Pressure Vessel Elliptical Head Design Calculator

Pressure Vessel Design and Calculators

The following are equations and a calculator to determine the wall thinkness and working pressure of an ellipsoidal head with t/L greater than or equal to 0.002.

The require thickness of a dished semiellipsoidal head in which one-half of the "minor axis" (inside head minus the skirt) is equal to one-fourth of the inside diameter of the head skirt.

The following equations apply:



Elliptical Section

 Do [in] - outside diameter
   tn [in] - wall thickness before forming operations
 tf [in] - thickness after forming 
 Ca [in] - corrosion allowance
1.500  St [in] - straight section length (Skirt)
 S [psi] - allowable stress 
 E - head longitudinal efficiency 
 P [psi] - interior pressure
Calculated Variables:
nt [in] =
Di [in] =
h [in] =
ho [in] =
Do/2ho = See Table A
Enter Value K = See Table A
Required Thickness:
Tr [in] =
Thickness Check
Maximum Pressure: 
Po [psi] =
Pressure Check


Do = outside diameter

tn = nominal thickness before forming

tf = thickness after forming

Ca = corrosion allowance

St = skirt length (straight section)

S = maximum allowable stress value

E = joint efficiency for, or the efficiency of, appropriate joint in cylindrical or spherical shells, or the efficiency of ligaments between openings, whichever is less.
For welded vessels, use the efficiency specified in UW-12. For ligaments between openings, use the efficiency calculated by the rules given in UG-53.

P = internal design pressure (see UG-21)

nt = tf - Ca = thickness with corrosion allowance removed

Di = D - (2nt) = inside diameter with corrosion allowance removed

h = D/4 = crown height

ho = h + nt = outside crown height

K = Interpolated from Table A (see Do/2ho calculated value)

Value of Spherical Rafius Factor K
Table A

tr = Required design thickness

Po = maximum operating pressure

References: ASME Boiler and Pressure Vessel Code

Contributed by:

Harsh Murugesan
Pune, Maharashtra India