Bracing Strength

[cool hand luke]

I'm trying to take a more engineering approach this year, (last year we just built a bunch of towers and saw what worked)

For a ladders and x's build, how strong do your ladders and x's need to be?

what about for an all x's?

[Random Human]

I'm trying to take a more engineering approach this year, (last year we just built a bunch of towers and saw what worked)

For a ladders and x's build, how strong do your ladders and x's need to be?

what about for an all x's?

It really depends, on the angle of the legs, density of the legs, and what your purpose of bracing is. I recomend you surf through last years towers forums, the answer lies in there.

[Balsa Man]

I'm trying to take a more engineering approach this year, (last year we just built a bunch of towers and saw what worked)

For a ladders and x's build, how strong do your ladders and x's need to be?

what about for an all x's?

It really depends, on the angle of the legs, density of the legs, and what your purpose of bracing is. I recomend you surf through last years towers forums, the answer lies in there.

CHL, congrats on understanding that a real engineering approach will get you a lot further than a, how should I say it, ...unstructured approach.

RH, you're absolutely right. I and a number of others posted very detailed info on how to figure it out last year. Adding a bit of refinement and... engineering approach to the good points you note - stuff that's discussed in great detail in the 2017 Towers archive;

The (buckling) strength of a set of braced legs depends on:
1) the unbraced buckling strength (which depends on the length, cross section, and modulus of elasticity.) Modulus of elasticity ("E" in Eulers Buckling Theorem) is related to density; higher density, higher E, but there is significant variation around the mean- you can have a bundle of sticks weighing the same, and their buckling strength can vary as much as +/-20%.) Its the lightest ones that have the buckling strength you need that you're looking for. Key thing to work out in design is the tradeoff between denser/stronger legs with wider bracing interval vs lighter/weaker legs with tighter bracing interval.
2)The angle of the legs (from vertical)- the force on a tower leg is proportional to 1 over the cosine of the angle from vertical. For towers, with 4 legs, and a 15kg load on the tower, leg forces will be (as I posted above) between 3.75kg to a hair over 4kg.
3) the braced buckling strength (which depends on unbraced buckling strength, the bracing interval- are you bracing at 1/2, 1/3, 1/4, 1/5, etc of the full leg length, and the bracing configuration (e.g., ladders and Xs, all Xs), which determines the "end conditions" of braced segments which determine the "effective length". Those factors work together to determine the braced leg buckling strength. And last,
4) the specific question you asked about- how strong the bracing pieces you use are. Ladders and Xs are easy to calculate. Ladders 'work' in compression- preventing incipient buckling of two adjacent legs toward each other. They fail by buckling, so same factors for figuring out leg strength apply. The loads on ladders will be in the 1-2kg range. Xs (in a ladders and Xs system) work in tension. You can easily test by "pull-testing"- the loads they need to carry are, again, in the 1-2kg range

[cool hand luke]

1-2 KG, that's perfect for what the kids are wanting to look into.

Balsa, you providing the effective length ratio (.55 for all x's, etc) is the piece I was missing last year that lead us to the "just throw it together" approach. I didn't have time to figure it out on the fly. Thanks for doing the hard work and letting us benefit.

[Balsa Man]

1-2 KG, that's perfect for what the kids are wanting to look into.

Balsa, you providing the effective length ratio (.55 for all x's, etc) is the piece I was missing last year that lead us to the "just throw it together" approach. I didn't have time to figure it out on the fly. Thanks for doing the hard work and letting us benefit.

Excellent, you're welcome!
As I've said before, I'm (still) working on getting a tight/predictive engineering handle on all Xs (like we developed for ladders and Xs- single finger pushdown BS measurement of leg material x effective length factor of 2.3 and inverse square calc looking at bracing interval to get the braced leg strength to force seen at full tower load, and sfpd BS test of ladder wood, x 2.3 and inverse calc at ladder length to get ladder strong enough to hold...approaching 2kg, w/ pull test to ~2kg for X strips).
The ~0.55 effective length factor for bracing w/ all Xs, as I've described before was 'reverse engineered' from some specs I got for a...high performing non-29cm circle bonus tower, using Xs cut 1/16" wide from 1/32 sheet weighing "just under 0.2gr/36" That equates to a 3" x 36" x 1/32 sheet weighing about 9gr. Two comments on that; a) when cutting/weighing and BS testing 1/32 x 1/16 strips (at 24cm, a bit longer than longest ones on the tower), found (no surprise), very significant variation in both BS and weight. This says that to control/optimize an all Xs design, you'll need to sort strips by BS, and use lightest that are above ... a certain strength, and that shorter Xs, higher up on the tower can be lower density. b) since we were reverse engineering from a narrower base, non-circle bonus to a wide base, circle bonus base, our lower 3 X sets were longer than lowest in a non-circle bonus tower- we dealt with that by laminating a second piece of 1/32 x 1/15 at the center for those longer Xs- we used 4cm, 3cm, and 2cm (coming up from the bottom) (no engineering/theoretical basis, just...a gut sense of additional strength needed). Given the 5kg in the circle bonus this year, going for it is the way to go, so lower Xs stronger than what worked in a non-circle bonus tower last year will be needed. Building and testing (keeping careful track of weight and BS of X strips) is one way to get to optimization/figure out strengths needed at what length for Xs. Hope to be able to get to guidance (like "ladders and Xs need to be able to carry ~2kg"), for forces/strengths that all Xs have to carry, and will be sharing what we find out (both in theory and testing). If we all share data, we can get (more quickly) to....valid, practical guidance range for everyone to work from (and then it becomes who can really fine tune that the best)...