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October 25th, 2019, 05:51 AM   #1
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Question Non-Linear Relation

Could someone tell me about the relation in the attached image.
One in the top follows the linear relation and extended length can be obtained through multiplying the height*angle.

What would be relation for bottom one?
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October 25th, 2019, 06:47 AM   #2
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Can you define the curve in some way?
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October 25th, 2019, 08:49 AM   #3
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Concave

It can be of conic, but it has to be a concave shape.

Thank you for your response..
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October 25th, 2019, 12:27 PM   #4
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Is this a design problem? As in, you are supposed to choose a concave shape, and then calculate the length?

A parabola, a hyperbola, a circular arc, and an elliptical arc are all conics that can be concave and can fit there. Once you have the shape (whether it be given, or whether you design it yourself), just write the equation as y = f(x). x is the vertical distance, and y is the horizontal distance. Then the ? is just f(h).

For example, the surface of the top shape is described by the equation y = ax. Substitute x = h, and y(h) = ah.
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October 28th, 2019, 05:04 AM   #5
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Post Question Explained

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Originally Posted by skipjack View Post
Can you define the curve in some way?
How to find the points for conic curve? You can find the explanation in the picture attached.
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October 28th, 2019, 05:59 AM   #6
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Quote:
Originally Posted by HazyGeoGeek View Post
. . . height*angle.
It looks like height*tan(angle) to me, where tan is the usual trigonometric tangent function.
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October 28th, 2019, 06:01 AM   #7
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Question Explained

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Originally Posted by DarnItJimImAnEngineer View Post
Is this a design problem? As in, you are supposed to choose a concave shape, and then calculate the length?

A parabola, a hyperbola, a circular arc, and an elliptical arc are all conics that can be concave and can fit there. Once you have the shape (whether it be given, or whether you design it yourself), just write the equation as y = f(x). x is the vertical distance, and y is the horizontal distance. Then the ? is just f(h).

For example, the surface of the top shape is described by the equation y = ax. Substitute x = h, and y(h) = ah.
Yes This is a design problem. And I have to create a concave curve. Could you plaese specify how to obtain the concave curve points. When I tried with the parabolic equation it doesn't work.
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October 28th, 2019, 06:06 AM   #8
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What do you mean by, "it didn't work?"
Your simple choices for conics are:
$y = \sqrt{r^2-x^2}$, where $r\geq h_5$
$y = \sqrt{a^2-\frac{a^2}{b^2}x^2}$, where $b \geq h_5$
$y = ax^2$, where $a > 0$
$y = \sqrt{\frac{a^2}{b^2}x^2+a^2}$, for any $a, b$

Last edited by DarnItJimImAnEngineer; October 28th, 2019 at 06:56 AM. Reason: Fixed hyperbolic equation for consistency
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