Distance is the numerical value by which two objects are physically separated, and travel distance (i.e., network distance) is an important factor in determining the accessibility to any destination in the transport and logistics sector [1
]. In most cases, since the network distance is longer than expected [2
], various distance analysis techniques were studied to estimate distance more accurately [3
]. Most studies of distance analysis used a distance estimating function based on the Euclidean distances of two points [1
The circuity factor of a road network, which is one of these distance estimating functions, is defined as the ratio of the shortest distance to the network distance in the road network for two different points [4
]. Because the regional circuity factor is influenced by terrain, rivers, facilities, and road density [3
], it can be used as an index to compare regional traffic efficiency [9
] and spatial characteristics [5
]. The circuity factor can realistically reflect the actual distance required in various plans [3
]. For example, the circuity factor for a target area can be calculated accurately after the road is constructed, so that the actual distance of the route to be planned can be estimated using the circuity factor for similar terrain or nearby areas [11
Studies of road circuity were mainly conducted to identify the characteristics of the network distance on national or urban scales [1
] using the weighted circuity factor [1
] or unweighted circuity factor [6
]. The aforementioned circuity factor can be defined as unweighted circuity [5
]; the weighted circuity is the average value of the circuity factor calculated by dividing the network distance into segments of unit length, which is applied because the circuity factor is affected by the network distance [4
]. This can be said to be a concept applied to minimize the effects of measuring distance. The accessibility of public facilities, such as public offices, hospitals, and schools, and spatial characteristics, such as the location analysis of residential space using commuting distance, were compared using circuity factors [3
]. These circuity factors estimate the actual distance with a certain level of accuracy within the urbanized area [12
], and several studies found an average circuity factor of 1.2 to 1.3 in urban road networks [1
]. However, in the case of non-urbanized areas, the deviation may be large [1
]. In particular, forest roads, which provide infrastructure for sustainable forest management [16
], are affected by their route alignments due to mountainous terrain; thus, most of the route is composed of complex linear shapes, and the circuity factors deviate considerably from region to region [11
]. To estimate the actual road distance for planning a road network or forest operation, estimating the network distance and calculating the circuity factor of the forest road network are necessary. Through this process, it is possible to more accurately and quickly estimate the transportation time and cost using various forestry machines. As the network distance on the road increases, the transportation efficiency decreases and costs increase; these differences can be used to assess the alignment of the road route in terms of its transportation efficiency.
Several studies reported on the circuity of forest road networks. Although their methods and objects differed (e.g., forest roads, public roads, and railways), their results can be converted into the circuity factor of the forest roads as follows: Sugihara and Iwakawa [17
], 1.57; Hujiwara [18
], 1.22–1.58; Cha et al. [19
], 1.33–1.63; Cha and Cho [20
], 1.02–1.88; and Nakazawa et al. [15
], 1.29–1.87. These studies reported that the effects of the circuity factor on plane factors (e.g., villages, forests, and streams) are greater than those of stereoscopic factors, such as elevation [1
]. The circuity factor appears higher in areas with rough terrain and rocky areas [20
]. Hujiwara [18
] reported that the circuity factor of mid-slope roads was higher than that of valleys because mid-slope roads are more affected by the terrain and moving distance than valleys. Nakazawa et al. [15
] also analyzed the circuity of road networks (e.g., highways, forest roads, and skid trails) and reported that circuity is influenced by road length, whereas the influence of the longitudinal slope is relatively small. As mentioned above, these studies related to forest road circuits were conducted locally on a single route. Research on such routes is lacking; thus, it is difficult to estimate how many forest road routes are generally bypassed compared to straight-line distances.
Thus, the purpose of this study was to determine how much the road distance differs from the Euclidean distance in mountainous areas. More specifically, this study (1) estimated the average circuity factor for 27 forest roads according to the vertical locations of the roads in South Korea, and (2) analyzed the factors affecting the circuity of forest roads.
As a result of this study, it was found that forest roads in South Korea exceed the Euclidean distance by about 1.6 times on average: ridge roads by about 1.4 times, mid-slope roads by about 2.1 times, and valley roads by about 1.1 times, according to the location of the mountain slope. The average circuity factor of the public road network in South Korea is 1.26 [1
]. Compared with the results of this study, the circuity factor of valley roads was lower than that of public roads, whereas those of ridge roads (1.36) and mid-slope roads (2.09) were higher.
In terms of unweighted circuity [6
], the circuity factors of the mid-slope roads tended to increase gradually with increasing network distance. The circuity factor of the studied routes was affected by the network distance in the general mountainous area. In particular, in the case of ridge roads, the circuit factor no longer increased in the section above 3500 m, because the average curve of the 500-m section was higher in the sections below 3500 m (mean 6.6) than the sections over 3500 m (mean 4.6). For the studied ridge and valley routes, the circuity factor was also low and the change range was small since the road alignment was relatively straight. Hujiwara [18
] reported a similar trend as found in this study. They found about a 30% difference between the mid-slope and valley roads due to changes in the mountain terrain. However, Cha and Cho [20
] reported that the circuity of the forest roads is affected by the frequency of valleys and streams but is not correlated with network distance. These results are different from the results of this study because the measurement length of their road circuity was too short (100–300 m) and their study route was locally selected.
Although directly comparing public road networks with forest road networks is difficult because public roads are longer than forest roads, the circuity factor of the public road networks is known to gradually decrease as the network distance traveled increases [1
]. According to Kim et al. [1
], the circuity of public road networks, including highways in South Korea, gradually increases to about 100 km of traveled distance and then tends to decrease. Other studies considered the increase of circuity to be caused by the influence of topography and other avoidance factors within relatively short sections (within 100 km); thereafter, circuity decreased due to the influence of the form of the route, that is, straightened wide-area networks, such as highways or the national road system. The road alignment is highly affected by the terrain; the linearity of this alignment can be achieved using tunnels and bridges, whereas forest roads are more influenced by changes in the mountain terrain. Therefore, the transportation efficiency of the forest roads in mountainous areas decreases as the network distance increases.
In terms of the weighted circuity based on 500-m sections, the average circuity factor was 1–1.6 times higher than the straight distance. Most studies on forest road circuity [15
] estimated the weighted circuity factors based on different interval distances. Although difficult to compare, Cha and Cho [19
] and Cha et al. [20
] reported that the average circuity of the forest roads in some areas of South Korea bypassed the average by 1.2–1.6 times compared to the straight-line distance. Hujiwara [18
] found that the average circuity of mid-slope roads (1.58) was higher than that of valleys (1.21), indicating a similar trend. A number of studies reported that the circuity of road networks is influenced by the shape of the road network, which is affected by planar and vertical factors [1
]. In particular, the horizontal alignment that affects the circuity of road networks is more influenced by the planar factor than the vertical factor [1
] and depends on the shape of the mountainous terrain and the frequency of ridges and valleys [19
]. For road networks on national scales, circuity is affected by multiple factors, such as the sample size of the city, road density and connectivity, lakes and seas, mountains, and conservation areas [3
The results of this study show that the road circuity is considerably influenced by the change in mountainous terrain. In mid-slope areas, roads are commonly constructed along the contour line at an average slope of less than 10% to prevent longitudinal erosion that may occur along the road’s surface and the periphery along the route [25
]. The mid-slope roads on these gentle gradients repeatedly pass through ridges and valleys; thus, the horizontal alignment of the lines has a winding shape. Therefore, the road routes detour further, and this is why mid-slope roads have a network distance about 1.6 times the straight-line distance based on the road’s beginning and end points. In whole-tree harvesting sites, it is important to build multiple log landings to increase transport efficiency [26
]. In general, the pre-hauling of ground-based harvesting is performed within the 500-m range [27
]. Therefore, ground-based pre-hauling using forest roads or skid trails can be applied in terms of weighted circuitry. On the other hand, estimates of timber transport distances using log trucks may apply unweighted circuity.
The circuity factors of ridge and valley roads were relatively low, and their variations were not large. These results indicate that the road alignments on ridges and in valleys were relatively straight compared to those of the mid-slope roads. The ridge and valley areas are thought to be less developed; I determined that few route detours occur because the routes in the mountain area pass through the ridges with a relatively small change. Consequently, the circuity of this route appeared to be low. The valley roads are constructed in mountainous areas where the development of ridges and valleys is remarkable. However, since this route has a gradient that builds relatively rapidly along the direction of the water system, I found less circuity than the mid-slope roads.
The proportion of seven or more curves in the planar line of the study route was about 77% for mid-slope, about 41% for ridge, and 10% for valley routes. This shows that the topographical changes in the mid-slope roads are relatively larger than those of the ridges and the valleys. In particular, the horizontal alignment of the route determines the curves and intersection angle depending on the shape of the terrain [20
]. The circuity of the forest road increases as the number of curves increases, and the intersection angles decrease. Even with the same frequency of curves, the circuity factor of the mid-slope roads was larger than the other sections, which is why the intersection angles of the mid-slope roads were smaller. The correlation coefficient between the weighted circuity factor (500-m intervals) and the average longitudinal slope was low, but the shape index was relatively bar-shaped in the area with a low degree of circuity. This is because the road route was arranged to evenly cross the target area. Thus, the horizontal alignment of the route has a close relationship with the mountainous terrain; these factors were shown to considerably influence the road circuity.
Road alignment plays a crucial role in ensuring the safety and smooth travel of a vehicle. However, since most roads have irregular and winding linear shapes due to rough and complicated terrain conditions, their speed is limited to ensure the safety of the traveling vehicle, which considerably influences transportation efficiency.
As a result of this study, the forest roads in the mountainous areas of South Korea were found to exceed the Euclidean distance by an average of 1.1–2.1 times, and the most detours occur on mid-slope roads. This study concludes that road circuity has a close relationship with mountainous terrain, and the changes in the mid-slope terrain are relatively larger than those of ridge or valley terrains. It was found that road circuity increases as network distance increases in mountainous areas; a longer route length of the road results in a lower efficiency of transport through the road network. To increase the efficiency of forest operations and transportation, it is important to locate the landings and properly connect them with public road networks.
The circuity of public road networks on the national and regional scales is somewhat different from the circuity of forest road networks. Since this circuity depends on various factors, including its measurement distance and method, a suitable method for estimating the circuity of forest roads is required. In the future, it is expected that it will be possible to use various aspects, such as the evaluation of the transportation efficiency of road networks, to estimate the network distance of planning routes and engage in operation planning.