The Engineering Safety Edition

On factors, structural engineering, and safety

Surjan Singh (SS) is a mechanical engineer who most recently worked at Virgin Galactic and is now on sabbatical. He writes at An Engineering Self-Study and previously published the excellent Stiffness Edition. Today’s WITI is a heavily edited version of a piece he published on his newsletter earlier this week. Be sure to check that out if you want to go deeper. - Noah (NRB)

Surjan here. By my estimation, a single number cost $1.5 billion on the Space Shuttle. Almost more amazing is what it represents and how it came to be. But for all its importance and intrigue, the number itself has an unassuming name—the factor of safety.

Image from NASA

Through engineering school and the start of my career, I didn’t think much of the factor of safety. The textbook definition is straightforward: it’s the breaking force divided by the expected force. So if you were making a chair with a factor of safety of 2, you’d design it to withstand twice your weight. In other words, the factor of safety is how much of the structure’s strength is “kept in reserve to assure its safe performance.”1

In day-to-day work as a mechanical engineer, that’s all you need to know. For example, if you’re designing an airplane wing, a loads engineer will tell you how much force the wing should experience and the FAA will tell you to use a factor of safety of 1.5. You can plug and chug and be good at your job.

But at some point, the safety factor started annoying me. As the joke goes, an engineer is someone who calculates to five decimal places, then multiplies by two. Why bother with all that detailed engineering work if we’re just going to slap a massive factor on it anyways?

Why is this interesting?

Safety factors started being formalized in the mid-1800s for bridge building, where factors as high as 6 were used to cover for the massive inconsistencies in the quality of early cast iron.5 So in its earliest definition, the safety factor was only intended to resolve the difference between a theoretical, flawless material and the imperfect reality. But the definition has changed over time and there doesn’t seem to be a lot of clarity on how or why different disciplines apply different factors.

And so I started to hunt. I figured aerospace was the best area to explore, because it has the most to gain from weight loss; the factor of safety would be examined critically from every angle.

Even under all that scrutiny, its origin remains unclear. In 1900, Wilbur Wright wrote to his father, “I am constructing my machine to sustain about five times my weight and am testing every piece. I think there is no possible chance of its breaking in the air.”9 If Wilbur wasn’t just lying to calm his dad down, the Wright brothers’ factor of safety was 5. By the early 1920s, it was down to 2, though that was not at all standardized.10

The first effort at rationalization came from a joint effort by the Army, Navy, and Civil Aeronautics Administration in the early 1930s. And it was from that group that 1.5 emerged as the factor of safety which has carried forward to this day.11 How did they come to their conclusion? The rationalization was that “airplanes were flying up to two-thirds and more of the ultimate load factor and nothing was happening to the structure; therefore, the evolution of thinking towards a lower factor of safety was a natural one.”12

Basically, pilots flew over the limit, but nobody died, so the limit changed. To go back to the chair analogy, it’s as if you designed the chair to support 2x your weight, but while making the chair, you gained 50% more weight by eating lots of donut holes. When you, at 1.5x your expected weight, sat on the chair, nothing bad happened, so you felt comfortable reducing your safety factor. 

In other words, the 1.5 factor was developed empirically. That one word—empirical—helped me understand the confusion around the definition and why it’s stayed the same for so long. You could argue until you’re blue in the face that the factor of safety only covers freak accidents and does not cover the simplifications we make when engineering. But the truth of the matter is that the extra margin is there and, even if you did not intend for it to, it could very well cover simplifications with or without you knowing.

The definition of the factor of safety is almost irrelevant. You can see why JE Gordon called it the “factor of ignorance”13 and the Department of Defense has renamed it to the “factor of uncertainty”.14

And the only way to reduce the factor of safety is to take on more risk. It’s no different than any other empirical knowledge. Your grandmother warns you not to eat some delicious-looking berries because her grandmother told her that her cousin died after eating the delicious berries. You suspect that your great-grand-cousin died from something else and the berries were a coincidence. You have only have one option to confirm your suspicion—you can eat the berries. Either you learn that they are harmless or you die.

Any attempt to reduce the 1.5 factor would be a similar step into the risky unknown. How did we get to 1.4 for spacecraft then? Who decided it was worth the extra risk for the weight savings? 

Apparently, the reduction to 1.4 was a one-time decision for one vehicle that somehow got absorbed and established as the standard for all spacecraft.16 Maybe to the engineering community, it looked like someone had tasted the forbidden berry and survived. That berry-taster was Boeing’s X-20 Dyna-Soar (what a great name). In fact, the manned portion of the X-20 was designed to the usual 1.5 factor. It was only the separable boosters that were designed to the reduced 1.4 factor. And even then, an additional factor was applied. The combination of factors came from a lab study that was focused on increasing structural efficiency for the particular use case and materials of the booster.17 Over time, the second factor and the context for the decision dropped away and only the 1.4 factor remained.

Boeing X-20 Dyna-Soar from Wikipedia

This whole thing might seem absurd, but engineering is a human endeavor with just the same quirks as any other. I think of the factor of safety as a modern-day version of the libation or offering. I’d rather keep pouring out the same amount of wine as my ancestors rather than skimping and risking offending the gods. That $1.5 billion pricetag, which seemed absurd when I began writing this, now just looks like the cost of being human. (SS)

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Thanks for reading,

Noah (NRB) & Colin (CJN) & Surjan (SS)

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