costs for the forest roads network depending on total road length in the management unit iljakovacka Dubrava II
6. Determination of annual costs for a forest roads network depending on the distance between roads in the management unit under consideration
Depending on the total road length, the opening will be according to formula (1)
The function of dependence of annual costs for a forest roads network (Tc) on the distance between roads can be determined from formulae (2), (3) and (4). Formulae (2) and (4) give the following results:
This expression for opening is substituted in formula (3) and we will obtain (T) depending on (e):
As formula (3) can only be applied to l > 13.5 km, then formula (5) is only held for e < 3146.6 m.
Calculation of wood extraction costs
In this management unit wood extraction to truck roads is done with forest tractors equipped with a reel and to do this job the following prices were determined depending on the length of extraction,
Table 2. Timber extraction prices for an average volume of 1000 kg/m3
Price in DM/m3
1. Determination of timber extraction costs depending on the distance between roads in the management unit iljakovacka Dubrava II
According to a theoretical model (Figure 6), timber species are extracted to a particular road at a distance 0 to e/3 from both sides. Therefore, the average extraction distance (ds) equals half this distance, i.e. is in a central position with respect to the extraction length.
ds = 0.25 · e
Due to the roughness of the soil (twisting of haulage ways in horizontal and vertical direction), the average extraction distance should be corrected by a "bypassing factor" which is:
· for low-lying areas: +10 percent
· for hilly areas: +28 percent
· for mountainous areas: + 40 percent
The corrected mean extraction distance will be called average extraction length (dp) and is:
dp = 0.275 · e
Equalizing extraction prices (Table 4) by a curve of square function according to a "method of mean values" the following formula was obtained:
Td = 3.022 · 10-5 · d2 + 0.036 · d + 6.0864 (DM/m3)
Td = extraction costs (DM/m3)
d = extraction length (m)
Figure 6. Wood extraction costs (Td) depending on extraction length (d)
In the above equation, if we substitute dp = 0.275 · e instead of (d), we get the equation for the extraction cost of 1 m3 of timber depending on the distance between roads:
Tc = 2.2855 · 10-6 · e2 + 0.01 · e + 6.0864 (DM/m3) (7)
2. Annual wood extraction costs in the management unit under consideration
Under the principle of "sustainability of production", it is assumed that the annual cut corresponds to the average annual increment of the timber volume.
In our management unit, the annual increment is 5.5 m3/ha and the determined average exploitation of cut timber volume is 82 percent. Therefore the net volume (En) that is extracted and transported each ear is:
En = 4.5 (m3/ha)
i.e. for the whole management unit it is:
En= 18349.88 (m3/year)
If we substitute this annual cut in formula (7), we obtain the function of annual extraction costs of timber volume (Tp) depending on the distance between roads (e):
Tp= 0.0419386 · e2 + 183.49875 · e + 111684.68 (DM/year) (8)
Calculation of optimum forest roads density
According to a theoretical model, the optimum density of a forest roads network (y0) is determined by the optimum distance between roads (eo), i.e. such a distance between roads that the sum of the costs for the roads (Tc) plus the extraction costs (Tp) is the lowest.
When these costs are expressed in the form of a function of road distance (5) and (8), they have the smallest value at a distance where the first derivative of sums of the mentioned functions equals zero:
S T = Tc + Tp
0.0838772 · e3 = 183.49875 · e2 - 1.1133328 · 108 = 0
e0 @ 680 (m)
Figure 7. Annual costs for a forest roads network and for wood extraction depending on the distance between roads in the management unit iljakovacka Dubrava II
To achieve the optimum forest roads density of 14.71 m/ha from formula (1), it follows that 62.5 km of roads are needed in our management unit.
This means that, apart from the already existing 44 km which give an opening ratio of 10.36 m/ha, additional 181.5 km of forest roads should be built. Then the forest roads network in this management unit would consist of:
· 6 km of public roads
· 56.5 km of forest roads, of which:· 7.5 of primary type
· 49 km of secondary type
The mean extraction distance (ds) would decrease to 170 m, i.e. the mean extraction length (dp) to 187 m.
Apart from the optimum density of the forest roads network, the optimum layout of forest roads on the area of the management unit should also be determined. Therefore, to calculate the optimum forest roads density by a theoretical model which is based on the minimum sum of combined road and extraction costs, the following steps should be taken in the following order:
· determine whether a particular management unit is suitable for the application of the theoretical model comparing the real terrain conditions with the assumptions on which the theoretical model is based;
· classify the existing forest roads;
· calculate the costs related to construction and maintenance of primary forest roads;
· calculate the costs related to construction and maintenance of secondary forest roads;
· find the functional dependence of annual costs for secondary forest roads on their respective distance;
· determine annual timber extraction costs which depend on road distance;
· determine optimum distance between roads which results in minimum total costs;
· calculate from the optimum distance between roads the optimum density of a forest roads network.
The topography of economic environment of this management unit, as well as its structural and habitat factors, support the determination of optimum forest roads density using this theoretical model. It is possible to calculate the optimum opening of the management unit iljakovacka Dubrava II comparatively quickly. Construction costs can also be reduced since they can be built in existing forest cuts. In addition, the forest management authority Velika Gorica provides a favourable business, organization and financial environment.
List of technical terms
· Optimum density of forest roads network: the relationship between road length and the area that gravitates towards them at the point where the sum of the costs for forest roads (construction and maintenance costs) plus timber extraction costs is lowest.
· Mean extraction distance: the distance from where the wood should be extracted so that extraction costs would be equal to those of extracting wood from various places in a stand.
· Average extraction length: mean extraction distance in view of the real conditions of the area considered, i.e. need to twist tractor haulage routes, both horizontally and vertically, corrected by a bypassing factor.
· Bypassing factor: a factor which, when multiplied by a theoretical mean extraction distance, results in an average extraction length in the concrete stands. It depends on the heterogeneity of the terrain both in horizontal and vertical directions. For low-lying areas it is + 10 percent; for hilly areas, + 28 percent; for mountainous areas, + 40 percent.
· Primary forest roads: roads that, according to the classification based upon frequency of use and need of maintenance, are in constant use and, therefore, require regular annual maintenance.
· Secondary forest roads: forest roads that are used only occasionally, when needed, and require periodic maintenance.
· Costs related to forest roads: costs that arise both when building forest roads or after that and include: amortization, current maintenance, periodic maintenance, loss of revenue due to unproductivity of the area converted into forest roads.
· Wood extraction costs: total extraction costs of felled timber from a particular area to the forest roads.
Arnautovic, R. 1975. Prilog istrazivanuj metoda odredivanja optimalne gustoce umskih komunikacija. Narodni umar 10-12. Sarajevo, pp. 344-362
Dürrstein, H. 1992. Detailed road planning using microcomputers. Proceedings IUFRO Workshop on Computer Supported Planning of Roads and Harvesting. Feldafing, Germany, pp. 57-66
Jelicic, V. 1983. umske ceste i putevi, skripta, SIZ odgoja i usmjerenog obrazovanja umarstva i drvne industrije SRH. Zagreb.
Löffler, H.J. 1991. Kllasifikacija terena za umarstvo. Mehanizacija umarstva 16, 1-4, Zagreb, pp. 25-44
Lovric, N. 1987. Metode planiranja otvorenosti umskih predjela i cestovne infrastrukture za potrebe prorjedivanja sastojina u nizinskim poplavnim podrucjima, umarski list 3-4, Zagreb, pp. 125-134.
Picman, D. 1993. Utjecaj konfiguracije terena i hidrografskih prilika na ekonomsku opravdanost izgradnje optimalne mreze umski prometnica, Doktorska disertacija, umarski fakultet Sveucilita u Zagrebu, 1-112.
Rebula, E. 1981. Optimalna otvorenost uma, Mehanizacija umarstva 6, 3-4, Zagreb, pp. 107-119.
Sabadi, R. 1992. Ekonomika umarstva, skripta, kolska knjiga, Zagreb.
Session, J. 1992. Using network analysis for roads and harvest planning. Proceedings IUFRO Workshop on Computer Supported Planning of Roads and Harvesting. Feldafing, Germany, pp. 36-41.
Shiba, M. 1992. Optimization of road layout in opening of forest. Proceedings IUFRO Workshop on Computer Supported Planning of Roads and Harvesting. Feldafing, Germany, pp. 1-12.
ikic, D., Babic, B., Topolnik, D., Knezevic, I., Bozicevic, D., vabe, Z., Piria, I. and Sever, S. 1989. Tehnicki uvjeti za gospodarske cete, Znanstveni savjet za promet JAZU, Zagreb.