Disdrometer Love
Rain on My Parade
By
Josh Molzan
Steve Gronstal
What the Heck is a Disdrometer
• An instrument to
measure the drop
size distribution falling
hydrometeors
• Three main types:
– Video disdrometers
– Acoustic disdrometers
– Impact disdrometers
An Impact Detector
Momentum
transferred:
– P = Mass *
Velocity
– Mass = f(size)
– Velocity = f(size)
Basically, Size is
EVERYTHING
Creating Our Disdrometer
Our Disdrometers
The piezoelectric device:
What is it and how does it work?
• Piezoelectricity is the ability of
some materials to generate an
electric field or electric potential
in response to an applied
mechanical stress.
• Basically, the harder you push
it, the bigger the voltage.
But its sooo small
• Is the detector
big enough to
accurately
measure the
rainfall
distribution?
Rainfall Rate
  N (d ) *V ( sam pled) *V (drop)
d
  N (d ) * A * v(d )dt *V (drop)
d
 Adh
R  dh   v(d ) * N (d ) *V (d )
dt
d
How many drops hit per second?
n   N (d ) *V ( sam pled)
d
  N (d ) * A * v(d )dt
d
R
but  N (d ) * v(d ) 
V (d )
d
n
  V (Rd ) * A
dt d
So how many drops hit?
Rainfall Intensity
Rainfall Rate
(mm/hr)
Average
Diameter
(mm)
Detector
Area
(mm2)
Hits
(#/s)
Light
< 2.5 mm/hr
1.0
1257
1.33
Moderate
2.5 - 10 mm/hr
1.5
1257
0.99
Heavy
10-50 mm/hr
2.0
1257
2.08
Experiment 1
Examining
the signal
of a drop
on each
sensor
The Good (Head 3)
2
1.5
1
0.5
0
0
-0.5
-1
-1.5
-2
-2.5
20
40
60
80
100
120
140
160
180
200
The Bad
0.1
0
0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
5
10
15
20
25
30
The Ugly (Head 1)
2
1.5
1
0.5
0
0
-0.5
-1
-1.5
100
200
300
400
500
600
700
Analyze lots of drops per detector
2.5
3:42:15 PM
3:42:16 PM
3:42:17 PM
2
3:42:18 PM
3:42:19 PM
1.5
3:42:20 PM
3:42:21 PM
3:42:22 PM
1
Voltage
0.5
0
-2000
-1000
0
1000
2000
3000
-0.5
-1
-1.5
-2
-2.5
Time
4000
5000
6000
7000
8000
Experiment 1:
Results
Peaks
Oscillation Period
Decay Rate
Amplitude (V)
Percent
Deviation
Per Event
StDev
Average
St. Dev
Average
St. Dev
Average
St. Dev
Head 1
135.818182
155.770497
3.491192
0.669199
0.048031
0.079475
-0.312816
0.561897
-179.63
Head 2
31.647059
12.504260
3.963884
0.560468
0.037397
0.028595
-1.226879
0.289811
-23.62
Head 3
31.476190
4.377431
5.120894
0.114121
0.021697
0.005515
-1.797458
0.207548
-11.55
Head 4
Failed
Head 5
32.500000
9.042827
2.461976
0.246496
0.022683
0.003937
-0.728157
0.306096
-42.04
Head 6
31.666667
4.779182
5.822552
0.116779
0.021119
0.003954
-1.822322
0.126192
-6.92
Head 7
Failed
Head 8
Failed
Experiment 2
• Examine how much
size matters.
– Drop 4 different size
drops onto our
favorite detectors.
– Find the relationship
between Voltage
response and drop
size.
Creating Drops
Head
Fall
Height
(cm)
25G
166.0
2.38
7.085
4.356
7.26
21G
165.8
2.86 12.240
4.710
7.85
18G
168.3
3.55 23.400
5.142
8.57
Buret
181.5
4.55 49.365
5.412
9.02
Diameter
(mm)
Mass/
Drop
(mg)
Estimated
Velocity
(m/s)
Terminal
Velocity
(m/s)
This Signals (H3, Buret)
8
4:38:15 PM
4:38:16 PM
6
4:38:17 PM
4:38:18 PM
4
4:38:19 PM
4:38:20 PM
2
0
-2
900
-4
-6
-8
-10
1000
1100
1200
1300
1400
1500
1600
1700
Analyzing the Signal
• Damped Harmonic
Oscillator
• (i.e. a spring)
V (t )  A sin(t ) * e
  2 / Period
k  decay
A  Am plitudemax
t  tim e
 kt
Results…. But…
What does it mean?
Peaks
Head
Drop
Mass
Average
Period
St.Dev.
Average
Decay
St.Dev.
Average
Amplitude
St.Dev.
Average
St.Dev.
Voltage Offset
Average
St.Dev.
3
7.085
17.06
3.316
7.463
1.4767
0.005065
0.00155
-1.12
0.119
0.1158
0.03371
3
12.240
16.50
2.710
16.090
5.9211
0.004162
0.000925
-1.40
0.139
0.1569
0.02095
3
23.305
17.94
3.490
18.708
5.6337
0.004838
0.000938
-2.04
0.095
0.1982
0.01894
3
49.365
38.26
4.348
34.525
4.1816
0.003699
0.000384
-7.86
0.012
-0.0415
0.01222
6
7.085
21.60
5.400
10.667
3.6000
0.007038
0.001653
-1.49
0.298
0.0635
0.01683
6
12.240
18.94
3.725
18.283
4.5605
0.007626
0.001581
-2.57
0.268
0.0075
0.02701
6
23.305
15.32
2.593
20.938
5.6411
0.007875
0.001468
-3.39
0.455
0.0659
0.05093
6
49.365
39.94
3.247
24.208
2.4057
0.006065
0.000394
-7.82
0.016
-0.0881
0.01578
Voltage Relationships?
• Possibility One:
– Model our system using Electrical Potential
Energy
– V α KE?
• Possibility Two:
– Model our system as a spring.
– V2 α KE
Electric Potential Energy
• Assumptions
– The KE of the raindrop is completely
transferred to the detector
– The initial KE is then converted into
Electric Potential Energy.
– The Voltage Change acts like a pt charge
moving in an electric field.
KE  U  V
Is V α KE??
0.00
0.0000
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
-0.50
Head 3
Head 6
-1.00
y = -1.9049x - 0.8737
R2 = 0.9995
Voltage (V)
-1.50
-2.00
-2.50
-3.00
y = -3.6374x - 1.2454
R2 = 0.8984
-3.50
-4.00
-4.50
KE (mJ)
Linear (Head 6)
Linear (Head 3)
Energy of a Spring
• Assumptions
– The KE of the raindrop is
completely transferred to the
detector
– The initial KE is then
converted into Spring
Potential Energy.
– For Piezoelectric materials, a
change in stress results in a
change in potential
– Capacitors have the same
relationship!
x
 V
D
KE  PE  V
2
Is V2 α KE??
12
y = 18.249x + 0.5608
2
R = 0.9547
10
Voltage^2
8
Head 3
Head 6
6
Linear (Head 6)
Linear (Head 3)
y = 6.1317x + 0.3785
2
R = 0.998
4
2
0
0
0.1
0.2
0.3
0.4
KE
0.5
0.6
0.7
Log D vs Log A
0.6
0.5
Log Amplitude
0.4
y = 2.0465x - 0.5719
R2 = 0.9459
0.3
0.2
y = 1.5194x - 0.5313
2
R = 0.9901
Head 3
0.1
Head 6
Linear (Head 3)
Linear (Head 6)
0
0.35
0.4
0.45
Log Diameter
0.5
0.55
Diameter3 vs Amplitude2
14
12
10
Amplitude Squared
y = 0.2883x - 1.0448
R2 = 0.9686
8
Head 3
Head 6
Linear (Head 3)
Linear (Head 6)
6
4
y = 0.0959x - 0.1359
R2 = 0.9933
2
0
10
15
20
25
30
Diam eter Cubed
35
40
45
50
Conclusion
• After analyzing 250,000,000 lines of data,
our results indicate Kinetic Energy is
proportional to Potential Squared.
• More data points are needed to confirm
the relationship between particle diameter
and voltage response!
• With more work, a piezoelectric transducer
will make a decent disdrometer.
Future work to do:
• Experiment with smaller drop sizes
(< 2mm diameter).
• Experiment with drops at terminal velocity.
• Experiment with an oscilloscope that can
handle larger voltages.
• Determine the voltage variation due to
drop impact location.
• Move analysis to real-time…..