after planting some more willow this moring, i decide to take a little break, and i saw this video on the front page youtube... YT@BI: Why A Mile-High Skyscraper Is Almost Impossible | The Limit https://www.youtube.com/watch?v=9DaEmvKWsEA ...and it got me thinking about a little recurring daydream i have, and before i knew it, there went the afternoon: Burj Khalifa[1] Architectural height: 828 m (2,717 ft) Top floor 585.4 m (1,921 ft) Mt Everest[2] peak elevation: 8,848.86 m (29,031.7 ft) "...The air pressure at the summit is generally about one-third what it is at sea level..." 1 mile = 1.609 kilometers[3] Earth's atmosphere[4]: Exosphere: 700–10,000 km (435–6,214 mi) Thermosphere: 80–700 km (50–435 mi) Mesosphere: 50–80 km (31–50 mi) Stratosphere: 12–50 km (7–31 mi) Troposphere: 0–12 km (0–7 mi) 1 meter = 3.281 ft [5] U.S. Standard Atmosphere Air Properties[6]: alt. temp. grav. press. density(10^-4* (ft) (°F) (ft/ (lb/ slugs/ s^2) in^2) ft^3) 0 59 32.174 14.696 23.77 =sea-level 5000 41.17 32.159 12.228 20.48 ~1,500M(approx. 1 mile - 5280ft) 30000 -47.83 32.082 4.373 8.91 ~9,000m(approx. everest peak ~1/3 pressure) 50000 -69.70 32.020 1.692 3.64 ~15,000m(in stratosphere ~1/10th pressure) 60000 -69.70 31.990 1.049 2.26 ~18,000m(in stratosphere ~1/10th density) 100000 -51.10 31.868 0.162 0.33 ~30,000m(in stratosphere ~1/100th pressure & density) 250000 -88.77 31.415 0.000 0.00065 ~75,000m(in mesosphere ~basically vacuum) Specific Strength of Various Materials:[7] Mater. Tensile. Str. Density Specific Strength (MPa) (g/ (MPa• cm^3) cm^3/g) Steel 400 - 2,000 7.85 50 - 255 Alum. 200 - 600 2.7 74 - 222 H.wood 100 - 150 0.6-.9 111 - 250 Tensile strength shows how much pull it takes. Stainless Steel 304 has 90,000 PSI. Yield strength shows bend-resistance. Metal Strength to Weight Ratio Chart [8] Metal Tensile Str Yield Str Density (MPa) (MPa) (g/cm^3) Steel 400-2500 250-1500 7.8 Alum. 70-600 30-400 2.7 Titan. 480-1150 275-950 4.5 1 MPa = 145.038 psi [9] Wood Beams - Strength of Material[10] Wood Hori. Hori. Comp. Comp. Comp. Comp. Shear Shear Perp. Perp. Par. Par. Wet Dry Wet Dry Wet Dry Birch 1417 1668 477 715 960 1200 Fir 1417 1668 417 625 1360 1700 Maple 1271 1495 410 615 880 1100 Oak 1369 1610 590 885 920 1150 Pine 1222 1438 223 335 960 1200 Redwood 1320 1553 433 650 1200 1500 Metal Engineering Materials - Properties[11] Mater Density Tensile Tensile Spec. Spec. (10^3 Mod. Str. Mod. Str. kg/m3) (GPa) (MPa) Iron 7.15 100 140 14.3 0.02 Steel 7.7-8 205 585 26.3 0.073 Alum. 2.7 73 450 27 0.17 2045-T4 Alum. 2.7 69 270 25.5 0.10 6061-T6 for comparison Compression and Tension Strength of common Materials[12] Mat. Comp. Comp. Tens. Tens. Str. Str. Str. Str. psi MPa psi MPa Bricks 1000 7 50 0.35 Granite 19000 130 700 4.8 Limest. 9000 60 300 2.1 Cement 3000 21 500 3.5 Concre. 6200 43 400 2.8 Some of the mechanical properties of various species at 12 percent moisture content. (From Wood Handbook, 1999)[13] (note: MOR is for flexure. it looks like the sheer test was along grain - different) type MOE MOR Comp. Sheer Spec. (psi) (psi) (psi) (psi) gravity Fir 1,950,000 12,400 3,780 900 0.48 Spruce 1,570,000 10,200 5,610 1,150 0.40 W Pine 1,240,000 8,600 4,800 900 0.35 Cedar 880,000 8,800 3,520 1,010 0.47 R Pine 1,630,000 11,000 6,070 1,210 0.46 Cott.W. 1,100,000 6,800 4,020 790 0.34 R Oak 2,200,000 13,400 6,540 1,850 0.54 Maple 2,200,000 13,400 6,540 1,850 0.54 W Oak 1,030,000 10,300 6,060 1,820 0.64 Walnut 1,680,000 14,600 1,010 1,370 0.55 source: [1] https://en.wikipedia.org/wiki/Burj_Khalifa [2] https://en.wikipedia.org/wiki/Mount_Everest [3] https://www.unitconverters.net/length/miles-to-km.htm [4] https://en.wikipedia.org/wiki/Atmosphere_of_Earth [5] https://www.unitconverters.net/length/meters-to-feet.htm [6] https://www.engineeringtoolbox.com/standard-atmosphere-d_604.html [7] https://www.samaterials.com/content/specific-strength-and-material-science.html [8] https://www.partmfg.com/metal-strength-chart-a-pro-guide-2025/ [9] https://www.unitconverters.net/pressure/megapascal-to-psi.htm [10] https://www.engineeringtoolbox.com/wood-beams-strength-d_1480.html [11] https://www.engineeringtoolbox.com/engineering-materials-properties-d_1225.html [12] https://www.engineeringtoolbox.com/compression-tension-strength-d_1352.html [13] https://extension.okstate.edu/fact-sheets/strength-properties-of-wood-for-practical-applications.html continued https://en.wikipedia.org/wiki/Specific_modulus https://web.archive.org/web/20100609005909/http://www.csudh.edu/oliver/chemdata/woods.htm note, woods as a category are of simliar specific stiffness to steel and other hard metals: https://upload.wikimedia.org/wikipedia/commons/5/5a/Specific_stiffness_of_materials.svg https://periodictable.com/Properties/A/YoungModulus.al.html https://periodictable.com/Properties/A/Density.al.html note cypress 1010 kg/sq.mm ~= 10 GPa https://www.unitconverters.net/pressure/kilogram-force-sq-millimeter-to-gigapascal.htm divide by 0.433 g/cm^3 = 23.1 compare to iron 211 GPa / 7.874 g/cm3 = 26.8 not that different https://www.hlc-metalparts.com/news/what-is-flexural-strength-78043665.html worthwhile charts(graphical rep of specific stiffness vs specific strength for color-coded classes of material): https://www-materials.eng.cam.ac.uk/mpsite/interactive_charts/spec-spec/basic.html note overlap in bubbles for woods metals and composites same for strengths-to-toughness: https://www-materials.eng.cam.ac.uk/mpsite/interactive_charts/strength-toughness/NS6Chart.html worth revisiting(stress/strain, Hooke's law, Poisson's ratio...): https://mechanicalc.com/reference/mechanical-properties-of-materials https://en.wikipedia.org/wiki/Specific_modulus https://www.engineeringtoolbox.com/young-modulus-d_417.html https://www.engineeringtoolbox.com/timber-mechanical-properties-d_1789.html https://www.novausawood.com/stiffness-chart-all-species https://www.samaterials.com/content/specific-modulus-of-engineering-materials.html https://en.wikipedia.org/wiki/Strength_of_materials https://www.testresources.net/blog/flexural-strength-vs-tensile-strength-what-are-the-similarities "Flexural versus tensile strength is typically higher in flexure strength than in tensile strength. A material’s flexural strength would be the same as the tensile strength if the material is completely homogeneous. In fact, most materials have small (or large) defects in them which concentrate the stresses locally, effectively causing a localized weakness. When a material is bent only the extreme fibers are at the largest stress so, if those fibers are free from defects, the flexural strength will be controlled by the strength of those intact ‘fibers’. However, if the same material was subjected to only tensile forces then all the fibers in the material are at the same stress and failure will initiate when the weakest fiber reaches its limiting tensile stress. Therefore it is common for flexural strengths to be higher than tensile strengths for the same material. Conversely, a homogeneous material with defects only on its surfaces (e.g. due to scratches) might have a higher tensile strength than flexural strength..." https://en.wikipedia.org/wiki/Flexural_strength https://workshopcompanion.com/know-how/design/nature-of-wood/wood-strength.html https://workshopcompanion.com/Img/the-nature-of-wood/wood-strength/wood_strength_chart.pdf https://workshopcompanion.com/know-how/design/nature-of-wood/wood-strength.html#wood-poplar https://www.atlasfibre.com/understanding-flexural-strength-guide-to-flexural-strength-in-materials/ "...Metals, such as steel and aluminum, also exhibit noteworthy flexural strength. Steel, known for its high tensile strength and durability, has a flexural strength that can range from 370 to 520 MPa depending on the specific alloy and heat treatment. This high flexural strength makes it an excellent material for construction and manufacturing. On the other hand, aluminum, while not as strong as steel, is much lighter and has a flexural strength that ranges from 70 to 700 MPa. This makes aluminum a preferred choice for applications where weight is a critical factor, yet a certain degree of flexural strength is still required..." https://www.origen.co.za/2019/01/01/tensile-versus-bending-strength/ "...For a particular material, the flexural strength would exhibit the same value as the tensile strength, if the material was homogeneous and isotropic. In practice, however, the material contains flaws or defects, even on a microscopic scale, which can cause localised stress concentration or weaknesses. In bending, the outermost ‘fibres’ of the loaded material would experience the largest stresses, but these would be applicable only for a relatively small region on the very surface of the component and would decrease linearly towards the centre of the sample/component (neutral axis) to become a compressive stress (in bending), on the opposite side as shown in the figure..." note why modulus numbers are so much higher than strength numbers: https://en.wikipedia.org/wiki/Young%27s_modulus https://en.wikipedia.org/wiki/Elastic_modulus https://en.wikipedia.org/wiki/Flexural_modulus "elastic modulus describes an object's or substance's resistance to being deformed elastically... ...The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region..." seems to be a photo-pdf and missing values for many entries: https://www.bestech.com.au/wp-content/uploads/Modulus-of-Elasticity.pdf https://en.wikipedia.org/wiki/Structural_load i feel like maybe i should include these guys because they seem so sure of themselves: https://buildsteel.org/technical/light-yet-mighty-steels-strength-to-weight-surpasses-wood-and-concrete/ "...Steel outperforms wood in strength, resisting tension, compression and shear forces more effectively. Despite being denser, steel creates lighter structures by requiring less material, thus reducing overall building loads... ...Concrete excels in compression but requires steel reinforcement to handle tension. Steel offers excellent tensile strength and greater flexibility for diverse applications. Because concrete is heavier, it demands more substantial foundations and higher transportation costs. Steel is lighter, easy to transport and better equipped to withstand seismic forces..." https://www.eng-tips.com/threads/difference-between-wood-and-steel-beams-in-theory.478690/#google_vignette note EI stands for elastic modulus and second moment of a beam's cross section. https://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory from eng-tips - "The wood will also be more sensitive to Shear deformations and experience creep deflection over time. On a material level steel is isotropic while wood is anisotropic." https://github.com/buddyd16/Structural-Engineering https://github.com/open-struct-engineer https://calcs.com/blog/creep-deflection-in-structural-wood-beam-design "Wood is a viscoelastic material, exhibiting both viscous and elastic characteristics when undergoing deformation. As a result, it suffers from creep behavior under long-term loading. Creep is the permanent sag caused by the stretching and adjusting of the wood fibers to the long-term loads on them, such as the weight of the member itself, the deck it supports, and other building components. It is a time-dependent deformation from constant stress that develops over years, and accelerates with frequent and drastic temperature and moisture content changes. Creep is an important factor to consider in the design and durability of timber structures..." Here, i found the engineered wood people!. right, wood is better than steel! it is solved(with the only exception being form-factor): https://binkleyconstruction.com/news/wood-beams/choosing-between-steel-or-glulam-benefits-to-consider/ "...Glulam boasts impressive strength compared to steel. It has a strength-to-weight ratio of approximately three times higher. This not only makes it suitable for structural applications but facilitates easier installation. It’s considerable for maneuvering beams into tight spaces or lifting large elements with cranes. Additionally, the reduced weight of glulam frames allows for smaller foundations. This can further contribute to cost and resource efficiency. Steel results in smaller members compared to equivalent glulam counterparts. While steel typically has a higher allowable stress, glulam’s lighter weight offers its advantages. As a general guideline, the depth of glulam required to perform a comparable task to steel ranges from 1.5 to 2 times greater. In scenarios where space constraints are a concern, steel may be a more practical choice... ...Although it may seem counterintuitive, wood demonstrates notable fire resilience compared to steel..." https://binkleyconstruction.com/news/mass-timber/cross-laminated-timber-beams-applications-installation/ "...CLT beams have many benefits compared to steel and concrete. They are lighter, which makes them easier to move and work with. This can help save money during construction..." ...for later: https://www.bucklandtimber.co.uk/blog/steel-or-glulam/ https://bioresources.cnr.ncsu.edu/resources/comparison-of-mechanical-properties-according-to-the-structural-materials-of-lumber-glt-clt-and-ply-lam-clt/ "MOR of lumber was 60.7 MPa (13.1), the highest among materials, followed by GLT 50.2 MPa (19.3%), ply-lam CLT 42.7 MPa (11.8%), and CLT 39.4 MPa (20.2%)." https://bioresources.cnr.ncsu.edu/resources/shear-strength-of-cross-laminated-timber-based-on-larch-lamina-combination/ https://pmc.ncbi.nlm.nih.gov/articles/PMC10672904/ Pyramid Volume = (1/3)Bh 30-60-90 triangle: (x/2)^2+(sqrt(3)x/2)^2=x^2 ... 11,999,999,999,999cu.m for a 30,000m tall equilateral square pyramid or 323,999,999,999cu.m for a 9,000m tall equilateral square pyramid https://www.fao.org/4/Y1997E/y1997e07.htm "The year 2000 estimate for the global volume of forests was 386 billion cubic meters..." construction could take awhile. perhaps it wouldn't have to be completely solid? space-launch mega-pyramid Rocket sled launch pyramid https://en.wikipedia.org/wiki/Non-rocket_spacelaunch https://en.wikipedia.org/wiki/Rocket_sled_launch The Big Lifters https://en.wikipedia.org/wiki/StarTram https://startram.com/ StarTram MagLifter i knew someone must have thought of this before. it looks like neat ESA was going to build a sled-launch space-plane, and got as far as building a prototype and doing a drop test: https://en.wikipedia.org/wiki/Hopper_(spacecraft) https://www.freepatentsonline.com/6311926.pdf it's not really obvious how they intended to get the end of the tube up into the high atmosphere? in the drawings it appears to be floating in the sky? https://startram.com/wp-content/uploads/2020/12/StarTram2010.pdf "... Magnetically levitated and propelled Gen-1 cargo craft accelerate in a 100 kilometer long evacuated tunnel, entering the atmosphere at the tunnel exit, which is located in high altitude terrain (~5000 meters)..." right, it just goes up a mountain. sounds like an opportunity for a mega-engineering project. like a space-pyramid. do you think it is doable?