Scioly.org

Any glue can work, most work about equally well, IF used correctly. Some are more convenient than others.

See http://www.soinc.org/sites/default/file ... weight.pdf for a lot of hints and tips on light/strong glue joints. Written for the old Wright Stuff event, applies about equally well to all the construction events where light weight strength is critical.

Jeff Anderson
Livonia, MI

Have any of you tried a three-tiered tower? Those seem to work rather well...

can you explain what you mean by three-tiered tower? like instead of having a base and a chimney it has a base, chimney and middle portion?

As opposed to having 4 support strips of wood, you have 3, making a triangular shape instead of a square one.
So instead of having something like this:
You would have something like this:
Also, curving it upwards to make the width smaller makes for less weight to be reckoned with--you don't need that middle support beam that way.

Ah, three- tiered = three-legs (vs 4).
We went that route last year. This, like a number of other design factors is a matter of trade-offs.

At first look, it seems like a good idea - 3 legs would be 3/4 the weight of 4 legs. As you get deeper into the details, the "price" for that appparent weight reduction emerges:
First, each leg has to carry 1/3 of the load instead of 1/4. That means heavier/denser/stronger leg wood, or closer spacing of the "ladder" bracing (cutting the "exposed column length" between bracing down), or some combination of the two. By "ladder" braces, I'm refering to the horizontal brace pieces between the legs.

Second, in the base/lower part, the legs will have to have more of a lean-in angle (to clear the test platform hole at the bottom, and lean in enough to get inside the 8cm clearance circle at 15cm above the platform). As that lean-in angle increases, the load/compression force on the leg increases (that increase is a function of one over the cosine of the angle off vertical). For example, at a 15 kg tower load, a leg in (the base section of) a 3-legger will be seeing about 5.7kg; in a 4-legger, its around 4.1 kg. In the upper part, with very little lean-in angle, the difference is pretty small- a fraction of a kilogram, but in the 3-legger, a bit over 5kg, and in the 4-legger a bit over 3.25 kg.

Third, it is easier to put together an accurate jig for a 4-legger than for a 3-legger.

Fourth, the 90 degree angle between ladder brace pieces in a 4-legger vs. 60 degree angle in a 3-legger has two advantages. First is the ease of cutting/glueing/fitting exactly. Second is how compression loading gets put on the ladder pieces. In a 4-legger, as a leg starts to bend under compression load, a compression load is put onto the ladder - but that load is straight onto/into the centerline of the ladder. In a 3-legger, that force is not aligned with the axis of the ladders; there is a component in toward the centerline of the tower, and that means a bowing force is put on the ladders.

So, bottom line, we are back to 4-leggers this year.

As to curved legs, one could theoretically do it with either a 3-legger or a 4-legger; much easier and less curve needed in a B-tower than a C-tower. Getting evenly curved legs is not an easy matter (we used curved legs a few years ago). As to the "middle support beam" you mention, with a curved leg, you are going to need a stout ladder set near the middle of the curve. With the curve, the inward force against the ladders at the middle of the curve- where the leg is trying to bow more, is going to be more than in the ladders at the top of the base in a "two-piece" tower design.

Balsa Man wrote:Ah, three- tiered = three-legs (vs 4).
We went that route last year. This, like a number of other design factors is a matter of trade-offs.

At first look, it seems like a good idea - 3 legs would be 3/4 the weight of 4 legs. As you get deeper into the details, the "price" for that appparent weight reduction emerges:
First, each leg has to carry 1/3 of the load instead of 1/4. That means heavier/denser/stronger leg wood, or closer spacing of the "ladder" bracing (cutting the "exposed column length" between bracing down), or some combination of the two. By "ladder" braces, I'm refering to the horizontal brace pieces between the legs.

Second, in the base/lower part, the legs will have to have more of a lean-in angle (to clear the test platform hole at the bottom, and lean in enough to get inside the 8cm clearance circle at 15cm above the platform). As that lean-in angle increases, the load/compression force on the leg increases (that increase is a function of one over the cosine of the angle off vertical). For example, at a 15 kg tower load, a leg in (the base section of) a 3-legger will be seeing about 5.7kg; in a 4-legger, its around 3.8 kg. In the upper part, with very little lean-in angle, the difference is pretty small- a fraction of a kilogram, but in the 3-legger, a bit over 5kg, and in the 4-legger a bit over 3.25 kg.

Third, it is easier to put together an accurate jig for a 4-legger than for a 3-legger.

Fourth, the 90 degree angle between ladder brace pieces in a 4-legger vs. 60 degree angle in a 3-legger has two advantages. First is the ease of cutting/glueing/fitting exactly. Second is how compression loading gets put on the ladder pieces. In a 4-legger, as a leg starts to bend under compression load, a compression load is put onto the ladder - but that load is straight onto/into the centerline of the ladder. In a 3-legger, that force is not aligned with the axis of the ladders; there is a component in toward the centerline of the tower, and that means a bowing force is put on the ladders.

So, bottom line, we are back to 4-leggers this year.

As to curved legs, one could theoretically do it with either a 3-legger or a 4-legger; much easier and less curve needed in a B-tower than a C-tower. Getting evenly curved legs is not an easy matter (we used curved legs a few years ago). As to the "middle support beam" you mention, with a curved leg, you are going to need a stout ladder set near the middle of the curve. With the curve, the inward force against the ladders at the middle of the curve- where the leg is trying to bow more, is going to be more than in the ladders at the top of the base in a "two-piece" tower design.

Well...it's not really so bad if you have the right materials and you know what you're doing. We did it last year as well and were very successful init--the jugs really helped. You just need to build a good jig to build a good tower, which really isn't so hard. I've done it before.

foreverphysics wrote:Well...it's not really so bad if you have the right materials and you know what you're doing. We did it last year as well and were very successful init--the jugs really helped. You just need to build a good jig to build a good tower, which really isn't so hard. I've done it before.

I couldn't agree more on the importance of good jigs; see last year archive for a number of posts I did on ways to do do really precise jigging. Over 9 yrs of coaching, 5 of those w/ towers, have worked through/with a lot of different ways to do it- 3-leg, 4-leg, curved legs, straight legs, spiral legs; 40 to 60cm. With the 70cm height this year, there's even more importance on precise jigs. Last year, our symmetry/precision around the center axis at the top (40cm) was better than 0.2mm, approaching 0.1; won Regionals by a hefty margin, ended up 4th at State because of a rushed build job of a 1.5gr lighter than Regionals version.

My comment that it's easier to build a precise 4-leg than a 3-leg was just one of a number points on 3- vs 4-leggers, and it was the most minor of those points.
What's important for anyone considering the apparent advantages of 3-legs is the trade-offs in leg density, load, and ladder spacing, and the non-axial compression loading you get in the ladders at 60 degrees. RJM has mentioned this downside to 3-leggers over the years more than once. I didn't fully appreciate it till we did some testing with a safety tower this summer; we were able to see it happen. So it means ladder pieces have to be both longer than in a 4-legger, they have to be stronger (denser/stronger wood).

It may be a little easier to build a four legged jig, but ultimately, the three legged one will be better if you know what to do with it. Triangles are more stable than quadrilaterals, and in addition to that, it's a lot lighter. Like, if you do it right, you can make it 1/2 the weight of a 4-legged one. The wood doesn't have to be stronger; in fact, last year, we built the entire thing out of 1/16 inch balsa wood. It still held more than 15 kg and it weighed a little less than 7 grams. Curving it...just make it part of the jig.

foreverphysics wrote:... Triangles are more stable than quadrilaterals... it 1/2 the weight of a 4-legged one.

It is good to know that you have made the 3 legged configuration work for you, and your jig is effective in reducing construction and geometric imperfections when building your towers.

On the issues of stability and weight, here are a few comments.

It is generally true that a triangular form is more stable than a quadrilateral (say, rectangular) form when the loads are applied in the plane of the members, like the towers shown below.



In the case of 3 vs 4 legged towers, if we look at the towers from the top, we see something like this:



Note that here the loads are not in the plane of the triangle or rectangle. That is, the members that are forming the triangle and the rectangle are not really carrying much of the applied loads. Therefore, we cannot conclude that the 3 legged tower is more stable than the 4 legged one. To draw any such conclusions, we need to examine the entire tower. To make the point, here is an example of a less stable 3 legged tower, compared to a 4 legged one.


The 3 legged tower is less stable because the members along the sides of the tower (the ones actually responsible for carrying the loads) do not form a triangular pattern. Of course, the tower can be made more stable simply by adding diagonals along the sides, as shown below.



Furthermore, everything else equal, I fail to see how a 3 legged tower could be made to weigh 1/2 of its 4 legged counterpart. Where does this 50% saving of the material come from?

Lastly, our experimentation, consistent with the theory of structures, suggests that a 3 legged base is more susceptible to torsion (twisting) than a 4 legged base. Because:

1. Construction and geometry imperfections could result in unequal distribution of the load among the legs which in turn leads to the development of a twisting force at the base of the tower.
2. A rectangular/square 4 legged base (having two axes of symmetry) better reduces any twisting force that could develop at the base of the tower than a triangular 3 legged base (with one axis of symmetry only).

Although it is plausible to suggest that a 3 legged tower could be made to weigh less than its 4 legged counterpart (I am not sure by how much though), but the former is more sensitive to geometric and construction imperfections than the latter.

As long as you build the jig correctly and you use equilateral triangles, 3 legged towers do work better. We were able to conserve a lot more material because we used less struts in the triangular tower--and it worked. You already have 1/4 of the weight shaved off; take off the midpieces by curving the structure and that takes away 1/8 of the weight. Using less struts because of the structure (which we did) made it plausible to literally reduce the weight by 1/2.
Now, I realize that 3 legged towers are difficult to build correctly. But if you do, and you have the right kind of jig, it will ultimately give you the best score. In a correctly built triangular tower, there's really not much twisting in it. And by using a jig, you can eliminate most geometric and construction difficulties.