Torispherical Dome
A torispherical dome is the surface obtained from the intersection of a spherical cap with a tangent torus, as illustrated above. The
radius of the sphere
is called the "crown radius,"
and the radius
of the torus is called the "knuckle
radius." Torispherical domes are used to construct pressure vessels.
Let
be the distance from the center of the
torus to the center of the torus tube, let
be the radius
of the torus tube, and let
be the height from
the base of the dome to the top. Then the radius of the base is given by
. In addition,
by elementary geometry, a torispherical dome satisfies
|
(1)
|
so
|
(2)
|
The transition from sphere to torus occurs at the critical radius
|
(3)
|
so the dome has equation
![]() |
(4)
|
where
|
(5)
|
The torispherical dome has volume
![]() |
(6)
| ||
|
(7)
|
![{x^2+y^2+z^2=R^2 for sqrt(x^2+y^2)<r; (c-sqrt(x^2+y^2))^2=a^2-[z-(R-h)]^2 for r<sqrt(x^2+y^2)<a+c,](/images/equations/TorisphericalDome/NumberedEquation4.gif)
![pi/6[3a^2cpi+4R^3-2sqrt((a-c-R)(a+c-R))×(2a^2+c^2+2aR+2R^2)+6a^2csin^(-1)(c/(a-R))]](/images/equations/TorisphericalDome/Inline9.gif)
torispherical dome