Towers B/C

[musicalwhang]

What would you recommend me do if I had a limited supply of balsa? I get all my wood from a local store and I cannot control which wood density they have at one time. Often times, I find that 1/16 by 1/16 wood isn't cut properly and the shape ends up being like a rectangle. What should I do?

[BuildingFriend]

What would you recommend me do if I had a limited supply of balsa? I get all my wood from a local store and I cannot control which wood density they have at one time. Often times, I find that 1/16 by 1/16 wood isn't cut properly and the shape ends up being like a rectangle. What should I do?

Order online with National Balsa or Specialized Balsa. Their quality is pretty good (can only speak for Specialized Balsa) but I cannot guarantee the time shipping is accurate or if the wood will break. My team has had much trouble with their shipping times and usually, they are backed up on orders (warehouse may not have densities or sizes you want) and once my package was snapped in half but they sent the same order again free of charge on express shipping (fastest). Their customer service isn't bad either.

[Balsa Man]

What would you recommend me do if I had a limited supply of balsa? I get all my wood from a local store and I cannot control which wood density they have at one time. Often times, I find that 1/16 by 1/16 wood isn't cut properly and the shape ends up being like a rectangle. What should I do?

Ordering from Specialized Balsa could get you exactly what you need, but sounds like that's not an option for you. So, sounds like a situation where you have to work around the limitations you have to deal with as best you can…. You can do that by, first, knowing the numbers you’re working with, then finding a best fit with the wood you have access to.

First a quick check on something you said about leg buckling strength, just to make sure we’re on the same page. You said the legs on the tower you tested had a BS of 80. I assumed that meant doing one finger push-down testing, you were seeing about 34.8gr (34.8 x 2.3 =80).

(1/8”) Sticks (36”) with this BS, btw, will typically weigh…1.4 -1.5gr. When you do the inverse square calcs on a BS of 80, braced at 1/5 interval, you get a braced strength of leg at about 6200gr; significantly more than you need for a 1/5 braced interval (4600gr would give you a ~20% safety factor). A measured BS about 26gr (26.1 x 2.3 = 60) will give you a braced leg strength ~4600gr; sticks with the BS should be at about 1.15 to 1.25gr/36”. So, what this is saying is you can go to lighter legs than you used at 1/5 bracing interval. But, the ones you used (1.4 – 1.5, measured BS ~35gr (x2.3=80)) are not strong enough to drop down to a ¼ interval, btw; at ¼ interval, they’d get you a braced strength about 3900gr (almost no safety factor). To get enough leg strength to go to a ¼ bracing interval, you’d need to be seeing a BS of about 39.7 on the scale (39.7 x 2.3 = 91.3; braced to ¼ interval, 91.2 gets you a braced leg strength about 4530gr (a 20% safety factor). These sticks would typically weigh 1.6-1.7gr. Note, I’ve pulled the numbers above from our B-Div spreadsheets, for tower meeting the 29cm circle bonus. If, as it looked in the pics, yours is not going for the bonus, the strength needed numbers would be just a hair lower. The methodology for measuring/calculating BS (1 finger push-down x 2.3, then inverse square calc from that to get braced strength when installed in the tower) is as has been discussed at length in past posts (review if any questions).

To not just be shooting in the dark, you’ll need to take your scale to the store. At an absolute minimum, you need to weigh sticks. Ideally, you do one finger push-down buckling testing. What you’re looking for is the lightest set of 4 that gets you a minimum 36” single finger push-down reading of about 26/27gr (for a tower running 1/5 interval bracing), or 40gr (for a tower running ¼ interval bracing). You might want to go for two sets, one to build for testing, one to build for competition…….

I noted earlier the numbers for ladder BS- First, if the sticks aren’t cut right, forget them. See if any 1/16 sticks get you needed BS for the lower 2 ladders. If not, go up to 3/32- you should be able to find ones that are strong enough at 3/32. As with legs, you want the lightest with enough strength. Then you build with the best set of sticks you were able to get, whether that turns out to be at 1/5 or ¼ bracing interval. That's how I'd handle things in your situation.
Hope this helps; good luck!

[musicalwhang]

I think I've been measuring BS wrong this whole time. I realized that my local store has been selling 1/8th by 1/8th in 24" sizes. I've been seeing 80gr strengths in 24" sticks. If I were to go run to that store, what density and BS should I be picking up?
Thank you for all your help!
Scratch that^
I went to the store and found 4 36" sticks all weighing 1.2 gr. The BS of these sticks are all about 20.5 gr. Should I still stick with the 1/5th bracing intervals? Or should I go up to 1/6th?

[Yackback]

FM posted an efficiency of ~3000 at NY States Competition.

[JZhang1]

FM posted an efficiency of ~3000 at NY States Competition.

Impressive. Pictures? Bonus?

[MattH2018]

FM posted an efficiency of ~3000 at NY States Competition.

Impressive. Pictures? Bonus?

No bonus. I also don't have pics. Actual score was 2959.

Edit: added actual score

[Alke]

I am in Division C and attempting the bonus. The 1/8th inch with a push-down test of 27 grams. The ladders and X's are 1/16th. First, I designed everything with AutoCad and printed everything out to scale.
https://drive.google.com/file/d/0Bx2Ru2 ... sp=sharing
Then I built the tower face.
https://drive.google.com/file/d/0Bx2Ru2 ... sp=sharing
Tommorow, I am going to use a normal "3D" jig to align/connect the faces together. Do you guys see any flaws so far?

[Balsa Man]

I think I've been measuring BS wrong this whole time. I realized that my local store has been selling 1/8th by 1/8th in 24" sizes. I've been seeing 80gr strengths in 24" sticks. If I were to go run to that store, what density and BS should I be picking up?
Thank you for all your help!
Scratch that^
I went to the store and found 4 36" sticks all weighing 1.2 gr. The BS of these sticks are all about 20.5 gr. Should I still stick with the 1/5th bracing intervals? Or should I go up to 1/6th?

OK
So, the questions you’re asking really come down to, how do you do and use an inverse square calculation? Been over this…many times, in multiple posts, but to save digging back through a lot of pages, I guess its worth going over, at this point, one more time, in detail, for you and a) anyone who hasn’t gone back and studied and come to understand, or b) anyone who did, and … went through too quickly, and didn’t take the time to really get to understanding, or for whatever reason didn’t really get to understanding. Once you really do understand, its REALLY helpful, and its pretty straightforward and easy to use. It may take reading the following discussion two or three times, carefully, to understand. It turned out pretty long, but it compiles and explains all the information needed to figure things out. I’m not just going to hand the answers to your questions to you, I’m going to try to teach/explain to you, and anyone else interested, how to figure the answers out yourself. After all, the rules do say, “students must be able to answer questions regarding the design, construction, and operation of the device.” (3 i)

Starting with some basics:
As explained way back at the start of the season, if you have a stick of length L, and it has a buckling strength (BS) of X, if you cut that length in ½, it will have a BS of 4X, cut it in 1/3, it will have a BS of 9X, etc. This is how an inverse square relationship works. This all comes from “Euler’s Buckling Equation”, which describes buckling behavior in thin columns of an elastic material under axial loading. By bracing a (longer) leg in a tower, you turn it into a set of shorter, ‘stacked columns’, so the BS of the longer (unbraced) leg becomes the higher BS of the shorter (stacked) column sections. So, if you know the BS at some length (L1), to figure out the buckling strength at some other length (longer or shorter, call it L2) the BS = 1/(Proportion (of L2 to L1) squared).

We can measure the buckling strength of a stick (from which we want to cut a piece to become a tower leg, or ladder), by putting it vertically on a scale, and pushing straight down until it buckles (bows out in the middle….an inch or two). These readings are approximate, but if you do this measurement consistently (there’s lots of discussion about this in past posts), then the relative readings between any two sticks will be… sufficiently accurate and useable

Example; the general form of inverse square calculation: where L2 is ½ of L1; the proportion of L2 to L1 is ½ (or 0.5). The proportion squared is ¼, or 0.25. 1 over 0.25 = 4; 1 over ¼ = 4; cut the length in half, quadruple the BS; BS of 1 becomes a BS of 4; BS of 25 becomes BS of 100, etc..

Another example, specific this time: at 24”, a stick shows a BS (one finger push-down test) of 80gr. So, applying this calculation, what BS would it show at 36”? L2 is 36”, L1 is 24”. The proportion of L2 to L1 is 3/2, or 1.5; 1.5 squared is 2.25; 3/2 squared is 2.25. This is saying that a stick testing at 80gr at 24” length would, if it were the same, test at 1 over the proportion squared; 1/2.25 (which = 0.444); 0.444 x 80 = 35.55gr.

Getting into buckling a little more deeply:
Now there’s one more twist/complication in translating what you measure on the scale, doing single finger push-down testing, to the buckling strength you’ll get when the tested piece is in-place, and braced, in the tower. The length term in Euler’s equation is actually expressed as “effective length.” This term depends on the “end conditions” of the column/piece in question I’ve explained this in detail in the thread “Measuring/using Buckling Strength- New Information”.

Briefly, when you do the single finger push-down test, you’re applying/creating “pinned/pinned” end conditions. At each end of the stick being tested, the end is able to rotate- as the stick buckles, and the part near the end deflects from vertical, the end, instead of staying horizontal…tips/rotates. Now when its in-place in the tower, and braced, looking at each of the braced points, the end of each braced segment is not free to rotate; its held in place; the ends of each braced segment is firmly attached to, is a part of the adjacent braced segment. This end condition is described as “fixed-fixed.”

The effective length of a column in pinned-pinned end conditions is 1; the effective length of a column in fixed-fixed end conditions is 0.65 Going back to our general equation BS = 1/(Proportion (of L2 to L1) squared), we calculate 1/0.65 squared, and we get 2.37 . What that’s saying is if a given stick is tested under pinned-pinned end conditions, if it were tested under fixed-fixed end conditions, the buckling strength measured will be about 2.3 times what it measured under pinned-pinned end conditions. You’d see something close to this result if you did single finger test, then glued the bottom of the stick to the scale pan, and glued the top to a plate (so it was perpendicular to the plate), and pushed the top plate in a way it stayed parallel to the scale pan.

Applying/using inverse square calculations:
So, to figure out in-tower buckling strength, from a single finger push down test, we multiply the single finger result by 2.3, and use that value (let me introduce a new term for it, ‘working buckling strength-WBS’) to do the inverse square calculations to see what the strength will be, in the tower, at shorter braced interval lengths. Its important to understand/remember this calculation/effective length factor applies to a bracing configuration that creates fixed-fixed end conditions- a ladders and Xs configuration, where the ladders (working under compression loading) prevent inward buckling of legs at the braced point(s), and the Xs (working under tension loading) prevent outward buckling of the legs at the braced point(s).

The inverse square calculation from WBS, for a 36” (91.6cm) stick (L1), goes like this (same formula as above); the numbers below are for a C- Div tower leg, in a tower meeting 29cm circle bonus- L=61.343cm.
½ of that = 30.67 (L2); the proportion of that to a 91.6cm stick is 0.335; 1/proportion squared = 8.92,
1/3 of that = 20.45 (L2) ; the proportion of that to a 91.6cm stick is 0.223; 1/proportion squared = 20.07,
¼ of that = 15.34 (L2) ; the proportion of that to a 91.6cm stick is 0.167; 1/proportion squared = 35.68,
1/5 of that = 12.27 (L2) ; the proportion of that to a 91.6cm stick is 0.134; 1/proportion squared = 55.74,
1/6 of that = 10.22 (L2) ; the proportion of that to a 91.6cm stick is 0.112; 1/proportion squared = 80.27.

If you take these 1/proportion squared numbers, and multiply the WBS for a stick by them, you get the braced BS for a given braced interval.

Example- you measure BS (1 finger push-down) of a 36” stick at 32.2gr; you multiply that by 2.3 (effective length factor) to get 74. That stick, if braced at a ¼ interval will give you a leg strength of 2640gr (74 x 35.68). That’s below the load on a leg at a 15kg tower load (3810gr; 4158 with a 10% safety factor-SF); legs from a stick like this, braced at a ¼ interval will not carry full load (should carry about 0.6x full load(15kg), or around 9kg. OK, let’s look at a 1/5 braced interval. 74 x 55.74 = 4125gr- very close to strength needed, with a 10% SF; this has a good shot at carrying full load.

Another example measured BS at 27gr, looking at 1/5 braced interval (a scenario Alke is wondering about a couple messages back). 27 x 2.3 = 62.1gr. At 1/5 interval, will brace to 3461gr (62.1 x 55.74). That’s not enough (significantly below the 3810 minimally needed. At 1/6 interval, 62.1 x 80.27, which = 4985gr, enough with more than a 20% SF……

Same data/discussion for a B-Div tower (meeting the 29cm bonus) (leg length- L=52cm):
1/3 of that = 17.33 (L2) ; the proportion of that to a 91.6cm stick is 0.189; 1/proportion squared = 27.93,
¼ of that = 13.00 (L2) ; the proportion of that to a 91.6cm stick is 0.142; 1/proportion squared = 49.65,
1/5 of that = 10.40 (L2) ; the proportion of that to a 91.6cm stick is 0.114; 1/proportion squared = 77.58,
1/6 of that = 8.67 (L2) ; the proportion of that to a 91.6cm stick is 0.095; 1/proportion squared = 111.71.

If you take these 1/proportion squared numbers, and multiply the WBS for a stick by them, you get the braced BS for a given braced interval.

Example- you measure BS (1 finger push-down) of a 36” stick at 23.9gr; you multiply that by 2.3 (effective length factor) to get 55. That stick, if braced at a ¼ interval will give you a leg strength of 2731gr (55 x 49.65). That’s below the load on a leg at a 15kg tower load (3840gr; 4180 with a 10% safety factor-SF); legs from a stick like this, braced at a ¼ interval will not carry full load (should carry about 0.7x full load(15kg), or around 10.7kg. OK, let’s look at a 1/5 braced interval. 55 x 77.58 = 4265gr- the strength needed, with a bit over a 10% SF; this has a good shot at carrying full load.

Let’s do another example; 36” stick testing (1 finger push-down) at 20.5gr (sound familiar, musical_whang?) 20.5 x 2.3=47.15gr , so at 1/5 interval, 47.15x77.58=3658gr (close, but a bit under 3840; at 1/6 interval, 47.15 x 111.71=5267, well over, with more than a 20% SF. So, that’s telling us with 36” stick(s) testing at 20.5gr, 1/5 interval won’t cut it, and 1/6 interval will be significantly stronger than it needs to be.

Density/stick weight vs BS:
Now, there’s one other set of data you’ll need, to have a full handle on design, and evaluating what density sticks to be looking for/ordering/buying (and figuring weight tradeoffs for stiffer legs with wider bracing interval vs lighter, weaker legs with tighter bracing interval; the relationship of density (stick weight) to BS (as measured for 36” stick, single finger push-down). The following data are for 1/8” (balsa) sticks. The values are picked off a graph plotting measured BS vs stick weight. As discussed many times before, there is significant (up to 20%) variation in balsa, in terms of what BS you will see at a given stick weight/density. The following numbers are approximate median values. “Good” sticks will have higher BS than the median, “bad” sticks will have lower BS:

At 36”- 0.8gr – BS ~18gr (same stick at 24” would weigh 0.667 of this; ~0.53gr, and have a BS ~2.25 x this = 40.5gr)
At 36”- 0.9gr – BS ~21gr (@24” ~0.6gr; BS 2.25x=47.25gr)
At 36”- 1.0gr – BS ~24gr (@24” ~0.67gr; BS 2.25x=54gr)
At 36”- 1.1gr – BS ~28gr (@24” ~0.73gr; BS 2.25x=54gr)
At 36”- 1.2gr – BS ~31gr (@24” ~0.8gr; BS 2.25x=63gr)
At 36”- 1.3gr – BS ~35gr (@24” ~0.87gr; BS 2.25x=69.75gr)
At 36”- 1.4gr – BS ~40gr (@24” ~0.93gr; BS 2.25x=78.75gr)
At 36”- 1.5gr – BS ~43gr (@24” ~1.0gr; BS 2.25x=90gr)
At 36”- 1.6gr – BS ~47gr (@24” ~1.07gr; BS 2.25x=105.75gr)

A note here, to musical_whang- your report of 1.2gr 36” sticks testing with a BS of 20.5gr doesn’t align very well with the data above (median in my data is about 31gr, almost 50% higher). You’d expect sticks with a BS around 20.5gr to be around 0.9gr… I’m honestly not sure what to make of this. Has to be some combination of error/difference in testing technique, and… pretty crappy sticks (in terms of BS vs density). With a BS measured at 23.9 (example above), good to go at 1/5 interval. One possibility, do the sticks have a perceptible bow in them? If so, they’re going to buckle…prematurely, in the direction they’re already bowed (you’ll read a weaker BS than you’d see in a perfectly straight stick). The way to handle this is to ….induce it to bow in the opposite way (finger pushing the bow back in the opposite direction), and averaging the two readings. If that’s what’s going on, you’ll get higher BS #, and the needed bracing interval may turn out differently…..

Ladders and Xs vs Xs only"
I’d noted in earlier posts discussing bracing approaches that I wasn’t saying/believing this bracing approach was the very lightest solution to bracing; I was saying it works, and I have a coherent, quantitative, engineering understanding of how and why it works and how to do predictive calculations around it, and I’ve shared that understanding and the data and calculations to use it in design. Data and information coming in for towers in the last few weeks, using an Xs only bracing configuration, seems to be saying a) it works, and b) correctly implemented, it results in lower bracing system weights. As yet, I have not been able to figure out the calculations apply/evaluate applications of this approach. Clearly, the end conditions it creates at braced points along the legs are something other than/less than fixed-fixed; the effective length factor is less than 2.3; you need a tighter braced interval, all other factors being equal, than you do for a ladders and Xs configuration. If you have leg strength where a 1/5 interval bracing configuration works, bracing those same legs with Xs only is going to need a….1/7, 1/8, 1/9, ? bracing interval. Hopefully, some testing in the next 2-3 weeks will shed some light on how to figure this out.

Whew, looong post, but I think its…..comprehensive. Hopefully helpful; have fun!

[Balsa Man]

I am in Division C and attempting the bonus. The 1/8th inch with a push-down test of 27 grams. The ladders and X's are 1/16th. First, I designed everything with AutoCad and printed everything out to scale.
https://drive.google.com/file/d/0Bx2Ru2 ... sp=sharing
Then I built the tower face.
https://drive.google.com/file/d/0Bx2Ru2 ... sp=sharing
Tommorow, I am going to use a normal "3D" jig to align/connect the faces together. Do you guys see any flaws so far?

See long post immediately above; you'll see that, with that push-down reading, it looks like you'll need to go to 1/6 (rather than 1/5) interval bracing....