User:Yakushima/AerovatorMT

(N.B. concept and most of the writing courtesy of Andreas Windemuth.)

The Aerovator is a transorbital megastructure for launching payloads into Earth orbit and beyond. It consists of a long ribbon rotating around a central hub on the Earth's surface. Aerodynamic lift elevates the ribbon above the atmosphere, allowing the outer parts to attain orbital velocity in near vacuum.

The Aerovator is related to the Space Elevator and the Rotovator, in both its purpose and its construction. The idea for the Aerovator developed in May 2006 in a discussion on the Yahoo Group on space elevators, and does not appear to have any known history before that.

Vertical Profile

Schematic of the aerovator in the baseline configuration. Two arms are only shown to indicate rotation. The baseline configuration has only one arm

The vertical profile of the Aerovator can be divided into two parts: The ascent section and the skim equilibrium section.

Ascent section

The ascent section is the innermost part of the aerovator and extends from the hub at the Earth's surface up to the upper atmosphere. It should be as short as possible to avoid excessive drag. The aerovator is kept in motion by pressure applied to the propulsion point. Calculations on the horizontal profile (see below) tell us that the propulsion point should be more than 20 km out from the hub (Mach 0.5), and less than 40 km (Mach 1). The altitude of the propulsion point should be low enough for efficient jet propulsion, say at the cruising altitude of a Boeing 747 aircraft (12 km). The ascent needs to be steep enough for the decreasing air pressure to balance the increasing speed enough to keep drag low. If possible, the ascent also should be shallow enough to allow the payload to slide upwards from centrifugal force alone.

Skim equilibrium section

At 100-200 km out, the ribbon extends high enough to settle into a skim equilibrium, i.e. its altitude at any point is the highest possible while retaining enough lift to carry its own weight. This simplifies the math significantly, because now we can assume lift equals weight, and drag equals lift/Cld (Cld: lift-to-drag ratio). The skim altitude increases from 60 km to more than 100 km as speed increases further out from the hub. Because of the Earth's curvature, the centrifugal force increasingly helps lift the ribbon, such that the net weight and thus lift and drag are reduced and become zero as the radial velocity approaches orbital. The preliminary calculations described below indicate that the power dissipation caused by drag does not exceed 1.5 W/m at skim equilibrium. Thus, the low air density sufficiently offsets the high velocity (up to Mach 24) for thermal load to not be a significant problem.

Horizontal Profile

Schematic of the horizontal profile of the aerovator. The profile is determined by the requirement of pure tensional load. To support the aerodynamic drag, the ribbon must curve with the concave side forward everywhere, except at the propulsion point

The horizontal profile is what the Aerovator would look like from above. The ribbon path is a balance between centrifugal force, drag, propulsion force, and ribbon tension. The section between the hub and the propulsion point is essentially a straight line, with some forward bending due to drag. At the propulsion point, the ribbon bends sharply back under the propulsion pressure. From the propulsion point on out, the ribbon bends forward again until it straightens out to the radial direction at the tip.

To derive the shape mathematically, we use a simple finite element approach. We look at each element of the ribbon in turn, starting with the tip. Each element has two external horizontal forces acting on it: centrifugal force and drag. We know the former from kinematics ($r\omega ^{2}$), and the latter from the skim equilibrium. To be balanced, these forces must be exactly opposite to the difference in tension between the previous element and the next. Because we know the forces, we can recursively calculate the tension for each element in turn. Because we do not allow shear, we can also calculate the angles between successive elements and thus the path of the ribbon. Because of drag, these angles will be non-zero, and the path of the ribbon will bypass the hub. The point of closest approach to the hub is the lever point, i.e. the closest point to the hub where the ribbon can be propelled. An attempt to drive it closer to the hub would result in it wrapping around. At the propulsion point, the ribbon bends around almost 90 degrees to sustain the driving force and then goes in a nearly straight line to the hub.

Baseline Properties

The following are reasonable properties of one particular configuration of the Aerovator. The numbers are based on a finite element simulation of only the horizontal profile, assuming that the lift/weight equilibrium holds throughout the whole length. This assumption is not strictly true, since the inner part of the aerovator needs to traverse the lower atmosphere. For now it is assumed that this part moves slowly enough, and rises steeply enough, to keep its contribution to total drag reasonable.

Property	Value
Length	1,000 km
Rotational period	13 min
Tip speed	8 km/s
Tip acceleration	4.9 g
Hub location	Earth's surface
Material strength	6 Gpa
Total mass	240 tons
Propulsion mode	Jet engines, detachable tug-planes
Propulsion location	20 km from hub
Propulsion airspeed	Mach 0.5
Propulsion force	5 Meganewton (about 20 Boeing 747 jet engines)

Aerodynamic Stability

Schematic of a small segment of the aerovator and the forces acting on it.

Forces acting on an aerovator ribbon segment, in polar coordinates, in a rotating reference frame.

(Image: Schematic of a small segment of the aerovator and the forces acting on it.)

The ribbon must be aerodynamically stable, i.e. orient itself by aerodynamic forces alone to present the optimal angle of attack for lift. This will most likely require the addition of stabilizers, e.g. very light feathered rods that extend downwind and are attached to the ribbon at the proper angle. The strong tension along the ribbon will provide structural integrity, otherwise the problem of stability is similar to that well-known from aircraft design.

Payload Launch

There are two possible modes of payload launch: clinging and free. In both cases, the payload vehicle is attached at the hub, moves outwards from there and detaches after reaching the desired velocity.

The clinging payload grabs onto the ribbon and moves outwards at a low, controlled speed. It gains the desired velocity (up to 8 km/s) from the tangential ribbon velocity alone. A set of wheels and a braking mechanism is sufficient to hold the payload to the ribbon, much like an aerial tram.

A free payload can move freely in the radial direction, and will be accelerated outwards by the centrifugal force. It can reach up to 11.2 km/s, and does not need braking, but it will require a special high velocity, low-friction attachment to the ribbon. Magnetic, gas cushion, or solid (ice?, teflon?) low-friction interfaces need to be explored as engineering solutions.

The need for the aerovator to rise up out of the lower atmosphere as close to the hub as possible may make it necessary to power the payload during the very first part of its trip while the centrifugal force is insufficient to overcome the gravitational force due to the uphill path.

Deployment

As opposed to other space transportation infrastructure projects, the Aerovator can be deployed entirely from the Earth's surface. The ribbon is played out from the rotating hub and lifts itself up aerodynamically as it is extended. The hub will need to rotate much faster initially than in the fully extended state, and the propulsion point will move outwards during extension. Deployment will put some additional constraints on ribbon design, which needs to be investigated.

Maintenance

The baseline version features tug-planes which dock to the ribbon for propulsion and bring their own fuel, leaving the ribbon no more than a thin strip of very strong paper. The ribbon can therefore be thought of as an expendable component of the system, and maintenance consists of regularly dropping and redeploying the ribbon.

Failure modes

The principal failure mode is severance of the ribbon. Parts of the ribbon would tangle up, lose lift, drop into the lower atmosphere and either burn up from increased air friction or flutter to the ground. No serious danger to personnel, structures, or the environment would be expected. Human transport vehicles would have to be equipped with heat shields and parachutes to allow a safe landing after ribbon severance or premature detachment.

Comparison with Space Elevator

The aerovator is a launch contraption, one of a large number of devices that have been proposed to cheaply launch payloads from Earth into space. The launch contraption with the longest history and one of the most advanced in the literature is the space elevator. Here is a list of advantages or disadvantages of the aerovator compared with the space elevator (SE), with the relative disadvantages marked in red:

Property	Space Elevator	Aerovator	Notes
Size	around 60,000 km long	1,000 km	Mass comparable
Required tensile strength	50-100 GPa	around 5-10 GPa	Zylon purportedly has an ultimate tensile strength of 5.8 GPa
Other unrealized technology	drive train, power beaming	none
Theory	very easy to describe mathematically and model	aerodynamic modeling more complex	Aerovator modeling requires many more variables
Location	Needs to be close to the equator	Can be anywhere, but covers much wider area
Deployment	Needs to be deployed from space, built up in a long process	Can be deployed from Earth-based hub in finished form
Space traffic	Needs to actively avoid satellites and orbital debris and be resistant to micro meteorites and atomic oxygen	Flies too low to be much affected by at least some of these
Reach	Can directly reach GEO and escape velocity, but needs additional rocket propulsion for LEO (2-3 km/s)	Can directly launch into LEO and escape, but needs some propulsion for GEO (1-2 km/s)
Travel time	A week or so to get anywhere	Can get to LEO in less than an hour, and GEO and escape in a few hours
Human transport	Problematic because of travel time and exposure to radiation belts	Safer and faster than rocket launch
Payload acceleration exposure	Not necessarily beyond 1 g (depending on climber velocity range)	Peaks at 5 g in baseline configuration
Throughput	Can launch one payload every few days	Can launch a similar payload (compared to its weight) every hour or so
Payload propulsion	Requires climbers to hoist up the payload vertically at high speed; drive train must have a specific power not currently feasible; power must be transmitted by laser beaming technology not currently in existence	Uses centrifugal forces thus needs no power, except possibly small amount at beginning near hub
Device propulsion	Needs propulsion only to avoid space traffic or debris	Energy required to keep rotating, about as much as needed by 10 airliners (baseline configuration)
Stability	Stationary with respect to the Earth and stable, like a bridge	Requires aerodynamic stability, like an airplane
Economics	More expensive to build	More expensive to operate	Throughput, travel time, human transport, and reach should make the aerovator more economical. The political economy of large-scale space projects would favor the aerovator.

Frequently Raised Objections

At this point, the aerovator is a new proposal with little history, meaning that it will encounter a large amount of healthy skepticism. The following is an incomplete list of frequently raised objections with attempts to briefly address those that are easily addressed.

• "It won't work."

Before you conclude that it just won't work, please do or imagine the following experiment: Grab a chain, hold one end in your hand, and start twirling it around. This demonstrates the essence of the dynamics of the aerovator, with all the essential ingredients except for lift. If your objection says this is impossible, think again. We will refer to this as the "chain experiment".

• "No material is stiff enough"

Like the chain in the chain experiment, the aerovator needs no stiffness whatsoever.

• "The horizontal profile will be a spiral, rather than that drawn in the illustration."

While this can be answered by looking at the result of calculations, it is not always certain that the calculations are correct, and it is worthwhile to try to deduce at least some properties of the shape by physical principles alone, if only to check the validity of the calculations. The shape of the ribbon is tightly limited by two principles:

• Lag -- At each point in the ribbon, the tension must exactly balance all of the forces acting on the entire outwards part of the ribbon. Horizontally, there are two such forces: Centrifugal force and drag. The former is radial, and the latter tangential, pointing backwards. To balance, the tension needs to point partly forward. Since there is no stiffnes, this means the ribbon needs to lag along its entire length, i.e. the direction of its path needs to have a positive angle with the radial direction everywhere. This is what causes the common misconception that the ribbon must be a spiral.
• Bend -- At each element of the ribbon, the forces acting on the element have to add up to zero. Horizontally, these forces are centrifugal force, drag, and the two tension vectors at each end of the element. Drag is pointed backwards, which means that the sum of the tension vectors needs to point forward. That means the tension vectors form an angle bending in the forward direction. Because both tension vectors must be parallel to the ribbon path, the ribbon path must curve with the concave side facing forward. This is analogous to a horizontal hanging chain, where the combination of curvature and tension counteracts the gravitational force to keep the chain suspended. This curvature is opposite to that of the spiral that most imagine after realizing the lag requirement.

The combination of these two principles leads to the shape shown in the horizontal profile schematic above. The results of the finite element calculation confirm this as well.

• "The ribbon will flutter, vibrate, resonate, etc. etc."

This is of course an important consideration, and requires much modelling to address properly. The issues are similar to those of the space elevator. The aerovator could fare better because it is shorter and because of atmospheric damping of oscillations. Or, it could fare worse, because the dynamic air drag provides many possibilities of feeding vibrational modes. There is hope, though, because the issue is successfully addressed in airplanes, and the aerovator is really just a gigantic airplane flying in circles.

• "There is no such thing as centrifugal force."

Let us at this point acknowledge for the purist that, indeed, there is no such thing. However, the entity of that name is a very useful construct when working in a rotating frame of reference and is indistinguishable from a true force. We will therefore use the term as if it were a real force, to simplify the discussions.

References

• Google groups discussion