End Caps SF & Knuckle Radius

I doubt that this is a calculated value. Instead, it is more likely a given, such as from a manufacturer's catalog. From the given numbers, one can then calculate the stress such a cap can withstand, if it isn't already rated. I can't speak for all manufacturers, but most weld-end caps I have seen look like 2:1 semi-elliptical rather than torispherical, and hence they do not have a constant knuckle radius. Likewise, pressure vessel heads can be formed in several types of shapes, typically with 1.5- to 2-inch skirts ( = straight face), but not restricted to this range.

please check out fig. 1 in B16.9 code

Hope this may be of assistance. In pressure vessel design the thickness of the cylindrical shell may be calculated simply as pd/2t. If the head is hemispherical then this is given as pd/4t or half the thickness of the cylindrical shell. In PV fabrication its normal to have the thickness of the cylindrical shell (strake) the same as the heads to facilitate a constant thickness butt weld. To facilitate a weld interface of constant thickness it can be shown mathematically that a semi-elliptical shaped head ( normally called a 2:1 head) achieves this. In Pipe fittings which are normally forged, using a die, this shape is easily achieved. In pressure vessels where the shell thickness is very much smaller than the diameter of the strake this is not the case. Forming machines tend to prefer a constant radius therefore they form what is called a torisherical shape comprising a crown radius and a knuckle radius which meet at a common tangent point. A 5% knuckle rad approxs to a 2:1 shape but a true 2:1 or semi-ellipse has a continuously changing rad over its entire shape. Rotate a coin slowly through 90deg to get an elliptical shape. Hope this assists.