## 4 Tether Materials  
This Section links the momentum transfer tether system architecture and environment discussion in Sections 1-3 with the mission design in Section 6 by providing guidelines as well as examples to the calculation of the physical properties of the tethers. In particular, tether strength and maintenance are discussed. The primary component of the bolo is the high-tension rope (tether), characterized by the critical tip velocity, dependent on strength to weight ratio. In 2001, [PERSON] [32] calculated an equation for the maximal permissible rotation speed (or maximal payload for given rotation speed) of tether with a payload attached to one end (See Equation (3a,b)). Figure 7: The energy (normalized) spent to spin-up a tether with a point-mass counterweight on one end, from standstill to fixed free tip velocity. _Aerospace_**2014**, \(1\)  
\[\omega_{\max}= \sqrt{\frac{F_{break}}{L(m_{p}+m_{t}/2)}} \tag{3a}\] \[m_{p}= \frac{F_{break}}{\omega^{2}L}-m_{t}/2 \tag{3b}\]  
However, using only ultimate tensile strength and density of material to calculate breaking force may lead to over-optimistic calculations of critical tip velocity and tether mass, as happened to [PERSON] [33], as the strength of the tether (rope) is mostly a function of defects present in tether material, not the material. For example, although the highest reported measured strength of microscopic alumina fibers was 22.3 GPa [34], the same material from the same manufacturer has a strength of 6.7 GPa [27] if made into long (0.5 m) fibers. Such a decrease of strength is a combination of the effect of the easy slip planes, surface imperfections, and voids inside the alumina fibers. In 2002, [PERSON] [27] published a detailed review of high-strength fibers and their failure modes, and any tethered-mission designer is strongly advised to read it. The following derating from the ultimate tensile strength should be used:  
1. If loads are periodic or constant (as opposed to impulsive), use maximal yield strength;
2. If brittle failure is possible in metal elements by a factor of 3 [27];
3. For time-dependent degradation (especially for Zylon);
4. For a maximal operating temperature (or up-rate, if operating temperature is low);
5. For ultraviolet light and radiation-induced degradation;
6. For the bundling of yarn (not all yarns are tensioned equally)--this penalty increases with tether diameter;
7. For the weaving of rope (bundles are twisted and pre-stressed);
8. For atomic oxygen erosion (for tethers on LEO) or decomposition catalysts present (copper on polyethylene);
9. For the creep during service life (most important for polymer ropes, especially UHMWPE) [35];
10. For the extra length of the tether compared to length of test specimens (variability of strength increases logarithmically with an increase in sample length). All derating coefficients may be cumulative. Typically, after all deratings, loading all of the potential tether materials beyond 30% of their respective ultimate tensile strength is dangerous, and some synthetic fibers (UHMWPE, polyester, Kevlar in marine environments) may be usable only up to 5%\(-\)20% of their ultimate tensile strength [27]. One is sometimes misled by the stated structural factors of 1.5 to 2.0 (corresponding to loads 67% to 50% of ultimate tensile strength) of the structural components (wings, for example) of aircraft. Such low structural factors are possible only if component is available for defectoscopy or is flying a very short time. The impressive reliability of modern aircrafts is the function not only of advanced materials, but also of inspection infrastructure. If one cannot monitor (and as necessary, repair) small cracks or scars before they grow to a dangerous size, it is better to double the structural factors of component in question. In addition, the geometry of the rotating tether is very unfavorable to timely crack detection, even if defectoscopy equipment is available during normal tether operation.