How to determine the horizontal length of a curve?

A steel bar is 25 drawing units long. I want to bend it against a round bar that is 50 units in diameter. The 25 unit steel bar now becomes curved, and the curve has a diameter of 50 units.

Before bending the steel bar, DIMLINEAR command would show "25" because it's 25 units long. After bending, DIMLINEAR would produce a dimension that's smaller than 25, say 22, because the steel bar has bent.

My question is: How do i accurately determine the horizontal length (22 or 23 or 21 etc) of the bent steel bar? Obviously it would be smaller than 25, as stated above, but how small?

By horizontal lenght, you mean lenght from end to end of the 25 unit steel bar?

hmm....you can quite easy draw it in AutoCAD and determine the length... how to calculate it on paper I don't know, I just liked simple trig

Ok, since I do like trig, I did some diggind in my old schoolbooks and this is how I did it.

With the formula: angle = 360 * (arclength / ( 2*pi*radius)) you can get what angle the 25 unit long steel bar encompasses.

When you have the angle, you have a triangle with two equally long sides (the radius of the circle = 50/2=25) and one known angle. Since the triangle have equally known sides, the two angles left have to be equally big, which is ((180-known angle) / 2).

from this you can split the triangle into two triangles, each with all the angles and one known side. Then you can use the sinus or cosinus formula to get the length of the wanted side, which is half of the horizontal lenght that you originally was after.

Do you follow me?

Is this a theoretical exercise or do you want to know what is actually going on ?

If you push the steel bar against a 50mm former, when you release the pressure, the ends of the bar are going to spring up, and the bar is no longer at the radius you wanted. You have to use a former that is of less diameter than you want to end up with. And that is not allowing for any stretching in the steel

If you want to do a theoretical exercise, then I would draw it out (saves having to search out the trigonometry tables). The bar would have an inside diameter of 50, and a diameter along its centreline of (50 + bar radius). Then it is simple to draw up the curved bar with a total length along its centreline of 25, and then take off the horizontal length.