help determining co-ordinates of offset points on a curve: need to find y dimension between flat horizontal and curved profile

[Sparky2008]

I'm a bit lost with this one so any help would be greatly appreciated!

I have a curve between two known horizontal points and known x axis offsets to defined positions at which I need to calculate the y dimensions between the flat horizontal and the curved profile. Below is an example, I know the radius of the curve is 91990.105mm but cant seem to find the correct solution to determine the dimensions I need. I have tried R2 = X2 + Y2 but the results appear to be incorrect.

 

[Dr.Peterson]

I'm a bit lost with this one so any help would be greatly appreciated!

I have a curve between two known horizontal points and known x axis offsets to defined positions at which I need to calculate the y dimensions between the flat horizontal and the curved profile. Below is an example, I know the radius of the curve is 91990.105mm but cant seem to find the correct solution to determine the dimensions I need. I have tried R2 = X2 + Y2 but the results appear to be incorrect.

View attachment 37356

You imply that the curve is an arc of a circle.

If the circle crosses the axis at x=0 and x=4289, then the center of the circle with radius [imath]R=91990.105[/imath] would be at [imath](x_c, y_c)[/imath], where [imath]x_c=2144.5[/imath] and [imath]x_c^2+y_c^2=R^2[/imath]. You can solve for [imath]y_c[/imath], and then the equation of the circle will be [imath](x-x_c)^2+(y-y_c)^2=R^2[/imath]. Solve for y in terms of x, and you will have a formula for the offset at any distance x along it.

Can you follow that?

Looking again, I see that you already know a point on the arc, [imath](2144.5, 25)[/imath]. Is the known radius derived from that? Yes, using the formula for R given here, I do get that value. So at least your information is consistent. And you could locate the center more easily using the 25 mm offset together with the radius; it's just [imath](2144.5, 25-91990.105)[/imath].