These formula are both simplified models of reality and as such should be taken with a pinch of salt.
Are they good models? Certainly not complete – factors like temperature. metal fatigue and thermal conductivity are ignored. As are the other important constructional features that affect strength: staying, joints, penetrations, and cylinder ends etc.
Both models seem to be based on Barlow’s Burst Formula for Pipes which will get order of magnitude right. Though Barlow broadly decides the answer, the models aren’t identical: the UTS model factors in Ultimate Tensile Strength, not wrong except the UTS of Copper varies by about 50% – it depends! Nonetheless, results are similar, but in both cases the maths generates ball-park estimates, not spot-on accuracy! Anyone care to calculate the error margin in these formula?
No matter! Both ensure the boiler gets nowhere near burst pressure by applying a Safety Factor. Remembering my maths is terrible, I decode the formula thus:
- they start by estimating the thickness of material that will just fail at design pressure, then
- the material thickness is increased by a safety factor, the size of which is left to the designer or the code he is following.
In the article, the YP example has a safety factor thickness x 3 whilst UTS applies thickness x 8. Quite a difference. In manufacturing safety factor varies between about x2 for non-critical items, up to about x25. The safety factor of an airliner is much higher than that of a guided missile because the latter only flies once!
The size of the safety factor makes a marked difference to the calculated shell thickness. Maybe the debate disappears in a puff of smoke because safety factor is an arbitrary multiplier!
Might put Bob Worsley’s mind at rest. His kit came with 2.5mm rather than 3mm Copper. Maybe someone decided to increase the Safety Factor rather than the 2.5mm boiler being dangerously weak. What does the boiler inspector think?
Though both mathematical models produce estimates rather than precision answers, large Safety Factors make them fit for purpose when designing model boilers. Unfortunately I feel their simplicity makes them less suitable for MEinThailand’s purpose; his desire to push the envelope requires better.
I’m all for pushing the envelope, and suggest 3D-CAD and Finite Element Analysis is the easiest way to tackle it. Barlow’s Formula was derived from a sharply focussed mix of theory and experimental data: he burst a lot of pipes made of many different metals and then did a regression analysis. To prove MEinThailand’s idea by applying Barlow and the other engineering formula needed to calculate stuff like tension and compression in stays and joints is hard work, even with spreadsheets. FEA is more general: it knows nothing of Barlow, so the operator need not either! Rather objects are triangulated so that the stress in each side of many triangles can be calculated. Accuracy depends on the number of triangles in the mesh and there can be millions of ’em. FEA’s mesh copes automatically with stays, joints, ends, shapes and complications of all kinds. Main problem seems to be getting the 3D CAD model to represent reality adequately and then to understand the results. Also hard work, too much for me!
Dave