Difference between revisions of "Specific Strength in Yuris"
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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.  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/m<sup>3</sup>) to its basic units yields (m/s)<sup>2</sup>  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  As if this wasn't enough, reducing the unit of Pascal/(kg/m<sup>3</sup>) to its basic units yields (m/s)<sup>2</sup>  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 quantity and another velocityunit quantity that characterizes a spinning celestial body, and this relationship determines just how possible it is to construct a Space Elevator on that body. See [[Velocitylike quantities]] for more on this, and also [[Astroid Tether Return]] and [[Disposable OneWay Elevator]].  
==Yuri==  ==Yuri== 
Revision as of 18:27, 7 July 2008
Title: Specific Strength in Yuris  
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Abstract
This article discusses the proper units to quantify tether material for use by the Space Elevator.
Motivation
Just like one cannot specify or measure speed in miles (hint  it must be done in milesperhour) 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  the measured quantity applies to the material, not the actual material sample. So in order to characterise a material, we test a cable sample, and divide the breaking force by the measures crosssectional area of the cable.
This works well for traditional bulk materials that are "fully dense". These units fail, however, for materials that have empty space within their structure, since it is impossible to determine their "real" crosssectional area. Should the empty space count? 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 really be looking at is "how much material" is in the cable. We do this by dividing the traditional material strength by the material density  if a material can have the same strength while being "full of air" it should be considered stronger  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/m^{3}) 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 GPacc/g, which is equal to 1E6 Pascal/(kg/m^{3})
As it turns out, we can arrive at the same unit by eliminating the crosssectional 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/m^{3}) 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 quantity and another velocityunit quantity that characterizes a spinning celestial body, and this relationship determines just how possible it is to construct a Space Elevator on that body. See Velocitylike quantities for more on this, and also Astroid Tether Return and Disposable OneWay Elevator.
Yuri
So. We covered GPacc/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 MegaYuri = 1 N/Tex = 1 GPacc/g.
To build a Space Elevator, we're looking for material in the 3080 MYuri range.
The traditional symbol used in engineering to denote stres is σ. We propose using τ as the symbol for Specific Strength or Tenacity. τ = σ/ρ
I am not sure what the procedure is to propose this the governing body of SI.