Ellipse Vertical Chord from Edge

The Ellipse Vertical Chord from Edge calculator computes the chord of an ellipse where the chord is vertical at a distance along the semi-major axis from the edge.

INSTRUCTIONS: Choose units and enter the following:

• (A) Semi-Major Axis
• (B) Semi-Minor Axis
• (d) Horizontal Distance from Edge

Ellipse Vertical Chord from Center (VE): The results are returned in centimeters.  However, these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Ellipse Vertical Chord from Edge equation computes the length of the vertical chord in an ellipse that is a distance from the edge

`VE = 2*(B/A) * sqrt(2*A*d-d*d)`

where:

• VE = length of the vertical chord
• A = length of semi-major axis
• B = length of semi-minor axis
• d = distance from the semi-minor axis.

Ellipse Calculators

An ellipse is defined by the semi-major axis (A) and semi-minor axis (B).

• Area of Ellipse: Computes the area of an ellipse based on the semi-major axis (a) and the semi-minor axis (b).
• Rumanujan's Circumference of an Ellipse 1 : The first of two of Rumanujan's approximations of the circumference (perimeter) of an ellipse based on the semi-major axis (a) and the semi-minor axis (b).
• Rumanujan's Circumference of an Ellipse 2: The second Rumanujan approximations of the circumference (perimeter) of an ellipse based on the semi-major axis (a) and the semi-minor axis (b).
• Circumference of an Ellipse (other) Another common estimation of the circumference (perimeter) of an ellipse based on the semi-major axis (a) and the semi-minor axis (b).
• Ellipse Axis Length: Approximates one axis of an ellipse bases on the circumference and the other axis.
• Eccentricity of an Ellipse  Computes the eccentricity of an ellipse which is based on the ratios of the semi-major axis (a) and the semi-minor axis (b).
• Linear Eccentricity of an Ellipse (f)  Computes the distance from the center to either foci (f), which is the linear eccentricity of an ellipse.  This is based on the semi-major axis (a) and the semi-minor axis (b).
• Mean Radius of an Ellipse  Computes the mean radius of an ellipse.  This would define a circle with the same approximate area, based on the ellipse's semi-major axis (a) and the semi-minor axis (b).
• Elliptical Volume  Computes the volume of a column with an elliptical base.

Ellipse Chords

• Ellipse Vertical Chord from Edge (VE): Computes the length of the vertical chord of an ellipse based on distance from the edge.
• Ellipse Vertical Chord from Center (VC): Computes the length of the vertical chord of an ellipse based on distance from the center.
• Ellipse Horizontal Chord from Edge (HE): Computes the length of the horizontal chord of an ellipse based on distance from the edge.
• Ellipse Horizontal Chord from Center (HC): Computes the length of the vertical chord of an ellipse based on distance from the center.

Ellipsoid (3D Elliptical Shape)

• Ellipsoid - Volume computes the volume of an ellipsoid based on the length of the three semi-axes (a, b, c)
• Ellipsoid - Surface Area computes the surface area of an ellipsoid based on the length of the three semi-axes (a, b, c)
• Ellipsoid - Mass or Weight computes the mass or weight of an ellipsoid based on the length of the three semi-axes (a, b, c) and the mean density.

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