# What fraction of Terminator Tape™'s drag comes from interaction with Earth's magnetic field as a function of altitude? Is it ever important?

This answer states that Terminator Tape™ uses the Earth's magnetic field to generate drag to shorten the deorbit time of a spacecraft in LEO. It links to https://sst-soa.arc.nasa.gov/12-passive-deorbit-systems which shows both Roll-Out DeOrbiting device (RODEO) which is a metalized film but uses aerodynamic drag, and Terminator Tape™ which is also a metalized film that acts as a "electromagnetic tether".

Looking at the abstract of The Terminator Tape™ : A Cost-Effective De-Orbit Module for End-of-Life Disposal of LEO Satellites it says

This tape will not only significantly enhance the aerodynamic drag experienced by the system, but will also generate electrodynamic drag forces through passive interactions with the Earth’s magnetic field and conducting ionospheric plasma, de-orbiting the satellite within 25 years.

Question: So Terminator Tape™ definitely provides aerodynamic drag, but what fraction of the drag it provides comes from interaction with Earth's magnetic field? Atmospheric density decreases exponentially with altitude and Earth's dipole field varies much more slowly as $$1/r^3$$ where $$r$$ is the distance from the center of the Earth, not the surface, so this fraction will definitely be altitude dependent and aerodynamics will always win at the end.

"Bonus points:" If Roll-Out DeOrbiting device (RODEO) doesn't use currents induced by Earth's magnetic field, why is it still metalized? (that could also be a supplementary answer to Why is “Terminator Tape” electrically conductive?).

Note that just dragging a long conductor in very slowly varying field does not generate much drag, the tape must support an electrical current and that means it must constantly emit electrons from one end and recover electrons from space at the other in order to generate drag. Read more in Tethers Unlimited's Cost-Effective End-of-Mission Disposal of LEO Microsatellites: The Terminator Tape

For comparison, here's an image of Roll-Out DeOrbiting device (RODEO) from here.

Figure 12.5: RODEO stowed. Image Courtesy of Composite Technology Development, Inc.

Composite Technology Development, Inc. has developed the Roll-Out DeOrbiting device (RODEO) that consists of a lightweight film attached to a simple, ultra-lightweight, roll-out composite boom structure. It was successfully deployed on suborbital RocketSat-8 August, 2013.

AAC-Clyde collaborated with the University of Glasglow to construct the Aerodynamic End-of-Life Deorbit system for CubeSats (AEOLDOS), where a lightweight, foldable “aerobrake” made from a membrane is supported by boom-springs that open the sail to generate aerodynamic drag against the upper atmosphere.

• – uhoh Jan 24 at 7:48

## 1 Answer

In the linked AIAA article, the bottom of page 4 (excerpted below) estimates numbers for a 250 m x 0.28 m tape. When 700 km high, electrodynamic drag and aerodynamic drag are both about 15 μN. Higher up, electrodynamic drag dominates.

To generalize this, into equation (4) plug in values for tape width w, a bunch of numbers ∆V me mi that I don't know how to estimate, and look up tables of plasma density n and magnetic field strength |B| as a function of altitude. Infer orbital velocity from altitude.

That's an awful lot of handwavium between the inputs and the outputs, though. The paper's authors resorted to "TEMPEST" simulation software, which has been described as

a nonlinear five dimensional (3d2v) gyrokinetic continuum code for studies of H-mode edge plasma neoclassical transport and turbulence in real divertor geometry.

I used to have one of those, but the wheels fell off.

• Thanks for your answer. I can't find a hold of a copy of this paywalled paper and most other readers won't be able to either, so all we'll know about this is what you choose to write here. Is it possible to at least include Equation 4 here and a description of its variables? – uhoh Jan 24 at 21:55
• if regenerating everything is a challenge, even a screenshot of a page would e most welcome, thanks! – uhoh Jan 24 at 22:17
• The screenshot of the relevant section is sufficient; I think I see a problem. It seems that it is saying that at 700 km the limiting factor is not the magnetic field strength, it's the ability to support the current flow that it would induce because of the dearth of ions available to accept electrons. They are using the entire area of the long strip as the collection surface to estimate current, but of course as I pointed out in the question you need to emit the electrons at one end and receive electrons at the other end in order to make full use of the current to generate a drag force. – uhoh Jan 25 at 0:02
• However if they at least collect electrons preferentially at one end while emitting them uniformly along the length, then it still works, it's just that the effectiveness is reduced by roughly half. Does the paper state how they collect electrons and how localized that is? – uhoh Jan 25 at 0:12
• The paper says nothing about how electrons or ions are collected or dissipated, nor about their distribution along the strip, so the process may be entirely a side effect of the induced current. I bet that the current varies along the strip. There sure isn't any Van de Graaff generator hiding in there! – Camille Goudeseune Jan 25 at 17:13