## So... What did it take to win your State?

Balsa Man
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### Re: So... What did it take to win your State?

Crtomir wrote:[quote="Balsa Man
Yeah (on the 5/32nd). For example, on our B tower, in 1/8. best stick > our design buckling strength was 1.22gr/36", w/ 110% of design BS. In 5/32, best is 0.97gr/36" w/ 120% design BS.

At the same density, going from 1/8 to 5/32 increases weight by a factor of 1.56, while "I" goes up by a factor of 2.44.
It sounds like you are on to something here! We never tried larger than 1/8" x 1/8" legs. I'm pretty sure most people thought the opposite. We even tried 3/32" x 3/32" once. The idea that you make it bigger to make it lighter and stronger is somewhat counter-intuitive to most people.[/quote]

Yup, its another example of how understanding the mathematical relationships that are.... in play is the key to optimizing design; where those relationships come from, how they... work.

Looking at the 3 key factors in Euler's buckling equation - buckling strength = E x I/effective length squares

The most important one is the inverse square relationship of buckling strength to length- it tells us that if a member (under compression loading) is made a bit longer, buckling strength falls off a lot, and the other way around, shortening a bit increases strength a lot.

Then when you look at E, the modulus of elasticity, its a linear relationship, but not 1:1; if you double the density, E goes up by around 2.25, saying higher density is... more efficient. A critical factor/relationship in the data of how E varies with density (that old Forest Service study) is the variability; there is a trend, but individual sticks vary around a mean. That tells us that if you have/look at a number of sticks at a given density, some will be stronger than others. You'll see a bell curve for strength vs weight- a few really weak, most in the middle, a few really strong. The further out the 'good end' of the bell curve you get, the higher performance of the stick.

And when you look at I (second moment of inertia), which, as you know, for a square is d (where d is the dimension of one side) is d to the fourth x12, it says a small increase in d gets you a....significant in crease in I, hence in buckling strength. When you run these numbers for 1/8 and 5/32, at same density I goes up more than the weight does. (x 2.44 vs 1.56)

The limitation lies in the fact that balsa has a bottom limit in density; only so light. At the loads on towers, 5/32 at pretty darn near the minimum density balsa exists in, gives you the needed buckling strength.
Len Joeris
Fort Collins, CO

Crtomir
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### Re: So... What did it take to win your State?

Balsa Man wrote:
Yup, its another example of how understanding the mathematical relationships that are.... in play is the key to optimizing design; where those relationships come from, how they... work.

Looking at the 3 key factors in Euler's buckling equation - buckling strength = E x I/effective length squares

The most important one is the inverse square relationship of buckling strength to length- it tells us that if a member (under compression loading) is made a bit longer, buckling strength falls off a lot, and the other way around, shortening a bit increases strength a lot.

Then when you look at E, the modulus of elasticity, its a linear relationship, but not 1:1; if you double the density, E goes up by around 2.25, saying higher density is... more efficient. A critical factor/relationship in the data of how E varies with density (that old Forest Service study) is the variability; there is a trend, but individual sticks vary around a mean. That tells us that if you have/look at a number of sticks at a given density, some will be stronger than others. You'll see a bell curve for strength vs weight- a few really weak, most in the middle, a few really strong. The further out the 'good end' of the bell curve you get, the higher performance of the stick.

And when you look at I (second moment of inertia), which, as you know, for a square is d (where d is the dimension of one side) is d to the fourth x12, it says a small increase in d gets you a....significant in crease in I, hence in buckling strength. When you run these numbers for 1/8 and 5/32, at same density I goes up more than the weight does. (x 2.44 vs 1.56)

The limitation lies in the fact that balsa has a bottom limit in density; only so light. At the loads on towers, 5/32 at pretty darn near the minimum density balsa exists in, gives you the needed buckling strength.

Balsa Man
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### Re: So... What did it take to win your State?

Crtomir wrote:
Balsa Man wrote:
Yup, its another example of how understanding the mathematical relationships that are.... in play is the key to optimizing design; where those relationships come from, how they... work.

Looking at the 3 key factors in Euler's buckling equation - buckling strength = E x I/effective length squares

The most important one is the inverse square relationship of buckling strength to length- it tells us that if a member (under compression loading) is made a bit longer, buckling strength falls off a lot, and the other way around, shortening a bit increases strength a lot.

Then when you look at E, the modulus of elasticity, its a linear relationship, but not 1:1; if you double the density, E goes up by around 2.25, saying higher density is... more efficient. A critical factor/relationship in the data of how E varies with density (that old Forest Service study) is the variability; there is a trend, but individual sticks vary around a mean. That tells us that if you have/look at a number of sticks at a given density, some will be stronger than others. You'll see a bell curve for strength vs weight- a few really weak, most in the middle, a few really strong. The further out the 'good end' of the bell curve you get, the higher performance of the stick.

And when you look at I (second moment of inertia), which, as you know, for a square is d (where d is the dimension of one side) is d to the fourth x12, it says a small increase in d gets you a....significant in crease in I, hence in buckling strength. When you run these numbers for 1/8 and 5/32, at same density I goes up more than the weight does. (x 2.44 vs 1.56)

The limitation lies in the fact that balsa has a bottom limit in density; only so light. At the loads on towers, 5/32 at pretty darn near the minimum density balsa exists in, gives you the needed buckling strength.
Thanks. We're looking forward to testing soon w/ the 5/32 legs; weight estimating spreadsheet says we can get to a....respectable score, with a tower meeting the circle bonus; hope it works.....
Two minor edits to the analysis-
BS = E X I/effective length squared
I = d to the fourth/12
Len Joeris
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S4BB
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### Re: So... What did it take to win your State?

At Illinois State Div B, the girls were able to take Gold with a score of 3092, 4.85g holding 15kg, and as stated it did break right at the end. The design was 4 sided with a square base, 10 X braces and each of the legs were 5.6# density, due to this from what I've read we spent too much weight on the bracing, 1/16 sq at 6# density, slightly heavier at the top and bottom. I was very happy for the team, but it was difficult to see Woodlawn break early, they had been in a league of their own during the season, they definitely made us work harder.

I have been intrigued by Crtomir's comments about using 11 X braces with all being in tension. In any simulations we looked at, we always saw the X braces alternate between tension and compression, so it never seemed right to go to 1/16 x 1/32 braces if they were in compression. Only thing I was thinking is if you put a slight outward bow on the legs you might be able to have all of the bracing work in tension. Can you elaborate on this? Thanks

Good luck at nationals to all that are going.

S4BB
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### Re: So... What did it take to win your State?

At Illinois State Div B, the girls were able to take Gold with a score of 3092, 4.85g holding 15kg, and as stated it did break right at the end. The design was 4 sided with a square base, 10 X braces and each of the legs were 5.6# density, due to this from what I've read we spent too much weight on the bracing, 1/16 sq at 6# density, slightly heavier at the top and bottom. I was very happy for the team, but it was difficult to see Woodlawn break early, they had been in a league of their own during the season, they definitely made us work harder.

I have been intrigued by Crtomir's comments about using 11 X braces with all being in tension. In any simulations we looked at, we always saw the X braces alternate between tension and compression, so it never seemed right to go to 1/16 x 1/32 braces if they were in compression. Only thing I was thinking is if you put a slight outward bow on the legs you might be able to have all of the bracing work in tension. Can you elaborate on this? Thanks

Another question, during the season the highest scores I have seen or read about have been Non-Bonus designs, all the math prior had seemed to indicate it was worth pursuing, did any state winners go for the bonus?

Good luck at nationals to all that are going.

Crtomir
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### Re: So... What did it take to win your State?

S4BB wrote: I have been intrigued by Crtomir's comments about using 11 X braces with all being in tension. In any simulations we looked at, we always saw the X braces alternate between tension and compression, so it never seemed right to go to 1/16 x 1/32 braces if they were in compression. Only thing I was thinking is if you put a slight outward bow on the legs you might be able to have all of the bracing work in tension. Can you elaborate on this? Thanks
First of all, congratulations on your team's tower performance at State. 3000+ is nothing to laugh at. We spent half the season chasing 2000 as I assume most teams did. We used only 9 X-braces (all tension members, no compression members) on our State tower without the bonus and scored about 3250. Most, if not all, 3000+ towers have not tried to go for the bonus. Also, I think they have all tried to use only X-braces. A lot of them used 10 X-braces, but they may have been copying each other without knowing why 10 and not 9 or why 10 and not 11. I was suggesting earlier that if you wanted to get over 4000, you would likely have to use 11 X-braces. I think the density of the braces is so low that they would not work as compression members. Also, because they are X-braces, I think if one piece of the X (say the "/" piece, for example) starts to feel a compression load, the other piece of the X (the "\" piece) would feel a tension load. As long as the "\" piece under tension could prevent enough of a displacement of the "/" piece under compression, the whole X-brace would not fail. That's just a theory. I'm not sure. But that might explain why this only seems to work well when the lengths of the X-braces are small (non-bonus design) and not when the lengths of the X-braces are large (bonus design).

An outward bow on the legs might be able to work. We didn't try that enough to be certain.

The teams wanting to push the limits always run the risk of premature failure. Some teams may try to play it safe, maybe not place 1st, but still in top 6 with significantly less risk, so they can preserve their team score. Other teams may go all out for gold in the towers event, willing to take that risk, because their team may or may not be contending for a top team spot.

Crtomir
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### Re: So... What did it take to win your State?

S4BB wrote: we spent too much weight on the bracing, 1/16 sq at 6# density, slightly heavier at the top and bottom.
A slight change in density of the bracing wood really starts to add up since there are so many X-braces on all sides. Also, be careful when stripping the balsa sheets to make the bracing members. There is a large variation in local density across the sheet. We had to measure each piece of stripped bracing member to see if it was low enough weight. Some where and some were not. You have to strip 2x to 3x what you need and then select only the best ones.

Juanyjose
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### Re: So... What did it take to win your State?

S4BB wrote:At Illinois State Div B, the girls were able to take Gold with a score of 3092, 4.85g holding 15kg, and as stated it did break right at the end. The design was 4 sided with a square base, 10 X braces and each of the legs were 5.6# density, due to this from what I've read we spent too much weight on the bracing, 1/16 sq at 6# density, slightly heavier at the top and bottom. I was very happy for the team, but it was difficult to see Woodlawn break early, they had been in a league of their own during the season, they definitely made us work harder.

I have been intrigued by Crtomir's comments about using 11 X braces with all being in tension. In any simulations we looked at, we always saw the X braces alternate between tension and compression, so it never seemed right to go to 1/16 x 1/32 braces if they were in compression. Only thing I was thinking is if you put a slight outward bow on the legs you might be able to have all of the bracing work in tension. Can you elaborate on this? Thanks

Another question, during the season the highest scores I have seen or read about have been Non-Bonus designs, all the math prior had seemed to indicate it was worth pursuing, did any state winners go for the bonus?

Good luck at nationals to all that are going.
About your first question, that's what I've done all year on accident. And yeah it works, thanks for pointing that out to me (on accident?). I build without a jig (yeah I know, bad idea) so the tower is always a little bit "inflated" when I finished, the columns with a 'slight outward bow'.

I'm surprised no one thought of that before. And wow that answered so many of my questions.

Juanyjose
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### Re: So... What did it take to win your State?

Juanyjose wrote:
S4BB wrote:At Illinois State Div B, the girls were able to take Gold with a score of 3092, 4.85g holding 15kg, and as stated it did break right at the end. The design was 4 sided with a square base, 10 X braces and each of the legs were 5.6# density, due to this from what I've read we spent too much weight on the bracing, 1/16 sq at 6# density, slightly heavier at the top and bottom. I was very happy for the team, but it was difficult to see Woodlawn break early, they had been in a league of their own during the season, they definitely made us work harder.

I have been intrigued by Crtomir's comments about using 11 X braces with all being in tension. In any simulations we looked at, we always saw the X braces alternate between tension and compression, so it never seemed right to go to 1/16 x 1/32 braces if they were in compression. Only thing I was thinking is if you put a slight outward bow on the legs you might be able to have all of the bracing work in tension. Can you elaborate on this? Thanks

Another question, during the season the highest scores I have seen or read about have been Non-Bonus designs, all the math prior had seemed to indicate it was worth pursuing, did any state winners go for the bonus?

Good luck at nationals to all that are going.
About your first question, that's what I've done all year on accident. And yeah it works, thanks for pointing that out to me (on accident?). I build without a jig (yeah I know, bad idea) so the tower is always a little bit "inflated" when I finished, the columns with a 'slight outward bow'.

I'm surprised no one thought of that before. And wow that answered so many of my questions.
Why my towers broke in the columns and not the bracing, like they should've considering I don't use ladders in the bracing.

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### Re: So... What did it take to win your State?

Kansas C 1st was ~2200
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