Specific strength

${\displaystyle L={\frac {T_{s}/\rho }{\mathbf {g} }}}$

where ${\displaystyle L}$ is the length, ${\displaystyle T_{s}}$ is the tensile strength, ${\displaystyle \rho }$ is the density and ${\displaystyle \mathbf {g} }$ is the acceleration due to gravity (${\displaystyle \approx 9.8}$ m/s${\displaystyle ^{2}}$)

The data of this table is from best cases, and has been established for giving a rough figure.

Note: Multiwalled carbon nanotubes have the highest tensile strength of any material yet measured, with labs producing them at a tensile strength of 63 GPa,[33] still well below their theoretical limit of 300 GPa. The first nanotube ropes (20 mm long) whose tensile strength was published (in 2000) had a strength of 3.6 GPa, still well below their theoretical limit.[38] The density is different depending on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid).[34]

The International Space Elevator Consortium uses the "Yuri" as a name for the SI units describing specific strength. Specific strength is of fundamental importance in the description of space elevator cable materials. One Yuri is conceived to be the SI unit for yield stress (or breaking stress) per unit of density of a material under tension. One Yuri equals 1 Pa⋅m³/kg or 1 N⋅m/kg, which is the breaking/yielding force per linear density of the cable under tension.[39][40] A functional Earth space elevator would require a tether of 30–80 megaYuri (corresponding to 3100–8200 km of breaking length).[41]

The null energy condition places a fundamental limit on the specific strength of any material.[37] The specific strength is bounded to be no greater than c² ~ 9×10¹³ kN⋅m/kg, where c is the speed of light. This limit is achieved by electric and magnetic field lines, QCD flux tubes, and the fundamental strings hypothesized by string theory.

Tenacity is the customary measure of strength of a fiber or yarn. It is usually defined as the ultimate (breaking) force of the fiber (in gram-force units) divided by the denier. Because denier is a measure of the linear density, the tenacity works out to be not a measure of force per unit area, but rather a quasi-dimensionless measure analogous to specific strength.[42] A tenacity of ${\displaystyle 1}$ corresponds to: ${\displaystyle {\frac {1{\rm {\,g}}\cdot 9.80665{\rm {\,ms^{-2}}}}{1{\rm {\,g}}/9000{\rm {\,m}}}}={\frac {9.80665{\rm {\,ms^{-2}}}}{1/9000{\rm {\,m}}}}=9.80665{\rm {\,ms^{-2}}}\,9000{\rm {\,m}}=88259.85{\rm {\,m^{2}s^{-2}}}}$ Mostly Tenacity expressed in report as cN/tex.

• Specific modulus
• Space elevator
• Space tether

• Specific stiffness - Specific strength chart, University of Cambridge, Department of Engineering