Vertical Parabolic Curves Summit

Question 1

Also known as BVC (beginning of vertical curve)

Answer 1

Point of Curvature (PC)

Question 2

Also known as EVC (end of vertical curve)

Answer 2

Point of Tangency (PT)

Question 3

Also called PVI (point of vertical intersection)

Answer 3

Point of Intersection of the Tangents (PI)

Question 4

It is the projection of the curve onto a horizontal surface which corresponds to the plan distance

Answer 4

Length of Parabolic Curve (L)

Question 5

Horizontal distance from PC to the highest (lowest) point of the summit (sag) curve

Answer 5

S1

Question 6

Horizontal distance from PT to the highest (lowest) point of the summit (sag) curve

Answer 6

S2

Question 7

Vertical distance between PC and the highest (lowest) point of the summit (sag) curve

Answer 7

h1

Question 8

Vertical distance between PT and the highest (lowest) point of the summit (sag) curve

Answer 8

h2

Question 9

Grade (in percent) of back tangent (tangent through PC)

Answer 9

g1

Question 10

Grade (in percent) of forward tangent (tangent through PT)

Answer 10

g2

Question 11

Change in grade from PC to PT

Answer 11

A

Question 12

Vertical distance between PC and PI

Answer 12

a

Question 13

Vertical distance between PT and PI

Answer 13

b

Question 14

Vertical distance between PI and the curve

Answer 14

H

Question 15

Formula of Vertical Distance between PC to PI

Answer 15

a = ½g1L

Question 16

Formula of Vertical Distance between PT to PI

Answer 16

b = ½g2L

Question 17

Formula of Horizontal Distance from PC to Summit

Answer 17

S1 = g1L/g1+g2

Question 18

Formula of Horizontal Distance from Summit to PT

Answer 18

S2 = g2L/g1+g2

Question 19

Formula of Vertical Distance between PC to Summit

Answer 19

h1 = ½g1S1

Question 20

Formula of Vertical Distance between PT to Summit

Answer 20

h2 = ½g2S2

Question 21

Formula of Height from PI to the Curve

Answer 21

H = ⅛L(g1+g2)

Question 22

Formula of Parabolic Relationship

Answer 22

x²/y = (½L)²/H