Designs

[mrsteven]

Me and my partner made a tower, it was perfect exept the base was to small, it was humiliating, DONT DO THIS! IT SUKS!

that stinks :/ keep in mind the smallest (but still fitting over the hole ) base is the best. Dont make them 20 cm away from each other. the shortest distance is from mid point to mid point!!

[Balsa Man]

Me and my partner made a tower, it was perfect exept the base was to small, it was humiliating, DONT DO THIS! IT SUKS!

Wow, bet it was. Some learning experiences are not fun.
I'm curious - like way too small, or just a bit?
Didn't have/read the rules to know what size it needed to be, or you did, but your measurements were off?

Better luck next time - like to hear how that perfect tower works with a full-size base!

[LKN]

Balsa Man or SLM:

I joined with a team mate this year who builds only square bases while I prefer to build rectangular (similar towers to SLM's post of a 6.7g tower in last year's forum). We have been discussing stability because it is going to become the primary concern for us once we get past regionals. With that being said, here is what I have been pondering about:

I build my rectangular bases to meet with the testing surface with a 5cm x 20.1cm gap between legs. The legs are rectangular 1/16 x 1/4 with a "centerlined" lamination piece and bracing that uses two glueing surfaces for the bracing to inside of the legs. I am currently bracing with medium density, about .40g 36" sticks balsa in-between the legs.

With your past experience, is this too thick? Can I go lower on the cross section for this bracing? I am not quite sure; would the bracing, although diagonal with no horizontal ladders, be under compression as well as tension? From what I have been following, if the bracing would be under some form of compression the cross section and density is much more vital rather than if the bracing was under tension.

At 16.5cm high on the base, the legs of the base have narrowed a gap that can support 1/16 x 1/16 chimney legs that are 2.8 cm apart where they connect to the base. From the 2.8 cm space between chimney legs, the chimney is 53cm long, making the tower 69.5 cm. At the top, the space between chimney legs has narrowed to 2.5 cm.

My team mate thinks that building a square base, tapering the base legs to 5cm at 15cm tall, and then having the chimney legs taper down to about 3cm at the top of the tower would be our best bet. I agree that this is more stable than my design. But, how much "more worth it" is the extra stability and tapering? I believe my design would come out much lighter (and has been so far) because there would be less distance to cover with the bracing, especially on the chimney, yet the slight tapering should be enough for the competition. How much "tapering" would be needed to be "secure" on a 70cm tower? Does the overall tower stability have an exponential relationship with the distance tapered in the legs? I realize that I am cutting it close, and that many assumptions are going to be in theory as if the rest of the design is perfect, and even with a great jig it is going to have to be a feat to pull it off repeatedly and shave off the last few grams, but I would like to know how far a little bit of tapering will go on a 70cm tower.

[SLM]

Balsa Man or SLM:

Here are my thoughts:

I build my rectangular bases to meet with the testing surface with a 5cm x 20.1cm gap between legs.

I would be a bit anxious if my rectangular tower had a width of 5cm. I feel it is too narrow for such a tall structure. Unless you have successfully tested a tower with a similar width, I suggest you start from a more conservative position. I’ve advised my team to use a width of around 9 cm as the starting point. After you have generated some data, you can then start narrowing the width.

The legs are rectangular 1/16 x 1/4 with a "centerlined" lamination piece and bracing that uses two glueing surfaces for the bracing to inside of the legs. I am currently bracing with medium density, about .40g 36" sticks balsa in-between the legs. With your past experience, is this too thick? Can I go lower on the cross section for this bracing?

My guess is that these dimensions don't give you a near "optimum" design for the legs. But, I may be wrong. What is the average weight of a leg?

...would the bracing, although diagonal with no horizontal ladders, be under compression as well as tension? From what I have been following, if the bracing would be under some form of compression the cross section and density is much more vital rather than if the bracing was under tension.

Let’s assume each pair of adjacent legs defines a trapezoidal area bounded, on the top and bottom by horizontal members, and the area is filled with horizontal and/or diagonal bracings.

Furthermore, the trapezoid is subjected to vertical (or almost vertical) loads at the two top vertices causing its bottom to stretch and top to shrink, as shown below.

This deformation of the entire trapezoid affects the members within it. Some of the members are going to be compressed and some will be elongated. Common sense suggests that members in the top part of the trapezoid are compressed and those in the bottom part are stretched. This observation, of course, is not very accurate, but does convey the idea that some of the members (mainly in the top part) are in compression and some of the members (mainly in the bottom part) are in tension. This is prior to the reign of buckling.

When the axial force in the legs (the sides of the trapezoid) gets too large, buckling starts to take form. At this point the sides (legs) start bending inward excessively compressing the bracings in between them. The net force in each of these bracings, therefore, equals to the force in the member due to the applied load + the compression force due to buckling. If a member was in compression initially, then the buckling effect makes it worse (more compression). Otherwise, depending on the magnitude of the two interacting forces (tension + compression), the member may end up being compressed slightly or remain in tension. Without knowing the exact geometry of the base and the bracing pattern, I am hesitant to suggest which diagonals will be in tension and which ones will be in compression.

You are correct, because of buckling, compression members generally need more attention than tension members.

I am currently bracing with medium density, about .40g 36" sticks balsa in-between the legs.

In our experience, medium density 36”-long balsa sticks that weigh around 0.40 g are adequate for bracings. That is what we used last year. The only way to know if you can get away with lighter sticks is testing!

At 16.5cm high on the base, the legs of the base have narrowed a gap that can support 1/16 x 1/16 chimney legs that are 2.8 cm apart where they connect to the base. From the 2.8 cm space between chimney legs, the chimney is 53cm long, making the tower 69.5 cm. At the top, the space between chimney legs has narrowed to 2.5 cm.

I feel your starting point for the size of the chimney (2.8 x 2.8 to 2.5 x 2.5) may not produce the result you are looking for. For me, this would be the “optimum” size, not the initial one, assuming no testing has taken place yet.

How much "tapering" would be needed to be "secure" on a 70cm tower? Does the overall tower stability have an exponential relationship with the distance tapered in the legs?

As you correctly stated, this year the height of the tower could pose stability problems. Instability here means undesirable movement of the tower, which in this case primarily means its sidesway, the leaning of the tower to the left or right. This could happen because:

(1) The tower was not built straight to begin with,
(2) The load of the sand bucket is not aligned with the tower’s centerline (eccentric loading),
(3) The platform itself is not level,
(4) The bucket starts swinging,
(5) Any combination of 1 through 4.

Let’s say, due to one of the above factors, the chimney wants to lean to the right, as shown below.

This means the long vertical member (labeled A) wants to turn clockwise a bit going from a perfectly vertical position to an inclined (right-leaning) position. By making the chimney tapered, you are, in effect, orienting A in a left-leaning position making it more difficult for the load to cause sidesway.

Here, the load has to do more work to cause the same amount of deformation. That, in a nutshell, is why tapering a tower adds to its stability.

Obviously, the more tapered the chimney, the better. But, I don’t see an exponential relationship between stability and the angle of inward inclination of the chimney. Furthermore, there are practical limitations to consider. Everything else equal, your teammate’s chimney ends up being more tapered (stable) than yours, but that does not mean yours wouldn’t be effective. The only way to know for sure is to build and test.

It would be interested to see a performance comparison (in terms of weight and load capacity) between the two towers.

[ckssv07]

I have built a three legged tower that worked preety well what scores have you been geting

[Balsa Man]

Some good, interesting questions, LKN. As usual, some excellent analysis/info from SLM
A couple specific question back – x-sect on your bracing? Both in base and chimney -?
I see the leg x-sect dimensions(for base & chimney), and 0.4gr/36 density on bracing, but don’t see a size on the bracing. I can add to what SLM’s said by saying at 3/32nds – in the chimney, for ladders in the length range of a bit over to a bit under 5cm, 0.4 to 0.5gr/36 works. With the much longer ladder length (s) in the base, more stiffness is needed. With 1/16th legs in the chimney, I’m guessing 1/16th bracing-yes?. Should work, at some bracing interval – the question is, what is that (optimum) interval
Next, just confirming, the 2.5cm apart spacing for legs at the top – rules call for clearing a 3cm eyebolt head- quick sketch looks like you’ll be awfully close – make sure there is enough room.
Agree w/ SLM that a 5cm wide rectangular is.....inviting sideways stability issues. Lean-in in the base (as well as in the chimney) would help

[LKN]

SLM and Balsa Man - I'll get a picture up soon and dimensions so you two can see what I am looking at. Good news, the base weighs 3.7g and definitely holds 16.5 kg and was not built "perfectly", some geometry was off, densities were well measured though. I think I can do some light design changes and shave off another .25g to .5g hopefully.

The legs for the base were 1/16 x 1/4 weighing 1.6g in a 36 inch stick. The legs didn't use the whole stick, so about 1.3 or 1.4 in the legs for the base. I laminated and braced with 1/16 x 1/16. I also did the tensional bracing across the bottom of the structure (literally underneath the legs) from the long rectangular side. The bottom of the legs met up with a 1/16x1/16 .65g piece of balsa (one on each long side) in more of a butt joint, so there was 1/16 x a little more than 1/4 for the gluing surface area. Now, something else I did, as a build off of hearing about a horizontal "brace" plate for the connection on perfectly rectangular towers to connect the chimney and the base, as well as some concepts from bridge building, I also created a small lap joint (on one side of the base leg/tensional member connection) on top of the already glued butt joint. I think that this would create a much stronger seal, even though I know we have discussed that the glue is practically infinitely strong if there is absolutely no gaps, even molecularly) between the wood being glued. I think that, because the legs come out to 5cm at the bottom of the base, which creates legs that are not on the same tilt with each other, the extra lap joint will help secure the tensional members if the legs pressure down on the tensional member and subject it to twisting and failing to something other than tension. I might be totally wrong with this idea, but that is my rational. Maybe the force of the legs that comes down with some vertical components on the tensional member is "enough" to keep it from any force but tension. I'd like to hear your ideas.

I also think a good bet would be to try to go down to 1/32 or 1/64 x 1/16 high density balsa for the tension members mentioned above.

SLM
The reason for my guess that there could possibly be an curved relationship to stability and lean in, is that in the past while building bases that came into a lean, I began with 8cm coming in to 3.9cm. These bases would not tilt side ways and I really had very little worries about the stability factor. I got to try keeping the half-base for top of base relationship, eg. 5cm (bottom) --> 2.5cm (top) only a few times last year and the stability still did not seem like a big deal. I didn't experiment too much, but that is what I hope this year is for... experimenting with lean-in rectangular bases. That is why I was taking a guess at that sort of relationship of lean in and stability. Your thoughts?

Balsa Man
Yes, I want to try to go 1/16 x 1/16 higher density on the chimney while keeping a fair density for the bracings, also 1/16 x 1/16. I want to see if I can get my chimneys any lighter because that is what I struggle with most as a builder. I am thinking about 4cm gaps, time and testing will tell.

On the eye bolt, I realize that it can be up to 3cm. At the NC state competition, the eye bolt and chain was much under the max dimensions, so I am not too worried. The team I joined this year has been going to nationals every year, and my thought is that we can turn the block 45 degrees just like you do the square base of a tower. I know that this is cutting it extremely close, so close that every thing else from a balance perspective must be perfect to keep the chain from contacting the tower. If I cannot pull it off then I will probably scrap the idea and go wider.

As I mentioned earlier, I will try and get some pics up on the image gallery. Balsa Man, thanks for your input and suggestions for cutting the thin strips and creating a plexiglass jig. And as always, thanks SLM for the analysis and diagrams.

[Cheesy Pie]

My tryout tower - Regional scoring - is 50 cm tall, basswood and a little balsa, and I don't know the mass. Although I think it will be moderate. Do you have any hypotheses on the score? Thank you! I need it to do well - I spent a lot on it.

[mrsteven]

My tryout tower - Regional scoring - is 50 cm tall, basswood and a little balsa, and I don't know the mass. Although I think it will be moderate. Do you have any hypotheses on the score? Thank you! I need it to do well - I spent a lot on it.

well without the mass or how much it held, I don't think it was be helpful to ponder on it. Its completely up in the air from my view since you don't know a range of where the mass might be, but i wish you luck on your tryout! I'm glad some teams have organization where that happens xD

[SLM]

SLM
The reason for my guess that there could possibly be an curved relationship to stability and lean in, is that in the past while building bases that came into a lean, I began with 8cm coming in to 3.9cm. These bases would not tilt side ways and I really had very little worries about the stability factor. I got to try keeping the half-base for top of base relationship, eg. 5cm (bottom) --> 2.5cm (top) only a few times last year and the stability still did not seem like a big deal. I didn't experiment too much, but that is what I hope this year is for... experimenting with lean-in rectangular bases. That is why I was taking a guess at that sort of relationship of lean in and stability. Your thoughts?

To relate stability to the amount of tapering of the chimney using a mathematical relationship, we first need to define the terms using variables. Here is a simple way of doing this. The chimney has a trapezoidal shape, as shown below.

Where h is height of the chimney and w is the amount that the chimney is tapered on each side. Also, since here stability has to do with sidesway, and maximum sidesway occurs at the top of the chimney, then we can use the horizontal displacement at the top (denoted by D in the above diagram) as a measure of the tower’s stability. The higher the displacement, the more unstable the tower becomes.

So, to relate the amount of tapering to stability, we can relate the ratio h/w to D. This relationship can be established for two scenarios.

Scenario 1: The sand bucket swings a bit creating a horizontal force at the top of the chimney as shown below.

In this case, stability (D) is proportional to cube of h/w. This relationship is nonlinear, but not exponential.

Scenario 2: The load block is not placed correctly on top of the chimney causing the chain to be off the centerline by a small distance denoted by e in the following diagram.

In this case, D is proportional to square of (h/w).

Related to the first scenario above, there is another stability consideration that is independent of the amount of tapering, but dependent on the distance between the legs of the tower. For a rectangular base, in the long direction where the distance between the legs is 20 cm, a 70-cm-tall tower tips over if the angle of swing becomes greater than 8 degrees. In the narrow direction where the distance between the legs is set to 5 cm, however, it takes an angle of 2 degrees to cause a tip over.