Let me tell you about Dave. Dave was a project manager. Dave cut corners on pressure vessel calculations. Dave isn’t working in engineering anymore.

Torispherical heads—the funky, dished ends on tanks and boilers—look simple. They’re not. I learned this the hard way early in my career. A client needed a storage tank. I eyeballed the material needed for the head. Big mistake. The fabricator laughed when he saw my quote. Turns out, surface area math isn’t optional.

Here’s the deal: a torispherical head has two curves. The big, fat curve at the top (the crown). The tighter bend near the edge (the knuckle). Mess up their proportions, and your tank might as well be a modern art sculpture.

The Formula That Actually Works

After with ASME codes I write this down::

A = π × D² × [0.0833 + 0.25(r/D) + 0.5((R/D) − (r/D))((R/D) + (r/D) − 0.5)]

Let’s unpack it:

D = Inside diameter of the tank. Measure twice. R = Crown radius. Usually about 90% of D for standard designs. r = Knuckle radius. Typically 6% of D. Tiny but mighty. Plug in numbers for a 2-meter tank (D=2000mm, R=1800mm, r=120mm):

A ≈ 3.14 × 2² × [0.0833 + 0.25(0.06) + 0.5((0.9) − (0.06))((0.9) + (0.06) − 0.5)]

Do the math. You’ll get ~7.2 square meters. That’s 7.2 square meters of metal you can’t afford to guess.

Why Your Gut Is Wrong

I once saw a junior engineer swap a torispherical head for an ellipsoidal one to “save time.” The tank failed hydrotesting. Water sprayed like a broken fire hydrant. Humiliating.

Torispherical heads aren’t hemispheres. They aren’t cones. Their hybrid shape balances strength and cost. But that knuckle radius? It’s a stress magnet. Get the surface area wrong, and you’ll under-order material. Or worse—overpay by 20%.

Pro Tip: When Excel Fights Back

Still scribbling on napkins? Stop. Use a calculator like PV Elite or Codeware. But understand the formula first. I keep a dog-eared notebook with this equation. Next to it, a coffee stain and the words: “Dave’s Revenge.”