Developing a gravimeter

and analyzing gravity

By: Chatura Dilshan Kuruppu

1

Proposed Gravimeter

Vibration Absorbers

Rotatable Jaw

Dash Board

Vacuum

Tube

Sprite level

Adjustable Stand

2

newmovie.exe

Prototype 002

3

sfull.MTS

Tripod was chosen as the structure

of the gravimeter

4

Modified Electromagnet

5

Robot Arm

• To receive the ball precisely.

• Positioning the ball according to the needs

of measurements.

• Maximizing data production rate.

Requirements:

6

Schematic Diagram of Robot Arm

7

Secondary Tray

• To receive falling ball precisely.

• Re Positioning the ball to the primary tray

before taking measurements

• Maximizing data production rate.

Requirements:

8

9

Design and Construction:

Electronics

• Robot arm controlling System

• Micro switch Array

• Photo Diode Circuit

• LASER Diode Driver

• Motherboard

• Serial Communication Interface

10

Robot arm controlling System

• To control stepper motor associated with

the robot arm.

• To control stepper motor associated with

the secondary tray.

• Receiving and processing feed back data.

• Controlling LASER modules.

• Receiving and processing logic values

from Micro switch array.

Requirements:

11

Robot arm controlling System

12

13

• In order to detect the disturbance made by

steel ball on the LASER beam photo

diodes were used.

• Prototype 001 and 002 contain

HAMAMATSU S5971 photo diodes.

• The maximum possible frequency that can

be detected via this photo diode was

100MHz.

• Relatively cheap package.

Photo Diode Circuit

Features:

14

15

LASER Diode Driver

• In order to illuminate photodiodes LASER

modules were established.

Requirements:

16

Motherboard

• Converting analog to digital logics.

• Generating timer interrupts.

• Handling LCD module.

• Displaying results and messages.

• Transmit raw data to the computer

Requirements:

17

18

19

Software Design

MATLAB

PICKit2

20

Robot arm behavior

• Detecting logic values associated with

switches connected to input pins.

• Processing changes of the logic values of

those switches.

• Running correct set of commands

correspond to input logic changes.

• Receiving feedback from external

peripherals and process.

21

Motherboard behavior

• Detecting logic values associated with

comparator outputs..

• Processing changes of the logic values of

those comparator outputs.

• Running timer interrupts to calculate

associated time value in terms of

instruction cycles.

22

• Finalizing time measurement as a raw

data.

• Dividing 32-bit integer value to four of 8-bit

data packets.

• Sending 8-bit data packets via RS232.

Motherboard behavior

(Continued…)

23

Data acquisition and analysis.

• Evaluating Random Errors on Circuits.

• Measuring Gravity on an arbitrary location.

• Simple Pendulum Measurements.

24

Evaluating Random Errors on

Circuits.

Date Time Raw Data Time Value (s) Relative g Val Rounded

5-Jan-13 20:26:16 18054607 1.504550583 0.441760024 0.442

5-Jan-13 20:26:30 18029238 1.5024365 0.443004103 0.443

5-Jan-13 20:26:44 18004140 1.500345 0.444240071 0.444

5-Jan-13 20:26:56 18045469 1.503789083 0.442207541 0.442

5-Jan-13 20:27:08 18021287 1.501773917 0.443395096 0.443

5-Jan-13 20:27:22 18062579 1.505214917 0.441370165 0.441

5-Jan-13 20:27:43 18037958 1.503163167 0.442575888 0.443

5-Jan-13 20:27:55 18013523 1.501126917 0.443777394 0.444

5-Jan-13 20:28:08 18054577 1.504548083 0.441761492 0.442

5-Jan-13 20:28:21 18030337 1.502528083 0.4429501 0.443

5-Jan-13 20:28:35 18004993 1.500416083 0.444197979 0.444

5-Jan-13 20:28:50 18046416 1.503868 0.442161132 0.442

5-Jan-13 20:29:03 18020907 1.50174225 0.443413796 0.443

5-Jan-13 20:29:15 18062071 1.505172583 0.441394992 0.441

5-Jan-13 20:29:27 18036928 1.503077333 0.442626436 0.443

5-Jan-13 20:29:39 18012884 1.501073667 0.44380888 0.444 25

Results And Analysis

Mean 0.442871986

Sigma 0.000938465

Upper Limit 0.445687381

Lower Limit 0.440056591

26

0.4405

0.441

0.4415

0.442

0.4425

0.443

0.4435

0.444

0.4445

0.445

0.4455

0 10 20 30 40 50 60

Trial

Scatter Plot for Random error Analysis

27

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0.44 0.441 0.442 0.443 0.444 0.445 0.446

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Results

Histogram for trials

28

Measuring Gravity on an arbitrary

location

29

Date Time Raw Data time relative rounded Approximated g

12-Jan-13 22:36:12 3013300 0.251108333 15.8590712 15.9 9.858

12-Jan-13 22:39:12 3018085 0.251507083 15.80882378 15.8 9.796

12-Jan-13 22:41:33 3022563 0.25188025 15.76201617 15.8 9.796

12-Jan-13 22:44:05 3020185 0.251682083 15.78684698 15.8 9.796

12-Jan-13 22:47:19 3018101 0.251508417 15.80865616 15.8 9.796

12-Jan-13 22:49:59 3011735 0.250977917 15.87555731 15.9 9.858

12-Jan-13 22:53:06 3007020 0.250585 15.92538201 15.9 9.858

12-Jan-13 22:55:27 3001600 0.250133333 15.98294698 16 9.92

12-Jan-13 22:56:10 3027398 0.252283167 15.71170994 15.7 9.734

12-Jan-13 23:00:14 3014133 0.25117775 15.85030664 15.9 9.858

12-Jan-13 23:02:34 3001762 0.250146833 15.98122188 16 9.92

12-Jan-13 23:03:45 3026621 0.252218417 15.71977805 15.7 9.734

12-Jan-13 23:09:47 3019338 0.2516115 15.79570544 15.8 9.796

12-Jan-13 23:14:31 3001494 0.2501245 15.9840759 16 9.92

12-Jan-13 23:21:01 3027285 0.25227375 15.71288291 15.7 9.734

12-Jan-13 23:23:48 3020777 0.251731417 15.7806599 15.8 9.796

12-Jan-13 23:33:09 3012349 0.251029083 15.86908621 15.9 9.858

12-Jan-13 23:39:09 3012688 0.251057333 15.86551511 15.9 9.858

12-Jan-13 23:42:01 3013997 0.251166417 15.85173709 15.9 9.858

12-Jan-13 23:46:04 3009933 0.25082775 15.8945719 15.9 9.858

12-Jan-13 23:57:12 3028767 0.25239725 15.69750979 15.7 9.734

13-Jan-13 0:00:04 3013997 0.251166417 15.85173709 15.9 9.858

13-Jan-13 0:04:20 3014166 0.2511805 15.84995957 15.8 9.796

13-Jan-13 0:38:35 3029084 0.252423667 15.69422441 15.7 9.734

13-Jan-13 0:53:30 3027482 0.252290167 15.71083808 15.7 9.734

13-Jan-13 0:54:59 3018707 0.251558917 15.80230968 15.8 9.796

13-Jan-13 1:06:21 3013107 0.25109225 15.86110292 15.9 9.858

13-Jan-13 1:07:26 3005587 0.250465583 15.9405714 15.9 9.858

13-Jan-13 1:10:55 3023286 0.2519405 15.75447829 15.8 9.796 30

Results And Analysis

sigma 0.085369

mode 15.85174

mean 15.83774

Lower Limit 15.58163

Upper Limit 16.09385

Minimum 15.7

Maximum 16

Bin Frequency

15.6 0

15.7 11

15.8 15

15.9 23

16 5

16.1 0

Total 54

31

32

9.7

9.75

9.8

9.85

9.9

9.95

0 10 20 30 40 50 60

g (m

s-2

)

Trial

Scatter Plot for gravity Analysis

33

Simple Pendulum Measurements

Length (m) Time Measurements (s)

Number of Oscillations Time Period (T) T2

0.6 62.44 40 1.561 2.436721

0.8 53.52 30 1.784 3.182656

1 59.19 30 1.973 3.892729

1.2 64.69 30 2.156333333 4.649773

1.4 69.69 30 2.323 5.396329

1.6 76.91 30 2.563666667 6.572387

1.8 77 30 2.566666667 6.587778

34

y = 3.7029x + 0.2306 R² = 0.9826

2

3

4

5

6

7

8

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9

T2 (

s2)

length (m)

Plot of T2 Vs length

35

y = 4.0109x - 0.0569 R² = 0.9917

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

0.6 0.8 1 1.2 1.4 1.6 1.8

T2 (

s2)

length (m)

Plot of T2 VS length

36

Results And Analysis

By considering worst case T can be taken as 1 and l

can be taken as 1.8. Since

Therefore:

and

. Also (

)=0.0005 and

(

37

By substituting above values for equation

ms-2

Therefore g = 9.8ms-2

But average value measured by

prototype 002 was 9.796

ms-2

Results And Analysis

(Continued…..)

38

Future Developments

• Mechanical Design

• Sensors

• Electronic Circuitry

• Software Design

39

Conclusions

40

• Falling body technique can be utilized to

construct gravimeters.

• Random error due to horizontal motion

make significant contribution to Random

Errors.

• Random errors can be minimized by

taking large amount of data within small

time intervals.

• If the gravimeter is calibrated properly with

the reference point it can be used to find

out absolute gravity of a particular

location.

41

Questions ?

42

43

Variation of g around the world

From N.A.S.A

G.R.A.C.E Project.

44

Sir Arthur C Clerk’s Prediction about the “Space Elevator”

https://www.youtube.com/watch?v=uZSrAoMzRm8

45

https://www.youtube.com/watch?v=uZSrAoMzRm8