General Discussion

[rjm]

I'm glad you're having success with your three-legged towers. It is a considerable challenge to build them competitively. It takes perseverance to do it well.

The disadvantages of three legged towers go beyond the geometric imperfections discussed by SLM. BalsaMan mentioned the fundamental problem in his post when he talked about the tower faces not being perpendicular to one another, and I've written about this in previous years.

Legs tend to buckle under compressive loads; the direction of the buckling depends on the cross section shape of the leg and the manner in which they are braced by the crossbracing in each tower face. In general, the direction of buckling will be in whatever direction in least supported, of course. Bracing in very light towers will be slender strips of wood with high tensile strength and low capacity for compressive axial loading, because the bracing itself will buckle along its length (between the legs). Bracing is really only strong when loaded axially, in tension, and that happens when the direction of the buckling of the leg coincides with the plane of the tower face. Bracing doesn't do so well resisting forces which have a component normal to the tower face.

When the tower faces are perpendicular to one another, any tendency of a leg to buckle is resisted by the tensile reaction of the bracing. If there is a component of buckling of a leg which is not in the plane of one face, that component is resisted optimally by bracing in the adjacent face, also an axial reaction in that bracing. If the tower faces are not perpendicular and the buckling happens to occur in a direction not in the plane of either face, then there is a component of the buckling which must be resisted by a bending force in the bracing of both faces. Bracing can only resist bending if it is relatively heavier than bracing with axial forces only.

Triangular base towers must either have legs with a cross section which tends to buckle in the planes of the faces, or they must have bracing which is heavy enough to pick up at least some bending load. Either way (or both ways) the savings in weight from omitting a leg and a side are offset by the extra mass required to resist the buckling. This isn't hard to demonstrate. Build both types of tower, using similar construction densities and cross sections, then apply enough load to cause strain in the bracing, but not so much that the tower collapses. In a three-sided tower, you can see the bracing bending in or out (or both) under such a partial load. A square base tower may bend also, but it won't be nearly as pronounced. Bending of the bracing is a design problem to be eliminated.

My daughter spent two years (1995 and 1996) building three-legged towers, taking a third place medal at Nationals her senior year. It can be done, but it's not really worth it. It took us a long time to understand what was happening in the bracing.

Bob Monetza
Grand Haven, MI

[Balsa Man]

Thank you, Bob, for adding/refreshing this information, which first leads me to a general comment about this board, and encouragement to all on how to use it to best advantage:

Over the years, important issues/aspects of the various events have been discussed over and over. Some of that discussion is just chatter; some just plain wrong; and some of it is from very knowledgeable people with years of experience and training/education (e.g. engineering/physics), and is REALLY good and helpful. The time spent to go back over the archived posts will be of great value. There are many real gems of information just waiting to be absorbed and used.

A few important examples for tower (some of which is under discussion of bridges & boomilevers) include use and types of glue, how column failure works under compression loading (Euler’s Buckling Theorem and the inverse square relationship of exposed column length to buckling strength), the pros and cons of various bracing configurations, wood properties and selection, jig design and building, and how to do structure testing in a way that you will know what piece breaks first and how/why, and 3-legged vs 4-legged tower designs. Do yourself a favor, take the time to explore, read and understandThat said, back to topic.

foreverphysics, I also think its great you’re having good success with both a 3-legged and curved leg approach. Having successfully worked through the design and building challenges involved in both aspects, understand and appreciate what you’ve accomplished.

The downside of non-axial compression force on bracing in a 3-legger is, as Bob has explained in more detail, absolutely real, and inherent in a 3-leg design. With proper testing, you can see it happen. With proper building, yes, it can be overcome, but there is a weight price to doing so.

So, now, as to your discussion of cutting the weight in ½ (a 50% reduction) going from a 4- to 3-legger, I’m not following your math.

Let’s look closely at the actual math for a C-Div tower.

First, the base section. In a 3-legger, just clearing the outside of the test plate hole, and the inside of the 8cm circle at a height of 15cm, the leg angle on a 3-legger is 28.6 degrees, and on a 4-legger, 24.1 degrees. The compression forces at a 15kg tower load - on each leg - are 5.67kg on the 3-legger, and 4.11kg on a 4-legger. That’s a 38% higher force on the leg in a 3-legger. Leg weight on a 3-legger would seem at first to be 25% less (=3/4). From some compression/culumn failure testing, though, the weight/density increase needed to get a 38% column strength increase is about 28%. So, let’s assume you have a 4-legger, where the legs are just sufficient in strength to carry the load; we’ll call the weight of each 1.0- total leg weight =1.0+1.0+1.0+1.0=4. So, in a 3-legger, with the 28% heaver legs you need to carry the additional force, we have 1.28+1.28+1.28=3.84. Lighter? Yes, it is, but it’s 96% of the 4-legger; a savings of 4% (not 25% - “1/4 of the weight shaved off”).

Now let’s look at the upper chimney part. Here the angles (from vertical) are close enough the same, and close enough to vertical that the increase in force from vertical to angled is negligible. Force on the leg in a 3-legger is 5kg; on a 4-legger, it’s 3.75kg; that’s a 33% increase in force. The weight/density increase needed to get a 33% increase in column strength is roughly 24%. So, again, let’s assume you have a 4-legger, where the legs are just sufficient in strength to carry the load; we’ll call the weight of each 1.0- total leg weight =1.0+1.0+1.0+1.0 =4. So, in a 3-legger, with the 25% heaver legs you need to carry the additional force, we have 1.24+1.24+1.24=3.72. Lighter? Again, yes, but it’s 93% of the 4-legger; a savings of 7% (not 25%).

The length of upper section is 3.67x the length of the bottom (55/15), so a 7% savings in the upper portion, and a 4% savings in the lower works out to about a 6.3% savings in overall weight. The ladder (and diagonal) bracing lengths in the upper portion are close enough to the same it doesn’t matter, and in the base, because of the wider spread at the base, a tad longer, but not enough to be significant.

Per increment of height, the weight of bracing is maybe half that of leg weight, so to reduce overall weight by ½, you’d have to use ¼ of the amount/interval of bracing. Looking at a 55cm tall upper section with bracing at bottom, ¼ of the way up, ½ the way up, ¾ of the way up, and at the top- you have 4 bracing sections, each about 13.75 cm long. Let’s say you go to a single brace point at the middle, so you get two braced sections, each at 27.5cm; half the bracing weight, at half the weight per unit height of the legs, you’ve saved 25% on overall weight. But by cutting the bracing interval from 13.75 to 27.5 – doubling the effective/exposed column length, you have reduced it’s column strength by a factor of 4 (1/22, which = ¼) – while the force has gone up by 33% (5/3.75). Basic physics – Euler’s Buckling Theorem – makes it plain that just won’t work. If a leg in the 4-legger was just barely carrying 3.75kg, and you double it’ s exposed column length, it will now carry 0.94 kg (3.75/4) before column failure, and it will be seeing a force of 5kg.

So, if you have legs in a 4-legger that are just strong enough to carry at a given bracing interval, and you go to 3-legger with the same legs, you have to reduce the bracing interval enough to increase the column strength by 33% - that works out to about 13% decrease in the bracing interval – i.e., more bracing, not less bracing.
Bottom line, and with all due respect for what you’ve done, I find myself echoing SLM’s question: “.... 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?

[jma]

If the testing block is 5x5, do I build the chimney smaller than that or do I rotate the testing blook 45 degree so it can fit on the tower? I saw someone mentioned 5.5x5.5 .

[blazinasian27]

A four legged tower would have better joints because for a three legged tower, the square shape of the balsa cannot be used as the base angles would be 60º. You would need to cut the ends of the cross supports and connect that to the side instead of the side to the side bond. An endjoint to side bond is always weaker than a side to side bond

[nejanimb]

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.

Wouldn't surprise me if you were able to reduce the weight of the towers you were building by 50%. But that doesn't mean that a 3 legged tower is, in theory, 50% lighter than a 4 legged tower. Certainly it's easy to see how over the course of a season of improvements, you can shave off half of the weight with design improvements, and you may have considered moving to three legs a design improvement. But the explanations given by Balsa Man, SLM, and rjm are pretty clear.

If the testing block is 5x5, do I build the chimney smaller than that or do I rotate the testing blook 45 degree so it can fit on the tower? I saw someone mentioned 5.5x5.5 .

Rotate the block however you like so it's situated well with respect to your tower. Generally probably is better to have the posts of your tower easily fit within the 5x5 square so the block sits fully on the tower.

An endjoint to side bond is always weaker than a side to side bond

Not really. For some compression uses, and certainly with good gusseting, butt joints can be quite useful, and are definitely not always weaker.

[hpfananu]

For the loading block thing:
I'm not sure if this is 100% correct, but when we tested a lot of towers last year, we found that if the block didn't sit exactly on the 4 legs, one leg always broke prematurely (not at the load we estimated).
Also, we once had a rectangular (:OO) block. Our tower broke a lot fast because the load wasn't even between the legs. Couldn't this also be a disadvantage with triangular towers?

[SLM]

For the loading block thing:
I'm not sure if this is 100% correct, but when we tested a lot of towers last year, we found that if the block didn't sit exactly on the 4 legs, one leg always broke prematurely (not at the load we estimated).
Also, we once had a rectangular (:OO) block. Our tower broke a lot fast because the load wasn't even between the legs. Couldn't this also be a disadvantage with triangular towers?

That is right, if the load is not distributed equally among the main compression members in the chimney, then one or more members have to carry a larger share of the load which generally results in their premature failure.

If the tower has four legs, then its top is either rectangular or square in shape. If the tower has three legs, its top is (has to be) in the shape of an equilateral triangle. To ensure equal distribution of the load, you need to place the loading block on the tower such that the center line of the eye-bolt/chain passes vertically through the center of the area of the rectangle/square/triangle at the top of the tower.

Both types of towers could be adversely affected by unequally distributed (eccentric) loading.

[Balsa Man]

For the loading block thing:
I'm not sure if this is 100% correct, but when we tested a lot of towers last year, we found that if the block didn't sit exactly on the 4 legs, one leg always broke prematurely (not at the load we estimated).
Also, we once had a rectangular (:OO) block. Our tower broke a lot fast because the load wasn't even between the legs. Couldn't this also be a disadvantage with triangular towers?

That is right, if the load is not distributed equally among the main compression members in the chimney, then one or more members have to carry a larger share of the load which generally results in their premature failure.

If the tower has four legs, then its top is either rectangular or square in shape. If the tower has three legs, its top is (has to be) in the shape of an equilateral triangle. To ensure equal distribution of the load, you need to place the loading block on the tower such that the center line of the eye-bolt/chain passes vertically through the center of the area of the rectangle/square/triangle at the top of the tower.

Both types of towers could be adversely affected by unequally distributed (eccentric) loading.

A few additional thoughts on this....

As is so often the case, there are trade-offs involved. And, the questions and answers here tie into a couple other discussion threads going on – testing on a level, or not so level surface and the effects of a leaning tower, and the pros and cons of 3 legs vs 4 legs.

First, 3 vs 4 legs and the problem of uneven leg loading.

With 3 legs, the block will sit, with load equally divided between the legs-assuming its geometrically centered- no other ifs, ands, or buts. That’s because 3 points define a plane.... It doesn’t matter if that plane’s not level- the 3 points define it. In terms of actual tower precision, within limits – a degree, or so off level – a millimetre, or maybe even 2mm difference in elevation of the leg tops- as long as the block is centered, it won’t matter. However, because 3 points define a plane, when you go to four points, you run into an inherent issue. 3 points will fall into contact- the 4th point/leg top, unless you are really lucky and/or precise, will be either above or below the 3-leg contact plane. If its low, the block will put disproportional load on two legs – it will “rock” along the diagonal axis, and things won’t “steady up” until those two diagonally opposite leg tops have been “pushed down” far enough to bring all 4 into the same plane. If its high, it, and the leg diagonally opposite it will become the “rocker points.” Depending on how far the leg tops are “out of plane”, the pushing down of the two “rocker point” legs may well cause leg failure. Very careful sanding (fine paper on a flat block that’s larger than the top of legs square, and sand-check, sand-check, etc.) can get you close. At a minimum, you need to do that. Even when you have sanded to what really seems to be full/even, 4-point contact, it will be likely there is some “out-of-planeness”– a thousandths of an inch or two difference. That will cause some degree of non-proportional loading on two legs. If its small enough, it won’t cause overload/breakage. There is a way help things beyond a good sanding. Once you’ve sanded to the best evenness you can get, cut some little balsa strips the width of the cross-section of your legs- an eighth, 3/32nds – whatever you’re using. You want fairly low density wood to do this with. As to thickness, depends on how good you are sanding things even. If you’re good, 1/64th, even sanded down thinner will do. I wouldn’t go any thicker than 1/32nd- maybe 1/32nd sanded down a bit. With a tiny glue spot, glue the strip across a leg top, then trim so you have a “pad” the same cross-section as the leg; repeat for the other 3 legs. What you have crush-zones-cushions that allow the block to settle in more evenly, and more evenly distribute the load equally.

Next topic - SLM is absolutely correct on the importance of having the load carried down the vertical centerline – the geometric center of the tower.

If the load is off-center, one or two legs will see more force, and will be the first to break. Two things have to happen to achieve this. First, the geometric center of the load block- the point through which the eyebolt runs – has to be aligned with the geometric center of the tower. Second, the tower has to be vertical.
There are some reasonably easy ways to get the load block centered – for either 3- or 4-leg towere. Get a piece of thin plexiglass- 1/16th or 3/32nd of an inch works fine. As precisely as you can, cut out a 5cmx5cm square. Take a sharp point and scribe (as in scratch) lines joining the diagonal corners. These lines will cross at the (geometric) center. With a square (or rectangular) top tower, its cake to line things up. Get a couple pieces of fine thread. Run them between your leg tops, diagonally, joining opposite corners. A tiny dot of glue will work; it can be done with tape, but its trickier…. The threads cross at the tower’s centerline. Now put your plexi square on top. Move it around till its center lines up with where the threads cross. If your top is truly square, the diagonal lines on the plexi will line up with the diagonal threads. If your top is, at the outside corners of the legs, exactly a 5cmx5cm square, you’re done- everything lines up; when you go to test, just use your eyes and fingers to align the corners of the load block with the outside leg corners.

There is a good reason to have your top (square or rectangle) smaller than 5x5. Having the upper/chimney legs lean in a bit helps with the overall stability of the tower. If the base of your chimney just fits within the required 8cm clearance circle, and the top fits under the 5x5cm load block square, you are going to have a bit of lean-in; the diagonal of a 5x5 is 7.07cm. The diagonal distance between opposite legs that just fit an 8cm circle is, of course, 8cm. BTW, you want the bottom of the chimney legs out as close to the limits of the 8cm circle as you can, to minimize the lean-in angle of the base section legs – the more they lean in, the higher the force (for a given tower load) they will have to carry. The amount (i.e., angle) of lean in for the basic fit of the chimney will, of course be greater for a B-tower than a C-tower, because the C-chimney is significantly longer. The limit for the amount of lean-in at the top is the need to fit the eye of the load block eye bolt through (looking vertically, a 3cm x ¼ inch rectangle). For a B-tower, going down to 5x5 at the top is probably plenty sufficient; for a C-tower, you'll probably want to pull it in a tad more.

So, if your legs lean in to smaller than an exact 5x5, the plexi square and string arrangement gives you what you need to get perfect block alignment. Get the block diagonals lined up with the string diagonals. Look through the plexi to see how far in your leg edges are from the edges of the block. Cut some little bitty pieces of really light balsa to about the length/thickness of the gap between the outsides of the leg edges and the block edges. Carefully glue these on the two outside leg edges, at two diagonally opposite corners. Trim/sand/file till the edges of these “corner guides” line up with the edges/corners of the block. Now you can accurately place the actual load block in a centered alignment, using fingers and eyes to line up two opposite corners with your tower corner guides.

This alignment process is a bit trickier/more complex getting centered alignment for a triangular top. We came up with nice alignment tool for doing this last year. Here’s how to make it. Cut a piece of thin plexi into a rectangle, oh, 6-ish cm x 9 or 10cm. On one of the 6cm sides, cut in a 60 degree “V.” Cut a plexi triangle that just fits your leg tops. Mark/scribe the (lines that define/will intersect at the) geometric center of it (be careful, the location of the geometric center of an equilateral triangle can be visually non-intuitive to some. You need to run perpendicular lines from the mid-points of the sides, they intersect at the geometric center; that point is closer to one side than some “think it looks like it should be.” The next step takes more than 2 hands….Put your triangle on top of your 5x5 plexi square, so that the centers are lined up. Rotate the triangle so that one apex, and the perpendicular line from the middle of the opposite side are lined up- one point of the triangle will be ‘pointing at” one leg. Move things around until the corners of the triangle are right on top of the leg ends. One edge of the triangle will be parallel with one diagonal of the square. Once you have this positioning, apply gentle down pressure to hold it all securely in place. Then, put the V-plate in place, sliding it into position just underneath the square, so that the apex of the V-cut is pushed up against one leg (btw, come back when you’re done, and mark that leg with a magic marker, and use the same leg to do actual load block placement). Now what you need to do is get two strips of wood in place that run up against/along 2 adjacent edges of the square. You can carefully mark where the line of the edges of the square run along your V-plate, or if you can hold the triangle/square, and v-plate stack in-place, you can glue the strips up against the sides of the square. These wood strips will form a 90-degree V. With these strips glued in-place, you’re good to go. To position the load block, push your V-plate up against your (marked) leg, so the top surface of the plate is just barely below the leg tops (one person holding the tower firmly in-place, one person positioning the plate and load block – and practice this before competition!) Position the load block so that its tight up against your wood strip V. Put a finger in place on the top of eyebolt in the load block so it doesn’t move around. Your partner can then get the load bucket hooked up/ready to go; you can re-check alignment just before loading…

OK, we’ve covered how to get the load equally onto the leg tops, and how to get it centered at the top. The last consideration is getting that evenly distributed, centered at the top load so its pulling down the centerline of the tower all the way through the bottom. Just as off-center loading at the top will cause one or two legs to get disproportionate loading (and break first), if the load is not pulling straight down the vertical centerline of the tower, same thing will happen. Leaning towers (especially at 70cm high) = break early and score low towers. To get your tower aligned vertically, you have to start with a level surface. “Level” is, of course, a subjective thing- how level is level…..You do the best you can, and you (have to) over-build to some extent to be able to handle off-axis loading (you may be able to get a very level surface to work from- there are no guarantees how level the test platforms at competition will be….).

You can get a decently level surface with a good level. Take time and care- the closer you get it, the better off you’ll be. If it’s a nice hard, smooth surface, like a piece of glass, a ball bearing or marble can help check. If it rolls, you’re not level- work till it doesn’t. Now, that 5cmx5cm plexi load block alignment piece I discussed above comes into play. Drill a really small hole in the center. Glue a piece of thread almost the height of your tower centered in that hole. Attach something with a bit of weight, and a sharp, centered point – a plumb-bob. You want the length to be such that the pointed tip of the plum-bob is just above the bottom of the tower – a millimeter or two if you can. Now you need a bottom plate to go with it- again, thin plexi works great. Put your tower on it, mark leg positions carefully. Scribe the lines needed to get your geometric center. You may want to put little brace blocks on to hold the bottom leg ends in correct position. Now, if you put your tower on the bottom plate, and put the top plate with plumb-bob in-place and lined up so its centered, you’re ready. If you are incredibly good and lucky, and your work surface is level, the tip of the plumb-bob will settle in right over your bottom center point. Likely, it will be off some, though.

Just as with the top, with a 4-legger, you have the 3 points define a plane, and getting a 4th point into that plane is a bear problem. While within reason, the angle of that upper plane compared to level doesn’t matter, it DOES with the bottom. What you’re trying to get to, is all 4 legs in equal contact AND at lengths that align the tower vertically to that plane. As you sand/adjust the bottom ends to get the plumb-bob centered on your bottom center mark, you need to keep checking/adjusting for good 4-point contact. Bringing both these aspects together is a tedious process that can be frustrating. It is a process that will pay great rewards, though. You’re going to need to sand leg bottom ends until you get the tower sitting firmly on all 4 legs, and the plumb-bob hanging straight above your bottom center point. Best sort of tooling setup for this is a thin piece of metal with some fine sandpaper glued on it. Identify the leg that needs shortening. Hold it an inch or two above the bottom; slide the sanding plate under. Letting the other legs rest/slide on your work surface, press gently down on the leg you’re holding, and slide the tower back and forth by a few centimeters. Especially if things are close, gently, gently- sand just a little, and check often. If you sand a long leg too far, you’re going to have to sand all the other legs to get back to alignment. When you think you’re done, holding the tower at the “waist” (top of base/bottom of chimney), put a good downward push on. You may find it’s gone out of vertical as the base “settles in” under some load. If it does, its time for more sanding, till its true with some load on. Patience. When you’re done, you can decide if little crush pads (like discussed for the top) make sense. Feel for the in-plane-ness (under some load). If you can’t feel any “rock”, you’re probably good to go. If you can feel anything, a touch more fine sanding, or a set of pads all the way around.

Last, jma, your comment about having heard of a 5.5x5.5cm top configuration. If you have your leg tops in a 5.5cm x5.5cm square, it is geometrically impossible to have the load block sit on/cover all 4 legs. Try it – take some graph paper; cut out a 5x5 square, and cut out a 5.5x5.5 square; rotate away; there is simply no way to get the 5x5 square to cover the 5.5x5.5 square. The maximum number of legs you can cover is 2.... That, obviously, won’t work.

[LKN]

I know there was some discussion last year on laminating legs, but it was pretty general. Here is what I am referencing:
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"if done properly, lamination will significantly strengthen the wood while adding less than 1g. I personally would suggest using it with two light and flimsy pieces of wood. I usually like to laminate on the base. So basically, what i do is build the base and my partner builds the chimney and we both connect it.
so, i will build the base normally first but use moderately light pieces of wood for the four 1/8^2 primary compression members. Then i will take an extremely light and spongy stick of balsa (with a mass of roughly 1gram per 48 inches). Then i cut out a piece from it that is a tad bit shorter than my primary compression members, apply glue to one entire side and glue it to a primary compression member. Do this until each of the four members has a stick laminated to it... i find that this only adds about 0.4-0.6 grams to the base to make a 3g base. However, the strength benefits are worth it imo.

Laminating for the chimney is an abject disaster because the primary members are too long so instead, we just put more bracing  but if someone has an easy method for that, i would really be interested in knowing it."
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I have had success with laminating, but I am wondering "is it worth the weight"? What percent of weight are you saving by laminating the legs compared to using more bracing? I usually laminate one side with a very thin strip of low density balsa, but what about laminating multiple sides? How about gluing the bracing: should the lap joint be on top of the lamination or on a side of the leg that is not laminated? Would it be reasonable to laminate the chimney?

[Balsa Man]

I know there was some discussion last year on laminating legs, but it was pretty general. Here is what I am referencing:
----------------------------------------------------------------------------------------------------------------------------------
"if done properly, lamination will significantly strengthen the wood while adding less than 1g. I personally would suggest using it with two light and flimsy pieces of wood. I usually like to laminate on the base. So basically, what i do is build the base and my partner builds the chimney and we both connect it.
so, i will build the base normally first but use moderately light pieces of wood for the four 1/8^2 primary compression members. Then i will take an extremely light and spongy stick of balsa (with a mass of roughly 1gram per 48 inches). Then i cut out a piece from it that is a tad bit shorter than my primary compression members, apply glue to one entire side and glue it to a primary compression member. Do this until each of the four members has a stick laminated to it... i find that this only adds about 0.4-0.6 grams to the base to make a 3g base. However, the strength benefits are worth it imo.

Laminating for the chimney is an abject disaster because the primary members are too long so instead, we just put more bracing  but if someone has an easy method for that, i would really be interested in knowing it."
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I have had success with laminating, but I am wondering "is it worth the weight"? What percent of weight are you saving by laminating the legs compared to using more bracing? I usually laminate one side with a very thin strip of low density balsa, but what about laminating multiple sides? How about gluing the bracing: should the lap joint be on top of the lamination or on a side of the leg that is not laminated? Would it be reasonable to laminate the chimney?

Well, you’re onto perhaps the most fundamental design question. What is the best weight trade-off between heavy, stiff – strong - legs with little bracing between them, and light, floppy – weak – legs with lots of bracing. Before getting into how lamination can play into this, back to some critical basics.
The rules pretty much define the tower’s shape. The legs are long columns in axial load (the load runs along their long axis). Their failure will happen in what is called “buckling.”

Hit Wikipedia on buckling. There you will see this:

Euler’s buckling equation:
F = pi squared times E times I divided by KL squared

Where F is the force at which buckling failure happens, E is the modulus of elacticity (simply put, how inherently strong the wood is), I is the area moment of inertia (simply put, how big is the cross-section, and how is the mass arranged around the long axis) and KL is the effective column length- this is also referred to as the exposed column length. It is the length between bracing- the bracing interval- where the bracing is configured to hold the points it is attached to securely in space..

What’s important is inverse square relationship between F and (KL) in this equation– between the load and the exposed length of the sections of a longer leg.

What this equation means for us is, if we have pieces leg wood (same size and density) 10 cm long, 5cm long, and 20cm long, and the 10cm piece carries 5kg, the 5cm piece (1/2 the length), will carry 1/4 the load (1/22), and the 5cm piece will carry 4 times the load
The piece 5cm long (1/2 the length) will carry 20kg- 4x the load –
1/(1/2)^2 = 1/1/4 = 4
The piece 20cm long (2x the length) will carry 1.25kg - 1/4 the load.
1/2^2 =1/4


Also search the archived posts- there is a lot of good, detailed discussion on this, and on the merits of various bracing approaches & configurations. This is really basic and important information you need to understand to get to an effective design. There is also as you’ve seen, a good deal of discussion on laminating.

So, as you correctly understand, you can go with stronger legs with the bracing points further apart, or floppier legs with the bracing at tighter intervals. Without changing the bracing interval, you can get legs stronger in 3 ways. You can stay with the same (cross-section) size and increase density. In Euler’s equation, doing this, you are increasing E when you do this. You can increase the cross-sectional size; you can generally go to a somewhat lighter density at bigger cross-section and get increased strength. In Euler’s equation, doing this, you are increasing I. You can, with a leg that in its current size, density, and braced length not strong enough, add lamination. In Euler’s equation, doing this also increases I.

As to how much weight do you “save” by laminating is totally dependent on how you laminate what; there is no, “laminating saves you 8.375%” answer. The only way to know if you have gained more in strength compared to what you lost in weight gain is trying and testing. You can do this testing in a whole tower (a pain, of course), in a single section – remembering, it is the between your bracing intervals that matters- if the legs in a chimney section 18cm long (braced at the ends and in the middle- giving you an effective column length of 9cm) holds, then a chimney 54cm long, braced at 9cm intervals (theoretically) will hold. Perhaps the best way – if you can get or make the tools to do it - is actual column compression testing; some high schools, most colleges, geotechnical or structural engineering companies/labs are a possibility to get a “real” test machine. You can build one, too. This way, you can test a piece of leg material. The length, within reason, doesn’t really matter. If you get data at some convenient length, you can put together an inverse square relationship look-up table, and see, for instance (real data here), if a piece 8.5 cm long tests at 7.25 kg, at a length of 10cm, you can expect it to break at 5.238kg…. There are a couple of photos of the compression testing rig we put together in the Image Gallery (2009). It took a day or so to build. Somewhere there is a post explaining how it was built, too.

To, finally cut to the chase. This is based on testing we’ve done over a number of years – I don’t know, 20 or 30 tests, of un-laminated, and laminated in various ways. I don’t claim to have “the answers”- as I said, there are a lot of ways; some are “beneficial”, and some aren’t. Some folk have had good success, again, with various configurations.

In general:

Doing effective long laminations – like tower chimney legs - is a real challenge. You will mess a number up before you get it right.

The easiest possibility that you may be able to get some advantage from is “doubling”- like if you’re using 1/8th stock, and its too weak, put two strips of 1/16th x 1/8th of somewhat lower density together.

More difficult is thin strip lamination along one side, or 2 adjoining sides (“angle-iron” lamination). When I say thin strips, I’m talking 1/64th, maybe even sanded down thinner. With low density core, and high density strips, there is some advantage to be had. Beware, though, it takes a fine hand with the glue to get both a tight lam, and not loose your weight advantage in excess glue. The glue layer in a lamination adds a lot of the overall strength increase.

Laminating a much lighter (lower density) to a higher density piece is essentially only going to get you the increased strength the glue layer provides to the initial piece (that’s what will increase I in Euler’s equation). It is a waste of time.

For any lam to be effective, you need to get a tight fit, and need to have the glue all along the laminated surfaces- gaps in glue = sections where the added lam strength is pretty much lost, and if that’s in the middle of the exposed length, bye-bye.