Skip to main content
Adding explanaition for corrected calculation of the other mass and correction of the mass values
Source Link
Sergiy Lenzion
  • 6.5k
  • 1
  • 20
  • 59

Update 2

The taper ratio formula seems to be correct. The crosscheck stress calculation error mentioned in the Update 1 below is found to be due to:

a) incorrectly calculated tether volume (and therefore mass). I assumed a linear change of cross section area across the tether length. In fact, to achieve the uniform strength, a logarithmic increase in erea is required. enter image description here

b) not accounting for varying gravity across the altitude (from 8.87001 m/s2 at the surface to 8.72529 m/s2 at 50 km altitude).

The tether mass values are now corrected in the text of the Update 1 below.

Update 1: Apologies for making already long answer even longer, but I forgot to mention few other very important factors in the above list:

Now that we've accounted for hot venusian climate (tensile stress reduction), let's see what our tether is going to look like in order to have a similar safety coefficient as originally planned (**total SF **willtotal SF will be 3.3 for the following example):

SF for tension = 5: operating tensile stress 2.1GPa/5=0.42GPa. Taper ratio formula gives us the ratio of 16.9 (by the way, it looks like the OP has simplified the formula from the referenced answer and, when I use the formula from the body of the current question, the taper ratio is not very accurate, which is highlighted by the fact that I always receive a higher stress when doing the cross check: (mass of probe + mass of tether)×gravity/(larger diameter of the tether))(by the way, it looks like the OP has simplified the formula from the referenced answer and, when I use the formula from the body of the current question, the taper ratio is not very accurate, which is highlighted by the fact that I always receive a higher stress when doing the cross check: (mass of probe + mass of tether)×gravity/(larger diameter of the tether)) The error has been attributed to incorrectly calculating tether volume (therefore mass) and not accounting for varying gravity across the height. The tether mass values in the examples below are now updated to the corrected ones.

The tether mass now grows from 270kg to quite disappointing 2,093 21,093kg604 kg.

  • Total SF 4.5 (6.5 for tension and 15 for bending) Taper ratio 39.5; Areas: 2.75 to 108.4 sq.mm; Diameters: 1.87 to 11.75 mm; Bend radius: 3.5 m (I list the figure for single wire purely for comarison, remember it will be smaller for rope); Tether mass: 5 5,778 3,778884 kg.
  • Total SF 5.2 (8 for tension and 15 for bending) Taper ratio 92.2 Areas: 3.38 to 311.6 sq.mm; Diameters: 2.07 to 19.92 mm; Bend radius: 6.05 m (again, only for comparison, rope will accomodate smaller); Tether mass: astonishing 15,640 159,640199 kg.

Update: Apologies for making already long answer even longer, but I forgot to mention few other very important factors in the above list:

Now that we've accounted for hot venusian climate (tensile stress reduction), let's see what our tether is going to look like in order to have a similar safety coefficient as originally planned (**total SF **will be 3.3 for the following example):

SF for tension = 5: operating tensile stress 2.1GPa/5=0.42GPa. Taper ratio formula gives us the ratio of 16.9 (by the way, it looks like the OP has simplified the formula from the referenced answer and, when I use the formula from the body of the current question, the taper ratio is not very accurate, which is highlighted by the fact that I always receive a higher stress when doing the cross check: (mass of probe + mass of tether)×gravity/(larger diameter of the tether))

The tether mass now grows from 270kg to quite disappointing 2,093kg.

  • Total SF 4.5 (6.5 for tension and 15 for bending) Taper ratio 39.5; Areas: 2.75 to 108.4 sq.mm; Diameters: 1.87 to 11.75 mm; Bend radius: 3.5 m (I list the figure for single wire purely for comarison, remember it will be smaller for rope); Tether mass: 5,778 kg.
  • Total SF 5.2 (8 for tension and 15 for bending) Taper ratio 92.2 Areas: 3.38 to 311.6 sq.mm; Diameters: 2.07 to 19.92 mm; Bend radius: 6.05 m (again, only for comparison, rope will accomodate smaller); Tether mass: astonishing 15,640 kg.

Update 2

The taper ratio formula seems to be correct. The crosscheck stress calculation error mentioned in the Update 1 below is found to be due to:

a) incorrectly calculated tether volume (and therefore mass). I assumed a linear change of cross section area across the tether length. In fact, to achieve the uniform strength, a logarithmic increase in erea is required. enter image description here

b) not accounting for varying gravity across the altitude (from 8.87001 m/s2 at the surface to 8.72529 m/s2 at 50 km altitude).

The tether mass values are now corrected in the text of the Update 1 below.

Update 1: Apologies for making already long answer even longer, but I forgot to mention few other very important factors in the above list:

Now that we've accounted for hot venusian climate (tensile stress reduction), let's see what our tether is going to look like in order to have a similar safety coefficient as originally planned (total SF will be 3.3 for the following example):

SF for tension = 5: operating tensile stress 2.1GPa/5=0.42GPa. Taper ratio formula gives us the ratio of 16.9 (by the way, it looks like the OP has simplified the formula from the referenced answer and, when I use the formula from the body of the current question, the taper ratio is not very accurate, which is highlighted by the fact that I always receive a higher stress when doing the cross check: (mass of probe + mass of tether)×gravity/(larger diameter of the tether)) The error has been attributed to incorrectly calculating tether volume (therefore mass) and not accounting for varying gravity across the height. The tether mass values in the examples below are now updated to the corrected ones.

The tether mass now grows from 270kg to quite disappointing 2,093 1,604 kg.

  • Total SF 4.5 (6.5 for tension and 15 for bending) Taper ratio 39.5; Areas: 2.75 to 108.4 sq.mm; Diameters: 1.87 to 11.75 mm; Bend radius: 3.5 m (I list the figure for single wire purely for comarison, remember it will be smaller for rope); Tether mass: 5,778 3,884 kg.
  • Total SF 5.2 (8 for tension and 15 for bending) Taper ratio 92.2 Areas: 3.38 to 311.6 sq.mm; Diameters: 2.07 to 19.92 mm; Bend radius: 6.05 m (again, only for comparison, rope will accomodate smaller); Tether mass: astonishing 15,640 9,199 kg.
added 1 character in body
Source Link
Sergiy Lenzion
  • 6.5k
  • 1
  • 20
  • 59

Achieving designs for safety factors in the range of human-rated lifting (if we ever wanted to utilise such an option on Venus) seems to be out of question even infor this relatively short 50km space elevator.

Achieving designs for safety factors in the range of human-rated lifting (if we ever wanted to utilise such an option on Venus) seems to be out of question even in this relatively short 50km space elevator.

Achieving designs for safety factors in the range of human-rated lifting (if we ever wanted to utilise such an option on Venus) seems to be out of question even for this relatively short 50km space elevator.

deleted 5 characters in body
Source Link
Sergiy Lenzion
  • 6.5k
  • 1
  • 20
  • 59
  • Stress components from various types of loading (like tension and bending) conform to superposition principle, i.e. they add "on top" of each other. This means that in the example above the bending stress of 0.3GPa (Safety factor (hereinafter referred to as SF) of 10) adds to tensile stress of 1GPa (SF 3). Therefore the total stress in the most loaded point (first bending loop on the reel just above the straight section) is 1.0+0.3=1.3GPa. This gives us the real SF figure of 3GPa/1.3GPa = 2.3 (which is a significant reduction).

  • Reduction of ultimate tensile stress with the increase of temperature (kudos to @Uwe for pointing this out this in the comments!). What this means is all above calculations would have been applicable only if the temperature in the atmosphere of Venus was 20degC. But it's quite a bit hotter than that. Wikipedia states 460degC at the surface.

  • Stress components from various types of loading (like tension and bending) conform to superposition principle, i.e. they add "on top" of each other. This means that in the example above the bending stress of 0.3GPa (Safety factor (hereinafter referred to as SF) of 10) adds to tensile stress of 1GPa (SF 3). Therefore the total stress in the most loaded point (first bending loop on the reel just above the straight section) is 1.0+0.3=1.3GPa. This gives us the real SF figure of 3GPa/1.3GPa = 2.3 (which is a significant reduction).

  • Reduction of ultimate tensile stress with the increase of temperature (kudos to @Uwe for pointing this out this in the comments!). What this means is all above calculations would have been applicable only if the temperature in the atmosphere of Venus was 20degC. But it's quite a bit hotter than that. Wikipedia states 460degC at the surface.

  • Stress components from various types of loading (like tension and bending) conform to superposition principle, i.e. they add "on top" of each other. This means that in the example above the bending stress of 0.3GPa (Safety factor (hereinafter referred to as SF) of 10) adds to tensile stress of 1GPa (SF 3). Therefore the total stress in the most loaded point (first bending loop on the reel just above the straight section) is 1.0+0.3=1.3GPa. This gives us the real SF figure of 3GPa/1.3GPa = 2.3 (which is a significant reduction).

  • Reduction of ultimate tensile stress with the increase of temperature (kudos to @Uwe for pointing this out in the comments!). What this means is all above calculations would have been applicable only if the temperature in the atmosphere of Venus was 20degC. But it's quite a bit hotter than that. Wikipedia states 460degC at the surface.

Added two important factors and examples of some more calculations
Source Link
Sergiy Lenzion
  • 6.5k
  • 1
  • 20
  • 59
Loading
Improved formatting
Source Link
Machavity
  • 8.2k
  • 1
  • 31
  • 72
Loading
deleted 5 characters in body
Source Link
Sergiy Lenzion
  • 6.5k
  • 1
  • 20
  • 59
Loading
added 79 characters in body
Source Link
Sergiy Lenzion
  • 6.5k
  • 1
  • 20
  • 59
Loading
added 79 characters in body
Source Link
Sergiy Lenzion
  • 6.5k
  • 1
  • 20
  • 59
Loading
Source Link
Sergiy Lenzion
  • 6.5k
  • 1
  • 20
  • 59
Loading