October 25th, 2019, 05:51 AM  #1 
Newbie Joined: Oct 2019 From: France Posts: 4 Thanks: 0  NonLinear 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? 
October 25th, 2019, 06:47 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,124 Thanks: 2332 
Can you define the curve in some way?

October 25th, 2019, 08:49 AM  #3 
Newbie Joined: Oct 2019 From: France Posts: 4 Thanks: 0  Concave
It can be of conic, but it has to be a concave shape. Thank you for your response.. 
October 25th, 2019, 12:27 PM  #4 
Senior Member Joined: Jun 2019 From: USA Posts: 386 Thanks: 211 
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. 
October 28th, 2019, 05:04 AM  #5 
Newbie Joined: Oct 2019 From: France Posts: 4 Thanks: 0  Question Explained How to find the points for conic curve? You can find the explanation in the picture attached.

October 28th, 2019, 05:59 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 21,124 Thanks: 2332  
October 28th, 2019, 06:01 AM  #7  
Newbie Joined: Oct 2019 From: France Posts: 4 Thanks: 0  Question Explained Quote:
 
October 28th, 2019, 06:06 AM  #8 
Senior Member Joined: Jun 2019 From: USA Posts: 386 Thanks: 211 
What do you mean by, "it didn't work?" Your simple choices for conics are: $y = \sqrt{r^2x^2}$, 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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