Class8 Inertial v2 Ayb

7/29/2019 Class8 Inertial v2 Ayb

1/67

MAS836Sensor Technologies for Interactive Environments

Lecture 8Inertial Sensors


2/67

2

AYB4/06

Inertial Sensing

Measures the inertial properties of a bodyi.e. thosehaving to do with dynamics (time derivatives ofcoordinates) Exploit only the properties of objects moving in space

> Black-Box devices require no external field or reference (ideally). But they do respond also to gravity (more later)

> Where does inertial come from (Machs Principle, Higgs field, etc.)?

Sensors include accelerometer, gyroscopes, velocity sensors,tilt switches, compasses and more.

Note that multiple measurements from a locationsensing technology can also be used to infer inertialmeasurements (e.g., obtain the time derivatives) Magnetic, acoustic, radiolocation, GPS, etc.

But this is generally backwards from what people want to do> Plus measurements can be noisy (more later)


3/67

3

AYB4/06

Inertial Sensors:Accelerometers

One of the two main inertial sensors, accelerometers

measure the translational acceleration exerted on a body

relative to some reference frame

Key uses: Airbag triggers

Simple biomedical sensing

Human computer interfaces Borehole and missle/aircraft/spacecraft navigation (high end!)


4/67

4

AYB4/06

Inertial Sensors:Gyroscopes

The other main inertial sensor, gyroscopes

measure the rotational rate of a body about a

fixed axis

Key uses:

Video camera stabilization

Automotive roll-over detection

Human-computer interfaces

Again, navigation (once more, high end)


5/67

5

AYB4/06

Inertial Sensors:Miscellaneous

There are number of other sensors which couldfit under the rubric of inertial sensors. Two keyones are:

Tilt switches for translational acceleration> Used for very low frequency, low resolution systems, we

will comment on a few later on

Compasses for rotational position> Useful for navigation in areas ofconsistentmagnetic field.

>Not inertialexploit an outside magnetic field.

> Covered in the previous lecture.


6/67

6

AYB4/06

Why measure inertialparameters?

Infrastructure free Simplifies task Only body of interest is instrumented

Vastly increases areas of use Cannot provide infrastructure for the whole world

> Well, actually, you can (aircraft navigation (LORAN),

GPS) but it is extraordinarily expensive

Self-contained

Cannot be jammed or fooled

> Unless you have a huge mass laying around!


7/677

AYB4/06


The problem with derivates (1) It is certainly possible to derive acceleration,velocity, rotational rate, tilt, etc from

conventional positioning system

Both from large scale systems such as GPS and

small scale systems such as the Flock of Birds

The design problem with this is that you are

measuring one quantity and then processing it tocalculate another quantity, which could have

been measured directly in the first place.


8/678

AYB4/06


The problem with derivates (2) There are also two key mathematical problems Time lag

> The more accurate your derivative (ie, the more points

back in time you look), the greater the delay.> Now consider that acceleration is the second derivative

Frequency noise

> A pure differentiator provides a linearly increasing gain

with frequency. This amplifies high-frequency noisewhich can swamp out the signal.

> Often have to low-pass before and/or after high-passing(see above).


9/679

AYB4/06


More direct measurement Most importantly, inertial parameters are oftenthe ones of fundamental interest.

Simple example with airbag

> I dont care where the car is, just if it stopped suddenly

More complex example with human muscle motion

> Unconstrained motion minimizes jerk

> Acceleration signal provides motion parameters trivially


10/6710

AYB4/06

Inertial Measurement Units:Basics

An inertial measurement unit (IMU) is a sensor package

containing three orthogonal axes of rate sensors (gyros)

and three orthogonal axes of acceleration sensors

(accelerometers) Often supplemented with additional sensors for

calibration (i.e., magnetometers provide a rudimentary

degree of orientation reference)

Historically used for inertial navigation or tracking

out of price range for HCI

Typically on the order of $1000 and 10 cm3


11/6711

AYB4/06

Inertial Measurement Units:Brief Survey

Made by: Xsens Motion Technologies http://www.xsens.com

MicroStrain http://www.microstrain.com

Cloud Cap Technology http://www.cloudcaptech.com

Intersense http://www.isense.com

Crossbow http://www.xbow.com

Us: http://www.media.mit.edu/resenv/Stack

and:

4/06
http://www.xsens.com/http://www.microstrain.com/http://www.cloudcaptech.com/http://www.isense.com/http://www.xbow.com/http://www.media.mit.edu/resenv/Stackhttp://www.media.mit.edu/resenv/Stackhttp://www.xbow.com/http://www.isense.com/http://www.cloudcaptech.com/http://www.microstrain.com/http://www.xsens.com/


12/6712

AYB4/06

Inertial Measurement Units:Gimballed

Most early IMUs were placed on a platform which stayedfixed relative to the inertial or earth frame

Still used for very accurate systems

Allows for gyros to measure a much smaller range, since

they only detect the small deviations (more linear, moreaccurate)

Simplifies transforms

Platform is servoed

> Zero rate

However

Very expensive

Suffer from gimbal lock

4/06


13/6713

AYB4/06

Inertial Measurement Units:Gimbal Lock

Given a fixed set of movements, it is possible toalign all three axes on the gimballed platform,

causing it to lock up and topple

Can be fixed by adding a fourth gimbal (expensive)

AYB4/06


14/6714

AYB4/06

Inertial Measurement Units:Strapdown

Far easier than gimballing, wecan simply fix the IMU in theframe of the device.

Mechanically much simpler andstronger, but increases thecomplexity of the math if worldframe position/orientation isneeded

Most useful if body frame itself

has meaning Makes choice of alignment key

Virtually all IMUs for HCI arestrapdown

AYB4/06


15/6715

AYB4/06

Position Calculations

X = ax d2t

q = w dt

Lots of ways to integrate (Polynomial, Simpsons Rule, etc.)

Note that gravity complicates thingsrotation measurements must

compensate for the change in the gravitational vector, which needs to besubtracted from the accelerationalso note that this is done in the body frame

usually should be transfored to inertial coordinates.

But, theres more..

AYB4/06


16/6716

AYB4/06

Inertial Measurement Units:Fundamental Error Source

Bias drift

Changes over time in the baseline (zero input) outputof the part

Scale factor drift Changes over time in the slope of the input-output

curve

Drift results in an additive noise which causes anerror proportional to t in angle and t2 in position

These noises/errors are separate from theadditive white noise seen on all sensors

AYB4/06


17/6717

AYB4/06

Inertial Measurement Units:Tracking (1)

IMUs are traditionally used for navigation or

dead-reckoning.

Given a known starting position and orientation, data

is integrated forward to get current position and

orientation

The most common algorithm for doing this is a

Kalman filter, which combines knowledge about theerror in the measurements and the error in a model of

the system propagation to give a (linearly) optimal

results (minimizes mean-squared error)

AYB4/06


18/67

18

AYB4/06

Inertial Measurement Units:Tracking (2)

However, IMUs made from low-cost parts quickly

diverge from reality because of both poor drift and

random walk noise

When noisy data is summed, the is increased by afactor of t

For example, in a gyro, this creates an error in the orientation

estimate

That error then couples into the position estimate (dx = rdq)

The only solution is to use external information to reset

the orientation or position at regular intervals

AYB4/06


19/67

19

AYB4/06

A Brief Interlude:Expressive Footwear

http://www.media.mit.edu/resenv/danceshoe.html

AYB4/06
http://www.media.mit.edu/resenv/danceshoe.htmlhttp://www.media.mit.edu/resenv/danceshoe.htmlhttp://localhost/var/www/apps/conversion/tmp/scratch_1/Vids/Byron1-trim.mpghttp://localhost/var/www/apps/conversion/tmp/scratch_1/Vids/Haim-MOS.mov


20/67

20

AYB4/06

Principle of Acceleration

Acceleration (a) is the second derivate of position withrespect to time (x)

Newtons 1st Law: An object in motion remains in

motion unless acted upon by outside forces Einsteins Principle of Equivalence: The acceleration

due to gravity is indistinguishable from otheraccelerations.

Gamow vs. Draper

> Gravity gradient (at least for a nonconstant g)

> Rotate the inertial platform as the earth curves away underneath

Schuler Tuning (add pendulum dynamics, with the mass @ earths core)

AYB4/06


21/67

21

AYB4/06

Principles of Accelerometry

Newtons 2nd Law F=ma

Since force is a fundamental quantity, we derive theacceleration by determining the force on an object of

known mass (ie the proof mass) This proof mass is usually attached to a spring of

some style allowing us to use Hookes Law

F = -kx

As F = ma, a = -x(k/m)

Deflection can then be converted into accelerationusing knowledge of the mass and spring constant

AYB4/06


22/67

22

AYB

Accelerometers:Fluid Inclinometers

Not used as an accelerometer per se, but very useful for

determining the tilt of a slowly moving object

Inclinometers are most often built as a small bubblefilled with electrolytic fluids.

These devices have slow response and

tend to be sloshy. However, in steady state, differences of

0.5 or better can be detected

Check out Spectron Glass

AYB4/06


23/67

23

AYB

Accelerometers:Inclinometers (bubble

levels)

C1C2

- Bubble (white) in fluid (blue) changes capacitance when

it moves across plates

- (C1C2) / (C1 + C2) = relative bubble displacement

- Can also read bubble position optically

Level is accurate to 0.5 arc seconds (0.00003"/ft or .0025 mm/M)

- [Also available with 0.1 arc second accuracy]

Large measuring range of +/-1000 arc seconds (0.06/ft or 5 mm/M)

EL-905 ELECTRONIC BUBBLE LEVEL

(Hamar Laser, CH)

AYB4/06


24/67

24

Accelerometers:Tilt Switches

Effectively a threshold on a single angle (with respect

to gravity), tilt switch draw virtually no power and are

excellent for simple motion detection

Mercury tilt switch

Connection between two pins made or

broken by bubble of mercury

Pinball tilt switch

Cross between mercury tilt switch and

inclinometer

ALPS SPSF100100

SMT version of ball in cup 3-axis Ball in Cup

Mechanical tilt switches can also bespring-mounted for higher acceleration

thresholds

AYB4/06


25/67

25

Accelerometer switches and piezo cantilevers

Acceleration switch

e.g., proof-mass reed, ball in magnetic can (old airbagsensors!)

Made by many companies

Piezoelectric Cantilevers

Made by MSI

Spring Steel Proof Mass displaces under

acceleration

Closes switch above threshold

Proof Mass

AYB4/06


26/67

26

Giveaway Sensor Schematic

100 ms dead timer prevents multipulsing Ultra low powerbattery lasts up to shelf life

Extremely cheape.g., under $1.00 in large quantity

MSI

Minisense 100Gated single-transistor

300 MHz RF oscillatorCould be mechanicaltamper switch

Th Wi l J k S


27/67

The Wireless Jerk Sensors

Very simple motion sensor

Cantilevered PVDF piezo strip with proof mass

Activates CMOS dual monostable when jerked Sends brief (50 ms) pulse of 300 MHz RF

Glued into a tube for simple handheld use

Front Back

AYB4/06


28/67

28

Demos

Early conductor mapping in Lab

AYB4/06
http://localhost/var/www/apps/conversion/tmp/scratch_1/Vids/Mark-single-sensor.mov


29/67

29

Accelerometers:Piezoelectric

Piezoelectric accelerometers use a cantilevered beam asa combination proof mass and spring

Beam is deflected by acceleration, creating a charge

related to its mass and flexibility This charge can be measured to find the acceleration.

ACH-04-08 from MSI (3 axis)

Range: 10g to 250g

Size: 0.3in x 0.3in x 0.2in

Bandwidth: 5 kHz

Noise: 250mg

Cost: $25

AYB4/06


30/67

30

Accelerometers:Piezoelectric - Circuitry

Also have digital versions

AYB4/06


31/67

31

Whats inside (complex folded beam)

AYB4/06


32/67

32

Piezoelectric accelerometers for rugged,sensitive vibration measurement

Lamerholm,EndevCo, Etc.

AYB4/06
http://news.thomasnet.com/images/large/2002/12/17162.jpg


33/67

33

Accelerometers:MEMS

Most MEMS accelerometers are based on a

system of interdigitated capacitors, as shown at

right.

Motion unbalances

the pair of capacitors

shown, unbalancing a

driven signal. The most common MEMS accelerometer is the

ADXL203 from Analog Devices, and is a staple

of low cost inertial sensing.

AYB4/06


34/67

34

Sidebar:What are MEMS?

Micro-Electro-Mechanical Systems (MEMS) is theintegration of mechanical elements, sensors, actuators,and electronics on a common silicon substrate.

This combination not only reduces costs, but the closeintegration of sensor and signal processing greatlyreduces system noise

MEMS have been used for everything for sensors to

microgenerators. Many companies make MEMS accelerometers now

Analog Devices, Motorola, Silicon Designs, STMicroelectronics

Some make 3-axis devices!

AYB4/06


35/67

35

Accelerometers:ADXL203

ADXL203 from Analog Devices (2 axis)

Range: 1.7g

Size: 5mm x 5 mm x 2 mm

Supply Current 0.7mA Max Bandwidth: 2.5 kHz

Noise: 0.8mg (@50Hz)

Cost: $12

Older model (ADXL202) includes duty-cycle output

for easy interfacing

AYB4/06


36/67

36

ADI single-chip 3-axis accelerometers:ADXL330

ADXL330 from Analog Devices Range: 3g

Size: 4mm x 4mm x 1.5mm

Supply Current: 0.2mA Max BW: 1.6 kHz (X,Y)

0.5 kHz (Z)

Noise: 2mg (@50Hz) (X,Y)

2.5mg (@50Hz) (Z)

Cost: $6

AYB4/06


37/67

37

Accelerometers:Thermal

A heated bubble of air can also act as aproof mass.

Its shifts with acceleration can be detectedby a quadrant of temperature sensors

giving a two-axis system. MXR7202GL from MEMSIC (2 axis)

Range: 2g

Size: 5mm x 5 mm x 2 mm

Bandwidth: 20 Hz

Noise: 1.3mg (@20Hz)

Cost: $3

Pin for pin same as ADXL203

AYB4/06


38/67

38

Accelerometers:Interferometric

Enormously small accelerationscan be detected based on

interfermetry.

In the device at right, deflectionof the proof mass changes the

intensity of the 0th order output

Resolution of 2g achieved See Cooper et alApplied Physics

Letters v.76 n.22 for more details

AYB4/06


39/67

39

Accelerometers Particle Trap

PhD Thesis of Rehmi Post

Electrostatically suspended multiple charged particles

in a tiny homemade electrostatic trap

Used a video imager to observe orientations andpositions

Ideally particles stay inertially stable, and platform

rotates around them Particles deflect (crystal deforms) under acceleration

Very preliminary workmany loose ends

AYB4/06


40/67

40

Rehmis Particle-trap Accelerometer

Actual image of oscillating particle clusters in trap

AYB4/06


41/67

41

Rotational Hough Analysis

Hough Xform looks at angles of linear structurespeak indicates orientation

AYB4/06


42/67

42

Accelerometry Based Applications:Pedometry and Body Position

Analog Devices App. Note 602

Real-Time Motion Classification for

Wearable Computing Applications

http://www.media.mit.edu/~rich

AYB4/06
http://www.media.mit.edu/~richhttp://www.media.mit.edu/~rich


43/67

43

Accelerometry Based Applications:Human-Computer Interfaces

Microsoft Sidewinder Joystick

http://www.microsoft.com/hardware/sidewinder/

Itsy Pocket Computer

http://research.compaq.com/wrl/projects/itsy/

AYB4/06
http://www.microsoft.com/hardware/sidewinder/http://research.compaq.com/wrl/projects/itsy/http://research.compaq.com/wrl/projects/itsy/http://www.microsoft.com/hardware/sidewinder/


44/67

44

Gyro from Displaced Accelerometers

Sum is gravitydifference is acceleration. Need large lever arm for accuracy

Must subtract out gravity, etc.

a1 a2

AYB4/06


45/67

45

Principles of Angular Velocity

Angular velocity (w) is the first derivate of anglewith respect to time (q)

Note the relationship between angular velocityand translational velocity (instantaneous) v = w x r

Angular momentum, like translational

momentum, is conserved Figure skater (change in moment of inertial)

Toy gyroscope (would have to change w to fall)

Processional Torque is t = w x HAngular Momentum

Body Rotation

AYB4/06


46/67

46

Principles of Gyroscopes

The Coriolis force is a fictitiousforce exerted on a body when itmoves in a rotating reference

frame. ac = -2v x w

The Sagnac effect is the change in

path length experienced by lighttraveling in a rotating referenceframe.

)/8( cAN

AYB4/06

G
http://localhost/var/www/apps/conversion/tmp/scratch_1/Vids/coriolis.movhttp://localhost/var/www/apps/conversion/tmp/scratch_1/Vids/coriolis.movhttp://localhost/var/www/apps/conversion/tmp/scratch_1/Vids/coriolis.mov


47/67

47

Gyroscopes:SDFG

The simplest mechanical gyroscopes, the single

degree of freedom gyroscope consists of a

rotating wheel attached to torsion bars

Rotation

perpendicular to the

axis of the wheel will

cause a deflection dueto the conservation of

angular momentum

AYB4/06


48/67

48

MEMS Implementation

AYB4/06

G


49/67

49

Gyroscopes:Tuning Fork

The tuning fork gyroscope was designed to be amuch simpler mechanical structure than SDFG.

Consists of two masses, connected to a common

base, oscillating out of phase with each other.Note that there is therefore no net motion.

Output is proportional to tine velocity and input

rotational rate, and is usually measured as a twistat a stiff base

AYB4/06

G


50/67

50

Gyroscopes:Vibrating Reed

This technique is quite similar to the tuning forkgyroscope, and uses piezoelectrics both as input

and output

A central vibrating reed drives two others,creating equal piezoelectric output.

A rotation deflects the velocity, driving one reed

more than the other, creating a differential output

w

Stationary Case Driven Case

drive

output 1output 2

drive

output 1output 2

coriolis

AYB4/06

G


51/67

51

Gyroscopes:Murata ENC03J

ENC03J from Murata (1 axis) Range: 300/sec

Size: 0.6in x 0.3in x 0.2in

Bandwidth: 50 Hz

Noise: 0.5/sec (@50 Hz)

Cost: $40

AYB4/06

G Wi l


52/67

52

Gyroscopes Wineglass(or hemispherical resonator)

Standing wave modal pattern of vibrations in ashell is perturbed by rotation

Wave propagation velocities around shell are

unequal in the presence of rotation Coriolis force effect

AYB4/06

G


53/67

53

Gyroscopes:Interferometric

Interferometric gyroscopes rely on the Sagnac

effect in light traveling in very long loops

(usually a small package with many turns).

Rotation causes a phase difference, which can be

converted to a magnitude by mixing the signals

Suffer from reflection

and limited by shot

noise

AYB4/06

G


54/67

54

Gyroscopes:Fizoptika VG941-3AS

VG941-3AS from Fizoptika (1 axis)

Range: 600/sec

Size: 50mm x 24mm dia

Bandwidth: 1 kHz


Cost: $1300

AYB4/06

G


55/67

55

Gyroscopes:Ring Laser

Ring laser gyros achieve far better results than IFOGsin a smaller volume by creating a loop within a lasing

resonator.

Finite number of wavelengths must fit in cavity, hence lasing

frequency must change with rotation Suffer from lock-in due to scatter and coupling

These gyros achieve tactical

performance levels

Military, aviation,

spacecraft

AYB4/06

Gyroscopes:


56/67

56

Gyroscopes:MEMS

Several companies now make MEMS gyros

Analog Devices, Delphi, ST Microelectronics, Silicon Sensing Systems,

Applied MEMS inc.

Analog Devices now makes a MEMS gyroscope very similar in

principle to their MEMS accelerometer

An oscillating mass with capacitive fingers is driven relative to

fixed finger on the substrate

Perpendicular rotation will create an imbalance

AYB4/06

Gyroscopes:


57/67

57

Gyroscopes:Analog Devices ADXRS300

ADXRS300 from Analog Devices (1 axis)

Range: 300/sec

Size: 7mm x 7mm x3mm

Bandwidth: 40 Hz


Cost: $33

AYB4/06

Gyroscopes:


58/67

58

Gyroscopes:Extending the range of the ADXRS300

Human motion easily exceeds 300 deg/sec Reduce internal amplifier gain with external

resistor

Works up to ~ 4x increase in range (45kmin)

Reduce sensitivity of internal drive circuitryby overriding internal 12V regulator withexternal reference voltage

Can be accomplished easily with external

Zener diode

7.5V Zener gives ~ 10x increase in range

Together, a 7.5V Zener and a 120 k externalresistor can be used to extend the range to

roughly 10,000 deg/sec !

AYB4/06

IMU Based Applications:


59/67

59

IMU Based Applications:Medical Data Collection

Gait Shoe

http://www.media.mit.edu/resenv/GaitShoe/

AYB4/06
http://www.media.mit.edu/resenv/GaitShoe/http://www.media.mit.edu/resenv/GaitShoe/http://localhost/var/www/apps/conversion/tmp/scratch_1/Vids/gaitlab.movhttp://localhost/var/Talks/MPEGs/sidebyside.mov


60/67

60

Position Calculations

X = ax d2t

q = w dt

Lots of ways to integrate (Polynomial, Simpsons Rule, etc.)

Note that gravity complicates thingsrotation measurements must

compensate for the change in the gravitational vector, which needs to besubtracted from the accelerationalso note that this is done in the body frame

usually should be transfored to inertial coordinates.

But, theres more..

R t t d F t Pit h


61/67

Reconstructed Foot Pitch

Z-gyroscope

integrated once

with respect to

time, over a

single leg swing.

maximum pitch minimum pitch

-3 -2 -1 0 1 2 3 4-400

-200

0

200

400

600

Calibrated Gyro-Z Output

AngularVelocity[deg

rees/sec]

Time [sec]

Calibrated Gyro-Z DataIntegration Bounds

-3 -2 -1 0 1 2 3 4

-40

-20

0

20

40

60

Final Results of Gyro-Z Integration

Angle[degrees]

Time [sec]

Linearly Integrated DataSpline-Fit of Integrated DataBML Foot Pitch

Integrated Data [zero offset adjusted,

iteratively, per integration].

AYB4/06

F t Pit h R lt


62/67

62

Foot Pitch Results

-20 -15 -10 -5 0 5 10 15 20 25 300

50

100

150

[count]

Magnitude Difference, Max Pitch

[degrees]

-20 -15 -10 -5 0 5 10 15 20 250

50

100

150

[count]

Magnitude Difference, Min Pitch

[degrees]

Recommendation: Consider replacing Murata Gyroscopes with Analog Devices Gyroscopes

AYB4/06

Stride Length: Accelerometers


63/67

63

Stride Length: Accelerometers

Accelerometers measure dynamicand static acceleration;pitch used

to subtract static component of

gravitational acceleration.

X- and Y- accelerometer

outputs can be combined

to determine acceleration

in room coordinates (also

requirespitch).

Axdynamic

Ax

Axstatic

Xroom

gsin=Ax

static

g

y

Ay-shoedynamic

Xroom

Ax-roomdynamic

Ay-roomdynamic

Yroom

Ax-roomdynamic

Ay-roomdynamic

Afoot

x

Ax-roomdynamic

Ay-roomdynamic

Ax-shoedyny

Ax-shoedynx

Xshoe

Yshoe

Ax-shoedynamic

Ay-shoe

dyn

x

Ay-shoe

dyn

y

cosx sin

x

cosy sin

y

Ax-shoedynamic

Ay-roomdynamic

Ax-roomdynamic

Ay-shoedynamic=

=

Ay-roomdynamic

Ax-roomdynamic

+

+

AYB4/06

Stride Length


64/67

64

Stride Length

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5-30

-20

-10

0

10

20

30

[m

/s2]

Acceleration Lower integration boundUpper integration boundA

x-room

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.50

1

2

3

4

5

[m/s]

Velocity

Vx-room

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.50

1

2

3

4

5

6

[sec]

[m]

Displacement

Displacementx-room

BML reference displacement

Dynamic component along room x-axis integrated twice with

respect to time, over a single leg swing.

AYB4/06

Stride Length Results


65/67

65

Stride Length Results

-60 -40 -20 0 20 40 600

10

20

30

40

50

60

70

[count]

Magnitude Difference, Stride Length using AX-room

[cm]

Recommendation: Improve pitch, incorporate all IMU outputs, Kalman filter

AYB4/06


66/67

66

What if Money is no Object? (1)

The state of the art in IMU design is the system used inthe MX missile, known as the Advanced Inertial

Reference System (AIRS).

Uses the best accelerometers and gyroscopes available

(strangely, from 1986)

The two part spherical structure is gimballed by floating

the outer sphere in fluorocarbon fluid and maintaining

the orientation of the inner sphere via hydraulic thrustvalves.

Circular error probable (CEP) of 100m

Will fall within that range 50% of the time.

AYB4/06


67/67

What if Money is no Object? (2)

Ask Joe what he did as a UROP!

Documents

Class8 Inertial v2 Ayb