I’ve discussed/explained this in a number of past posts, but its worth going over.Random Human wrote:Balsa Man, when you say "20% safety factor" what exactly do you mean?Balsa Man wrote:Designed to carry full load w/ a 20% safety factorparvatipatel wrote:
Nice plan! I am planning on using it- thanks! Do you know how much that should carry?
In all technicality, when you test structures, you do understand if this design or whatever works or not. In competitions, you can be the unlucky one, and somehow have a "hole" or something, wrong with your wood, you never know.
Is that what you mean by safety factor. I was always told that in a competition, there is a +- 10% level of uncertainty of how your tower will perform.
From Wikipedia- “Factors of safety (FoS), also known as (and used interchangeably with) safety factor (SF), is a term describing the load carrying capacity of a system beyond the expected or actual loads. Essentially, the factor of safety is how much stronger the system is than it usually needs to be for an intended load. Safety factors are often calculated using detailed analysis because comprehensive testing is impractical on many projects, such as bridges and buildings, but the structure's ability to carry load must be determined to a reasonable accuracy.
Many systems are purposefully built much stronger than needed for normal usage to allow for emergency situations, unexpected loads, misuse, or degradation (reliability).
So, when I say designed to carry full load with a 20% safety factor” I mean exactly that.
“Design” encompasses two things- the configuration, the ‘geometry’; dimensions and shape; this is driven a) by the rules; base ends of the legs far enough apart to span the base opening (or 29cm circle); top ends of the legs close enough to support the load block, and b) by your choice of the bracing interval (and system/pattern) to use. The choice of bracing interval (heavier, stiffer legs with/requiring less bracing (wider spacing of braced points), or lighter less stiff legs with more/closer bracing interval can be made by comparing estimated tower weight, using estimated densities (stick weights) of components. The same approach can be done to evaluate bracing system weights.This has all been discussed in some detail in many past posts, with factors to do these calculations discussed.
The calculations to make the legs and bracing design decision are based on your “design load”- 15kg. In a 4 legged tower (built precisely/symmetrically, which a jig allows you to do), each leg will be carrying ¼ of the design load. (15/4= 3.75kg). However, because the legs are slanted (slope in toward the top), the force each leg sees with a 15kg tower load is a bit more than 3.75kg; for a B tower (meeting the 29cm circle bonus) leg force is 3840kg, for a C tower 3810kg. Again, as discussed in depth in past posts, the wood to use is selected based on measuring the buckling strength of sticks from which you cut your legs , then calculating the increased buckling strength of the leg sections between bracing points (using ‘inverse square’ calculations/table. You’re looking for the sticks that will give you the buckling strength you need/want at the lightest weight. Applying a 20% safety means that instead of using 3840, or 3810 as your design load, you use a design load that incorporates your safety factor; for a C tower, with a 20% safety factor, 3810gr x 1.2 = 4572gr, and for a B tower, 3840gr x 1.2 = 4608gr. As discussed before, calculating forces on bracing system members is…beyond my current understanding/knowledge, but from years of experience, I know if bracing system components can handle a force on the order of 1kg, they generally will work. With a 20% SF, that would be 1.2kg.
And why should safety factors be used? The short answer is to control variables. The biggest variable (but one that is straightforward to deal with, and control is shape/symmetry. If your legs are exactly the same length, at exactly the same angle, oriented symmetrically, and the bracing intervals are all the same (e.g., 1/3, ¼, 1/5, etc., then the force the legs will see at design load, and the strength of legs between bracing points will be equal. If alignment is off, forces and strengths quickly will become unequal. The more precise your construction is, the less of a safety factor you need to account for/deal with unequal loading. The more difficult variable to control is the inherent variability in wood- its grown, not manufactured to some precise physical properties specifications. Each stick is different. However, there is a relationship between density and strength.
If you take, say 100 1/8” x 1/8” 36” sticks, all weighing 1.5grams, most of them will have a buckling strength at 36” (measured by pushing down on the top with one finger when the stick is put vertically on a scale about 35 grams). Some will have more, or less; a few will test as high as 43, 44, a few will test as low as 28, 29 (approaching ~20% weaker). With a large enough sample size, you’ll see “a bell curve distribution” of buckling strength vs density. By increasing your design load by 20%, and picking sticks that display the buckling strength needed to carry that load, you “protect yourself” against sticks that are ‘to the weak end’ of the density vs strength spectrum. Understand that the inherent variability in wood is not only in/between sticks, but within each stick. If you were to measure buckling strength of a stick at 36” (in our example here, a 1.5gr stick testing at 35gr), and then cut it into 5 equal length pieces, you’ll see the same kind of distribution of buckling strength- weaker or stronger sections within the stick. If you’re really into looking for absolute maximum performance, you can reduce the unseen/undetected variability by cutting pieces just a bit longer than your finished legs will be, and doing buckling strength testing on them. If you do this, you can reduce the safety factor needed to be pretty sure the weakest still has the buckling strength needed to hold your design load.
The factors discussed above are the main objective/quantifiable factors to consider using/applying a safety factor to control the variables in play. There are a couple of subjective factors to think about, too.
Choosing what safety factor to use is a strategic decision; how close do you want to ‘push the limits; how important is it to have/take a shot at medaling, winning? Maybe you approach Regionals conservatively, 20%, or maybe even a bit more, and at State push the SF down to 10%, or even less.
And, as you noted, there is, to some extent, the…. in the heat of actual competition, under time pressure, everyone watching, factor. You could approach putting some control on this factor by making your tower a little stronger (hence a little heavier) by using design safety factors. I would suggest the better approach is a) quality control- building carefully, inspecting carefully, transporting carefully, and practice with the setup and testing process; doing this till you and your partner are comfortable doing everything right.
