Catostrophic failure of the Liberty Ship

A cracked bicycle frame

The first approach, absolute analysis, means the engineer will do their best to reproduce the loads, cycles, geometry and materials as close to reality as possible. The engineer will build a computer simulation model with these inputs which will then be used to predict what the fatigue life should be for that particular design.

So after putting all these inputs into the computer, the engineer determines that the design should last at least 10,000 hours before cracking. This single answer translates to a number that does its best to reflect the reality.

The problem with absolute analysis approach is we often do not know our loads, number of cycles and material properties to any high degree of accuracy. In fact estimates at these are often plagued by huge variability of +/- 100%. For example, if the engineer thinks the load is 100 newtons, in reality it could be 200N or 50 N. So when you add up all the uncertainties of the input, the final answer has a large degree of inaccuracy .

Unfortunately many engineers do not understand that inaccuracy is cummulative with your inputs. So the greater number of inputs you have, the more uncertainty your final answer will have. The final answer has a large variance and can become almost meaningless without having a reference point to compare to.

The second approach engineers take is called relative analysis. What this involves is ignoring absolute numbers but instead focusing on relative changes in designs to predict a relative change in outcome. In our car frame example, outcome would be fatigue life till crack starts. Using relative analysis, the engineer only needs to compare the failed car's operating environment to identical cars running without problems .

In other words, the engineer uses their field population and field history to determine what differences are accounting for the change in reliability. It could well turn out that the cracked frame car is being driven in harsh bumpy off-road conditions which results in x% higher average loads relative to the field population. So the engineer can quickly use rules of thumb to tell that x% higher loads typically corresponds to y% lower field life. Since cycles, material properties and geometry are the same, the engineer can throw them out of the picture. The engineer can make accurate predictions of fatigue life by just focusing on what is relatively different, i.e the loads in this case.

The important concept to understand here is that is irrelevant what the actual loads and material properties are. All that matters is what percent different they are than a typical baseline or average design. From these relative differences, engineers can predict with far more accuracy what the expected life should be. For this reason relative analsysis is also referred to as 'comparative analsysis' since the engineer is only comparing back to an established design.

In fatigue the equation to calculate fatigue life improvements for welded steel is proportional to the ratio of the loads raised to the third power. So if the failed design sees twice as high loads as the average, then its fatigue life is 2 raised to the third power, or 8 times lower ! What this means is if an average car lasts for 10,000 hours, then the same car operating under the harsh conditions will only last 1,250 hours. Clearly small changes in load correspond to the large differences in expected life.

It is quite amazing that engineers can use relative analysis with great confidence so long as they have a large population of similar designs operating under a diverse set of conditions. Field history is perhaps the single most important factor in determining how new designs get built. With no field history you have to rely on absolute analysis which is riddled with too much uncertainty. For this reason, almost all awesome designs you see, i.e skyscrapers, trucks, airplanes and ships are all based on incremental improvements to an established design with a field history. No engineer is going to build the 3 mile high skyscraper without having successfuly built a 2 mile high skyscraper!

Why does human nature prefer doing absolute tpye of analysis if the answer is fraught with uncertainty? For one reason, engineers incorrectly think more complicated must be better. When you are observing complex phenomena it is natural to assume the solution must also be complex. In reality simple incremental changes summed up over time are enough to give the semblance of complexlity . A good scientist needs to be able to look at each simple incremental change independently to understand how the complexity has evolved.

Another take on why complex analysis is preferred to simple comparative analysis is best captured by the famous American science writer, Gary Taube. He wrote a famous article on the proliferation of fad diets for the New York Times, What if It's All Been a Big Fat Lie? Below, is an excerpt from a 2002 interview of Gary Taube on the Charlie Rose Show. Although he is talking about diets and health, his comments are equally applicable to science and engineering.

" The science is surprisingly complicated. The human body is incredibly complicated. All people are different, diseases are divergent and different. You have people and their genetic elements and physiological elements and lifestyle elements .

When you actually get around to trying and test it you end up with this morass of confusing and conflicting data out of which people can pick just the elements they want to support their pre-conceived opinions. And that sometimes make the particular researcher look very sure he knows the answer but unfortunately that is not how you do good science. "