Bonus weight in Towers B

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Bonus weight in Towers B
Question: Our team is trying to decipher the 29cm diameter bonus rule in Towers B. I want to confirm that any parts of the tower that touch the base (say its on 4 legs) must be outside that circle to qualify....even if parts of the tower itself span across (but do not touch) the space between the 20cm square and the 29cm circle.
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Re: Bonus weight in Towers B
Standard Disclaimercaryjrtmkmk wrote:Question: Our team is trying to decipher the 29cm diameter bonus rule in Towers B. I want to confirm that any parts of the tower that touch the base (say its on 4 legs) must be outside that circle to qualify....even if parts of the tower itself span across (but do not touch) the space between the 20cm square and the 29cm circle.
Your interpretation seems right to me; after all, the tower would necessarily have to span the intervening space to support the loading block over the hole.

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Re: Bonus weight in Towers B
So, is the bonus worth going after??
A little analysis:
From discussion in the other tower thread of some math “basics”, we have the basis to understand and evaluate this bonus. While I haven’t seen/gotten this year’s rules, hence don’t know what the tower height parameters are, nor what/how much building to get the bonus gets you, we can understand/discuss to get a reading.
For purposes of discussion, I’ll use a 60cm height, 4 leg configuration, top at 5cm square. In overview, the legs in a tower spanning the 29cm circle will have a greater leanin angle from vertical; they’ll see higher force from a given load they’ll need to be longer and stronger (stiffer higher buckling strength) than the legs in a tower spanning the 20cm square. So, the legs (and bracing) will also be heavier. The question is, does the bonus overcome the additional tower weight (provide a higher efficiency score)?
To span (as in leg bottoms sit just outside of) a 29cm circle, each opposite pair of leg bottom ends will be a bit over 29 cm apart (let’s say 29.5cm). To span a 20cm square, each opposite pair of leg bottoms will need to be just over 20 cm apart (let’s say 20.5cm). At the top, for both, each opposite pair of leg tops will need to be just over 7cm apart (7.07cm the diagonal of a 5cm square).
When you lay these dimensions out, and look , for one leg, at the right triangle formed by top end of leg, bottom end of leg, and point where vertical line dropped from top end of leg hits the test base surface, you see that for the 29cm circle version, the angle from vertical is about 10.3 degrees, and for the 20cm square version, the angle from vertical is about 6.6 degrees Hmmm.. that’s about a 56% greater angle for the 29cm version; that seems like quite a bit, however….
Looking at the cosines for these angles (cos6.6 degrees =0.9934 , cos10.3 degrees = 0.9836, and then the inverse of these cosines carrying ¼ of the force from a 15gk tower load which would be 3.75gk, if the leg were vertical the 29 cm circle version leg gets a force of about 3.81kg, while the 20cm square version leg gets a force of about 3.77kg. So more force in the 29cm circle case, but only about 1% more; that’s not much. If you look at the lengths of the legs, 29cm circle version needs 61cm length, 20cm square version needs 60.4cm again, about 1% more for the 29cm circle version. Now, if you look at the inverse square relationship of length to buckling strength, and linear relationship of density to buckling strength, you’ll find you’ll need about 2% higher density (leg weight) in the 29cm circle version to carry the load. Last, length and strength (hence weight) of bracing will be somewhat higher in the 29cm circle version. When you figure out how much more, you’ll have the answer to whether the bonus is worth going for; it sure looks like it may be.
A little analysis:
From discussion in the other tower thread of some math “basics”, we have the basis to understand and evaluate this bonus. While I haven’t seen/gotten this year’s rules, hence don’t know what the tower height parameters are, nor what/how much building to get the bonus gets you, we can understand/discuss to get a reading.
For purposes of discussion, I’ll use a 60cm height, 4 leg configuration, top at 5cm square. In overview, the legs in a tower spanning the 29cm circle will have a greater leanin angle from vertical; they’ll see higher force from a given load they’ll need to be longer and stronger (stiffer higher buckling strength) than the legs in a tower spanning the 20cm square. So, the legs (and bracing) will also be heavier. The question is, does the bonus overcome the additional tower weight (provide a higher efficiency score)?
To span (as in leg bottoms sit just outside of) a 29cm circle, each opposite pair of leg bottom ends will be a bit over 29 cm apart (let’s say 29.5cm). To span a 20cm square, each opposite pair of leg bottoms will need to be just over 20 cm apart (let’s say 20.5cm). At the top, for both, each opposite pair of leg tops will need to be just over 7cm apart (7.07cm the diagonal of a 5cm square).
When you lay these dimensions out, and look , for one leg, at the right triangle formed by top end of leg, bottom end of leg, and point where vertical line dropped from top end of leg hits the test base surface, you see that for the 29cm circle version, the angle from vertical is about 10.3 degrees, and for the 20cm square version, the angle from vertical is about 6.6 degrees Hmmm.. that’s about a 56% greater angle for the 29cm version; that seems like quite a bit, however….
Looking at the cosines for these angles (cos6.6 degrees =0.9934 , cos10.3 degrees = 0.9836, and then the inverse of these cosines carrying ¼ of the force from a 15gk tower load which would be 3.75gk, if the leg were vertical the 29 cm circle version leg gets a force of about 3.81kg, while the 20cm square version leg gets a force of about 3.77kg. So more force in the 29cm circle case, but only about 1% more; that’s not much. If you look at the lengths of the legs, 29cm circle version needs 61cm length, 20cm square version needs 60.4cm again, about 1% more for the 29cm circle version. Now, if you look at the inverse square relationship of length to buckling strength, and linear relationship of density to buckling strength, you’ll find you’ll need about 2% higher density (leg weight) in the 29cm circle version to carry the load. Last, length and strength (hence weight) of bracing will be somewhat higher in the 29cm circle version. When you figure out how much more, you’ll have the answer to whether the bonus is worth going for; it sure looks like it may be.
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Re: Bonus weight in Towers B
I belive you are correct but make sure you don't add to much weight to you're tower because of the bonus, it could bring your efficiency down
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Re: Bonus weight in Towers B
You're right, it could.arv101 wrote:I belive you are correct but make sure you don't add to much weight to you're tower because of the bonus, it could bring your efficiency down
The factors I noted earlier are correct;and having now gotten this year's design/analysis spreadsheets pretty much worked up, I can tell you the added weight to get outside the 29cm circle is on the order of 0.250.35 grams on a 10ish gram tower (that incudes added leg length, slightly increased leg loading (so a touch higher density legs), and a bit heavier bracing, down toward the bottom where the span is longer).
Simple score calculation tells the story; a 10gr tower (that spans the 20cm square) carrying full 15kg scores 1500; a 10.5gr (spanning the circle) tower carrying 15kg + 2kg bonus (=17kg) scores 1619; you'd have to bump it to 11.3; adding 1.3gr) to get close to even (1504). This bonus is definitely well worth it
Len Joeris
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Re: Bonus weight in Towers B
Hey I'm having trouble with the four supports that meet on the top square can you help?

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Re: Bonus weight in Towers B
Do you mean the legs, and what sort of "trouble"??Llamastwaimzjf wrote:Hey I'm having trouble with the four supports that meet on the top square can you help?

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Re: Bonus weight in Towers B
Yes. And that is the fastest breaking point of my tower, I plan on using balsa . Would you recommend that?
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