#### Problem (1)

PVI station and location are 74+26.50 and 772.30 ft. What are the endpoints' stations and elevations of a 750.00 ft long curve with incoming and outgoing grades of -4.00% and +2.00%?

#### For problems (2) through (4), compute the following items

##### (a) Curve table at full station interval. Include curve point grades.

(b) Stations and elevations of the curve's highest and lowest points?

#### Problem (2)

PVI station and location are 56+50.00 and 1325.00 ft. Incoming and outgoing grades are +5.0% and -3.5%. A 500.00 ft long vertical curve will be used.

##### (a) Curve Table

Station | d_{i}, sta |
Elev_{i}, ft |
g_{i}, % |

59+00 EVC | 5.0000 | 1316.250 | -3.5 |

58+00 | 4.0000 | 1318.900 | -1.8 |

57+00 | 3.0000 | 1319.850 | -0.1 |

56+00 | 2.0000 | 1319.100 | +1.6 |

55+00 | 1.0000 | 1316.650 | +3.3 |

54+00 BVC | 0.0000 | 1312.500 | +5.0 |

Math checks in red.

##### (b) Highest and lowest points

Because this is a crest curve, the lowest point will occur at either the BVC or EVC.

In this case lowest point is at BVC: 54+00.00 @ 1312.50 ft

Highest:

#### Problem (3)

A 425.00 ft long curve ends at station and elevation 88+00.00 and 1220.00. Its initial and final grades are -4.00% and +2.75%.

*Only the answers are given, computations left to the reader.*

##### (a) Curve table

Station |
d_{i}, sta |
Elev_{i}, ft |
g_{i}, % |

92+25 EVC | 4.2500 | 1217.344 | +2.75 |

92+00 | 4.0000 | 1216.706 | +2.35 |

91+00 | 3.0000 | 1216.147 | +0.76 |

90+00 | 2.0000 | 1215.176 | -0.82 |

89+00 | 1.0000 | 1216.794 | -2.41 |

88+00 BVC | 0.0000 | 1220.000 | -4.00 |

Math checks in red.

##### (b) Highest and lowest points

Sag curve so either BVC or EVC is highest point

__Highest: BVC, 88+00.00 @ 1220.000 ft__

__Lo____west: 90+51.852 @ 1214.963 ft__

#### Problem (4)

A curve begins at station 32+00.00 and elevation 912.00 ft; it ends at station 38+00.00 and elevation 915.00 ft. The PVI elevation is 918.00 ft.

*Only the answers are given, computations left to the reader.*

##### (a) Curve table

Station |
d_{i}, sta |
Elev_{i}, ft |
g_{i}, % |

38+00 EVC | 6.0000 | 915.000 | -1.00 |

37+00 | 5.0000 | 915.750 | -0.50 |

36+00 | 4.0000 | 916.000 | 0.00 |

35+00 | 3.0000 | 915.750 | +0.50 |

34+00 | 2.0000 | 915.000 | +1.00 |

33+00 | 1.0000 | 913.750 | +1.50 |

32+00 BVC | 0.0000 | 912.000 | +2.00 |

Math checks in red.

##### (b) Highest and lowest points

This is crest curve so the lowest point will be at BVC or EVC.

__Lowest point: BVC, 32+00 @ 912.000 ft__

__Highest point occurs at grade = 0.00%: 36+00 @ 916.000 ft__

#### Problem (5)

A 400.00 ft vertical curve begins at station 29+00.00 and elevation 954.00 ft. Its initial and final grades are -1.00% and -2.25%.

#### Part (a)

What are the station and elevation of the curve's midpoint?

The midpoint is *not* the PVI. It has the same station as the PVI, but is located on the curve.

Alternate solution

#### Part (b)

What are the stations and elevations of the curve's highest and lowest points?

Because both grades are negative, the highest point is the BVC, lowest is EVC.

Highest: 29+00.00 @ 954.00

Lowest: