Torispherical head: the practical and efficient choice for low-pressure applications

In the world of pressure vessels, tank construction and industrial processing equipment, the choice of vessel head plays a crucial role in determining both performance and cost. Among the different head types available, the torispherical head, also known as a torispherical dish end, stands out as one of the most practical and efficient options for low-pressure applications. In this article, Ralph Hofman, Sales Engineer at Antonius, shares his expertise on the characteristics, production, and applications of these vessel heads.

What is a torispherical head?

A torispherical head is a standardized type of vessel head used to close off the end of a cylindrical pressure vessel. Its shape is defined by two key radii: the crown radius and the knuckle radius. According to common industry standards, the crown radius (the large spherical section) is typically equal to the vessel diameter, while the knuckle radius (the smaller, curved transition to the straight shell) equals 0.06 times the diameter.

In simpler terms, a torispherical head can be defined as a relatively flat, shallow dome compared to other head types such as ellipsoidal or hemispherical heads. Because of this flatter shape, it is often used in applications that do not require high internal pressure resistance.

As Ralph Hofman of Antonius, one of Europe’s leading manufacturers of vessel heads, explains: “The torispherical head is a relatively flat head shape. The flatter you make the head, the more difficult it becomes to handle pressure. A hemispherical head is the most perfect shape for high pressure, but it also takes up a lot of space. A torispherical head, on the other hand, is very practical when you don’t need high pressure.”

Torispherical head vs. ellipsoidal head and hemispherical head

When selecting the right head type, engineers usually compare torispherical vs. ellipsoidal or hemispherical heads. Each type has a distinct geometry that determines its mechanical performance and cost:

Hemispherical head: The ideal form for pressure resistance, as the stresses are evenly distributed. However, it requires more height and material, and is therefore more expensive and less space-efficient.
Ellipsoidal head: A compromise between pressure resistance and space efficiency, commonly used in medium-pressure vessels.
Torispherical head: The most economical option for low-pressure applications. Its flatter shape requires a thicker wall to withstand internal pressure, but it is more practical for many industrial settings.

Hofman explains: “The difference between these head types is essentially determined by the curvature. A torispherical head follows a normalized form, defined by a standard. If you know the diameter, you know exactly what the radii will be. That makes it predictable and efficient to produce.”

The torispherical dish end properties

The geometry of a torispherical dish end is determined by two parameters: the crown radius (R) and the knuckle radius (r). The torispherical head formula follows from the relationship:

Crown radius (R) = D (vessel diameter)
Knuckle radius (r) = 0.06D

For pressure calculations, the wall thickness can be calculated using the ASME formula.

Because torispherical heads are relatively flat, higher thicknesses are required as pressure increases.

Volume and surface area of torispherical heads

The torispherical head volume and surface area are important for calculating vessel capacity and material requirements. The exact torispherical head surface area formula depends on the specific geometry, but in general, torispherical heads have a smaller internal volume and surface area compared to ellipsoidal heads of the same diameter. This can reduce overall material use, especially for low-pressure vessels.

Manufacturing torispherical heads

At Antonius, torispherical heads are produced using the same advanced forming processes as other head types. The manufacturing process involves cold or hot forming, where large steel plates are pressed into the desired curvature. Hofman explains:

“The production process is exactly the same. We just press it slightly less far through. The press keeps stamping until the right radius is achieved. That might differ by 10 or 15 centimetres, but the process itself doesn’t really change. Throughout production, the shape of the head is constantly measured using a template, and once the head is finished, we make a measurement report to verify that it meets all required tolerances,” says Hofman.

Antonius can produce torispherical heads in one piece up to approximately 9 metres in diameter. Beyond that, the company fabricates the heads from multiple segments, which are welded together with extreme precision. “Above nine metres we work with segments,” Hofman notes. “That means the size is theoretically unlimited. We can build up to 30 metres if needed, as long as the components can be transported. Sometimes we even deliver segmented heads that are welded together on site.”

The maximum forming thickness for a single-piece head is around 30 mm. Beyond this, segmented construction becomes necessary due to forming limitations. This is, of course, not a problem for Antonius, we have many examples where segmented construction was the right solution for our client.

Materials and applications

Torispherical heads are available in a wide range of materials, from carbon steel to stainless steel and special alloys. However, for many modern applications, stainless steel is the preferred choice due to its corrosion resistance and hygiene properties. “In the food and beverage industry, where cleanliness is critical, stainless steel is standard,” says Hofman. “We can also polish or grind the surface to achieve a smooth finish so no residue can remain inside the vessel.”

Because of their geometry and cost-efficiency, torispherical heads are most commonly used in low-pressure vessels, such as:

Food and beverage processing tanks (for example breweries)
Storage tanks for non-pressurized or low-pressure liquids
Water treatment systems
Chemical and pharmaceutical mixing vessels

Why torispherical heads remain a solid choice

While torispherical heads may not be the most complex or high-pressure components in Antonius’ product portfolio, they remain essential across industries that prioritize practicality, cost efficiency, and easy maintenance. The combination of standardized geometry, predictable fabrication, and flexibility in size and material make them a reliable choice.

“The torispherical head may not be our most advanced product,” Hofman concludes, “but it’s a design that simply works. It’s efficient to produce, it performs well in low-pressure applications, and we can make them in virtually any size or material our customers need.”

With decades of experience and unmatched production capacity, Antonius continues to serve as a trusted partner for industries worldwide, providing everything from precision-engineered torispherical heads to complex, large-diameter vessel constructions.