CJ,
No problem. I should have cited my source and more importantly the "why"... The source is: myself, but more importantly the why...
First, BIG CAUTIONARY NOTES:
1) I am not a mechanical, materials or structural engineer. I am an electrical and software engineer by training, but no longer practice engineering in my career. I am only an interested observer and amateur practitioner of mechanical, structural, aerospace and other disciplines as it relates to the high power rocketry hobby.
2) The following commentary may be considered heretical in certain circles of the rocketry hobby. I am not attempting to start a firestorm here, I am simply providing my observations, opinions and conclusions in the area of shear pin use in high power rocketry flights. You may agree or disagree and either is fine, as they say, your mileage may vary.
3) Also, very important is my intent—in no way am I trying to disparage any individual in rocketry, and in particular, especially not Drake Damerau and all the wonderful work his had done for our hobby. I do not know Drake personally, but over the years have done a couple of financial transactions with him on rocketry equipment and he has always been a “gentleman and scholar.”
OK, a little background is probably useful… After doing ground testing for a dozen years over numerous airframe sizes and rocket designs I began to notice a continual and consistent trend, namely, my ground tests always had to be repeated more than once as they were always under-powered. In most cases I had to add 50% more BP to the charge, sometimes even more. This began to bother me, not just because I was wasting e-matches and BP, but it consumed considerable precious time of the limited time I can devote to rocketry. Being trained as an engineer and in another life working as a quality engineer, the results really began to get under my skin. If everything was “nominal” and on a normal distribution curve, I should be seeing just as many “overcharge” events as “undercharge” events, but this just wasn’t the case. Even more disturbing is that as I spoke to, and read of experiences of, fellow rocketeers, and the vast majority experienced the same thing, i.e., their initial calculations for ground testing led to weak separations.
So given the above, I began tracing the variables back one at a time. First it was the BP pressure/volume calculations, but they seemed solid. Next it was my construction and placement of the charges. After significant testing in this second area, I did make adjustments when utilizing centrifuge charge containers, but the vast majority of my charges are in 2X to 3X length copper tubing which fired consistently and with authority (this geometry has also since been verified as effective by Jim Jarvis on his high altitude flights). At this point, I began to look at the pins, but not directly related to shear. I thought there might be a significant contribution due to bending and the particular shear material, i.e., cardboard, phenolic, fiberglass, etc. I began to look at the shears under a microscope, note any bending or elongation of holes in material (in most cases I typically enhanced cardboard and phenolic with brass inserts to aid the cut which effectively eliminated any deformation of the airframe material). I then started to consider friction in the joint, but never could come close to accounting for the under-calculation of charges due to the minor contribution from friction. That is when I consulted an old mechanical engineering friend of mine. I described the problem and my observations and what I had gone through up to that point. His view was that I had looked at most everything but the pins themselves. Showing him the chart that you referenced above, he had a bit of heartburn, in that he didn’t feel you should see the type of combinatorial effect shown, i.e., a shear for a group of pins that were arranged in a symmetrical fashion should be more additive versus the reduction in per pin force as shown. In other words, if shear for one pin is 25 lbs for instance, the result of three pins in the test should be 75 lbs. I didn’t dismiss the shear pin test chart immediately, but I just asked him how he would calculate the forces involved and it was blatantly simple. I like simple, so I set out to gather data and calculate results.
So I began referencing a number of documents from
Fastenal Technical Guides to
NASA Fastener Design, just to make sure my friend wasn’t “full of it” and then to gather needed data. But quickly before presenting results, just a couple comments on my reading… The first thing that I noticed was that in the screw/bolt mechanical design world the term shear is thrown around in a “loose” fashion. I’m sure it works for those in the industry, but for the uninitiated, you can get confused easily and really have to study the context when the word shear is used. Just to be clear, we are interested in single mode (versus double, ref. above docs) screw thread shear when used as a pin (i.e., not under tension with a nut on the back side). The shear force is in the direction perpendicular to the longitudinal axis of the screw and should in no way be confused with thread shear which is a completely different stress mode. The second point in reading is that, for reasons I don’t understand, screw/bolt manufacturers generally do not publish and/or guarantee shear strength on their product; tensile strength yes, shear strength no. What mechanical/structural engineers do is take the tensile strength measurement and derate that by a factor based on the material. It seems like a rule-of-thumb is to multiply the tensile strength by 60% to get shear strength. The reason I mention this is because, again, in my literature search, I saw rocketeers doing this for nylon screws, which leads to inaccurate results.
So, the punch line… The force for a single pin shear is as follows:
Shear force = stress area * shear strength
And, shear force for an array of pins placed symmetrically and acted upon in the same force vector is:
Total shear force = shear force 1 + shear force 2 + shear force 3 + … + shear force N
And finally there is some effect from non-perfect shear (bending, material elongation, etc. which I try to eliminate) and friction from the joint. I have found this last factor to be somewhere between 5 and 10 lbs for high power rockets and skewed to the lower end of this range. This last factor has by no means been calculated and are simply based on observations from ground testing. Often this factor is negligible and can be ignored by sizing your charges with a 20% to 25% safety factor.
You are probably saying “That’s obvious!,” especially with respect to that first formula. And that is what I said. But to get it right you have to calculate it right using the correct inputs. First, make sure you are using the right units. Easiest for us here in the U.S. to find shear area in inches-squared and shear strength in pounds per square-inch (PSI). Next to calculate the stress area for the threaded portion of the screw you need to use the minimum pitch diameter including subtracting tolerances (see
Machine Screw Thread Dimensions). Finally as mentioned earlier, we need to use the real material shear strength (versus the tensile strength * 60% estimate used for steels/alloys). The nice thing is that 6/6 Nylon material is fully characterized and shear strength is readily available (see
6/6 Nylon Resin Mechanical Properties). So, punch line #2, the shear force for a 2-56 nylon screw is:
Shear force = 0.00370 inches-squared * 10,000 PSI = 37 lbs,
And for a 4-40 nylon screw we have:
Shear force = 0.00604 inches-squared * 10,000 PSI = 60 lbs.
In practice I use 35 lbs for 2-56 screws and 55 lbs for 4-40 screws and then add 5 lbs for joint friction, imperfect shear, etc. I then go about calculating my charge size and then add 20% to that as a safety factor. Again, the above works for me, and in the three or so years I have been moving this direction with my ground testing, I find it much more accurate in providing “good” separation.
So, just to conclude, I am not saying that the chart posted summarizing the Damerau results is inaccurate, in fact, I’m sure it is accurate given the test setup and measurements that were done. But, based on my research, I choose not to use those values and instead have adopted what I consider a “personal best practice.”
Sorry for the rambling,
Tim
P.S. Since developing these parameters, I have found other rocketeers that have used these same, or similar values. Of note are this webpage:
https://www.feretich.com/rocketry/Resources/shearPins.html and the contribution toward the end of this Info-Central article:
https://www.info-central.org/?article=303.