The Factor Of Ignorance

"Safety factor." It's probably one of the most common, and most misused, terms in engineering.

The "factor of safety" might be better described as a "factor of ignorance". It's a multiplier, applied to loads and/or structural components in a design, to account for things that weren't explicitly taken into account in the design calculations. Those things could include variations in material quality or workmanship, uncertain overload conditions, accidents, and other hard-to-predict conditions that could cause a failure.

Over-building something brings a weight penalty. When weight is critical, then – as is the case in aerospace work, or in race boats – it is desirable to reduce the factor of ignorance. We do this by tossing more time, effort and money at calculations and simulations to get a better understanding of the loads, allowing us to design with less and less of a margin beyond the expected, well-understood conditions.

To give a sense of scale, it's fairly common to use a safety factor of 3 for many things aboard a boat. You can think of this as meaning that if the calculations say a shroud will normally carry a tension of 10 kN when under sail, it will be sized to be able to handle 30 kN without breaking. In some cases, our ignorance of the loads is greater; the propeller shaft of a heavy, slow motoryacht might have a factor of safety of 6 to 10, to account for the difficult-to-analyze condition of sucking a log or ice chunk into the prop. In other cases, meticulous calculation of many likely conditions lets us cut back on ignorance; the Space Shuttle routinely flew with a safety factor of 1.4 (and NASA was reamed out by the Columbia accident investigation board for occasionally flying some components at 1.25).

Remember, the safety (or ignorance) factor is for conditions beyond what we expect in normal use. If that shroud with the 10 kN expected load were to part at 27 kN, we'd chock that up to severe overloading and perhaps a variation in the quality of the wire. If it failed in anything resembling regular sailing conditions, though, we would deem the design or specification to be flawed.

As an example, consider Richard Feynman's comments on the Space Shuttle Challenger investigation. The famous physicist had this to say about known problems with erosion of the O-rings that brought down flight 51-L:

For example, in determining if flight 51-L was safe to fly in the face of ring erosion in flight 51-C, it was noted that the erosion depth was only one-third of the radius. It had been noted in an experiment cutting the ring that cutting it as deep as one radius was necessary before the ring failed. Instead of being very concerned that variations of poorly understood conditions might reasonably create a deeper erosion this time, it was asserted, there was "a safety factor of three."

In fact, as Feynman pointed out in further commentary, the ring had already failed. There was no safety factor; the design wasn't even adequate for its routine operating conditions.

In the marine world, where production runs are small and most things are hand-built, the factor of ignorance is often going to be high. The designer is unlikely to know the distribution of void sizes in the laminates produced by a particular crew, for example. Things like this have to be accounted for by the factor of ignorance.

We must be careful of thinking that "safety factor" means "extra safety". It is really nothing more than a shorthand way of saying "here's our best guess at how much we think we don't know".


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