While going to college I had a professor who liked to reference the Zeno paradox. “That which is in locomotion must arrive at the half-way stage before it arrives at the goal.” He would make this point with an analogy.
An engineer and a mathematician are in a bar. They see a beautiful woman walk in. Both want to talk to her, but the mathematician states, “If I get up and try to talk to her, I will have to walk half the distance to her. Then I will have to walk half that distance, and again infinitely. It’s hopeless I can never reach her.” The engineer stands up and say, “You might never reach her, but I can get close enough for a kiss.”
My professor put it this way, as you are getting closer to your goal are you close enough to kiss it? We might never be able to reach the exact answer, and if we try to get a right answer those last several steps could involve extreme complex math. He would in essence ask, “Do you need to take those final steps?” Are you close enough when you calculate that your design can support 25,000lbs of load, but the exact calculation would be 25,005.25lbs?
Often with math or science we want an exact answer, but are limited by the assumptions made, the simplification of our models, or even round off errors, but as long as we can get close enough, we can get a usable result. The question then becomes how close do we need to get to trust the answer we have? This is a question we have to frequently ask ourselves as engineers when we analyze a design. With the information we have can we get close enough to an answer to be confident in the design’s performance?
This becomes crucial when designing equipment that is required to hold a person aloft. Often times engineers are instructed through standards, or regulations, that their design is suppose to have a safety factor on top of the expected loads. Usually if a safety factor of 2 to 1 is required, then the design should be able to take twice the expected loading before the design starts to fail. And while that is true, these safety factors are often there to help account for unknowns in the materials, manufacturing, or even dynamic effects (motion, impacts, etc.).
Even with these unknowns “taken into account” by using a safety factor, we still need to be careful in our designs. I have seen instances where a company will take the basic hand calculations, make sure they meet the safety factor required, and say “we nailed it.” Their testing later showed that with the effects of manufacturing and the dynamic motion of the device applied they were lucky to have a safety factor of ½ what it was supposed to be. Meaning this design should fail when it is used. This approach can lead to unsafe designs.
So how do we get close enough to kiss? Alpine Engineering and Design, Inc. has found that using Finite Element Analysis (FEA) early in the design process will help to size components and determine if the design performs as expected. We have also found that early implementation of FEA results in a better product and faster design process. But this is dependent on using proper constraints, or taking the right half step to the answers.
It has been said that with infinite amount of time a monkey sitting at typewriters hitting random keys could produce the complete works of Shakespeare. The same can almost be said for FEA, a “monkey” can make an FEA that gives you results, but if his half steps take you to the bathroom instead of the beautiful girl, are you going to want to kiss the toilet seat?
After the proper steps in FEA are taken for a design, it is important to perform physical tests and/or hand calculations. This helps to take one more step to assuring that your design will work in real life.
As my professor pointed out, in the design process you might never reach the perfect answer or design, In fact, another teacher pointed out that the only thing we actually know about FEA or other engineering analyses is that they are wrong. That being said, if you do it right, you will get close enough to the right answer that you can kiss it.
About the Author: Nathan Morrill is a licensed professional engineer (PE) and a certified safety professional (CSP). He is an engineering project manager at Alpine Engineering and Design, Inc. and has worked on the design of projects ranging from aerial lifts to lift gates, and dump trailers to zip lines. In addition to engineering work Mr. Morrill also provides expert witness services for patent and product liability cases.