Hello,

I need help regarding Dummy leg modelling in CAESAR-II using offset method. I have prepared an excel sheet for calculation using formulas given in application guide of CAESAR-II. I am not having the exact values as given in application guide because I am getting α = 41.4° using the formulas. The values given in CAESAR-II application guide is based on α = 45°. So if you could please explain me if I am making any mistake in calculating α based on the formula?
Also I have derived the formula for calculating x and y offset based on assumption that dummy leg is attached at 45°(file attached). So if anyone can check and validate it that will be great.

Long Radius
Assume OD = 2.
Assume Nominal R = 1.5 x OD = 3. (adjacent side)
Assume Outside R = Nominal R + 0.5 x OD = 4. (hypotenuse)

Alpha = acos (Nominal R / Outside R) = acos (3 / 4) = 41.4096°.

Short Radius
Assume OD = 2.
Assume Nominal R = OD = 2. (adjacent side)
Assume Outside R = Nominal R = 0.5 x OD = 3. (hypotenuse)

Alpha = acos (Nominal R / Outside R) = acos (2 / 3) = 48.1897°.

There is one issue with the equations you should note, however.

The elbow radius is a function of nominal size - not OD. So the numbers above are still slightly skewed.

I.E. NS 6" piping has an OD of 6.625" but a long radius elbow is 9". So for 6" piping alpha is actually 43.033°.

Thank you Michael for taking the time to reply. I have done the same thing but in Application Guide the values for offset method are calculated based on alpha 45° for NPS 10 bend radius 15, they did not calculate alpha based on the equation instead they assumed dummy to be attached at 45°.
x= 15(1-cos45)= 4.395
y= 15*tan45(1-cos45)=4.395
whereas according to equation alpha should be 41.4096.

So if it is a mistake in the application guide or should we assume dummy to be attached at alpha 45°.

The Application Guide states:
The dummy leg is attached near the 45º point on the bend. The centerline of the dummy leg should line up with the centerline of the vertical run of pipe.
"Near the 45 degree point". Have the dummy leg line up with the riser and use your trigonometry to find this angle. It is about 41 degrees for a long radius elbow.