## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Sites

#### 2.2. Computation of Circuity Factors

_{net}and D

_{euc}are the network and Euclidean distances between the two end-points in a given section of forest road route, respectively.

#### 2.3. Factors Affecting the Forest Road Circuity

_{i}is the shape index, p is the perimeter (m), and A is the area size (m

^{2}).

#### 2.4. Statistics

## 3. Results

#### 3.1. Circuity Factors Vary with Cumulative Network Distance at the Vertical Position of Forest Roads

#### 3.2. Circuity Factors in 500-m Interval Sections per Vertical Position of Forest Roads

#### 3.3. Correlation between Circuity and Each Influential Factor

^{2}) = 0.79). The intersection angles of the 500-m sections of the forest road were 129°–140° (mean 135.2°) on the mid-slope roads, which had the highest circuity factor. The ridge roads were 129°–146° (mean 140.7°), and the intersection angles of the valley roads, with the lowest circuity factor, were 135°–153° (mean 145.6°). However, the size of the intersection angle in each 500-m section of the forest road was found to be negatively correlated with the circuity factor in the 500-m sections (R

^{2}= 0.39). The average longitudinal slope of the measurement section was 4.9%–21.4% (mostly within 15%), but the longitudinal slope and circuity factor of the forest roads were not significantly correlated (R

^{2}= 0.14). The shape index of the study area had a relatively long form due to the large index value for ridge and valley routes with low circuity factors. The shape index of the study area was high for the ridge and valley roads with low circuity factors; Figure 3d shows that this shape index had a longer shape like a bar-type.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**The distribution of the cumulative circuity factors according to the network distance by forest road location.

**Figure 3.**Linear correlation between the circuity factors and influential factors according to the studied road routes in South Korea. Regression between the circuity factor and (

**a**) the average number of curves, (

**b**) the intersection angle, and (

**c**) the longitudinal slope of the 500-m section of the road routes; (

**d**) regression between the circuity factor and the shape index.

Road No. | Administrative District | Road Length (m) ^{1} | Elevation (m) | Longitudinal Slope (%) ^{4} | Vertical Location | |
---|---|---|---|---|---|---|

B.P. ^{2} | E.P. ^{3} | |||||

1 | Donghae, Kangwon | 5000 | 223 | 261 | 8.98 | Ridge |

2 | Chuncheon, Kangwon | 4779 | 537 | 624 | 15.29 | |

3 | Heongseong, Kangwon | 3229 | 992 | 1129 | 6.47 | |

4 | Milyang, Kyeongnam | 4417 | 721 | 1077 | 10.98 | |

5 | Yeongyang, Kyeongbuk | 5000 | 255 | 462 | 9.56 | |

6 | Uiseong, Kyeongbuk | 3384 | 171 | 271 | 4.31 | |

7 | Bukgu, Ulsan | 5000 | 128 | 218 | 9.54 | |

8 | Bukgu, Ulsan | 5000 | 286 | 389 | 10.54 | |

9 | Boryeng, Chungnam | 2512 | 202 | 498 | 11.84 | |

10 | Heongseong, Kangwon | 5000 | 720 | 853 | 9.96 | Mid-slope |

11 | Pyeongchang, Kangwon | 5000 | 323 | 638 | 16.44 | |

12 | Bonghwa, Kyeongbuk | 2444 | 405 | 523 | 7.65 | |

13 | Yeongdeok, Kyeongbuk | 5000 | 798 | 813 | 8.30 | |

14 | Yeongyang, Kyeongbuk | 3742 | 459 | 455 | 6.23 | |

15 | Yeongyang, Kyeongbuk | 5000 | 378 | 420 | 9.16 | |

16 | Gongju, Chungnam | 5000 | 291 | 399 | 5.06 | |

17 | Nonsan, Chungnam | 3835 | 58 | 159 | 7.83 | |

18 | Dangjin, Chungnam | 5000 | 78 | 142 | 7.32 | |

19 | Cheonan, Chungnam | 5000 | 203 | 360 | 10.70 | |

20 | Inje, Kangwon | 4273 | 635 | 963 | 12.98 | Valley |

21 | Heongseong, Kangwon | 2511 | 392 | 685 | 12.20 | |

22 | Bonghwa, Kyeongbuk | 4593 | 167 | 325 | 8.42 | |

23 | Munkyeong, Kyeongbuk | 1861 | 436 | 654 | 20.47 | |

24 | Yeongyang, Kyeongbuk | 2247 | 586 | 750 | 11.80 | |

25 | Yeongyang, Kyeongbuk | 1826 | 501 | 746 | 8.60 | |

26 | Geumsan, Chungnam | 1743 | 350 | 433 | 10.93 | |

27 | Chungju, Chungbuk | 2556 | 323 | 480 | 8.84 | |

Total | - | 104,952 | - |

^{1}Road length is the distance digitized from the satellite image.

^{2}Beginning point.

^{3}End point.

^{4}The average value of the longitudinal slope of each 500-m section on all routes.

**Table 2.**Computation of the circuity factors on forest roads and the results of the one-way ANOVA test per the vertical location of the studied roads.

Vertical Location | Road No. | 500-m Section Average Circuity Factor | Mean | SD ^{1} | F | p |
---|---|---|---|---|---|---|

Ridge road (n = 74) | 1 | 1.16 (n = 10) | 1.24 ^{a} | 0.328 | 3.041 | <0.01 |

2 | 1.18 (n = 9) | |||||

3 | 1.08 (n = 6) | |||||

4 | 1.14 (n = 8) | |||||

5 | 1.58 (n = 10) | |||||

6 | 1.36 (n = 6) | |||||

7 | 1.19 (n = 10) | |||||

8 | 1.12 (n = 10) | |||||

9 | 1.19 (n = 5) | |||||

Mid-slope road (n = 88) | 10 | 1.64 (n = 10) | 1.61 ^{b} | 0.482 | ||

11 | 1.50 (n = 10) | |||||

12 | 2.12 (n = 4) | |||||

13 | 1.69 (n = 10) | |||||

14 | 1.82 (n = 7) | |||||

15 | 1.54 (n = 10) | |||||

16 | 1.46 (n = 10) | |||||

17 | 1.39 (n = 7) | |||||

18 | 1.46 (n = 10) | |||||

19 | 1.73 (n = 10) | |||||

Valley road (n = 40) | 20 | 1.05 (n = 8) | 1.06 ^{c} | 0.057 | ||

21 | 1.05 (n = 5) | |||||

22 | 1.09 (n = 9) | |||||

23 | 1.13 (n = 3) | |||||

24 | 1.04 (n = 4) | |||||

25 | 1.03 (n = 3) | |||||

26 | 1.03 (n = 3) | |||||

27 | 1.04 (n = 5) |

^{1}SD: Standard deviation. Superscript letters (a, b, and c) represent a significant difference at α = 0.01.

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