SD Drain Parabolic Design

SD Drain uses the following information to create a parabolic ditch:

  • Parabolic Ditch width
  • Parabolic Ditch depth

Our parabolic shape is calculated so that the depth halfway between the edge and center of the parabola is 3/4 the depth of the parabola

 

Example:

  • Ditch width = 36 ft
  • Ditch depth = 2 ft
  • Ditch depth 1/2 way from ditch center to ditch edge = 1.5 ft

Cross section of example

Calculations:

    Parabola Formula

        y = a(x – h)^2 + k

    For our example:

    • h = 18 (horizontal center of the parabola)
    • k = 0 (minimum height at the vertex)
    • a = coefficient determining the curvature

    Solving for Coefficient a

    Using the point at 50% width from the center (x = 9 or x = 27, y = 1.5):

    • 1.5 = a(9 – 18)^2
    • 3/2 = a(81)
    • a = 2/(81*3) = 2/243 

    Final Equation for calculating height

    The equation of the example parabola is:

         y = (2/243)(x – 18)^2

    Height Calculations at Specific Points

    1. At 50% width from center (x = 9): y = (2/243)(9 – 18)^2 = (2/243)(81) = 0.66 ft or 8″
    2. At 50% width from center (x = 27): y = (2/243)(27 – 18)^2 = (2/243)(81) = 0.66 ft or 8″