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
0123456789
10111213141516171819
0.44 0.441 0.442 0.443 0.444 0.445 0.446
Fre
qu
en
cy
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