Aerodynamic Response

Space Elevator Response to Wind

Wind Environment

The area of the Pacific ocean considered to be optimal for location of the space elevator has little quantified data for the wind environment at altitudes above sea level; thus it was concluded that using “probability of occurrence” type of synthesized wind-altitude envelops would likely not be meaningful at present. Thus, for purposes of this study, a constant wind-versus-altitude profile was adopted as a reference environment. So, in this study, the space elevator is subjected to a variety of (peak) wind intensities modeled as constant in altitude and direction, but, varying in time. This time variation can be summarized as:

• the wind starts at zero velocity
• builds to a peak velocity in 2 hrs
• holds that peak velocity for a period of 2 hrs (unless otherwise specified)
• then, decays to zero velocity in 2 hrs

Thus, the wind velocity has usually returned to zero after 6 hours, and the simulation continues until about 10 hours so as to examine the ribbon rebound from effects of the wind.

This study did not address gusts, since such short term phenomenon will likely not have a insignificant overall effect.

Wind Levels

Since the elevator is envisioned as being anchored in the Pacific ocean, the typhoon wind categorization scheme was adopted for the study. The wind-levels spanned velocities between the two official categories below:

• Category 0 (average of 25 m/s, 55 mph, a tropical disturbance)
• Category 3 (average of 54 m/s, 120 mph, a full typhoon)

Elevator Configuration

Various combinations of possible elevator configurations are subjected to various wind environments. The configuration parameters are:

• whether the elevator is occupied by a climber (or unoccupied).

• If occupied, then the climber may be positioned at different altitudes.The location of the 20 metric ton climber is significant since it both alters the vertical tension profile in the ribbon, and, if the climber is positioned in the troposphere, it presents to the wind a significant localized aerodynamic area.

• the ribbon width (a 5 cm ribbon is used unless otherwise specified). The aerodynamic area subjected to the wind by the ribbon itself has a significant effect upon aerodynamic response.

Animation Conventions

Note: in all animations, the horizontal displacements are greatly exaggerated to show details of ribbon response; Maximum gross-ribbon librations shown in the animations correspond to only about 0.5 deg

Two types of animations are shown:

1. Conventional 3-D animations providing general perspectives; some are in 3-D perspective views, some are presented in 2-D views.
2. Special 2-D Animations that are timed snapshots of static engineering graphs of elevator displacements taken at 8.3 min intervals; in addition to providing a some sense of the response, these mainly provide accurate quantitative assessment of the extent of the response.

Note 1: In the Special 2-D animations, the troposphere is indicated by levels of graduated blue to portray atmospheric density.

Note 2: The Special 2-D animations are presented at different vertical scales, for example:

• Full Altitude: Shows the entire ribbon length of 100,000 km (thus, these movies have a grossly over-scaled horizontal axis).

• High Altitude: Shows what’s going on from Ground up to about 400 km

• Low Altitude: Shows what’s going on from Ground up to about 40 km

General Tips on Viewing Animations

• All simulation runs last 9.7 hours, so, any resulting wind-induced elevator in-plane natural libration response (with a period of about 5 days) will not be observable.

• Pay particular attention to the animation horizontal scales, as they vary drastically from case to case.

• Look for the progression of horizontal displacement reaching a maximum value and holding at that value in some runs, while displacement in other runs will continue to progress (due to exacerbating conditions like wider-ribbon or increased peak wind level, climber-on-ribbon effects, etc).

• Detail discussions of these case situations can be found in the Aerodynamic response paper (on the previous Wiki page).

The Animations

Configuration Summary and Overview

Animation 1: Unoccupied, Cat 0 wind

Animation 2: Unoccupied, Cat 0 wind, 10 cm Ribbon

Animation 3: Unoccupied, Cat 0 wind 5 vs 10 cm Ribbon

Animation 4: Unoccupied, Cat 0 vs Cat 3 wind

Animation 5: Climber @LEO, Cat 0 wind

Animation 6: Climber @LEO, Cat 0 wind, 4 hour peak wind

Animation 7: Climber @LEO, Cat 0 wind, 2 -vs- 4 hr peak wind

Animation 8: Climber @LEO, Cat 2 wind (full perspective view)

Animation 9: Climber @9km, Cat 0 wind (true linear scale view)

Animation 10: Unoccupied vs Climber @9 km, Cat 0 wind

Animation 11: Unoccupied, Cat 2 wind

Animation 12: Unoccupied, Cat 3 wind

Unoccupied, Cat 0 wind

Unoccupied, Cat 0 wind, 5 cm Ribbon.

- Note that ribbon displacement progresses to the point of peak wind, then stays there until subsiding as the wind decays.

Viewed in 2-D Low Altitude

Unoccupied, Cat 0 wind, 10 cm Ribbon

Unoccupied, Cat 0 wind, 10 cm Ribbon.

- Note that displacement continues to progress even with wind constant at its peak value.

- Ribbon Departure angles are approaching horizontal at anchor.

Viewed in 2-D Medium Altitude

Unoccupied, Cat 0 wind, 5 vs 10 cm Ribbon

Unoccupied, Cat 0 wind, 5 vs 10 cm Ribbon

- Displacement for 10 cm ribbon shows almost unabated progress even with wind constant at peak value (note: compare to 5 cm displacement), reaching significant horizontal displacements approaching 250 km down-range.

Viewed in 2-D High Altitude

Unoccupied, Cat 0 vs 3 wind

Unoccupied, Cat 0 vs Cat 3 wind, 5 cm Ribbon

- The ribbon is seen to be displaced almost 300 km downrange, by the time that wind starts to subside.

- This Case points out that once conditions are met in which wind-level can overcome the horizontal restoring ability of the ribbon, then, as long as wind persists, horizontal and vertical displacements will simply continue to progress (at least until new geometrical mechanisms come into play to inhibit it).

Viewed in 2-D High Altitude

Climber @LEO, Cat 0 wind

Climber @LEO, Cat 0 wind, 5 cm Ribbon

- In this animation the Climber’s position (initially at about 370 km alt.) is clearly seen as the sharp bend in the ribbon becoming evident about halfway through the movie.

- The climber is observed to be drawn continually downward in altitude as the wind builds; this is possible because the exceedingly low spring rate of the upper ribbon presents little to inhibit downward pulling tendencies.

Viewed in 2-D High Altitude

Climber @LEO, Cat 0 wind, 4 hr peak wind

Climber @LEO, Cat 0 wind, 5 cm Ribbon, 4 hour peak wind

- This illustrates that as long as the wind is at peak value, the horizontal displacement does not reach equilibrium but rather continues to grow.

- Here the earth's limb is shown to give a sense of perspective of the extent to which ribbon is being laid out near the earth's surface. As the wind subsides it is seen that a slackening ribbon may well pay a visit to King Neptune.

Viewed in 2-D Medium Altitude

Climber @LEO, Cat 0 wind, 2 vs 4 hr peak wind

Climber @LEO, Cat 0 wind, 5 cm Ribbon, 2 -vs- 4 hour peak wind'

- The ribbon trace (red) at its greatest downrange displacement shows an artifact of the animation's being displayed in a cartesian frame that does not reflect the curvature of the earth, which over a 300 km range represents a significant drop in altitude (relative to a horizontal plane through the anchor point)

Viewed in 2-D High Altitude

Climber @LEO, Cat 2 wind

Climber @LEO, Cat 2 wind, 5 cm Ribbon

- The climber's location is clearly seen being drawn down in altitude significantly as the Cat 2 wind has its way with the ribbon displacing it horizontally.

Viewed in 3-D Perspective FULL Altitude

Climber @9km, Cat 0 wind

Climber @9km, Cat 0 wind, 5 cm Ribbon

- The climber's location is obvious in this animation, and the fact that it is parked at an altitude for which the full effects of wind are felt is also notable.

- The vertical and horizontal scales are identical in this animation so a realistic picture of the near-surface ribbon geometry is shown; it can be seen that the climber, even though it was initially at 9 km, ends up near 1 km altitude.

Viewed in 2-D (true linear scale) Low Altitude

Unoccupied vs Climber @9 km, Cat 0 wind

Unoccupied vs Climber @9 km, Cat 0 wind, 5 cm Ribbon

- A climber in the atmosphere is shown to significantly amplify the effects of wind. Comparing the two ribbon shapes, they look similar because the altitude of the climber is very near the earth's surface on the vertical scale of this animation (compared to the previous animation that shows low altitude details of climber response).

Viewed in 2-D High Altitude

Unoccupied, Cat 2 wind

Unoccupied, Cat 2 wind, 5 cm Ribbon

- This full altitude perspective view of a Cat 2 wind encounter shows how atmospheric disturbances propagate the entire length of the elevator. Note the highly exaggerated horizontal scale of this animation; the actual libration angle at the ballast due to this wind is on the order of 0.2 degrees.

Viewed in 3-D Perspective FULL Altitude

Unoccupied, Cat 3 wind

Unoccupied, Cat 3 wind, 5 cm Ribbon

- This full altitude view of a typhoon encounter shows details of atmospheric disturbances propagating the entire length of the elevator. Note the highly exaggerated horizontal scale of this animation; the actual libration angle at the ballast due to this wind is on the order of 0.5 degrees.

Viewed in 2-D FULL Altitude

Discussion of Results

There were two general elevator behaviors exhibited in this study that bear specific discussion: (1). the absence of over-stress to wind loading even with resultant large horizontal displacements; and, (2). the apparent ease with which the wind could drive the ribbon out horizontally.

The absence of over-stressing can be attributed to a combination of the following:  

1. The overall ribbon has an extremely low effective end-to-end spring rate at earth on the order of .04 N/m. This mean that relative to local atmospheric disturbance, the ribbon can tolerate a significant amount of elongation without significant rise in tension.
2. A ribbon departure of even 200 km downrange, while appearing significant from an anchor-station viewpoint, and presenting a bizarre ribbon departure of near horizontal, in fact represents a minimal increase in overall strain of the 100,000 km long ribbon.
3. The fact that stress wave propagation time (approximately 1 hour to travel 100,000 km) is very short compared to the time it takes a strong wind to build up. This effectively defuses the possibility of localized stress at the source of the disturbance by quickly propagating stress gradients upward along the entire length of the ribbon, distributing strain.

Understanding the propensity for the wind to blow the ribbon horizontally downrange can be attributed to the aerodynamic model and the ribbon geometry as it yields to the relative wind. In order for the ribbon to sustain horizontal displacement, it is necessary for the vertical and horizontal components of air load to equilibrate respectively the vertical and horizontal components of ribbon tension. The aerodynamic source for this equilibration arises over a region of essentially uniform curvature as the ribbon departs the horizontal and proceeds upward to vertical.

The aerodynamics model used in this study predicts that if the relative wind has any component normal to the ribbon, then a pressure against the ribbon results, and a force normal to a tangent to the ribbon results. The vector-integral of this force distribution provides the required horizontal and vertical force components.