# Automated Parameter Determination for Horizontal Curves for the Purposes of Road Safety Models with the Use of the Global Positioning System

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Theory and Calculation

_{1}, E

_{2}, and E

_{3}(Equation (2)).

_{1}, E

_{2}, and E

_{3}were calculated (Equation (3)). With the above assumptions, we reformulate the necessary condition for the existence of a curve, which can be expressed as

_{1}, ΔE

_{2}, and ΔE

_{3}denote the maximum uncertainties for expressions E

_{1}, E

_{2}, and E

_{3}.

_{1}(red on the graph) and l

_{2}(green on the graph) which could be seen in Figure 2, could be described with functions (Equation (9)):

_{0}, a

_{1}, a

_{2}(consistent with Equation (12)). These transformations turn the circle equation into a second-degree polynomial (Equation (13)):

## 4. Results

## 5. Discussion

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Determining the intersection angle of two straight-line segments of the road, divided by a curve in the horizontal alignment.

Objected | Circle Diamete [m] | Length of Curve [m] | Beginning of Curve [m] | Middle of Curve [m] | End of Curve [m] |
---|---|---|---|---|---|

40 | 801.42 | 124.49 | 288,853.56 | 288,915.81 | 288,978.06 |

46 | 256.31 | 99.27 | 285,797.75 | 285,847.39 | 285,897.02 |

48 | 895.37 | 157.25 | 285,503.81 | 285,582.43 | 285,661.05 |

56 | 471.05 | 170.11 | 281,647.82 | 281,732.87 | 281,817.92 |

60 | 509.93 | 167.99 | 280,894.10 | 280,978.09 | 281,062.08 |

62 | 550.03 | 189.95 | 280,483.19 | 280,578.16 | 280,673.14 |

63 | 181.14 | 89.18 | 280,381.84 | 280,426.44 | 280,471.03 |

66 | 622.82 | 100.68 | 280,076.36 | 280,126.71 | 280,177.05 |

68 | 271.47 | 216.05 | 279,704.29 | 279,812.32 | 279,920.35 |

70 | 888.12 | 104.33 | 279,562.34 | 279,614.49 | 279,666.66 |

78 | 162.05 | 91.12 | 277,357.82 | 277,403.37 | 277,448.93 |

80 | 423.91 | 164.48 | 277,064.02 | 277,146.26 | 277,228.50 |

82 | 393.77 | 97.34 | 276,200.00 | 276,248.67 | 276,297.34 |

84 | 121.67 | 26.11 | 275,921.27 | 275,934.33 | 275,947.39 |

86 | 610.66 | 133.62 | 274,109.48 | 274,176.29 | 274,243.11 |

88 | 392.09 | 176.43 | 271,277.14 | 271,365.36 | 271,453.57 |

94 | 914.79 | 126.69 | 269,862.06 | 269,925.41 | 269,988.76 |

96 | 1648.89 | 175.97 | 269,208.75 | 269,296.74 | 269,384.72 |

98 | 754.86 | 159.12 | 269,036.61 | 269,116.18 | 269,195.74 |

100 | 394.50 | 113.36 | 268,666.87 | 268,723.55 | 268,780.23 |

108 | 535.59 | 251.16 | 266,850.73 | 266,976.31 | 267,101.89 |

110 | 419.80 | 154.17 | 265,571.92 | 265,649.01 | 265,726.10 |

112 | 731.21 | 173.12 | 265,269.80 | 265,356.36 | 265,442.92 |

114 | 304.73 | 103.93 | 264,963.62 | 265,015.58 | 265,067.55 |

Parameter | Value |
---|---|

Length of curve segments [km] | 5.758 |

Length of straight-line segments [km] | 18.200 |

Collisions on curves | 24 |

Collisions on straight-lines | 17 |

Numbers of collisions/1km curve | 4.16 |

Number of collisions/1km straight-line | 1.06 |

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**MDPI and ACS Style**

Budzynski, M.; Jamroz, K.; Pyrchla, J.; Kustra, W.; Inglot, A.; Pyrchla, K. Automated Parameter Determination for Horizontal Curves for the Purposes of Road Safety Models with the Use of the Global Positioning System. *Geosciences* **2019**, *9*, 397.
https://doi.org/10.3390/geosciences9090397

**AMA Style**

Budzynski M, Jamroz K, Pyrchla J, Kustra W, Inglot A, Pyrchla K. Automated Parameter Determination for Horizontal Curves for the Purposes of Road Safety Models with the Use of the Global Positioning System. *Geosciences*. 2019; 9(9):397.
https://doi.org/10.3390/geosciences9090397

**Chicago/Turabian Style**

Budzynski, Marcin, Kazimierz Jamroz, Jerzy Pyrchla, Wojciech Kustra, Adam Inglot, and Krzysztof Pyrchla. 2019. "Automated Parameter Determination for Horizontal Curves for the Purposes of Road Safety Models with the Use of the Global Positioning System" *Geosciences* 9, no. 9: 397.
https://doi.org/10.3390/geosciences9090397