3 Sided Tower?

[Balsa Man]

I have had this idea on having a 3 sided tower. All the 4 sided towers have been over 5 grams. I was thinking that if I get rid of 1 side... then I might be able to reduce the weight by possibly around 1-2 grams From what I'm imagining, it might not be as good as a 4 sided tower. Has anyone tried making a 3 sided tower or might know if this is a good idea?
Thanks.

I'm gonna try one, just for kicks and post back how it goes. If I remember, I have terrible memory.

I have leftover wood that I don't want to use for competition, so: the 3 columns are 3/16" x 3/16" weighing 2 g/36" each. That should hold everything, with enough bracing. It will go for the bonus.

Isn't compressional strength very dependent on cross sectional area of wood? If someone built a 3sided tower with 3/16" wood that weighed maybe 1.5, that would be pretty competitive, right? After you get over the fact it's harder to build.

Those 1.5gr/36" at 3/16" are gonna be pricey- they'll be right down at the lower limits that balsa exists in. 4.74 lbs/cu ft. At 1/8" that density gets you a 0.7gr/36" stick. Jake (Specialized Balsa) lists these at $6.95 each; it'll be more at 3/16". He doesn't list on his web site, but sometimes has a very few below 0.7. The very lightest I've ever seen was at 0.62; next lightest at 0.66- $9.95 each.

Just a terminology thing- 'compressional' strength refers to strength resisting crushing. What you're wanting/referring to is buckling strength. Buckling strength (as I've discussed/explained extensively in past posts, and as Crtomir explains in detail in the extensive info he's just posted) is, indeed dependent on cross section. Buckling strength is E times I, where E is the modulus of elasticity (aka Young's modulus), and I is the second moment of inertia, which for a square cross section is d (the dimension of one side) to the fourth power/12 divided by the effective length squared.
I for a 3/16 cross section is 5.06 times what it is for a 1/8 cross section. That's a big gain in buckling strength. Going up to 5/32" gives you 2.44 times what you have at 1/8"..... And, if you run the numbers, for both 5/32 and 3/16, the weight goes up by a smaller factor than the buckling strength does. That's why we've gone to 5/32 for Nationals towers
But, for the reasons a number of folk have brought up, a 3-legger is not going to provide an advantage over a well designed 4-legger. Been there, down that path. It'll be fun to play with, I'm sure.

[Crtomir]

Hey, I just wanted to say, its really great seeing someone else join the...brotherhood who believe its important to get real, detailed information and knowledge out there; to give everyone the opportunity to up their game. There's some very good stuff here. It always fascinates me how different people understand and communicate their understanding, and how different folk learn differently; same info said in a different way, and the lights go on. , Back at the beginning of the season, laid out the importance of understanding the important mathematical relationships you need to really design- engineer. I like your take on these things- nicely done.
First, hats off to have gotten to the scoring level you have; that's just plain awesome.
Second, great to see someone else picking up on the old Forest Service study; I think it was 3 years ago I first posted a link to it, and nobody had said anything about how useful that info is.
Third, one important thing that study ....reflects is the variability around the mean of E at any given density- if you look at both the graph and the data table, it jumps out at you. It is in/because of this variability, that ...high performance wood selection is another key to success- getting the lightest sticks in your....wood pile that have the design buckling strength. For instance, in this year's wood, in 1/8th at 1.4gr/36", we were seeing single finger push down buckling strength ranging from 26-40gr. This is an important variable to understand and work with.
One thing I'm still working on (as discussed in a number of posts) is how the Effective Length factor in Euler's equation works with different bracing configurations- understand how to use/apply for a ladders and Xs configuration; haven't gotten a good handle for Xs only- its very different between the two. I look forward to digging into your spreadsheet.
Gotta run, working w/ our two Ft Collins schools going to Nationals to see what we can come up with.
Thanks. Look forward to talking more when things slow down a bit.

Thanks "Balsa Man". Looking back through some of the old posts, I see you did provide a wealth of information. Unfortunately, I only discovered this after the season was pretty much over for us, but anyone who wants to know the "secret" to building a really great tower only needs to go and read through all your posts in this Towers forum. I kind of think that's what Science Olympiad is all about. The kids learn to approach a technical real-world problem from a rational point of view, using scientific and engineering principles to solve the problem. It is more important, in my opinion, that the kids learn the physics and engineering behind the problem than winning the top score, although it's nice to see that sometimes those two go hand-in-hand. Often, my kids included, kids just build randomly without really learning the science behind the design. What you and some others have done in this forum is to lay out all that science as a justification for a truly great design. It's interesting to watch the progression of design ideas in this Towers forum over months as experimental knowledge started pouring in. It shows how a real-world engineering problem is solved, which is really what I think these kids will take away with them and what makes Science Olympiad so great, in my opinion.

I am still puzzled about the "effective length factor" in Euler's equation. We just made sure our balsa sticks could hold well beyond what they needed to hold to get the segment length for the distance between bracing points. We just kept trimming down the balsa stick 1cm at a time and testing it. I think there must be better way to test it, but we didn't have time to rig one up.

I need to do a drawing of the X-braces design that shows how I did the length calculations in the spreadsheet.

Good luck to your teams at Nationals. The level of completion in Towers seems much higher than years ago when they last had this event in Division B.

[dholdgreve]

Recently at our State competition, the judges would "interview" the tower builders as permitted in the rules to confirm that they in fact did build the tower, or as least have some inkling of what it was all about. Most builders would go off on some tangent about how many towers they had to build to get there, that the design was all about triangles 'cause they're the strongest ya know, X braces versus Z braces, etc... Our 2 first year Division B girls got up there and started discussing with the Judges Euler's Buckling Theory, how they determined the number of bracing tiers they used, the safety factor they incorporated into their design, how their scores had gradually improved with each competition... The judges eyes got about the size of saucers, and I'm not sure they were ever able to get their jaw back in position...

I'm not sure if I have ever been more proud! Not that the tower carried the full load (which it did), but that all the concepts I have been preaching over the last 10 months or so really did sink in, and that they fully comprehended it! Now I just hope they go on to become Structural Engineers! My life would then be complete!

[Crtomir]

Recently at our State competition, the judges would "interview" the tower builders as permitted in the rules to confirm that they in fact did build the tower, or as least have some inkling of what it was all about. Most builders would go off on some tangent about how many towers they had to build to get there, that the design was all about triangles 'cause they're the strongest ya know, X braces versus Z braces, etc... Our 2 first year Division B girls got up there and started discussing with the Judges Euler's Buckling Theory, how they determined the number of bracing tiers they used, the safety factor they incorporated into their design, how their scores had gradually improved with each competition... The judges eyes got about the size of saucers, and I'm not sure they were ever able to get their jaw back in position...

I'm not sure if I have ever been more proud! Not that the tower carried the full load (which it did), but that all the concepts I have been preaching over the last 10 months or so really did sink in, and that they fully comprehended it! Now I just hope they go on to become Structural Engineers! My life would then be complete!

That's what it's all about. Kids like yours are the real winners.

[Juanyjose]

I have had this idea on having a 3 sided tower. All the 4 sided towers have been over 5 grams. I was thinking that if I get rid of 1 side... then I might be able to reduce the weight by possibly around 1-2 grams From what I'm imagining, it might not be as good as a 4 sided tower. Has anyone tried making a 3 sided tower or might know if this is a good idea?
Thanks.

I'm gonna try one, just for kicks and post back how it goes. If I remember, I have terrible memory.

I have leftover wood that I don't want to use for competition, so: the 3 columns are 3/16" x 3/16" weighing 2 g/36" each. That should hold everything, with enough bracing. It will go for the bonus.

Isn't compressional strength very dependent on cross sectional area of wood? If someone built a 3sided tower with 3/16" wood that weighed maybe 1.5, that would be pretty competitive, right? After you get over the fact it's harder to build.

Those 1.5gr/36" at 3/16" are gonna be pricey- they'll be right down at the lower limits that balsa exists in. 4.74 lbs/cu ft. At 1/8" that density gets you a 0.7gr/36" stick. Jake (Specialized Balsa) lists these at $6.95 each; it'll be more at 3/16". He doesn't list on his web site, but sometimes has a very few below 0.7. The very lightest I've ever seen was at 0.62; next lightest at 0.66- $9.95 each.

Just a terminology thing- 'compressional' strength refers to strength resisting crushing. What you're wanting/referring to is buckling strength. Buckling strength (as I've discussed/explained extensively in past posts, and as Crtomir explains in detail in the extensive info he's just posted) is, indeed dependent on cross section. Buckling strength is E times I, where E is the modulus of elasticity (aka Young's modulus), and I is the second moment of inertia, which for a square cross section is d (the dimension of one side) to the fourth power/12 divided by the effective length squared.
I for a 3/16 cross section is 5.06 times what it is for a 1/8 cross section. That's a big gain in buckling strength. Going up to 5/32" gives you 2.44 times what you have at 1/8"..... And, if you run the numbers, for both 5/32 and 3/16, the weight goes up by a smaller factor than the buckling strength does. That's why we've gone to 5/32 for Nationals towers
But, for the reasons a number of folk have brought up, a 3-legger is not going to provide an advantage over a well designed 4-legger. Been there, down that path. It'll be fun to play with, I'm sure.

Last second, my partner said we should use 1/8 x 1/8 columns weighing 2 g/36", which I thought was kinda pointless but this was a side project so whatever I went along with it. For bracing, I used 0.6 g/36", because, again, it was a side project so I'm not gonna use good wood on it.

Total it weighed 8.8g, and it held 13.7kg. 15700/8.8=1784. So, not very good. But... there is significant room for improvement:

1) I could use 3/16" squared columns, which would be more resistant. I'm not sure how much more, but if each leg holds 433 more grams it'll hold everything.

2) I could use 0.3 g/36" in bracing. That would take off 2 grams off the weight of the tower.

3) I found a 1.5 g/36" stick at 3/16" in a tower 'skeleton' (columns without bracing) in my 'useless' pile. I used to build everything with 3/16" wood, so my partner had started building a tower with 1.5, 2.4, 2.4, and 2.4 (g/36" and 3/16"squared) columns, but we finished a tower with 1/8" columns weighing much less so we just abandoned that project. The funny thing is that 1.5 g/36" piece cost me $1, not the $10 you said, because I get my wood from hobby stores, not specialized balsa. So if I could find 1.8 g/36" at 3/16" squared or so, that would be good.

That tower, with all the room for improvement filled, would weigh about 5.5 grams and hold more. Let's say I can't find 1.8 3/16" wood: then it would weigh 5.8 grams.

17000/5.8=2931. 17000/5.5=3090. That sounds pretty competitive to me, so I'll build one with no (or much less) room for improvement, and post back how it goes.

[Juanyjose]

I have had this idea on having a 3 sided tower. All the 4 sided towers have been over 5 grams. I was thinking that if I get rid of 1 side... then I might be able to reduce the weight by possibly around 1-2 grams From what I'm imagining, it might not be as good as a 4 sided tower. Has anyone tried making a 3 sided tower or might know if this is a good idea?
Thanks.

I'm gonna try one, just for kicks and post back how it goes. If I remember, I have terrible memory.

I have leftover wood that I don't want to use for competition, so: the 3 columns are 3/16" x 3/16" weighing 2 g/36" each. That should hold everything, with enough bracing. It will go for the bonus.

Isn't compressional strength very dependent on cross sectional area of wood? If someone built a 3sided tower with 3/16" wood that weighed maybe 1.5, that would be pretty competitive, right? After you get over the fact it's harder to build.

Those 1.5gr/36" at 3/16" are gonna be pricey- they'll be right down at the lower limits that balsa exists in. 4.74 lbs/cu ft. At 1/8" that density gets you a 0.7gr/36" stick. Jake (Specialized Balsa) lists these at $6.95 each; it'll be more at 3/16". He doesn't list on his web site, but sometimes has a very few below 0.7. The very lightest I've ever seen was at 0.62; next lightest at 0.66- $9.95 each.

Just a terminology thing- 'compressional' strength refers to strength resisting crushing. What you're wanting/referring to is buckling strength. Buckling strength (as I've discussed/explained extensively in past posts, and as Crtomir explains in detail in the extensive info he's just posted) is, indeed dependent on cross section. Buckling strength is E times I, where E is the modulus of elasticity (aka Young's modulus), and I is the second moment of inertia, which for a square cross section is d (the dimension of one side) to the fourth power/12 divided by the effective length squared.
I for a 3/16 cross section is 5.06 times what it is for a 1/8 cross section. That's a big gain in buckling strength. Going up to 5/32" gives you 2.44 times what you have at 1/8"..... And, if you run the numbers, for both 5/32 and 3/16, the weight goes up by a smaller factor than the buckling strength does. That's why we've gone to 5/32 for Nationals towers
But, for the reasons a number of folk have brought up, a 3-legger is not going to provide an advantage over a well designed 4-legger. Been there, down that path. It'll be fun to play with, I'm sure.

So, could I expect a piece of (x)cm long 3/16" squared balsa to hold 5.06 times as much wood as a (x)cm long 1/8" squared balsa? Is effective length the length of the piece?

[Crtomir]

So, could I expect a piece of (x)cm long 3/16" squared balsa to hold 5.06 times as much wood as a (x)cm long 1/8" squared balsa? Is effective length the length of the piece?

Yes, if the densities of both pieces of balsa were the same and they were both had exactly the same internal composition. As "BalsaMan" often points out, there is a distribution of strength among balsa of the same density. For a given density, some pieces are really week, some are really strong, and most are somewhere near the average strength.

In general the equation for how much load (or force) a long slender column (balsa stick) can hold before buckling is given by:

,

where is the critical load (max weight the stick can hold), is the Modulus of Elasticity (MOE) (or Young's Modulus) of the material, is the length of the stick (effective length = segment length between bracing points on your tower), and is the second moment of the cross-sectional area of the column (balsa stick). The second moment of the cross-sectional area of a stick with a square cross-sectional area is , where is the length of a side. In this case, we are talking about changing from " to ". The MOE () is a property of the material and is in general a function of the density of the balsa wood. The greater the density, the higher the MOE, and the larger the load you can put on the stick without causing it to buckle.

From this, you can do some optimization. If you increase the cross-sectional area of your balsa columns from 1/8" to 3/16", goes up by



However, to keep the same weight, you will have to drop the density of the 3/16"x3/16" sticks down. The volume of the stick is and density is mass/volume (, so since we want the mass of the 3/16"x3/16" stick to equal the mass of the 1/8"x1/8" stick, we have



which is



From this, we solve for the ratio of densities



So roughly, we have to half the density of the 3/16" balsa stick to give the same weight as the 1/8" balsa stick of the same length. The MOE is approximately linearly dependent on the density, so dropping the density by half also drops the MOE by half. This reduces the critical load that we can hold before buckling by half as well. However, we get about five times as much moment of cross-sectional area () with the 3/16"x3/16" sticks than with the 1/8"x1/8" sticks. So the critical load also goes up by five times. All-in-all, by switching from 1/8" square sticks to 3/16" square sticks, we increase the critical load we can hold before buckling () by about 5/2 = 2.5 times.

Now here is the clincher: if the critical load () is higher by 2.5 times, then we can increase the effective length of the stick () so that the critical load is the same as what we had with the 1/8" square columns. That means we can have a longer distance between X-braces (greater bracing interval) and use less wood for bracing, which saves more weight. This assumes that your original tower with 1/8" square legs (columns) could hold all the weight. The amount you can increase the effective length is given by



So you can hold the same amount of weight with a 3/16" square leg tower as with a 1/8" square leg tower but your X-bracing interval can be increased by about 1.5. That's a huge savings in weight, because you can use less X-braces. Saving weight = higher score!

[Crtomir]

However, to keep the same weight, you will have to drop the density of the 3/16"x3/16" sticks down. The volume of the stick is and density is mass/volume (, so since we want the mass of the 3/16"x3/16" stick to equal the mass of the 1/8"x1/8" stick, we have

Sorry, I meant to write



(left out the "=" sign)

[Juanyjose]

However, to keep the same weight, you will have to drop the density of the 3/16"x3/16" sticks down. The volume of the stick is and density is mass/volume (, so since we want the mass of the 3/16"x3/16" stick to equal the mass of the 1/8"x1/8" stick, we have

Sorry, I meant to write



(left out the "=" sign)

Thank you! That was so helpful

[Crtomir]

You're welcome. Let us know how your 3-sided tower performed. Most of the best scores this year, probably all the scores over 3000, were built with 4 sides, not going for the bonus, and 9-10 simple X-braces on each side. We did try 3-sided towers for a little bit, but never got much over 2000-2200 points with them.