Figure 4 shows three graphs of strength, σf (sigma underscore f) (MPa) on the vertical axis against density, ρ (rho) (kg per meter cubed). The scales are logarithmic, from 0.01 to 10 raised to the power of 5) MPa on the vertical axis and 10 to 100 000 kg per meter cubed on the horizontal axis.

Each graph is for a different time period. Each graph shows clusters (curved regions) containing points (density, strength) for the materials used at that time.

Top graph – 50 000 BCE. There are three separate clusters. Units omitted for brevity, values are approximate. Natural materials with density 100 to 1000, strength 1 – 100. These are mostly types of wood e.g. balsa, fir, pine, oak) plus leather. Each type of wood has a greater density parallel to the grain than the same wood perpendicular to the grain. Ceramics and glasses – density 1000 to 3000 and strength 50 to 500. This includes, bone, antlers, shell and stone. Metals, including gold, with density about 20 000 and strength 20 to 2000.

Middle graph – 1945. This contains the same clusters as 50 000 BCE with additions. Natural materials also include cork with lower density and strength than other woods. The selection of metal includes many more examples, including alloys, cast iron, zinc, bronze etc. They have density in the range 2000 to 20 000, strength 5 to 1000. This overlaps ceramics and glasses There is an additional cluster of polymers and elastomers. This includes epoxy acrylic, bakelite and rubber. It has a narrow range of density 800 – 1500, strength 10 – 80. This is a range of densities between natural materials and metals, similar strengths to these.

Bottom graph – 2013. This contains the same clusters as 1945 with additions. There are many more materials in polymers and elastomers, with density in the range 70 to 3000, strength 1 to 200. There are more metals and ceramics. Ceramics covers a much larger range of properties density 2000 to 20000, strength from 1 (concrete) to 10 000 (diamond) There is a new cluster of composites, including various glass reinforced polymers. These have similar strength and densities as the lowest density metals and ceramics. The last cluster is foams, showing a range of low density, low strength materials with density 10 to 500, strength 0.01 to 10. The strongest of these are like the types of wood.