Plotting a Parabola or a Parabolic Graph

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PLOTTING A PARABOLIC GRAPH.

The formula: Y squared = 4 times P times X.

PLOTTING a parabolic graph is easy. We will use the formula Y squared = 4 times P times X.

Where Y is the radius or ½ the diameter of a dish or a lineal parabolic and is plotted along the y axis..

X is the x axis of the plot. Normally the horizontal axis. X is the depth of the dish or lineal parabolic.

P is the focal length measured along the X axis from the bottom center of a dish, or a lineal parabolic, to the focal point. The bottom of the dish may also be refereed to as point D, or DirectX.

4 is a constant used in all parabolic plots.

To plot a parabolic, you need to know any two of the 3: Y, P, and X.

Lets say you wish to plot a parabolic that has a diameter of 8 units. Units can be feet, inches, meters or any other unit of lineal measurement.

A diameter of 8 means the radius or ½ the diameter is 4, and 4 squared is 16 = Y squared.

Now we can specify either the focal length (P), or the depth of the dish (X), one or the other not both.

If we specify P then we can calculate X from the formula. If we specify X then we can calculate P from the formula.

Lets specify P = 4. So to calculate X we divide Y squared by (P times 4) remember 4 is a constant in the formula so The formula is: X = 16 divided by 4 times 4 = 16/16 = 1. So X= 1. The parabolic is 1 unit deep.

Lets suppose you wanted a depth of 1 unit and the parabolic is 8 units in diameter and you need to know how far out on x is the focus.

Depth of the dish or lineal parabolic is 1 so X = 1. Radius is 4. and 4 squared is 16. Y squared = 16.

P = Y squared divided by 4 ( the constant ) divided by X.

P= y(2)/4/1= 4 or P =16/4/1= 4.

If this dish had a width of 8 feet, and the depth of the dish is 1 foot, then the focal point (P) is 4 feet from the bottom of the dish.

You have a dish 48" diameter and 6" deep. How far out is the focus measured from the bottom of the dish.

X = zero at the bottom of the dish. X= 6 at the lip of the dish.

The dish is 48" diameter, so the radius is ½ that or 24". Y = 24.

P = Y squared divided by 4 divided by X. Remember 4 is a constant in this formula.

P =24(2)/4/6. Or P = 576/4/6 = 24" . The focal point is 2 feet from the bottom of the dish.

How deep would the 48" dish be if the focal point was 12" from the bottom of the dish?

You will notice that the deeper the dish, the shorter the focal length, or the shallower the dish, the longer the focal point.

Dennis Cofield.

For more information e-mail us at acrosolar@elp.rr.com

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