# Could a rotating skyhook use a sail or wing to make orbital corrections to keep the structure in orbit?

Imagine a rotating skyhook with the majority of its length in the thermosphere, but whose hook side (as opposed to the counterweight side) has the ability to deploy wings or sails. Suppose that orbital and rotational parameters were chosen such that when the hook dips into the atmosphere, its translational velocity is similar to the average velocity of the local air currents - like a moving car's wheel rotating over the ground with static friction. Since wind currents vary, there would usually be a small (compared to orbital velocities) difference causing the hook side to experience winds. Now, obviously, we must be clever about which wind tool we choose and when we deploy it and how we trim it, but in principle, could there be enough available $$\Delta V$$ to counteract the loss in momentum from hurling payloads further into space?

While the question of a solar sail could change this calculus, I'm specifically asking about wind sails, kites, wings and other structures that would interact with the upper atmosphere.

Edit:

As you can see, a boring old wing acting directly against the tether with no wind helping would have a significant forward force component until nearly verticality. At this point, the wings would be either trimmed to reduce drag or deflated and reeled in. Naively, a downward force on the body acts in the wrong direction, but trading altitude for speed could actually help if one were clever about the timing and ellipticity. This and similar maneuvers could be repeated as needed to regain orbital velocity, rotational velocity and altitude until the next launch.

Supposing the tether releases its payload at the top of its arc (when the payload's velocity has no vertical (earth radial) component), the tether would then be moving more slowly than the atmosphere by some amount, and there would be an expectation of tailwinds on hook re-entry. To take advantage of these, the tether could deploy a boring old sail in addition to the wing.

• I think the atmosphere end could only exert a force down and opposite the orbital velocity because of the tether, you can't push a rope and move the counterweight up and forward. But I'm not 100% certain, so no answer, these dynamic orbital systems are complicated and give me headaches. Commented Jan 23 at 21:07
• @JoshKing People can walk (impart translational movement) while spinning a sling (including changing the rate of rotation). As the hook enters the atmosphere, a tensile force would have a substantial (orbitally) forward component. Commented Jan 24 at 8:23
• Put simply, no. You can only sail against the wind because there's something to push off of. In this case, since there's nothing to push off of, you can temporarily increase the speed of the hook through "tailwind" on a sail, but this will decrease the overall velocity of the system. Commented Jan 24 at 14:55
• @Dragongeek I believe you're referring to tacking which does indeed benefit from a keel. I would probably only use that sort of sail for latitudinal corrections. See the edit for a diagram of how catching a tailwind would impart orbital velocity to the tether. Commented Jan 24 at 18:50
• @user121330 see my answer. Tailwind cannot impart orbital velocity on the tether, because while it could speed up the hook, this would slow the angular velocity of the entire hook as it spins in the opposite direction. This results in a slower spinning tether, so a net loss of energy in the system Commented Jan 25 at 8:39

I'm not quite sure what you're asking, but the answer is no.

I've drawn a (grossly) simplified diagram to help me explain:

I've simplified a bit, but the skyhook does not fall to the ground because $$F_C$$, the centripetal "force", is equal to $$F_G$$, the force that gravity exerts on the skyhook. Here the "force" $$F_C$$ depends on $$V_O$$, which is the orbital velocity of the center of mass of the skyhook. If the orbital velocity, $$V_O$$ decreases, this means that $$F_C$$ would also decrease, bringing it out of balance, and causing the orbit to lower, potentially into the atmosphere and causing it to crash to Earth.

If the skyhook is rotating, indicated by $$\omega_{SH}$$, you can find a speed where $$V_H$$ is equal to zero relative to the ground once per revolution. Observed from the ground, the hook will come to a complete stop at the lowest point, and then accelerate, reaching maximum velocity (2x $$V_O$$) at the top of the rotation. This is the cycloid curve that's on the wikipedia page for rotating Skyhooks.

Now, if I understand you correctly, you want to apply some sort of force at the hook end of the skyhook.

The problem is that this drag force will decrease $$\omega_{SH}$$ and/or reduce $$V_O$$, both of which result in net energy loss of the system. There's no free lunch here: you can only do "trades":

For example, if you have a long tether in space and would like to "spin up", you could dip the hook end into the atmosphere with a "sail". This would essentially be trading $$V_O$$ for $$\omega_{SH}$$: your skyhook starts to spin, but gets slower overall.

Technically the answer is yes. A skyhook can be a cable that is slightly shorter than full space elevator, such that it dips into the atmosphere, yet is not anchored to the surface. Like a space elevator, it can also be made to rotate at the same rate as the Earth - once every 23 h 56 min 4.0905 sec. A sail at the lower end could help to give it energy and raise its orbit. With such a skyhook a sail or wing could make orbital corrections to keep the structure in orbit, since the winds will be able to push on the sail or wing and since this particular skyhook is not going to experience a lot of orbital decay or need a lot of corrections.

The reason this works is that we are maneuvering within an already inherently stable operating regime. Since the air currents will vary and will travel at a different speeds than the lower tip of the skyhook, there is an velocity differential that a sail or wing can take advantage of.

But, almost every other kind of rotating skyhook will not operate within an inherently stable regime. They will experience orbital decay - especially if they are constantly losing energy to lift payloads into higher orbits.

For these, it seems like it should be impossible to tap the wind's energy to make orbital corrections and replenish lost energy - but technically it is still possible.

To understand why, first image that we replaced the spinning skyhook with a spinning ring. Then it should be easier to see that a if one pushes up on one part of the ring while simultaneously pulling down on another, it will be possible to make the ring spin faster. Also, that the places where we push and pull can both be locations within the atmosphere.

It should also be apparent that wind can be used to apply pushing and pulling forces, as we are quite familiar with the concept of using sails and wings in an airstream to generate forces.

If the part of the ring in the atmosphere is travelling horizontally at the average windspeed, then, since windspeed and direction varies, it will sometimes experience a more east-west wind and sometimes it will see a more west-east wind.

If the ring deploys wings into the airstream and sets their angle of attack appropriately for the wind direction, these wings can apply the upward and downward push and pull forces needed to add energy to the ring. Because the relative wind direction will change from east-west to west-east and back again, the ring's rate of rotation can be maintained.

Therefore, it is possible to add energy to maintain the orbit of a ring while maintaining the ring's average rate of rotation.

Is it also possible for a ring with spokes? Yes, it is. Is it possible for a partial ring with just four spokes? Yes, still possible.

(not to scale)

Is this a "rotating skyhook"? Yes, I think what we're left with here can be classified as a rotating skyhook.

The question of whether more energy can be added than will be lost will depend on a variety of design decisions, wind patterns, and on the rate at which the skyhook it is used to launch payloads. But, the idea of an entirely wind-powered skyhook is at least plausible enough to be interesting.

When the wind is right-to-left, the wings are deployed as shown in the first figure (below) to generate a counter-clockwise torque on the skyhook.

When the wind is left-to-right, the wings are deployed as shown in the second figure (below) to generate a counter-clockwise torque on the skyhook.

• I don't see how any interaction with the atmosphere can result in net energy gain of the system unless you start ignoring forces. The energy of the wind can only be exploited by providing a counter-force. Windmills use their solid connection to the Earth, sailboats use their hull and keel to push against the water. Even the wacky cars that can drive up-wind using only wind power push against the earth through their wheels. Any interaction despite potentially being locally "positive" would result in net orbital velocity decrease. Commented Jan 26 at 11:44
• The counter force that you're wondering about is the inertia of the skyhook. I added two more figures to the answer to help illustrate. Keep in mind that the wind is assumed to alternate between left-to-right and right-to-left, relative to the lower end of the skyhook, over time. Inertia can be exploited as a counter force. For example, inertia is exploited for dynamic soaring Commented Jan 27 at 3:31
• Yes, you can "push against the inertia" of the moving skyhook, but this isn't a free lunch. By doing so, you are decreasing orbital velocity. In dynamic soaring, the wings transfer momentum into the still wind below the shear line to realize the maneuver. I don't think that a technique like dynamic soaring would work if one side of the loop is vacuum. Commented Jan 27 at 6:10
• Dynamic soaring was only mentioned to address your comment. It demonstrates that you don't need "a solid connection to the earth" or "keel to push against water" to exploit wind power. Other than that, it has no connection to the provided answer. The answer explains how to use winds to increase orbital velocity. I can't deduce the reasoning behind your opposite statement, "Yes ... by doing so you are decreasing orbital velocity". Commented Jan 27 at 7:05
• Airfoils conventionally have a lift and a drag component, and you are only considering lift. If you were to include the drag component, there are two scenarios: In your right-to-left scenario, the drag force would point towards the left and thus have a far larger lever arm / torque in the opposite direction of the rotation, slowing the skyhook. In your left-to-right scenario, the drag force would point towards the right, which would be pointing opposite of orbital velocity resulting in net velocity loss Commented Jan 27 at 8:48

Answer: Nice try, but this strategy is unlikely to work.

Note: I will assume that "Skyhook" refers to architecture similar to the HASTOL study: A tether rotating prograde in a circular equatorial orbit. I will focus on angular momentum (which is conserved) rather than kinetic energy (which is not).

Since the Skyhook is moving faster than the Earth’s surface, and drag always occurs counter to the direction of relative motion, any interaction between a Skyhook and the atmosphere will transfer angular momentum from Skyhook to the Earth. Depending on the rate of rotation and tether length, this momentum may come from the Skyhook’s orbital momentum or its rotational momentum or both.

Total angular momentum is always conserved. In a Skyhook system, this total angular momentum can be exchanged between

• The Earth

• Skyhook orbital momentum

• Skyhook rotational momentum

Payload launch involves transfer of Skyhook angular momentum to the payload. Following a launch, the Skyhook has a lower orbit and slower rotation.

Could a … sail or wing… make orbital corrections to keep the structure in orbit?

The strict answer to the title question is YES, but at the expense of lost rotational momentum. However, keep in mind that staying in orbit is not the end objective, launching payload is.

If the Skyhook rotation is fast enough that the grapple end is moving in a retrograde direction through the atmosphere, lift could increase the Skyhook’s orbital velocity. However, this maneuver comes at the cost of transferring angular momentum from Skyhook rotation to Skyhook orbital momentum. Total Skyhook angular momentum (orbital + rotational) has not increased, so neither has future launch capability.

However, during the maneuver, the wing has "pushed against the atmosphere", transferring some momentum from Earth to Skyhook. So the Skyhook could potentially have a net gain in angular momentum, despite rotational momentum lost to the Earth through drag.

could there be enough available ΔV to counteract the loss in momentum from hurling payloads further into space?

The devil is in the details. Can the micro effects of wing forces overcome drag to provide the macro amounts of angular momentum needed to launch payloads?

Bottom line: I suspect that no matter how clever you are with angles of attack and vectors, any contact between Skyhook and atmosphere causes angular momentum to be lost to the Earth.