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SUMMARY
The development ol a device for measuring raindrop impact force is described. The
apparatus records the amplitude olvoltage outputs produced by water-drops striking the sur-
face of a piezo-electric transducer. Voltage output can be calibrated in terms of kinetic energy
or impact lorce. The apparatus can record either the force of individual water-drop impacts or
the integrated impact force exceeding a particular threshold value. Impact force and trans-
ducer output signal are linearly related to each other. The effect of the height offall on impact
force is discussed. Transducer measurements are compared with amounts of sand splashed
by faling water-drops. The similarity of the results suggests that the apparatus is recording an
important erosive property of the water-drops used in the experiments.
CATENA Vol. 8, 83-96 Braunschweig 1981
THE MEASUREMENT OF WATER_DROP IMPACT FORCES
WITH A PIEZO_ELECTRIC TRANSDUCER
AC. Imeson, R Vis & E. de Water, Amsterdam
1. INTRODUCTION
Raindrop impact forces have been studied by many authors investigating soil detach-
ment and erosion (PALMER 1965, MUTCHLER & LARSON 1971, MUTCHLER &
YOLING 1915, HAGHSCHMIDT & BROGARD 1976 and GHADIRI & PAYNE 1977,
1979). Various methods ol obtaining a continuous registration ol successive water-drop
impact forces have been described, using, lor example, microphones or strain gauges
attached to rubber membranes (PALMER 1965). A promising approach described by
KOWAL et al. (1973), involves the use of piezo-electric transducers which convert raindrop
impact forces into voltage outputs proportional to the strains producing them (PERCY
1961).
This paper describes the development and calibration of a device lor measuring impact
forces based on this approach. The instrument may be used either in the laboratory or in the
field, lor as long as a month. Although it is based upon a similar principle to the instrument
developed by KOWAL et al. (1973), it is sufficiently different to require further description.
A1so, problems of calibration were encountered which made it impossible to interpret vol-
tage outputs in terms of drop-size distributions, as KOWAL et al . (1973) have done. Here, the
transducer output may be calibrated directly into values of impact lorce, or if required, values
of momentum or kinetic energy. Whilst calibrating the device, inlormation was obtained on
the effects ollall height on water-drop impact forces. This information is also discussed in
this paper.
84 IMESON. \4S & DE WATER
2, INSTRUMENT DESIGN
Design requirements
The principle design objective was to be able to record raindrop impact forces in the fie1d,
for periods as long as one month, in remote areas where no external power sources were
available. Further, the apparatus was needed to compare rainfall simulators both in the field
and the laboratory and to act as a control for more simple methods ofassessing rainfall impact
forces.
When used in the field lor long periods oltime, so many measurements are registered
that a system had to be used which made automatic data-processing via a computer terminal
possible. Raindrop impact lorces were to be measured concurrently with measurements of
temperature, river stage, turbidity, conductivity and pH and recorded with a data-logger.
Problems resulting from the use of the apparatus in this way were those olpower consump-
tion and data storage capacity.
2.1. THE TRANSDUCER AND ITS RESPONSE TO WATER-DROP IMPACT
The piezo-electric transducer used, and the one recommended by the manufacturer
(\'ERNITRON Ltd) lor our requirement, was the lead zirconate, titanate ceramic (PZT-5H)
transducer in the form of a 5 cm diameter, 1 mm thick disc. The output from the disc was
measured by placing it in the housing shown in Photo L The transducer is built into a 6,5 cm
diameter teflon cylinder (Fig. 1) and held in position along its edge by silicon rubber. Above
the disc, the cylinder is open so that water can drain from the transducer surface. Beneath it is
a chamber through which wires from the electrodes soldered onto the edge olthe transducer
pass. This is kept open to the air by means of a tube which allows pressure above and below
the transducer to become equalised. Beneath this chamber is a second airtight chamber
housing an amplifier which gives a high impedance to the output from the transducer disc
and a low output impedance to the cab1e. The cylinder is mounted onto a support with adjust-
able legs, enabling the transducer surface to be placed at an angle ofa few degrees to facilitate
drainage. The transducer surface was made water-repellent with a silicon coating. Setting the
transducer disc at a slight angle did not significantly influence the measurements.
The lorm of voltage output pulse produced by the impact of a water-drop is illustrated in
Figure 2. This output lasts lor only about I millisecond, provided that a water film is not
allowed to develop on the disc surface. The presence of a water fi[m results in a rather variable
secondary vibration which generates an output voltage with a period of 10-20 milliseconds.
These secondary pulses increase the time required between measurements. In practise water
droplets often remain on the surface ofthe disc and influence the output. This occurs most fre-
quently following the impact of drops having a low momentum. It was found that it was pos-
sible to reduce secondary vibrations by placing a moist sponge-rubber disc above the trans-
ducer. However, since this resulted in a loss of sensitivity, this modification was not adop-
ted. Water-drops lalling on the transducer housing can produce voltage pulses which are
subsequently recorded by the instrument. When used in the field this is prevented by placing
a funnel shaped shield above it. The shield is also used to cover the outermost 1 cm olthe
transducer disc, which has a rather variable voltage output. This is illustrated in Figure 3,
which compares peak voltage outputs produced by uniform water-drops striking various
points on the disc surface, with those produced at the disc centre. Although not sensitive to
WATER DROP IMPACT
l1
Photo l: The control unit and transducer mounting
noise, as used here, voltage outputs were sometimes produced by gusts olwind. The shield
placed over the instrument appeared sufllcient to remove this source of error, but the
apparatus has not been tested under storm conditions.
Since the amplitude of the voltage pulse is proportional to the strain producing it, it is
this parameter which is measured by the control system. This is in effect the same parameter
which KOWAL et al. (1973) measured manually lrom chart recorders and used to recon-
struct drop-size distributions of rainfall.
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Fig. 1: Cross section of the transducer mounting (1 is the piezo-electric transducer, 2 the amplifier
and 3 the position ol the cable carrying the power and output signal)
approx. time scale (mS)
Fig. 2: Form ofthe output signal produced by an impact ofa water drop on the piezo-electric trans-
ducer. The amplitude of the first pulse (a) is recorded by the instrument.
E
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o
WATERDROP IMPACT
Fig. 3: Variations in sensitivity olthe transducer surface. The
average voltage amplitudes produced bydrops striking the surlace
at the indicated point are shown as a percentage of'the amplitude
recorded atthe centre of the disc.
2.2. PROCESSING OFVOLTAGE OUTPUTS BYTHE CONTROL LTNIT
A schematic diagram of the control unit is shown in Figure 4. Basically this does one of
he two things according to the mode of operation chosen. In mode 1, used for calibration or
studying the impact olindividual drops, voltage outputs are converted into a digital output
which is directly stored on a cassette tape. In mode 2, used lor periods olprolonged field
measurement, the output is integrated in a memory which is printed on the cassette tape
when the memory storage is full.
The first step performed by the control unit is the digitisation olthe voltage pulse, by
means of amplifier B diode D and capacitor C, which perlorms the lunction of an analogue
memory for the amplitude olthe pulse. The voltage from capacitor C is led into a voltage to
frequency converter (V/F). The frequency ofthe outgoing pulses is proportional to the vol-
tage across capacitor C and to the amplitude of the transducer pulse. The output of the V/F
converter is gated by the control logic, which has a crystal controlled clock signal, so that the
number of pulses entering the BCD register is proportional to the original voltage pulse.
When the BCD counter has received its signal, the control logic sends a start signal to the
recorderand the content ofthe register is recorded on the cassette tape. The control logic
then resets the register, the capacitor is discharged via contact C and the equipment is ready
to record the next drop.
In the integrating mode, pulses from the V/F converter are fed into two cascaded binary
counters which are reset after a predetermined number ol pulses. A trigger signal starts the
measurement, together with a special flag which is written on the magntic tape. The logging
lrequency is preset with thumbnail switches and the elapsed time recorder between logging.
The cassette recorder used to record the measurements is a digital recorder lrom
Memodyne Inc., which is compatible with the Silent 700 terminal of Texas Instruments. The
recorder is used to log data lrom additional channels, and the results of raindrop impact
forces can be plotted by means ol a computer programme together with measurements ol
other physical parameters.
3. CALIBRATION OF VOLTAGE PULSES IN TERMS OF WATER-DROP
PARAMETERS
The control unit records the amplitude olvoltage pulses produced by the transducer as a
result of strain induced by the impact olwater-drops. KOWAL et al. (1973) based their
analyses of such peaks on a presur.ned linear relationship between the momentum of the
87
88 IMESON \TIS & DE WATER
Fig. 4: Circuit diagram of the control
drops intercepted by the transducer and the amplitude of the graph they recorded. They
verified this experimentally by plotting the amplitude of the signals against momentum.
From the relationship between momentum and drop volume, which they describe lor drops
larger than 2 mm in diameter, they relate drop size to signal amplitude. The transducer
signals are related directly to drop size for drops at terminal velocity. This approach was not
adopted here because the impact force of the drops themselves was the chief interest. Outilut
signals would not be proportional to drop size for impact velocities above or below terminal
velocities in windstill air. Further, it would seem lrom the measurements described below,
that only an approximate relationship could be established between voltage amplitude and
drop size.
Tab. 1: THE MEAN DIAMETER (cm) AND STANDARD DEVIATIONS OF WATER DROPS
USED DURING THE CALIBRAnON DGEzuMENTS (n : 120)
drop diameter standard deviation
0.577 0.005
0.395 0.0015
0.295 0.002
0.266 0 005
3.1. METHOD OFCALIBRATION
The apparatus was calibrated by recording the signals produced by water-drops of
known size, which were allowed to fall onto the transducer from heights of up to 12 m, at
intervals of 50 cm. At least 100 impacts were recorded for each drop diameter at each interval.
To avoid problems of turbulence in the building where the measurements were made, the
tests were performed in a 40 cm diameter pipe, that could be extended in sections and which
was closed at the top. Water-drops were produced lrom calibrated capillary tubes fed by a
constant head device. The reproducibility of the drops was extremely good (Table I ), and no
WATERDROP IMPACT
signihcant differences in size could be recognised between drops leaving th capiilary tube and
striking the transducer surface.
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r too ,i{ o
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Fig. 5: The range of voltage outputs produced by 0.395 cm diameter drops striking the transducer alter
different heights offall. Average values are indicated. The open circles give the amount olsand splash
lrom a container after similar heights of fall.
Tab.2: THE AVERAGE (x) AND STANDARD DEVIATION (9 OF 100 MEASUREMENTS OF
THE AMPLITUDE OF VOLTAGE PULSES PRODUCED BYWATER DROPS STRIKING THE
TRANSDUCERAFTERTHE INDICAIED HEIGHTS OF FALL
Height of fall Drop size (cm)
0.395 0.s77
0.266
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
'7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
is
253
104 16
t37 9
t74 15
220 20
218 17
266 15
244 31
2s9 48
254 50
295 45
287 4
262 64
320 50
314 64
322 65
384 s9
34t 49
370 65
381 76
363 72
326 79
344 70
334 '75
is
5 0.5
11 3.1
t6 2.0
t9 1.8
24 3.3
25 3.4
27 3.6
34 3.2
32 3.3
32 3.1
33 3.3
33 3.4
xs
19 2.4
32 2.2
62 2.8
80 3.3
98 5.0
108 6.8
118 12
122 10
114 19
108 12
145 12
141 18
131 18
153 13
r37 25
t46 29
171, 26
166 28
169 29
187 26
182 3'7
163 43
162 32
t57 32
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90 IMESON VIS & DE WATER
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9
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t@
120
100-
EO
60
40
20
drop diameter (cm)
o=O54
+ = 0395
. = 0266
. - 0.295
Fig. 6: The relationship between voltage output and momentum for different drop sizes. The regres-
sion equation shown is lor grouped data excluding the largest (0.54 cm) drop size (r : 0.98).
3.2. RESULTS
Examples of voltage outputs from the transducer are indicated in Table 2, where the
mean and standard deviations of I 00 impacts are given in terms of the number of registered
counts. In the figures, voltage outputs are expressed in both the number of counts and in mV.
Even though the drops are constant in size, a range ofoutput voltages is produced for each
height of fall. This range is very small for low fall heights and small drops, but increases with
fall height. It probably reflects the variability in sensitivity ofthe transducer surface illustrated
in Figure 3 and the presence or absence olsmall water droplets on the transducer surface. It
can be seen that above a given fall height, voltage outputs no longer increase linearly but fluc-
tuate within a certain range. This is demonstrated in Figure 5, which also shows the maximum
and minimum voltages recorded.
Using velocity data from LAWS ( 1 94 1), the momentum, kinetic energy and impact force
of the drops used in the experiment can be calculated and plotted against voltage outputs
(Figures 6 and 7). In the case olmomentum, it can be seen that different linear relationships
are produced for each drop size. According to LAWs (1941) data, terminal velocities and
WATERDROP IMPACT
o 1 2 3 1 5 6 1 I 9 10 11 12 13 E 15 16 17 ]a 19 m Z 22 23 21 25 2621 Jxio-4.....-
Fig. 7: The relationship between voltage output and kinetic energy lor different drop sizes. Equation A
is for all grouped data and equation B lor grouped data excluding the largest drop size. The correlation
coefficients for these relationships are respectively 0.98 and 0.99.
hence maximum values of momentum are reached by at least four or five drops of each drop
size, since 12 m is greater than the height required for them to attain this velocity.
Nevertheless, these drops produce a relatively wide range of voltage output (Figure 6). For
drops smaller than 4 mm, a good predictive relationship is found.
A better relationship was found between kinetic energy and output voltage. A good
predictive equation can be obtained to interpret output voltages in terms of kinetic energy for
grouped data (Figure 7). Values for the largest drop size class do tend to deviate from this
relationship at the higher ranges ofkinetic energy.
The equally good relationship between impact force Grl) and voltage output will be dis-
cussed below.
3.3. DISCUSSION
KOWAL et al. (1973) based their analyses of transducer data on an assumed linear
relationship between drop momentum and the amplitude ofthe voltage output. This is then
used with a relationship between the momentum of a drop at terminal velocity and drop
volume, for volumes greater than 4 mm3, to estimate drop size. The results described above
suggest that smaller drops having the same momentum as larger ones produce higher vol-
tage output peaks. This could be interpreted as indicating that the amplitude of the voltage
output peak is a function, not of the velocity (9, but of t'.
The voltage produced by the transducer is in fact proportional to the strain (PERCY
1967) in the material. GHARDIRI & PAYNE (1977)have recently discussed the nature of
raindrop impact force and stress. They point out that stress is proportional to f and that this
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92 IMESON \4S & DE WATER
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724
200
la0
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t?
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drop d ameter
o=054
r = 0395
. = 0266
(cm )
Force (N)
Fig. 8: The relationship between voltage output and impact lorce lor different drop sizes. The regression
equation is lor grouped data (r : 0.985).
may account for apparent correlations between the kinetic energy of rainfall and its erosivity.
The good relationship between the amplitude of voltage output and water-drop impact force
(Figure 8) indicates that this force is a somewhat better parameter for calibrating output from
the transducer than the kinetic energy. GHARDIRI & PAYNE ( 1977) further concluded that
the erosive capacity of a raindrop is related to the product of its diameter and the square of its
velocity. When such calculations were compared with voltage amplitudes, different linear
relationships were obtained for each drop size.
Values of impact force (F) plotted in Figure 8 were simply obtained from the
relationship
F: mr2
d
where m and d are respectively the mass and diameter of the drop. This equation at best only
gives an approximation of the true impact force partly because the value of d is derived from
the drop volume and the form of the water drop is not taken into account. Hower, this
relationship nevertheless provides a means of interpreting the output from the transducer.
The equation which is used to estimate the impact force from the voltage amplitude
measurements is given in Figure 8.
WATER DROP IMPACT
The degree of amplification of the output signal chosen for the instrument is somewhat
arbitrary. Lower amplification was found to reduce the sensitivity olthe instrument to drop
impacts which were empirically found to be capable of transporting sand grains. Higher
amplification resulted in an increased sensitivity to spurious vibrations. At the selected
amplification a scale deflection of about 20 coincided with the threshold impact force re-
quired to splash moist sand.
time (seconds) *
Fig. 9: Relationship betwen voltage output oltransducer and the time of lall lor 0.54 cm diameter
water drops.
4.THE EFFECT OF FALL HEIGHT ON IMPACT FORCE
During the calibration experiments it was repeatedly found for different drop sizes, that
the peak voltage amplitude increased linearly with the fall height of the drops for the first 4 or
5 metres of fall. For higher fall heights this increase became more variable (see Table 2 and
Figure 5). However, cerkin heights above the transducer consistently produced either low or
high average voltage outputs. The position of these maximum or minimum values varied for
different drop sizes. For example, for 0.395 cm drops (Figure 5), peak average values
occurred for drops which had fallen 5.5, 7, 8.5 and 10 m. Thus, even after reaching terminal
velocities, the impact force of the drops striking the transducer varied with the fall height.
A possible explanation for this seemingly periodic oscillation in impact force, might be
the way in which drops oscillate in shape after leaving the drop formers. The length-width ratio
of a drop would influence the deceleration time at impact. The troughs and peaks in the fall-
height voltage output relationship, consistently observed in repeated tests, might reflect the
periodicity olshape oscillations. If voltage output is plotted against the time of fall rather than
the height (Figure 9), such a periodicity becomes more apparent. Measurements were not
made at small enough intervals to determine any period oloscillation exactly but this would
93
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94 IMESON, \'IS & DE WATER
appear to be between 0.2 and 0.3 seconds. Such an explanation would require photographic
verifieation and would imply that water-drop impact forces are not simply related to drop
mass or diameter at terminal velocity. In nature such oscillations might possibly be brought
about when rain falls through vegetation canopies, or as a result of wind.
Tab. 3: GRAIN SIZE DISTRIBUTION OF SAND USED IN THE SPLASH E)GERIMENTS
class
interval (pm)
percent <75 75 105 150 210 300 420 600
105 150 210 300 420 600 850 > 850
0.20.2
0.8 10.2 37.5 50.7 0.4
;o
o
.N
I
g
o
o
E
drop drameter (cm)
o - 054
, = 0397
0 05 1 1.5 2 25 3 3.5 4 45 5 5s 6 65 1 7.5 8 85 I 9.5 10 10.5 11 11.5 12
height of fall (m) *
Fig. 10: Amount of soil in grams splashed lrom containers by 0.54 and 0.397 cm drops alter the indi-
cated heights offall.
5: TRANSDUCER MEASUREMENTS AND SAND SPLASH
An experiment was conducted to attempt to examine whetherwater-drop impact force as
measured by the transducer is a quantity which does in fact describe the erosivity of the water-
drop. To keep the experiment as simple as possible washed quartz sand purchased from a
chemical supplier was used. The grain size distribution is indicated in Table 3. The sand was
placed in 15 cm diameter, 15 cm deep beakers. The sand was levelled 2 mm below the beaker
rim and maintained at pF I by a syphoning device. The beakers were placed in 60 cm high
plastic bins and subjected to the impact from falling water drops in the same way as the trans-
ducer. The amount of material splashed into the plastic bins was collected after 25 drop
al
06
05
WATER DROP IMPACT
o 01 a2 03 04 05 06 01 .oo,x"n"o *li ,nnu l!"o,-ru",il, - r,
Fig. 1 1: Relationship between transducer output signal and amount olsplashed sand lor 0.54 cm and
0.39 cm drops. Regression A relers to the larger drops, regression B to the smaller drops and regression
C to the grouped data. The impact force ofthe drops is indicated by the scale to the right ofthe figure.
impacts, dried and weighed. Care was taken to ensure that water-drops did not lall in the
same place.
The amounts of material splashed by drops o10.54 and 0.397 cm in diameter are shown
in Figure 10, as a tunction of lall height. The resemblance between Figure 10 and Figure 5,
which shows the relationship between transducer voltage amplitude and lall height, is clear.
To lacilitate comparison, amounts olsand splashed by 0.397 mm drops are also shown in
Figure 5. Although not exactly the same, there is a rather similar oscillation in the amount of
sand splash at fall heights above 5.5 m, as in the transducer measurements.
When transducer measurements lor each drop size and fhll height are plotted against the
corresponding amount of sand splash that the drops produced, the relationship shown in
Figure I I is lound. The relationships are particularly good lor the lower fall heights and the
smaller drop sizes. The correlation coeflcient lor the grouped data is 0.93. It would seem that
a good predictive equation can be established to enable sand detachability to be estimated
lrom the transducer measurements.
As is to be expected, the regression equation shown in Figure 1 I intersects the Y axis
above the origin. This indicates that a scale def'elction ol30 (0. 125 N) has to be attained belore
the sand used in the experiment is transported liom the beaker.
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6, CONCLUSION
The relationship between the transducer measurements and the amount ol sand
splashed by water drops would seem to suggest that a relevant erosive property ofthe water-
drops studied is being recorded. The degree to which this is the case under field conditions is
at present being examined. The peak voltage outputs recorded by the instrument can be
used to estimate the impact force ol falling water-drops. By using the regression equation
shown in Figure 7 it is also possible to express the impact effect in terms of KE. It is not pos-
sible to estimate the momentum, however, since this is influenced by drop size (Figure 6).
When using the instrument in the integrating mode, only those impact forces are recor-
ded which exceed the threshold value required for particle detachment and transport. In the
case of sand at pF 1 this is the value indicated above. However this threshold can be varied to
take account of the erodibility of the soil.
One objection to the transducer measurements described here is that the surface area of
the transducer disc is too small. Clearly, if for example an average value of raindrop impact
force is required, many measurements will be necessary. It would seem, from the good
relationship between sand splash and transducer output amplitude, that calibrated con-
tainers of sand or other materials could be placed at many locations in the fieid to provide a
more extensive data base. This possibility is now being examined.
ACKNOWLEDGEMENT
We gratefully acknowledge the assistance and advice ofDr. H.J.M. vanZon, who helped with the
initial experiments and ofVernitron Ltd. of Southamptonwho helped us with the selection ola suitable
piezo-electric transducer. We thank Mrs, M.C.G. Keijzer-v.d. Lubbe for preparing the manuscript and
Mrs. O.M. de Vr6 and Mr. A Eikeboom lor preparing the figures.
REFERENCES
GHADIRI, H. & PAYNE, D. (1977): Raindrop impact stress and the breakdown olsoil crumbs. Joumal
ol Soil Science, 28, 247 -258.
GHADIRI, H. & PAYNE, D. (1979): Raindrop impact and soil splash. pp. 95-104 in: LAL, R &
GREENLAND, D.J. (eds) Soil physical properties and crop production in thetropics. J. Wley
HOGH-SCHMIDT, K & BROGAARD, S. (1976): The energy of raindrops. Geografisk Tidskrift, 75,
24-29.
KOWAL, J.M., KIJEWSKI, W & KASSAM, AH. (1973): A simple device lor analysing the energy
load and intensity of rainstorms. Agricultural Meteorology, 12,271-280.
LAWS, J.O. (1941): Measurement ol the lall velocity ol waterdrops and raindrops. Transactions,
American Geophysical Union, 22, 7 09 -7 21.
MUTCHLE& C.J. & LARSON, C.L. (1971): Splash amounts from waterdrop impact on a smooth
surflace. Water Resources Research, 7, 19 5 -200.
MUTCHLE& C.J. & YOUNG, RA (1975): Soil detachment by raindrops. pp. 113-117 in: Present
and Prospective techniques lor predicting sediment yields and sources. ARS. S-40, U.S.Dept.
Agriculture.
PALMER RS. (1965): Water drop impact forces. Transactions American Society of Agricultural
Engineering, 8,69-71.
PERCY, C. (1967): A guide to the use ol PZT piezoelectric strain, vibration and excitation ganges.
Vernitron Ltd. Bulletin 66022/8.
Anschrift der Autoren:
AC. Imeson, R Vis, E. de Water, Department of Physical Geography and Soil Science
University of Amsterdam, Dapperstraat 115, Amsterdam
