Towers B/C

[maxxxxx]

Are tripod towers allowed? I didn't see anything in the rules that would say otherwise, but I don't remember ever seeing one the last time this was an event.

[bernard]

Are tripod towers allowed? I didn't see anything in the rules that would say otherwise, but I don't remember ever seeing one the last time this was an event.

Sure, general rule 1: https://www.soinc.org/ethics_rules.

[baker]

Balsa Man,
Like you I've been around here for some time now. I still love reading your posts as they are full of solid discussion of what is important. The bracing issue you wrote about several years ago showed the importance of understanding this issue and again you make it clear... Thanks for sharing.

Quick review of three basic mathematical relationships that might help everyone, re discussion on leg angles, and the effects of those angles, and what the bracing of legs is all about. These apply to both tower legs, and the outer/end legs of bridges, btw… If you dig back through the archives, you’ll find plenty of detailed discussion (re: towers, bridges, and booms).

First, forces on a leg. For discussion, lets assume a 4-leg tower. Having not gotten this year’s rules yet, don’t know what the size of the hole in the test base the legs need to clear/be outside of.

So, let’s start with a simple case- a … hypothetical straight tower; legs vertical, on the corner of a 5cm square (so the 5cm square load block just sits/fits on top). With a 15kg load, each leg will carry 1/4th of that load- a 3.75 kg “axial compressive” force (i.e., the load puts a compressive force along the long axis of each leg). If the force is strong enough, or the leg weak enough, it will fail by “buckling”- the middle will bow outward due to the force, and the leg will break.

So what happens/what’s the math, if the legs are angled (wider at the base/bottom- to clear the defined base opening)? As discussed above, the “more angled” the legs are, the greater the force they have to carry (at a given load). If you do a vector analysis, you’ll find that force has an “inverse cosine “ relationship to the angle from vertical- the force is 1 over the cosine (1/cos) of the angle from vertical, times the load. If you drop an imaginary vertical line from the top of one leg down to the test base, you form a right triangle. The hypotenuse of that triangle is the leg. The imaginary vertical line is the other (adjacent) side of the angle from vertical. The cosine of the angle between the hypotenuse and the adjacent side is the length of the adjacent side divided by the length of the hypotenuse.

Looking at a few cosine values, 1/cos, and axial compressive force on one leg of a four leg tower with a 15 kg load
0 degrees; cosine = 1.0000; 1/cos = 1.000; axial compressive force = 3.75 kg
5 degrees; cosine = 0.9962; 1/cos = 1.0038; axial compressive force = 3.78 kg
10 degrees; cosine = 0.9847; 1/cos = 1.0155; axial compressive force = 3.81 kg
15 degrees; cosine = 0.9661; 1/cos = 1.0351; axial compressive force = 3.88 kg
20 degrees; cosine = 0.9397; 1/cos = 1.0642; axial compressive force = 3.99 kg
30 degrees; cosine = 0.8658; 1/cos = 1.1550; axial compressive force = 4.33 kg

The bottom line, until that angle gets pretty big, the effect of the angle on the force on the leg is pretty small. Even at 30 degrees from vertical, the increase in force (from that on a vertical leg) is about 15%

The second important relationship to understand is how the strength of a leg (resisting buckling) relates to its length. This is an “inverse square” relationship. Google up Euler’s Buckling Theorem to see the formula. What its saying is that if you have a column- a leg- a piece of wood say 60cm long, and it has a buckling strength of 0.5 kg, if you cut its length to 1/2, to 30 cm, its buckling strength goes up by a factor of 4 (to 2.0 kg); if you cut its length to 1/3, to 20 cm, its buckling strength goes up by a factor of 9 (to 4.5 kg).

You can see/get a feel for this important relationship by taking a (nice straight) balsa stick, place it on a scale, vertically, and push straight down. At some force/load, the middle will start to bow out (buckle)- that’s its buckling strength at that length. Be careful not to break it; just note/see the force/weight measured by the scale when it starts to buckle. Now, cut the stick in half, and do the same “axial loading” to the point buckling starts, and you’ll see the force on the scale is about 4 times what it was at full length. The numbers you get won’t be perfect; there will be some variation in the stiffness along/within the stick (that’s just the nature of wood- its not perfect/homogeneous), and its likely not perfectly straight, and without a pretty precise testing setup, the force you put on the top won’t be perfectly vertical, but you will see pretty close to 4 times the buckling strength.

What the bracing between the legs is all about is turning the long leg/column (with a low buckling strength) into a set of shorter, equal length, “stacked columns” (with much higher buckling strength). You can get a feel for this by repeating the ‘push down on a long stick on the scale” drill. Mark the midpoint on the stick- push down at full length, note the weight/load at which buckling starts. Now, push it to the start of buckling again, but with your other hand, hold the midpoint in place, so it doesn’t move in space, and what you’ll see is that at about 4 times the long length buckling load, one of the sections (above or below your fingers holding/bracing the midpoint) will start to buckle. There is good, detailed discussion in the forum archives on approaches to doing the bracing. Key is keeping the “braced interval” equal- if the exposed section of the leg between braced points is unequal, the longer exposed leg segment will break first.

The third/last important relationship to understand is the effect of density on the stiffness of a leg. This is pretty close to a linear relationship; if you have two sticks w/ the same size/cross section (e.g. 1/8” x 1/8”), and one weighs twice what the other weighs, the heavier one will have about twice the buckling strength at a given length. ( http://ir.library.oregonstate.edu/xmlui ... /1957/1286 )

Understanding these basic relationships gives you the basis for designing an efficient tower.

[Clueless Builder]

To clarify, I am only printing the loading block. It is nice 3D printed because it is super accurate.

[dholdgreve]

To clarify, I am only printing the loading block. It is nice 3D printed because it is super accurate.

"Clueless,"
It is not critical that the loading block be accurate... assuming you are building the tower for the block to sit on top of... It would work if it were anywhere between a 1/4" and 3" thick, and could be substantially over the 2" x 2" (5 cm x 5cm) spec... the only critical part is that the hole be drilled (or molded) 90 degrees to the block, and that it be centered in the block, whatever size you decide to use...

Something to consider: Use an oversize block (something in the 40 cm long range), then build some sort of skeleton about 45 cm cage about 45 cm high, that the tower can be placed in when you are testing your design (at home, not at a competition). Allow the wings of the oversize test block to overhang the skeleton cage. If / when the tower fails, you should be able to see the exact point of failure, as the loading block will be caught by the cage, and not destroy additional parts of the tower.

[jander14indoor]

I thought you were talking about 3D printing the test base, but my comment about rough vs slick surfaces still applies. Slick is worst case, I'd suggest testing your towers on that, not plain wood.

What happens is most towers have the bottom legs angled outwards. As a result there can be a force vector outwards as the legs try to spread when the load is applied.

On a rough surface the bottoms lock in place and provide the reaction force to prevent spreading.
On a slick surface the tower itself must prevent spreading, increasing the twisting loads on the legs and any cross bracing near the bottom.

If you only test on a rough surface and minimize the cross bracing to just short of breaking (what you need to do to win) you'll find they fail on a slick surface.


Comment on test blocks. Yes you can use a larger or smaller block, but make sure your design is insensitive to block size or do SOME testing with a correct block size. Testing with an oversize block reduces the local pressure loading (if you aren't careful) and going to correct size may introduce pressure points you didn't expect. Going from under size to correct size and you may find that it doesn't fit!!

Jeff Anderson
Livonia, MI

[batteryPack]

Does anyone know how to create an autoloader for testing? Preferably for sand.

[0ddrenaline]

Has anyone tried using hollow legs for towers? My coach insists that it would be better than typical legs. I know that people use hollow fuselages on freeflight planes, but those have boron strips along the length of the balsa tube to keep it from buckling. Considering that we can only use wood, do you all think that this idea is practical?

[bernard]

Has anyone tried using hollow legs for towers? My coach insists that it would be better than typical legs. I know that people use hollow fuselages on freeflight planes, but those have boron strips along the length of the balsa tube to keep it from buckling. Considering that we can only use wood, do you all think that this idea is practical?

Compression tubes are also used for motor tubes without boron; for instance, they are not used by some F1D flyers. I have also made rolled tubes for Science Olympiad haven't used boron. Many years ago, compression tube Boomilevers were often winning designs.

Sidenote: This topic is starting to get long. All the build events this year have forums because they tend to get long and complicated, so if you're bringing up a new subject, feel free to make a new topic!

[Balsa Man]

Has anyone tried using hollow legs for towers? My coach insists that it would be better than typical legs. I know that people use hollow fuselages on freeflight planes, but those have boron strips along the length of the balsa tube to keep it from buckling. Considering that we can only use wood, do you all think that this idea is practical

That's a really good question. Short answer, yes, theoretically, tubular legs would be the most efficient.....construction, but as a practical matter, for tower legs, you will not be able to realize that theoretical advantage. For a given amount/mass/weight of wood, having it in a thin walled tube does gives you the highest buckling strength. See archive discussions on boomilevers- the wood structure before bridges rotated in.

However, having been one of the folk that ...helped get this concept out there for booms, I can tell you that because of the BIG difference in forces involved, and inherent construction issues, tubes that will be small enough diameter and thinness to be more efficient than a solid leg are, I believe, probably not practical to build. In booms, with a single tubular compression member, you were looking at a 40 cm long boom, with a 40 kg axial compression force (at 15 kg load); that's an order of magnitude higher than what you're looking at in a tower leg (for a 4-legged tower). After exploring a couple of ways of constructing, we ended up with 5/8" diameter tubes, rolled from high density, C-grain 1/64th balsa sheet (high density, as in 15+ lb/cubic foot. Looking at about a 2.5 gram tube weight. Great for 40cm long member, carrying VERY high compression load. Way less efficient than solid leg w/ bracing for a tower, I believe. I haven't 'run the numbers, though to be certain.
It is very difficult do do rolled construction a lot smaller than this- precisely, at 50, 60, 70cm length. For efficiency > solid legs + bracing, likely looking at 1/100th of an inch thickness or less. If you look at attaching bracing, gets very difficult to avoid bracing pushing in the tube wall, and once circular cross section gets distorted, it will fail almost instantly.
You might, however, waant look into how rubber band flyers do smaller diameter rolled motor stick, though, to make sure there's not a workable angle. Jander14Indoor will have some useful insights on this