Toothpick Tower

[anatidaephobia]

This project is pretty much a standard tooth pick tower but with some weird parameters.

1. Only 750 flat toothpicks may be used
2. The base must be at least 100 square centimeters
3. It must be at least 36 centimeters tall

The tower that has the lowest mass to weight supported ratio gets extra credit, which is what I'm aiming for. Help please?

[arkain101]

Triangles

[Turtle]

flat tootpicks lend themselves to laminating. if that's allowed anyway.

think, glulam. >> Glued laminated timber - Wikipedia, the free encyclopedia

[UncleAl]

First, the glue. Carpenter's glue, then fully cured and dried (water is massive). Adhesive (vs. cohesive) failure would be a tragedy. Clamped very thin layer on both surfaces to minimize added mass. Second, stiffness vs. toughness. Heating toothpicks in an oven, temp and time, makes them stiffer but more brittle. Third, geometry. All triangles, of course, and fractal like the Eiffel Tower or perhaps a Sierpinski gasket,

Sierpinski triangle - Wikipedia, the free encyclopedia

HOWEVER... You must attach triangles with glue, perhaps sanding away (Dremel!) noncontact joint overlaps. Smaller emergent scale has its price in added glue mass for more joins. Stiffness of a beam varies as the cube of thickness. A wider, thicker toothpick that is slotted down the middle until the joins could give you a better strength to weight ratio. Would arches built of triangles bear more weight than a pile of triangles?

The volume of a pyramid is 1/3(base area)(height). (100)(36)/(3)(750) = 1.6 cm^3/toothpick. It must be airy! Cut off the thin ends? Should toothpicks be glued onto each other, or should anti-parallel pairs be interdigitated at the joins? Thicker = (stiffer)^3 A skin to establish base area and isotropic resistance vs. tipping plus a central pillar for main support, triangles at the base for attachment, sounds interesting. What would interstital filler add to strength against weight, cos(theta)? It must be airy! If you use anti-parallel pairs it must be twice as airy. Trace the force into the ground. Central outer belt plus trace internal struts to prevent buckling re flying buttresses?

Buy many boxes of toothpicks and only use the 750 perfect ones for the final construct. Look at imperfections, the direction of grain (off-axis shear failure), and the color (is heartwood stronger?).