Specific Strength in Yuris
Abstract
This article discusses the proper units to quantify tether material for use by the Space Elevator.
Motivation
Just like one cannot measure speed in miles (hint -it has to be in miles per hour) we must be careful to use the right units for material strength.
Is a cable that carries 100 kg "stronger" than a cable that carries 50 kg? In a way, it is, but what if the first cable is 2" thick and made out of wool, whereas the second one is less than 1 mm in diameter and made out of Kryptonite? In this case we'll say that the first cable is stronger, but the second cable *material* is stronger - obviously we're using the word "strong" for more than one property.
In conventional materials engineering, material strength is measured in units of Stress - Pascals, Pounds per Square Inch, or other units of force per area. Using this convention, it doesn't matter if our test cable is an inch thick or a mm thick - that area cancels out and the measured quantity applies to the material, not the actual material sample.
This works well for traditional bulk materials that are "fully dense". These units fail, however, for materials that have empty space within them, since it is impossible to determine their cross-sectional area. If a rope become thinner as it is pulled, which area should we use?
The answer is that we're looking at the wrong quantity again - what we should be really looking at is "how much material" is in the cable. We do this by dividing the material strength by the material density - if a material can have the same strength while being "full of air" we consider it better - and the resultant ratio is called the "Specific Strength", or the "Tenacity".
Units
Specific Strength is thus naturally measures in stress/density, or Pascal/(kg/m3) in the SI system. For tether materials, it is convenient to measure strength in GPa and density in g/cc, and so the everyday unit used is GPa-cc/g, which is equal to 1E6 Pascal/(kg/m3)
As it turns out, we can arrive at the same unit by eliminating the cross-sectional area from the original ratio - stress/density is exactly like force/linear density. (this shows why this unit is insensitive to the unknown "real" area of the tether - the area, whatever it is, simply cancels out). Measuring force in Newtons and linear density in g/km (a.k.a Tex) we get the equivalent form of the unit - N/Tex.
As if this wasn't enough, reducing the unit of Pascal/(kg/m3) to its basic units yields (m/s)2 - velocity squared ! This is quite striking at first - material strength is charaterized by velocity? Well, yes, and when looking at Space Elevator (and other space tether systems) it turns out that there is a direct relationship between this strength and another "velocity" unit that characterized a spinning celestial body, and this relationship determines just how possible it is to construct a Space Elevator on that body. See Velocity-like quantities for more on this.
Yuri
So. We covered GPa-cc/g, N/tex, and Mega-(m/s)2, which are all the same. Rather than choosing between the three, we propose to simply give all of them a name - a derived SI unit named after Yuri Artsutanov - 1 Yuri = 1 (m/s)2, and thus 1 Mega-Yuri = 1 N/Tex = 1 GPa-cc/g.
