Momentum Exchange Space Tethers

14 years of research at Edinburgh & Glasgow Universities

Matthew P. Cartmell

Department of Mechanical Engineering University of Glasgow G12 8QQ Scotland, UK.

1 st Scottish Space Systems Symposium

Momentum Exchange Space Tethers

US Naval Research Lab –

TiPS

on 20/06/96, Ralph (lower) and Norton (upper) joined by a 4km tether - the Tether Physics and Survivability Experiment.

• • •

Tsiolkovsky (1895)

– proposed exploitation of gravity gradient force for an elevator, and rotating structures for artificial gravity

Tsander (1910)

– suggested the use of a tapering cable to connect the Earth and the Moon

Artsutanov, Isaaks, and Pearson (1960s)

– re-invented the space elevator • • • • • • • • • • Gemini 11 & 12 – 1966 Oedipus A – 1989 TSS1 – 1992 SEDS1 – 1993 PmG – 1993 SEDS2 – 1994 Oedipus C – 1995 TSS1R – 1996 TiPS – 1996 ATEx - 1998

Team members and their projects (1998-2010)

Postdoctoral RAs: Dr Cristina D’Arrigo – Inertial parametric excitation of momentum exchange tethers Dr David I.M.Forehand – Analytical model and solutions for a librating MMET Dr Olga A.Ganilova – Payload soft landing dynamics Ph.D. Students: Dr Spencer Ziegler – MMET tether dynamics Dr David McKenzie – MMET tether dynamics & Space Web models Dr Christopher Draper – MMET risk & lifetime analyses, Dr Leo Yi Chen – MMET tether dynamics and control (discrete models) Christopher Murray – MMET Earth Moon mission architectures Norilmi Ismail – MMET tether dynamics (continuum models) M.Sc. Students: Gao Ji – Operational power budgets for MMETs Edith Mouterde – Simone Lennert – Feedback linearisation control simulations for MMETs Tether brake systems Claudia Gandara – Payload de-spin dynamics 1 Prabhanand Peerupalli – Payload de-spin dynamics 2 David Neill – Payload de-spin design concepts 1 Allan Barr – Payload de-spin design concepts 2 Amir Mubarak – Llewellyn Price – Gyratory propulsion systems 1 Gyratory propulsion systems 2 Ali Razavi – Payload soft landing dynamics David Dupuy – Design and material selection considerations for multi-line tethers

TiPs mission – 20 June 1996

Norton 4 km Tether Ralph Ralph & Norton - Ralph Kramden and Ed Norton, two US comedians who starred in the 1950s show

The Honeymooners.

Payloads connected together by a 4km tether to test gravity gradient stabilisation and libration effects.

Research Timeline 1981-2001

Edin. Univ. Abdn. Univ. Swan Univ. Edin. Univ. Glasgow Univ. 1981 Unstable beam – accident!

1983 1987 oscillators.

1991 Expt. verification Theoret. Models of energy flows through paramet. 1994 1995 1996 ‘Rotators’?

Q: can we scale up such systems?

How much?

Optimising KE?

In space?

- motor drive?

‘slingshot’ concept 1997 - Scale ESTEC contract #1 - Application #2 - Materials MMET – modelled!

1998 First Ph.D. student on ‘tethers’ – S.W.Ziegler

Publication: JSV, 2001 Definition of new combination instability in a parametrically excited beam  = ½(  B1 +  B2 ) Watt & Cartmell, ‘An externally loaded parametric oscillator’ Response to ESTEC call for ‘novel space propulsion concepts’ ESTEC contract #3 ‘Staging’ ‘Space Tether’ - Scale Model!

- re-invented yet again? Partly, but with refinements!

Symmetrical Motorised Momentum Exchange Tether

Research Timeline 2002 2008, and beyond…

Glasgow University ….. 2002 ‘Project Aurora’ propulsion technology roadmap – MMET included!

2005-2009 Thales-Alenia Aerospace contracts - 3 2002 Royal Society award and SSE participation.

2005-2006 Earth-Moon architecture 2006-2007 Space-Webs 1998-2008 -Deployers & brakes -Para. Ex, tether 2007-2009 Earth-Mars architecture -Continuum model -Control sims ‘Gyrator’ concept -SMAs & tethers Case1 : 1,2,3 Walk along the edges from sub span to next sub span symmetrical 100 50 0 -50 -100

Fundamentals

sub-span 2,

l

sub-span 1,

l

Propulsion Tether Outrigger tether E

V

0 

l



V

0

V

0 

l

  A Space Tether on an orbit around a planet will tend to ‘hang’ if left undisturbed. This is called Gravity Gradient Stabilisation (GGS) . A small tensile force is induced by this in the tether, causing it to appear to have some of the qualities of a rigid body.

This shows a Motorised Momentum Exchange Tether (MMET) on a circular Earth orbit. The motor raises the energy level in the system and overcomes GGS and perturbational effects to generate a spin. It is this spin which can be used for propulsion of the payloads.

If

V 0

is arranged to be around 7.62  km/s, then the outer payload will be at 10.77 km/s - and able to ESCAPE! This is using a tether for interplanetary transfer!

Gravity Gradient Stabilisation

An object of mass

m

, and radial position

r

Earth is subjected to a gravitational force: from the centre of the Earth, which is orbiting the

F

G

  

m

2

u

r r

The inwardly acting centripetal force on the body, due to its orbital motion, is given by:

F

C mr

2

u

r

CoM

r 0 z r

CoM

z r r 0

(1) Outer case (2) Inner case

r = r 0 + z r = r 0 - z F G



F C

at

r



r

0 At CoM:  

m r o

2  

mr

0  2    2

r

0 3   (1) Outer case

r F G F Zout

 

r

0

F C F Zout F G

 

F C

3

mz out

 2

r

  0   2   (

r

0

F Zout



z out

  )  

m

(

r

0

r

2 

r

0 3

z out

) 2

z mr

  for ‘short’ (2) Inner case 

F Zin

  3

mz in

 2 tethers!

F Zout

[Cartmell (2006)]

Dumb-bell Tethers in 3 Dimensions

In this early model (1996-1998) a ‘spin plane’ was defined whose inclination relative to the equatorial orbit plane was defined by

α

. The angular spin coordinate is

ψ

. This modelling concept was superseded by a ‘projected spin’ coordinate, together with an inclination

α

. Both coordinates are required to define spin fully.

E denotes the centre of the Earth and CoM is the centre of the tether – the location of the ‘facility’ which contains the motor drive, power supplies, controls, telemetry, etc.

[Cartmell (1996-1998), Cartmell & Ziegler (1998-1999)]

Generalised Coordinates:

R – length of position vector from E to CoM



- tether spin coordinate projected onto the ‘tether plane’



- angular coordinate denoting out-of-plane orientation of tether θ – true anomaly i – inclination of tether plane to Earth equatorial plane γ – roll coordinate (along tether’s long axis)

Modelling of the MMET in a non-equatorial Earth orbit γ E

R

5 scalar equations of motion – nonlinear ODEs Motor Drive excites equations in  and 

.

[McKenzie (2004), Cartmell, McKenzie, McInnes (2004-2006)]

Obtaining practically useful Increments using ‘staging’

5 1 3 - f r o - t o - f r o m m L T E E O E O a r t h t o t o L E L E O O 3 t o L T O V P , e e o  E E O E L  O 1 E L E O L L E V P O , l e o 5 L E O E E O P a L E O a P E O O E A series of calculations based on standard orbital mechanics gets the payload from Sub Earth Orbit (SEO), with an apogee velocity of 7.3810 km/s, to LTO with a velocity of

10.7285 km/s

.  V for this system is 3.3475 km/s.

The angular velocity of the facility in the rescue orbit PEO1 is 

peo1

= 0.01065 rad/s.

The tip velocities, relative to the centres of tether rotation, are

V leotip

=

0.8730 km/s

and

V eeotip

=

0.7980 km/s

.

Design calculations suggest that payloads of up to 1000 kg, and 3.25 GPa strength

Spectra2000 TM

can be used for the tether.

Environmental Design

The

Hoytether

TM

Load taken by Sec. Lines Broken Pri. Line Load also shared with other Sec. Lines

[Graphic: Tethers Unlimited Inc.] Problem: How do we prevent it stretching (and the cross-section reducing as it does so)?

Adding axial elasticity to an MMET model

k 1 k 2 m 1 c 1 M P - Payload mass c 2 m 2 k 1 =k 2 =…=k N+2 , c 1 =c 2 =…=c N+2 , m 1 =m 2 =…=m N k N

2

c N

2

m N

2

k N

2  1

c N

 1 2

k N

2  2

m N

 1

k N+1 m N k N+2 c N

 2 2

m N

 1 2

M M

–

Facility Mass(Rotor) c N+1 c N+2 M 0 - Outrigger mass M M0 - Facility Mass(Stator) i

 0

L T l i

  2

i

 1 

L T

2

N l x l i L x L

0

L x

 0

L l x

 

i L L

0 

L x

 We start by simplifying the model by using a circular equatorial orbit, so there are just two generalised coordinates:  and

L x .

Chen & Cartmell (2007), Chen (2010)]

Axial Elasticity Model – Initial Performance

Angular displacement of the tether as a function of time 0.01

0.4

0.005

0.3

0 0.2

-0.005

0.1

0 0 5000 Time (sec.) 10000 Axial displacment of the tether as a function of time 10 8 -0.01

0 0.5

6 4 2 0 3000 3500 4000 Time (Sec.) 4500 0 -0.5

0 2 Phase plane for  0.1

0.2

 (rad) 0.3

Phase plane for L x 0.4

4 L x (m) 6 8 10 [Chen & Cartmell (2007)]

Generating more data – scale model testing

MMET shown on ice at Braehead Centre, Glasgow, April 2001, with 9.4 kg payloads, 1 metre tethers, and 80 W motor drive power. Radio control used for (i) cold gas start-up thrusters (long cylinders on each payload), (ii) drive motor (contained in central facility and driving the alloy bar to which the tethers are connected), (iii) payload release actuators (stepper motor driven actuators on each payload). Length scale is 1:40000. Sponsored by ESA/ESTEC, April 2001. [Cartmell & Ziegler (2001)]

Lunar Mission MMET hardware - Payloads

cap container 2.3 m end cone 2.2 m Structure: 7000 series Al - longerons and rings, flange joints, estimated internal volume of the container: 5m 3 , attitude thrusters on the external surface, fuel pipelines divided into two parts re the container-cone joint, 8 external lugs integral with the primary structure for capsule lifting.

[Villanti, Canina, Cartmell, Vasile & Murray (2006)]

Payload Delivery & Retrieval hardware

-Passive payload -No expendables on the tether -Large capture volume with low mass -Only one active component -Minimises shock loading on the tether [Villanti, Canina, Cartmell, Vasile & Murray (2006)]

Can the Tether be extended, conceptually?

Yes! We have proposed a ‘Space-Web’ concept – reflectors, telescopes, interferometers, SBSP.

Telescope/reflector web Robot crawler Masses 1 to 3 could form the apex points of a triangular web. Other shapes are equally possible.

[McKenzie, Cartmell, Vasile (2006)]

Modelling the Web

Start with arbitrary shape – triangle and define edge nodes and midpoint, then divide into two and define new edge nodes and midpoints, then divide into three and re-define, leading to division into n divisions and definitions of edge nodes and midpoints.

C B A A B C

Simulation & Animation of Web Dynamics

Case1 : 1,2,3 Walk along the edges from sub span to next sub span symmetrical 0.4

0.2

-0.2

0 -0.4

-0.4

-0.2

CoM 0 0.2

0.4

Y 100 50 0 -50 -100