Designs

[AlphaTauri]

however, the thing i dont understand is that if an 8 cm hole needs to go through the top portion of the tower, how is the 5 cm loading block going to fit on the top of the tower?

Well, actually the tower is supposed to fit through the hole, so the top portion of the tower can be no further across than 8 cm at its widest point. If they had to have an 8 cm hole through the tower...that would sort of be an impossible building event.

[phillies413]

oh, i get it. Thanks!

[smartkid222]

however, the thing i dont understand is that if an 8 cm hole needs to go through the top portion of the tower, how is the 5 cm loading block going to fit on the top of the tower?

And also, it is better to divide the tower into the top vertical portion and the bottom more angled base, or just have it as one straight angled line going to the top?

The 8cm hole needs to go outside the tower
You have to make a top vertical portion and then a more angled base. If you had a straight angled line it wouldn't either fit inside the 8cm whole or span the 20cm x 20cm opening.

[Littleboy]

The top part of the tower has to go through the 8cm hole.

[Balsa Man]

In the “Base” thread, I discussed yesterday one of the key mathematical relationship for designing – how the force on angled legs increases with the angle away from vertical. That leads to the next important relationship; how to handle that force so that the legs don’t break. Let’s discuss this in “Design.” We discussed this last year for bridges- for the pieces in a bridge under compression loading – worth looking back if you didn’t see it last year.

Let’s start with a hands-on exercise to get a feel for what’s going on. In a B-tower, we are looking at “lower legs” (the legs below the level of the 8cm circle) a bit over 30cm long; in a C-Tower, we’re looking at upper legs about 35cm long. Each leg has to carry something over 5kg in a 3-leg tower, or something over 3.75 kg in a 4-leg tower.

So, take a stick of, say, 1/8th x 1/8th balsa. Cut a piece of it 30 cm long. Cut another 15 cm, and cut another7.5 cm long. Take the 30cm piece. Put it vertically on a hard surface; put your finger on the top, gently push down. At not very much pressure (load), it will start to bow. If you apply just a little bit more pressure, it will bow more and break. The way it breaks - its failure mode –is called “buckling’ and/or “column failure.”
Now, take the 15 cm stick. Do the same thing. It will take considerably more pressure to get it to buckle. Do the same thing with the 7.5 cm piece. It will take considerably more pressure than it took to buckle the 15 cm piece. Now, Google up “Euler’s Buckling Theorem.” The second hit you’ll see is http://en.wikipedia.org/wiki/Buckling

This provides a good discussion in the early parts, and the key formula – F= pi squared x EI/(KL) squared. The key relationship is how the force (needed to induce buckling) varies with the length (the “exposed length” of the column. Its an “inverse square” relationship. As explained, if you have a column of length L, and it buckles at load F, if you then have a column (of the same material) of length 2L (twice the length), F=1/2 squared, or ¼; it will buckle at ¼ of the load it took to buckle length L. Conversely, if you go to a length of L/2 (1/2 the length), it will buckle at 2 squared (4 times the load). That’s the mathematical relationship behind what you felt. It takes a lot more load to buckle a piece that’s ½ the length; 4 times as much.

That is what the bracing between the tower legs is all about. By putting in bracing, you break the long column into a stacked set of shorter columns; the “effective column length” becomes the length between bracing. Let’s say your initial 30 cm piece took 1/4 kg to buckle. Properly braced at the midpoint, (making the effective column length 15cm) it will now carry 4 times the load- 1kg. Brace the midpoints of the two 15cm sections (making the effective column length 7.5 cm), ant it will carry 4 times 1 kg; 4kg. Wow, on a 4-leg tower, we’re into the load range you’ll get at a 15 kg tower load……

This leaves thee areas to explore. The first two both involve trade-offs – a fundamental aspect of engineering design.

First is 3 legs vs 4 legs trade-off. 3 legs means ~50 cm less leg wood (25% less), but that leg wood is going to have to be heavier than in a 4-leg design because its carrying 25% more load) -either bigger cross-section, or higher density, or some combination- , or its going to have to be braced to a shorter exposed column length, or some combination of all three. Which will get you to a lighter tower??

Second is the leg weight vs bracing weight trade-off. Are you better off with lighter leg material braced at closer intervals, or heavier leg material braced at longer intervals??

The third is bracing configuration; how do you brace the legs so that the brace points are……effectively locked in space- so that the bracing really does break the long leg sections into shorter effective column length; X-bracing, Z-bracing, ladder pieces….? What are the forces on bracing pieces in various configurations?

I’m sure we’ll see some interesting discussion (and discoveries) on these aspects as the year progresses.

Cheers,

[smartkid222]

Excellent explanation!

[lllazar]

Balsaman that was an excellent way to put the basic objective of this event - i learned a lot from it, thanks!

Now when building a three legged tower you also have to consider the building process, it's harder to pull off than a 4 legged tower thats for sure. Make sure your comfortable building your structure because that honestly makes more of a difference when we're at such light towers (<8-9 grams).

As for the bottom legs, we've been using x bracing, two sets on each side of the base, to essentially split the force on the legs in half. However, we do feel there is a more efficient way of doing this - now my question is, instead of x bracing, what if you had an arrow shape...imagine a horizontal member from the midpoint of one leg to the other leg. Now, from one of the points where the bracing member is attached to the leg (Point A) apply another member from that same point to the opposite side, and up to the corner. Do the same thing down to the other corner, again starting from that initial point where the horizontal member and the leg met.

Less wood, by one member, and your still splitting the forces in half. Would the rigidity of the structure be compromised?

[Balsa Man]

Thanks, guys.

Understanding the basic engineering principles at work is key to doing well, be it tower, bridge, or boomilever.

IIIazar, you raise another very critical one; the importance of building precisely. You can have a superb design; you’ve figured out your loads/forces, what kind/size wood where – correctly, but if you don’t build it precisely and symmetrically, it won’t work. It takes surprisingly little variation from the “design configuration”- that set of straight lines, symmetrically aligned, that you have on paper, or in CADD, or whatever, to drive the actual forces well past the design forces; one leg a bit askew. A millimeter or two over the 50cm height can take a design that would work to something that doesn’t work (as in fails significantly below full load).

That says you need a way – a system – to get that precision; some kind of jig (probably 2 jigs, one for the upper portion, one for lower one (“upper = above the 8cm circle, “lower” below it). I preached the value of this on bridges for the last couple years – it for sure applies to towers. The other thing that you get by investing the time up front in figuring out and making good, precise jigging is control of variables. Some are harder to control- like the natural variability in wood – two pieces of balsa or bass, same size, same weight, are not necessarily of the same strength. Shape, configuration IS a variable you can control.

To some extent, you get into a …..development process; refining/perfecting a design. Say you build a tower; it fails at 12kg; you build another one like it, but with heavier/stronger wood in the places you think you need; it fails at 12.5kg. Did it fail because the heavier wood wasn’t strong enough, or in the right place(s), or did it fail because the shape was different – some part was seeing well over design load because it was mis-aligned by a millimeter or two? Or you build a tower, and it carries 15kg,; wow, it carries 17.5, so you go to lighter wood, and it fails at 13. Same question- is the wood selection not up to design load, or was the failure due to imprecise (different) structure shape ?? If you don’t know the shape – the configuration was the same (as close as you can get it, you don’t have a clue, and you don’t have a way to have a clue.

Its really not all that hard to make jigging that is very precise. The real key for towers is the legs. They need to be very precisely placed. The structure will be more tolerant of slight variations in bracing alignment. We can talk more about how, but I will say as a matter of fact two things:

a) my son’s jig for bridge last year – for building the sides, which then get assembled into a bridge, was symmetrical to about 1/10th mm. You could take a built side, lift it up out of the jig, flip it over, put it back in, and it would fit. Take a look in the bridge photos from last year (Balsa man folder) to see the jigging I’m talking about.

b) there is an easy way to get that same level of precision for a tower (my older son did towers back in 04/05). Takes <$20 in materials, and once you’ve worked out dimensions, takes about 2 hrs for top part, 2 hrs for bottom, holds the legs “in design configuration” while you put the bracing on. With that you have a tool to do real engineering development with.

BTW, like you, my initial thought was that building a 4-leg design was inherently easier than a 3-legger. Turns out, that's not true; with jig design I'm talking about in b), above, its the same. For a 4-legger, you'd have 4 pieces, 3 for a 3-legger. In each case, you have 3, or 4 pieces, carefully made to be the same shape. Ponder this; I'm not going to.....give away the store this early in the season. Think about the end-point I've just hinted at; think about the problem- positioning legs in space, precisely, and repeatably.

Let me ponder your bracing question; little short on time today.

Cheers,

[lllazar]

Thank you balsa man, i have been working on a design for a jig and i think i have it but i don't know if i can be sure of its precision...id rather take my time and build another one after reading that

[Balsa Man]

Let me be a little more precise about where the degree of precision is most critical.

Same situation/problem with 3- or 4-leg tower; let’s use a 4-legger for discussion, and let’s focus to the bottom part- from the test base up to the 8cm circle. What I’m about to talk about is easy to draw, but a bit harder to present with only words. Imagine the Great Pyramid. Whack the top off – take a slice parallel to the ground; you end up with a truncated pyramid; instead of a point at the top, you have a flat, square area, parallel to the ground. The “edges”, those 4, sloping lines where the faces of the pyramid meet, are your “leg lines.” If you were able to make/shape a solid that accurately shrunk that to “tower size”, you would have a very precise, useable jig. Put your 4 leg pieces up against the 4 edges – put on some …..bits that hold them/keep them from moving sideways, that align them with the edges, and the legs are in “design configuration.”

Now all you have to do is put your bracing on, then lift what you’ve put together off…. If you drew up your design configuration in CADD, and fed that into a $100,000 3-D milling machine, and had it shape a block of…..something, let’s call it unobtainium, you’d have a perfect jig. Most of us don’t have access to a set-up like that (Duh…..).

So, let’s look at the points and lines that we are trying to…..locate in space. What we want is some kind of material/structure that locates the legs, actually the end-points of the legs (the legs being straight lines that join those end-points) exactly as our “perfect jig block does. Holding the visualization of our perfectly aligned legs, there is one other line we need to add to the picture; the “center line.” For this shape, there is a vertical line running from the center of the bottom – let’s call it the “base plane”, to the center of the top – let’s call it the “8cm circle plane.”

In/on both planes, the end points of the legs are at the corners of a square. Draw the diagonals connecting opposite corners. These lines cross, at 90 degrees to each other, at the center. Our center line runs vertically from the center of the base plane to the center of the 8cm circle plane. In a C tower, the 8cm circle plane is 15 cm above the base plane; in a B tower, it is 30 cm above the base plane. So, looking at our two planes; on each, we have on each a “cross.” Visualizing our “points in space”- the leg end-points at the ends of the “crosses” – the center of both crosses is on our center line; one cross sits above the other. Now, let’s look at vertical planes defined by our crosses. Take a visual slice along one of our cross lines; the plane that passes through a pair of diagonally opposite legs. You have a trapezoid; flat top, parallel to a flat bottom, with both sides sloping in toward the top.

The rules tell us what we need to know about the lengths of those crosses. The bottom cross length has to be >20cm; the legs at the ends of the cross need to be farther apart than 20 cm, so they are outside the 20cm x 20cm hole in the test base, and sit on the base. The top cross length needs to be less than 8cm (because the legs need to fit inside an 8cm circle); actually, the length needs to be even less, to fit the dimensions of the leg wood, because the outsides of the legs need to be inside that 8cm circle. Let’s assume legs out of 1/8th square stock. 1/8th is about 4mm (you’ll have to check this, I didn’t look up or measure, but it is about 4mm). So, with 4 mm off each end, we’re looking at 8cm, minus 8mm = 7.2 cm.; actually <7.2 cm.

The center line bisects that trapezoid, splitting it into two, congruent trapezoids. Each of these trapezoids has a vertical side (defined by the center line). The length of this is about 15 cm in a C tower (actually a little bit less than 15 cm, so it is below the level of the 8cm circle the tower has to fit inside of), about (as in a bit <) 30cm in a B tower. They each have a parallel top and bottom. The length of the top is ½ the length of our “top cross” lines (<3.6cm, from above), and the length of the bottom is ½ the length of one of our “bottom cross” lines (>20 cm, from above). If we cut a trapezoid of that shape out of…..a sheet of something…..actually, if we cut 4 trapezoids of that shape, and we put them together, with the center line edges touching, so that they are aligned 90 degrees to each other, the outer, sloped edges define and locate in space the same lines that our unobtainium truncated pyramid did…….hmmmm…. For the next piece of discussion, let’s call these trapezoids; these pieces “leg plates.”

Finally, after all those words, we’re to the point I wanted to get to about precision.

The lengths of the centerline, and the top and bottom cross lines are not that critical; they just need to be < or > a defined dimension; how much clearance/margin for error (allowance for event supervisors that aren’t prepared to measure accurately….) you want to build in is up to you. What IS critical is that those 4 trapezoids – the leg plates - are, in order of priority a) as identical as possible, and b) that the angle between the center line side and the base cross line side is as close to 90 degrees as possible. If they’re identical, you can put the leg plates together (glueing them together along the center line side) and have a jig that gives you your design geometry. If they’re not identical, you will have a jig that induces the problems- the distortions, the lack of symmetricality we talked about earlier.

It is the precision in making these leg plates “identical” that is the key – the precision that matters most; and the precision that you want to be in the fraction of a millimeter range.

It’s cake to cut out one “shape” that matches your design geometry; make sure the top is short enough; make sure the bottom is long enough; draw it up, cut it out – thin cardboard, sheet plastic from the hobby store- lots of workable, easy possibilities. The problem we’re down to is how to make more that are “the same.” If you are very careful, and very good, you can get pretty darn close. That is certainly an option.

Consider, though, the possibility of making a jig for making a jig. If you were to take that first shape you’ve made, lay it down on a …..sheet of something (wood, plexiglass, foam board, etc.), and take strips of something (metal, wood, plexi, etc), and glue those strips such that they are butted up tightly against the sides of your “shape”, what do you have? You have a form with which you can build identical (i.e with that ~1/10th mm precision I talked about earlier that may have seemed crazy, and obsessive, and difficult and time-consuming to achieve) leg plates.

Cut wood strips the width/thickness of your legs – we’ll call them the “plate edges”. Put them up against the insides of your top, bottom, and sloped outside jig strips. Do a little measuring- cut out a shape that fits inside those plate edges – doesn’t need to be perfect ; just needs to be a bit smaller than the open space you have left. Make it out of something, the thickness of which is the same as that of your plate edges – plexi (recommended), plywood, aluminum, etc. – we’ll call it your leg plate core. The back edge –the edge that goes up against the center line side needs to be straight, the other edges don’t need to be- they can be off a little, wobble a little. With wax paper, or saran wrap, or glad wrap down on/over the jig so you don’t glue your leg plate core and edges to the jig, put in some glue to attach the core plate to the edges – like thick, 5-minute epoxy. Let the epoxy harden, lift out the almost finished leg plate. Repeat ad nauseum; make 2, or 3 more (or a hundred. They will all be the same shape, with the kind of precision we’ve been talking about…..

There is actually one last challenge/issue – the back edges- that go on the center line. The dimensions we’ve been talking about for the upper and lower sides are from the center line. If you take the plates you’ve built and put them together, with center line edges touching, you have a small square (or triangular hole if you’re doing a 3-legger version), and the edges are out too far, by the size of that hole. Number of solutions- adjust your top and bottom dimensions to allow for that hole – so the outside edge is out from the center the right distance, or use/make a triangular plate edge strip along the center line edge, or sand/file/saw – bevel, the center line edge so that the edge line , centered in the thickness of your plate forms the edge.

Whew, that took a while to describe. If it doesn’t make sense, re-read, play/try. There are a lot of ways to skin a cat. This is just one way to skin this one. I’m sure there are other, and maybe better ways. This one, though, does work. Food for thought; a place to start from. Lots of other challenges to work through to a winning tower, but this approach does bring one very important variable under your control.

Have fun,
Cheers.