Apparatus and Techniques 

for Measuring Bedload

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1748
Apparatus and Techniques 

for Measuring Bedload

By D. W. HUBBELL

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1748

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1964
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

First printing 1964 

Second printing 1967

The U.S. 'Geological Survey Library has cataloged this publication as follows :

Hubbell, David Wellington, 1925-

Apparatus and techniques for measuring bedload. Washington, U.S. Govt. Print. Off., 1964.

v. 74 p. illm, diagra, profiles, tables. 24 cm. (U.S. Geological 

Survey. Water-Supply Paper 1748)

Bibliography: p.. 72-74.

1. .Sedimentation and deposition. 2. Hydraulic measurements. 

3. Hydraulic engineering Instruments. I. Title. (Series)

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.G. 20402 - Price 30 cents (paper cover)
CONTENTS

Page

Abstract_______________________________________________________ 1

Introduction. _____________________________________________________ 2

Some aspects of measuring sediment discharge ________________________ 3

Calibration of bedload samplers.____________________________________ 5

Determining the total load____-----___-________-____-_____________ 7

Early bedload-measuring apparatus__________________________________ 9

Box or basket samplers_______________________________________ 9

Pan or tray samplers_________________________________________ 13

Pressure-difference samplers___________________________________ 14

Slot or pit samplers__-__--____-________________________________ 16

Recent bedload-measuring apparatus_______________________________ 16

Direct-measuring apparatus___________________________________ 18

Indirect-measuring apparatus ___________________________________ 27

Acoustic instruments_____________________________________ 27

Ultrasonic bedload sampler_________________________________ 31

Tiltmeter_____________________________________________ 36

Some new possible apparatus and methods for measuring bedload______ 39

Portable pit sampler___________________________________________ 40

Photography_____________________________________________ 40

Tracking of dune movement, particularly by ultrasonic sounding-___ 42

Pressure transducers___________________________________________ 65

Ultrasonic sounding of large particles.___________________________ 65

Conclusions.__ ____________________________________________________ 70

Literature cited ___________________________________________________ 72

ILLUSTRATIONS

Page 

FIGURE 1. Variation of sampled bedload discharge.___,____---_-----_ 5

2. Results of bedload collections during one hour in a laboratory

flume.._________--__-_______________-____--__--_---_-_ 6

3. Mtihlhofer sampler____________________-_-____-__-_---_- 11

4. Ehrenberger sampler frame._____________________________ 11

5. Nesper sampler.__-_-_-_______________-_-_--_-_-------_ 12

6. Swiss Federal Authority sampler.________________________ 13

7. Losiebsky sampler.___________________-__-______-------- 14

8. Polyakov sampler.______________-_____--__-__--_-----_- 14

9. Scientific Research Institute of Hydrotechnics sampler._____ 14

10. Arnhem sampler._-_____-_________________------__---- 15

11. Mtihlhofer pit sampler____________-________-____------_- 17

12. Enoree River sampling installation.______________-_-_---_ 18

13. The Sphinx sampler__________________-_-__----_-------- 19

in
IV CONTENTS

Page

FIGURE 14. Experimental sampler of U.S. Army Corps of Engineers, 

Little Rock, Ark.: A, Parts diagram; B, Sampler in 

lowering position.____________________________________ 20

15. Interior of Karolyi sampler._____________________________ 21

16. VUV sampler: A, Sampler in operating position; B, Top and

side views of sampler; C, Flow pattern through the sampler. 22

17. Sampler B of the Irrigation and Power Research Institute,

Punjab____________________________________________ 25

18. Suction-type sampler proposed by Hiranandani____________ 26

19. Hydrophonic detector of d'Electricit6 de France..-_________ 28

20. L'Arenaphone: Operating position__._____________________ 30

21. L'Arenaphone: Fork and transducer______________________ 31

22. Ivicsics' acoustic bedload recorder: A, Operating position;

B, Plan view-_-___-----------___--------__________ 32

23. Variation of acoustic energy and sampled bedload discharge,

Rajka gaging station__________________________________ 33

24. Smoltczyk ultrasonic bedload sampler.____________________ 35

25. Diagram of Zollner pendulum suspension._________________ 37

26. Relation between water level and tilting angle.____________ 38

27. Tiltmeter chart, Kokidaira in Tone River system, September

27-28----------------------------------------------- 38

28. Relation between water level and tilting angle, Kokidaira in

Tone River system, September 27-28___________________ 39

29. Diagrammatic sketch of portable pit-type bedload sampler. _ 41

30. Time required to pump material from the bed at different

slurry concentrations and pumping rates ________________ 42

31. Relation of pump speed and brake horsepower to the discharge

of a 2-inch pump for 20- and 40-foot heads._____________ 43

32. Motion-picture apparatus.______________________------_- 44

33. Idealized diagram of dune movement if particles are transported only from the upstream to the downstream side of a 

dune_ _______________________________________________ 46

34. Idealized diagram of dune movement if only one of every 

three particles eroded from a dune is deposited on the 

downstream side of the same dune and the other two pass 

on to the next dune___-_________________-__--------- 48

35. Bed-contour plat, Little Blue River near Fairbury, Nebr.,

May 28, 1958_-________-_________.____________ 51

36. Relation between the dune height and the vertical dune area,

Little Blue River near Fairbury, Nebr., May 28, 1958_-__ 52

37. Longitudinal profiles, Little Blue River near Fairbury, Nebr.,

May28, 1958_.____________.______-________--------_- 53

38. Change in bed elevation with time at stations along line O,

Little Blue River near Fairbury, Nebr., May 28, 1958___ 57

39. Longitudinal profiles, Middle Loup River at Dunning, Nebr.,

August 7, 1958-__________-___-__---------_---------- 58

40. Relation between the dune height and the vertical dune area,

Middle Loup River at Dunning, Nebr., August 7, 1958__ 59

41. Change in bed elevation with time at single points, Middle

Loup River at Dunning, Nebr., August 7, 1958_________ 59

42. Longitudinal profiles, Middle Loup River at Dunning, Nebr.,

Augusts, 1958_______---___._______-_______ 60
CONTENTS V

FIGURE 43. Relation between the dune height and the vertical dune area, Page 

Middle Loup River at Dunning, Nebr., August 8, 1958__ 61

44. Change in bed elevation with time at single points, Middle

Loup River at Dunning, Nebr., August 8, 1958. _________ 61

45. Diagrammatic sketch of a dual pressure transducer. ________ 66

46. Determination of radius of spherical particle from a recorder

trace by ultrasonic sounding___________________________ 68

47. Minimum number of times a spherical particle will be scanned. 69

TABLES

Page 

TABLE 1. Simplified formulas for computing the total sediment discharge

of a size range.______________________________________ 10

2. Results from sampler calibrations by Novak_______________ 23

3. Computation of bedload discharge by the dune-tracking 

method, Little Blue River near Fairbury, Nebr., May 28, 

1958___ _______ __ ___ ___ _ __-___ 54

4. Computation of bedload discharge by the dune-tracking 

method, Middle Loup River at Dunning, Nebr., August 7, 

1958 __ __ -_ _ _ .___ _ 62

5. Computation of bedload discharge by the dune-tracking 

method, Middle Loup River at Dunning, Nebr., August 8, 

1958__--_-____-___----______--_---__----_-___-_--__- 63

6. Bedload discharges computed by the dune-tracking method

from flume data_____--_______---_--__--_----_________ 64
APPARATUS AND TECHNIQUES FOR MEASURING

BEDLOAD

By D. W. HUBBELL

ABSTRACT

The need for accurate determinations of the total sediment discharge of particles of bedload size has prompted this investigation of available and possible 

measuring apparatus and procedures. The accuracy of measurements of sediment discharge made with trap-type samplers is affected by the variability of 

sampler efficiency, by the oscillatory variation of bedload discharge, and by sampler placement. Equations that were developed for determining total discharge 

from measured bedload discharge and measured suspended-sediment discharge 

are simplest if the bedload apparatus measures only the true bedload.

Early bedload samplers are generally unsatisfactory. Recently developed or 

suggested apparatus include various improved samplers of the pressure-difference 

type, a pumping sampler, a magnetic sampler, acoustical instruments that measure the magnitude of the sound of particle collisions, an ultrasonic bedload sampler designed to measure and integrate electronically the concentration and 

velocity, and a tiltmeter designed to measure the total sediment discharge from 

the ground tilt that results from the passage of flow. All the pressure-difference 

samplers are improvements over early samplers, but none are void of the inherent 

shortcomings of trap-type apparatus; probably the Sphinx (Dutch) and VUV 

(Hungarian) samplers are the most satisfactory. The acoustical instruments 

are capable of measuring only the relative discharge. The ultrasonic sampler 

and the tiltmeter are not adequate without further development.

Some new possible apparatus and means for measuring or aiding in measuring 

bedload discharge are small pit samplers, ultrasonic sounders, pressure transducers, and photography. A small pit sampler for measuring bedload discharge 

was designed to provide self-placement and portability; however, its practicability and efficiency are undetermined. Exploratory films show that by using slowmotion photography the discharge of particles larger than about pea size can be 

determined provided the flow is clear; however, photography generally is not 

practical. Ultrasonic sounders provide continuous and accurate data on bed 

configuration and dune movement for use in equations that were developed for 

computing the bedload discharge. Computations with the equations indicate 

that the interpretation of the sounding data needs further study. Pressure 

transducers placed beneath the bed surface possibly can be used to provide 

information on dune movement; however, their installation would be difficult. 

The time required for collecting data on bed configuration and dune movement 

throughout a cross section could be substantially reduced by using several transducers simultaneously In conjunction with an ultrasonic sounder. A modified 

ultrasonic sounder that provides information on the shape and velocity of large 

particles and a method for determining the discharge of such particles were 

proposed; the method seems most feasible for particles of high sphericity.
2 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

INTRODUCTION

One of the principal concerns in studies of sediment transport is 

the determination of the total sediment discharge of coarse sediments 

those particles of bedload size. Such particles do not always move as 

bedload but sometimes move as suspended-sediment load. Because the 

suspended sediment can easily be measured, the main problem is the 

determination of bedload the sediment that slides, rolls, or skips 

along in almost continuous contact with the streambed.

In the past, attempts have been made to determine the bedload discharge in three general ways: By direct measurement with some type 

of apparatus; by definition of physical relations from which the 

bedload could be estimated; and by quantitative measurements of the 

results of some sedimentation process, such as erosion or deposition. 

Unfortunately, direct-measuring apparatus have been useful for only 

a very limited range of sediment and hydraulic conditions; the definition of physical relations has not been complete enough to estimate 

precisely the bedload discharge; and the quantitative measurements 

have supplied information only on the characteristics of the reach that 

was studied. As a result, no single apparatus or procedure, whether 

theoretical or empirical, has been universally accepted as completely 

adequate for the determination of bedload discharge over the wide 

range of sediment and hydraulic conditions in nature.

The need for adequate determinations of bedload discharge 

prompted an investigation on the measurement of bedload. This report presents the results of a review and evaluation of the existing and 

contemplated apparatus and techniques that were studied as a part 

of the investigation.

Because the majority of previous development work and study on 

the measurement of bedload was done outside the United States, much 

of the literature had to be reviewed through translations. Many of 

the translations of publications on early bedload samplers were furnished by the U.S. Waterways Experiment Station, the U.S. Soil Conservation Service, the U.S. Bureau of Reclamation, the National Bureau of Standards, and the University of California. Publications 

and other informational material on some of the recently developed 

measuring apparatus were kindly supplied by some foreign laboratories of the International Association for Hydraulic Research, by the 

U.S. Corps of Engineers, and by Mr. Sam Shulits. The publication 

by Smoltczyk (1955) was translated partly by Dr. A. N. Zervins and 

partly by Mr. Donald Steinmetz. Mr. William Thordarson of the 

Geological Survey and Mr. Istvan Takacs translated the articles by 

Juniet (1952) and Ivicsics (1956), respectively.
APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD 3

SOME ASPECTS OF MEASURING SEDIMENT 

DISCHARGE

The total sediment discharge of any size fraction includes the 

suspended-sediment discharge and the bedload discharge of the size 

fraction. Theoretically, both of these discharges can be determined 

either by measuring the weight of sediment that passes a section in 

a given time or by combining the concentration, the area of flow, and 

the velocity of the particles. However, in practice, the suspendedsediment discharge is usually computed by the concentration method, 

and the bedload discharge is usually computed by the weight method. 

Different methods are vised because suspended-sediment particles are 

transported for sustained periods of time at about the same velocity 

as that of the flow, and bedload particles usually are transported 

intermittently at velocities less than that of the flow. Thus, suspended-sediment discharge can be computed from a concentration 

and a water discharge (the product of particle velocity and area of 

flow equals water discharge), whereas the bedload cannot.

Seemingly, the simplest and most practical method for measuring 

the weight of bedload passing a section in a given time would be to 

collect the sediment for a given time in some kind of portable sampler; 

this method has been used in most efforts to measure the bedload 

discharge. However, because with this method the sampler must 

rest on the bed, the flow pattern and the bedload discharge in the 

vicinity of the sampler are altered to some extent. The degree to 

which the bedload discharge is altered by any particular sampler 

depends on many factors, such as the stream velocity and depth, the 

magnitude of the bedload discharge, and the particle size of the bedload. For accurate bedload discharge measurements, the sampler 

must be designed so that the bed-load discharge is virtualy unaltered. 

Also, it must be designed to sample the largest and the smallest 

bedload particles, to accumulate and retain the bedload particles, 

to be stable on the bed, and to orient vertically and horizontally so 

that all particles have an equal opportunity for entrance. These 

criteria, collectively cannot be completely satisfied. As a result, samplers must be calibrated to determine their efficiencies. The efficiency 

of any given sampler may vary with any or all of the following factors : velocity, depth, particle size, bedload magnitude, degree of filling, and bed configuration. Inasmuch as all these factors vary in 

a natural stream, efficiencies are highly variable and uncertain.

The bed configuration is a particularly important factor because 

its effect on efficiency is superimposed, through sampler orientation 

and stability, on the other factors. Although discussions of the 

effects of bed configuration on efficiency are not available from the
4 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

literature, certain effects seem probable. If the bed relief is formed 

by dunes that are large relative to the sampler, the sampler location 

and orientation with respect to the dunes would cause the efficiency 

to vary radically. Thus, variability in efficiency is the least when 

the bed relief is low, except possibly if high velocity makes the 

sampler unstable. Also, if the bed relief is formed by antidunes, 

which are usually unstable, sampler stability, and therefore efficiency, 

probably will be affected adversely. Inasmuch as bed relief can 

be approximated roughly according to the Froude number, certain 

generalities about the variability of efficiency can also be made according to the Froude number. Tranquil flow over movable material 

generally forms, successively, ripples, dunes, a so-called transition bed, 

and possibly antidunes as the Froude number increases. Rapid flow 

generally forms a transition bed and then antidunes as the Froude 

number increases. Hence, in tranquil flow, sampler efficiencies might 

be expected to be least variable at low Froude numbers, highly variable at Froude numbers from about 0.3 to 0.6, only fairly variable at 

Froude numbers from about 0.6 to 0.8 (if the sampler remains 

stable), and highly variable at Froude numbers from about 0.8 to 1.0 

and throughout the rapid-flow regime.

Besides variable and uncertain efficiencies, other factors cause inaccuracy in bedload sampling. Probably the factor that contributes most to inaccuracy is the oscillatory variation in the bedload 

discharge. This phenomenon has been commented on by many investigators. From measurements made with bedload samplers, Ehrenberger (1931) was able to characterize the variations in the Danube 

and Inn Rivers with an almost constant period of oscillation, AZOT . 

(See fig. 1.) Einstein (1937) also measured variations during his 

laboratory calibration tests of the Nesper bedload sampler (fig. 2). 

The significance of the variations in the measurement of bedload 

lies in the fact that short-term measurements at a point are very 

likely to be unrepresentative of the mean bedload discharge at the 

point. Thus, each sampling point must be sampled many times over 

a long period in order to achieve any reasonable accuracy. Ehrenberger concluded that greater accuracy can be achieved by measuring 

a few verticals for a long time than by measuring many verticals for 

a short tune. Also, Einstein (1948) has pointed out that many samples at each point are required and that, consequently, sampling a 

single cross section may take as much as a whole day. Because of 

the time element, bedload sampling with an apparatus that measures 

the load at a point for only short periods of time is not accurate with 

changing flow conditions.

Another factor that contributes to inaccuracies in bedload sampling is the inadvertent collection of bed material. Because of hy-
SOME ASPECTS OF MEASURING SEDIMENT DISCHARGE

1500-1

1000-

1500-,

1000-

10:00 11:00 TIME 3-.00 4:00 5:00

A, B, DANUBE RIVER AT VIENNA 

(measurements by Ehrenberger)

10:30 ii:00

C, INN RIVER AT KIRCHBICHL 

(measurements by Muhlhofer)

FIGURE 1. Variation of sampled bedload discharge (from Ehrenberger, 1931).

draulic resistance, most samplers are subjected to a large downstream 

drag force and must be supported by an elaborate cable system. As 

the sampler is lowered into layers of progressively decreasing velocity, 

the drag force continuously decreases. As a result, the sampler 

achieves an upstream motion from its own weight and from the elasticity of the front stay lines. If the motion is not arrested before 

the sampler reaches the bed, the sampler may scoop up bed material. 

Also, once the sampler is on the bed, the turbulence causes the drag 

force to fluctuate; as a result, the net force on the sampler oscillates 

and may cause th# sampler to move back and forth and scoop up bed 

material. The scooping of bed material is probably most likely if 

the sampler is inadvertently lowered into a trough in the bed.

CALIBRATION OF BEDLOAD SAMPLERS

The sampling efficiency of a bedload sampler can be defined as the 

ratio of the weight of bedload collected during any single sampling 

time to the weight of bedload that would have passed through the
APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

1600

800

25 30 35

MINUTES

FIGURE 2. Results of bedload collections during one hour in a laboratory flume (from

Einstein, 1937).

sampler width in the same time had the sampler not been there. 

Needless to say, truly representative sampling efficiencies for prototype samplers are extremely difficult, if not impossible, to determine. 

Ordinarily, the sampling efficiency of a sampler can be determined 

most easily and accurately through tests in a laboratory flume; however, even under controlled conditions in a flume, several difficulties 

are encountered. The difficulties result not only from the variation 

of efficiency with several hydraulic and sediment variables (see under 

"Some aspects of measuring sediment discharge") but, also from 

several other physical restrictions. One difficulty is the determination of the bedload that would have passed through the width occupied by the sampler had it not been there. Because the magnitude 

of the bedload discharge oscillates and varies laterally across the 

flume, a bedload discharge that is measured at a particular time across 

the end of the flume or across some part of the end will not necessarily 

reflect the bedload discharge for the same time and the same lateral 

location at a given cross section in the flume. Thus, some corrective 

procedure must be applied to the measured loads so that they will 

be representative of the discharge at a given place upstream in the 

flume. Another difficulty arises because full-size samplers are generally so large that they alter the flow pattern in common-size laboratory flumes to such an extent that the calibration is invalid; therefore,
DETERMINING THE TOTAL LOAD 7

scale models must be used. However, the use of models produces 

the problem inherent in most sediment model studies the lack of 

similarity.

Bedload samplers have been calibrated both in flumes with fixed 

beds and in flumes with movable beds. Ehrenberger (1932) calibrated his sampler in a flat-bottomed laboratory flume by placing 

models of the sampler in the middle of the flume at a point downstream from the sediment injecting device where the sediment was 

assumed to be transported along the flume bottom in a normal manner 

and evenly distributed across the width of the flume. By knowing 

the amount of sediment injected into the flow, 6??, the amount retained 

in the sampler, G, and the ratio of the flume width to sampler width, 

W/w, Ehrenberger computed the efficiency, in percent, from Eff.= 

(G W/Gtw)lQQ. With this type of calibration, the following facts 

are ignored: The bed material, the bed shape, and the vertical orientation of the sampler may affect the efficiency; the sediment and 

flow conditions are not mutually related as they are in a natural 

stream; the sediment probably is not transported at the same rate 

everywhere across the flume; and the bedload discharge may vary 

along the flume.

Einstein (1937) used a calibration procedure that was intended to 

indicate, as nearly as possible, the efficiency a sampler would have in a 

natural stream. The procedure differed from Ehrenberger's procedure in several respects the flume contained bed material scaled to 

the river material in approximately the same proportion as the modelprototype ratio, the lateral distribution of bedload discharge upstream 

in the flume was determined by special measurements, and individual 

measurements were treated as statistical quantities. The efficiency 

was determined by comparing the average bedload discharge measured at the end of the flume with the average local bedload discharge 

determined from sampler measurements that were adjusted in accordance with the lateral distribution to represent the load for the entire 

width.

DETERMINING THE TOTAL LOAD

The determination of the total sediment discharge is not necessarily the simple summation of the measured suspended-sediment discharge and the discharge from a bedload measuring apparatus. For 

many conditions, the determination of total load becomes somewhat 

complicated and is dependent on theoretical considerations. The 

reasons for the complications are that the measured suspended-sediment discharge is not necessarily the total suspended-sediment discharge and that some bedload measuring apparatus measure more
8 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

than the bedload discharge. Normally, the measured concentration, 

which with present-day suspended-sediment samplers represents only 

the concentration from the water surface to 0.3 or 0.4 foot from the 

streambed, is multiplied by the total flow and a constant to give the 

measured suspended-sediment load. Consequently, if the concentration of a particular size range in the unsampled depth is greater 

than that in the sampled depth (if a concentration gradient exists), 

some of the load in the unsampled depth will not be included in the 

computation. Therefore, if the measured suspended-sediment load 

for the size range is summed with the results of a bedload measurement that represents only the bedload, the total load of the range 

will be low. Whereas, if the measured suspended-sediment load is 

summed with the results of a bedload measurement that represents 

the bedload plus some of the suspended-sediment load, the total load 

of the range may be either too large or too small; the direction of 

error depends on how much of the unsampled depth (depth from 

lowest point measured with suspended-sediment sampling equipment 

to streambed) is measured by the bedload apparatus.

For all conditions the following general formula is applicable for 

determining the total sediment discharge of a size range:

T=Dle+Q.M +Qu.M1 -FQ.M+(l-Ele)Qt.a 

where

T is the total sediment discharge of the size range.

D is the discharge of the size range as measured with the bedload

apparatus. If the apparatus measures more than the bedload

discharge, D includes some of the suspended-sediment discharge.

If the apparatus measures only the bedload discharge, D=B.

e is the efficiency of the bedload apparatus in measuring the bedload

discharge of the size range.

Q,M is the measured suspended-sediment discharge of the size range. 

It equals the product of the total water discharge, a units 

conversion constant, and the velocity-weighted mean concentration in the sampled zone.

QuiMl is the unmeasured suspended-sediment discharge of the size range 

in the depth between the lowest point measured by the supsendedsediment sampler and the highest point measured by the bedload 

apparatus. It equals the product of the water discharge in this 

depth, a units conversion constant, and the difference between 

the velocity-weighted mean concentrations in the sampled 

zone and in this depth.

F is the fraction that the flow in the depth measured by the bedload 

apparatus is of the total flow.

E is the efficiency of the bedload apparatus in measuring the 

suspended-sediment discharge of the size range that passes 

through the depth measured by the apparatus.

Qts2 is the total suspended-sediment discharge of the size range through 

the depth measured by the bedload apparatus.

Simplifications of the general formula can be made for different 

combinations of particle-size ranges (expressed as bedload or suspended load), vertical distribution of suspended-sediment concen-
EARLY BE DLOAD-MEASURING APPARATUS 9

tration, and type of bedload measuring apparatus. Table 1 shows, 

for each combination, the equivalent of each factor in the general 

equation and the simplified formula. The formulas in table 1 indicate 

that for particle-size ranges transported only as suspended load, the 

least effort is involved in the computation if a bedload apparatus that 

measures only the bedload is used; for particle-size ranges transported 

only as bedload, any type of bedload measuring apparatus is equally 

convenient; and for particle-size ranges transported as both bedload 

and suspended load, the apparatus that measures only the bedload is 

possibly the most convenient. These facts for individual size ranges 

lead to the following general conclusion: For all streams, regardless 

of how any particle-size range is transported, an apparatus that 

measures only the bedload is preferable.

EARLY BEDLOAD-MEASURING APPARATUS

Before about 1940, most bedload measurements were made with 

direct-collecting samplers. Many of the samplers developed up to 

that time have been described in detail in Report 2, "Equipment 

Used for Sampling Bed Load and Bed Material," of the Federal InterAgency River Basin Committee (1940) and will be mentioned only 

briefly here. In general, all these samplers can be classified according 

to one or a combination of the following types: box or basket, pan 

or tray, pressure difference, and slot or pit.

BOX OB BASKET SAMPLERS

Box or basket samplers operate by retaining sediment that is deposited in the sampler because of a reduction in the flow velocity and 

(or) that is screened from the flow. Usually, box samplers are open 

only at the front and top; and basket samplers are open, but screened, 

on all sides except the front and possibly the bottom. In general, the 

basket type has been adopted in preference to the box type. Several 

of the most highly developed and tested basket samplers are those 

designed by Miihlhofer (Ehrenberger, 1932), Ehrenberger (1932), 

Nesper (1937), and the Swiss Federal Authority (1939). (See figs. 

3-6.) All these samplers are similar in design, but each is an improvement over its predecessor. The Miihlofer sampler had a solid bottom ; each of the others had a bottom of loosely woven iron rings that 

conformed to the shape of the bed.

In general, the average efficiency of a basket sampler is about 45 

percent. However, Einstein (1937) measured efficiencies with the 

Nesper sampler from about 90 to 20 percent, depending on the particle 

size and discharge of the bedload; Ehrenberger (1932) determined 

efficiencies for his sampler from about 92 to 80 percent, depending on
TABLE 1. Simplified formulas for computing the total sedimen

[/3, bedload; s, suspended sediment having a uniform vertical distribution; a, suspen

bution; W, measures only bedload; Y, measures bedload plus suspended sedime

plus suspended sediment in part of unsampled depth]

Particle-size 

range transported as 

s

s

s

a

a

a

ft

ft

ft

fts

fts

fts

ft, ff

ft, ff

ft, a

Type of 

bedload 

measuring 

apparatus

W

Y

Z

W

Y

Z

W

Y

Z

W

Y

Z

W

Y

Z

Equivalent

D/e

0

(E/e)Q ts2

(E/e)Q t ,2

0

(E/e~)Q ta2

(E/e~)Q ts2

B/e

B/e

B,'e

B,'e

B/e+(E/e')Qts2

B/e+(E/e-)Q ti2

B'e

B/e+(E/e-)Q tS2

B/e+(E/e)Q ts2

QsM

QsM

QsM

QsM

QsM

QsM

QsM

0

0

0

QsM

QsM

QsM

QsM

QsM

QsM

QusMl

0

0

0

QusM1

0

QusM1

0

0

0

0

0

0

QusMl

0

QusMl

F

0

F

F

0

F

F

0

F

F

0

F

F

0

F

F

Q,

0

FQsM

FQsM

0

Qts2

Qt*2

0

0

0

0

FQsM

FQsM

0

Qts2

Q»>

1 or Q,M-\-Qu*M where QU sM is unmeasured suspended-sediment discharge in unsa
EARLY BEDLOAD-MEASUEING APPARATUS 11

FIGDKE 3. Miihlhofer sampler (from Ehrenberger, 1932).

FIGURE 4. Ehrenberger sampler frame (from Ehrenberger, 1931). Mesh basket is inserted

into frame.
12 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

FIGURE 5. Nesper sampler (from Einstein, 1937).

the bottom velocity, the particle sizes of bedload, and the degree of 

filling of the sampler (he later revised these efficiencies downward 

after recalibrating his sampler in a flume having a movable bed rather 

than a metal floor) ; and the Swiss Federal Authority (Federal InterAgency River Basin Committee, 1940) computed efficiencies for their 

sampler and found that they varied with the sampling time and the 

bedload discharge.

Because basket samplers have a large capacity, they are suited for 

measuring large particles. However, small particles, including suspended-sediment particles, can also be collected if the screen openings 

are sufficiently small.

The most extensive use of basket samplers was in Europe in the 

1930's. Although the samplers were used primarily as an aid in the
EARLY BEDLOAD-MEASURING APPARATUS 13

FIGURE 6. Swiss Federal Authority sampler (from Swiss Federal Authority, 1939).

solution of specific river problems, they also were used for checking 

the validity of bedload formulas. The Schoklitsch formula was 

checked by both Ehrenberger (1931) and Schoklitsch (1934), who 

used the data from Ehrenberger's sampling of the Danube Kiver at 

Vienna, where particle sizes from about 5 to 75 mm were collected. 

An early form of the Meyer-Peter and Miiller equation was checked 

with bedload measurements and other field data by Miiller (1937) as a 

part of a study of the Rhine River, where the coarse sediment is mainly 

from 5 to 100 mm. The study, which was proposed by Meyer-Peter, 

also included the calibration of the Nesper sampler by Einstein (1937) 

and the use of the sampler in the field by Nesper (1937).

PAN OR TRAY SAMPLERS

Pan or tray samplers operate by retaining the sediment that drops 

into a slot or slots after it has rolled, slid, or skipped up an entrance 

ramp. Hence, this type of sampler collects mainly bedload. Shamov 

(1935) has described and tested the operation of several different 

models of pan samplers that have been used principally in Russia for 

measuring the bedload discharge of sands. He found that average 

efficiencies for the Losiebsky (fig. 7), Polyakov (fig. 8), and Scientific 

Research Institute of Hydrotechnics (SRIH) (fig. 9) samplers were 

38 percent, 46 percent, and 75 percent, respectively, and that the effi-
14 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

SECTION 

FIGURE 7. Losiebsky sampler (from Federal Inter-Agency Hiver Basin Committee, 194*0).

>7s777S777777777S77777/77777777777777777~77

SECTION 

FIGURE 8. Polyakov sampler (from Federal Inter-Agency River Basin Committee, 1940).

ciencies increased as velocities increased from 1.3 to 1.75 feet per second but decreased markedly when the velocities were greater than 2.1 

feet per second (partly because some of the bedload moved as suspended 

sediment). He concluded that the upstream ramps of the Losiebsky 

and Polyakov samplers contributed to their low efficiencies by creating 

mounds of sediment in front of the ramps, whereas the SRIH sampler 

with its conelike entrance did not create this condition. The tests also 

showed that the series of slots in the Poyakov and SRIH samplers were 

superior to the single slot of the Losiebsky sampler because they did 

not create a large eddy over the slots.

Several writers (Polyakov, 1932; Einstein, 1948) have recommended 

that this type of sampler be limited to applications in streams having 

low velocities and low bedload discharges.

PRESSURE-DIFFERENCE SAMPLERS

In the operation of ordinary basket and pan samplers, the flow 

resistance of the sampler produces a decrease in the velocity at the

SECTION

FIGURE 9. Scientific Research Institute of Hydrotechnics (SRIH) sampler (from Federal 

Inter-Agency River Basin Committee, 1940).
EARLY BEDLOAD-MEASURING APPARATUS

15

theKm r Was made by G°ncharov; 

the SKIH sampler and the sampler developed by J. M. Terry of the

Inte 7 T^ "5° ^ °f the P^-diflerence ty^e (FedInter-Agency Eiver Basin Committee, 1940). Probably the best Sn ^s type rf sampier is the Imhe- - DU*<* -mS

10). This sampler ls composed of a rigid rectangular entrance

FIGUEE 10. Arnhem sampler (from Einstein, 1948).

that is connected by a diverging rubber neck to a basket of 0.2- to 

0.3-mm mesh. Because of the mesh size, the sampler is capable of 

measuring the discharge of particles as small as medium sand The
16 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

sampling efficiency of the Arnhem sampler is about 70 percent 

(Meyer-Peter, 1937).

Although the results of specific measurements with the Arnhem 

sampler are not readily available, this author is familiar with some 

measurements that were made by L. C. Fowler (written communication) in 1954 on the Middle Loup River at Dunning, Nebr. In 

these measurements the computed average bedload discharge was 

low in comparison with the difference between the total sediment 

discharge as measured at the turbulence flume (Benedict, Albertson, 

and Hatejka, 1955) and the suspended-sediment discharge as measured at a normal stream cross section. However, the most striking 

thing about the measurements was the variability in the sampling 

rate, which ranged from 11 to 112 cc per minute at one point. The 

variability of the sampling rate probably accounts in a large part 

for the low computed discharge and confirms the fact that numerous bodload samples are required for an accurate determination of 

the bedload discharge.

SLOT OB PIT SAMPLERS

Slots or pits that catch the sediment as it moves along the streambed h|ve been used by several investigators to determine characteristics of the bedload transport. Miihlhofer (Federal Inter-Agency 

River Basin Committee, 1940) trapped sediment with the arrangement shown in figure 11, to determine the size distribution of the 

bedload. Other investigators have determined the bedload discharge 

by measuring the time required for a pit of known volume to fill. 

Probably the most elaborate installations were those of the Soil Conservation Service on the Enoree River and Mountain Creek near 

Greenville, S.C. (Federal Inter-Agency River Basin Committee, 

1940; Einstein, 1944). Although the Enoree River apparatus (fig. 

12) is a permanent installation and the Mountain Creek apparatus 

is semiportable, both operate on the same principle the continuous 

withdrawal and weighing of the bedload after it falls into the slot 

or pit.

Experiments have shown that samplers having slot widths of 

100- to 200-grain diameters are capable of collecting nearly 100 percent of the bedload (Einstein, 1944). The disadvantage of slot or 

pit samplers is that they must be placed into the streambed and 

cannot be emptied except by pumping or digging.

RECENT BEDLOAD-MEASURING APPARATUS

Recently developed bedload equipment generally can be classified 

as direct- or indirect-measuring apparatus. With the exceptions of 

a pumping sampler and a magnetic sampler, the direct-measuring
RECENT BEDLOAD-MEASURING APPARATUS 17

FIGURE 11. Miihlhofer pit sampler (from Federal InterAgency River Basin Committee, 1940).

apparatus basically are improved models of the early pressure-difference samplers. On the other hand, the indirect-measuring apparatus, 

which measure some consequential characteristic of sediment movement rather than bedload discharge directly, are radical departures 

from any type of early sampler. Inasmuch as the indirect approach 

to the determination of bedload discharge is relatively new, some of 

the apparatus are not fully developed. Also, some of the apparatus 

are intended only as aids in studying the nature of bedload movement.
18 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

FIGURE 12. Enoree River sampling Installation (from Dobson and Johnson, 1940). 

DIRECT-MEASURING APPARATUS

Vinckers, Bijker, and Schijf (1953) have described a bedload sampler that measures grain sizes smaller than 0.40 mm and that was 

developed by the Research Department of the Rijkswaterstaat and the 

Hydraulic Laboratory at Delft, Netherlands. In this sampler, called 

"Sphinx," (fig. 13) the flow enters through a rectangular nozzle that 

gradually becomes circular, then through a series of settling chambers, 

and then out a wide exit at the rear. The sampler has been designed 

so that the hydraulic efficiency the ratio of water discharge through 

the sampler to the product of the undisturbed mean velocity of the 

stream at the nozzle location and the area of the nozzle entrance is 

about 1.09 for clear flow, slightly lower for fairly high loads, and 

between 0.9 and 1.0 for extreme conditions. Sampling-efficiency tests 

indicate that about 8 percent of the sediment that enters the sampler 

passes on through when the median grain size is slightly greater than 

0.2 mm and that 12 to 15 percent passes through when the sand is finer 

than about 0.09 mm. However, no information is available on the 

absolute sampling efficiency.
RECENT BEDLOAD-MEASURESTG APPARATUS 19

0.60m 0.03m

0.05 m

FIGURE 13. The Sphinx sampler (from Vinckers, Bljker, and Schijf, 1953).

The Corps of Engineers, Little Hock, Ark., U.S. Army Engineer 

District, (written communication) have developed an experimental 

bedload sampler that measures sand and gravel and that contains some 

of the basic features of the SRIH and Terry samplers. The sampler 

(fig. 14) consists of a diverging rectangular box with a series of canted 

baffles (or slots) that retain the skipping, rolling, and sliding particles 

and any other sediment deposited as a result of the decrease in velocity. 

Mean entrance velocities have been made about equal to mean stream 

velocities at the sampling points by making the lower part of the rear 

gate, which remains in the closed position except when the sample is 

removed, a specific height. During sampling, the entrance ramp is 

pressed against the bed by means of a spring, and the supporting 

frame for the side weights, which is attached to the sampler with 

sleeves, settles into the bed independently of the sampler. Both the 

entrance ramp and the upper part of the rear gate automatically retract and close off the ends whenever the weight of the sampler is 

supported by the suspension cable. The large fin is necessary in raising and lowering the sampler in high velocity flow. Although the 

sampler has not been calibrated and its sampling efficiency is unknown, 

it has been used successfully to determine the sizes of particles transported, the stage at which appreciable movement begins, the relative 

amount and size of material transported at various locations on the 

bed, and the approximate accuracy of various tractive-force bedload 

formulas.
20 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

FIGURE 14. Experimental sampler of U.S. Army Corps of Engineers, Little Rock, Ark. 

(U.S. Army photographs) : A, Parts diagram ; B, Sampler in lowering position.
RECENT BEDLOAD-MEASURING APPARATUS 21

FIGURE 15. Interior of Karolyi sampler (from Karolyi, 1947).

Karolyi (1947) developed a pressure-difference sampler (fig. 15) 

for measuring the bedload discharge of coarse sand and gravel. The 

principal feature of the sampler is a horizontal curved dividing wall 

that is about midway between the top and bottom of the rear of the 

sampler. This wall, which divides the lower sediment-retaining part 

of the sampler from the upper direct-flow-through part, is perforated 

at the rear. In the operation of the sampler, the bedload laden flow 

passes beneath the wall, rises through the perforations, and passes 

out the exist of the sampler. This action causes the load to be deposited at the rear of the sampler. (See fig. 15.) Other features of 

the sampler include a rubber-sheeting bottom at the entrance to insure conformation with the bed, an exit closure that operates automatically and is open only when the sampler is on the bed, signal 

lights to indicate the beginning and ending of sampling, and a side 

door for emptying the trap. In large rivers, this sampler, like most 

other traps, requires an elaborate suspension and anchor system to 

insure stability of the sampler on the bed.

Karolyi used the sampler in the field and assumed that it had a 

relatively high sampling efficiency if the sampling periods were short. 

However, Novak (1957) found in laboratory calibration tests that the 

hydraulic efficiency was about 80 percent and the sampling efficiency 

was about 45 percent. Although these efficiencies are relatively low, 

they do not vary radically with velocity or particle size as do the 

efficiencies of most other trap-type samplers.

Novak (1957) has developed a pressure-difference type sampler, 

called the VUV sampler, for measuring the discharge of sediment 

particles from 1 to 100 mm in diameter. The sampler (fig. 16), which 

is basically an improvement of the Karolyi sampler, is 130 cm long, 

45 cm high, and 50 cm wide and collects about a 25-kg sample. Like 

the Karolyi sampler, the VUV sampler has a perforated dividing
22 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

FIGURE 16. VUV sampler (from Novak, 1957) : A, Sampler in operating 

position; B, Top and side views of sampler ; C, Flow pattern through 

the sampler.

wall; however, the perforations consist of 1 large and 8 small mesh 

windows. (See fig. WB.) Flow through the sampler exits from the 

unobstructed section above the dividing wall and from a 5.5-cm meshcovered canted slot just below the dividing wall. The entrance and
RECENT BEDLOAD-MEASURING APPARATUS 23

exit areas have been designed to give a hydraulic efficiency of about 

100 percent. The flow pattern through the sampler is shown in 

figure 16 0.

Novak determined the sampling efficiency of the VUV, Karolyi, 

Nesper, and Ehrenberger samplers and a wire-mesh sampler. His 

laboratory studies, which were extremely comprehensive, were made 

in flumes 60, 100, and 250 cm wide and with sampler models that 

had scale ratios of 1:1,1: 2,1:4, and 1: 8. Kuns were made with the 

samplers placed on concrete floors (Ehrenberger method) and on 

movable beds (Einstein method), with particle-size mixtures and individual fractions of bedload that ranged from 0.1 to 100 mm, and 

with mean velocities that ranged from 0.6 to 2.2 meters per second. 

The model scales, particle-size ranges, and velocity ranges were 

selected so as to maintain an approximate similarity with the flume 

size. Sampling efficiencies were determined according to the concept used by Einstein that the efficiency is the ratio of the weight 

of sediment retained by the sampler to the weight of sediment that 

would normally pass through the area occupied by the sampler. Efficiencies for all the samplers tested are given in table 2. The field 

efficiencies recommended by Novak are 70 percent for the VUV 

sampler, 40 percent for the Nesper sampler, and 60 percent for the 

Ehrenberger sampler. Both the 40 percent and the 60 percent agree 

reasonably well with the efficiencies previously established by Einstein 

and Ehrenberger.

TABLE 2. Results from sampler calibrations by Novak (1957) 

[Sampling efficiency: 1, concrete bed; 2, movable bed]

Sampler

VUV.-. -.--

Karolyi-.. ....

Ehrenberger. .....

Scale 

ratio 

(model 

to prototype)

1:1 

1:2

1:4 

1:8

&

1:4 

1:8 

1:1 

1:2 

1:4 

) 1:1 

I 1:4 

f 1:1 

\ 1:4

Ratio of flume width 

to sampler width in 

indicated flnme

250cm

5 

10

3.9

7.8

5 

10

5

5

100 cm

4 

8 

16

3.7 

6.25 

12.5

4 

8

8

8

60cm

4.8

3.75

7.5

4.8

Sampling efficiency, in 

percent, as determined 

in indicated flume

250cm

1

82 

70

92

75

55 

?7

75

80

2

52 

64

64

40

34

100 cm

1

75 

93

sa

80 

85 

75

47

67

65

74

2

30 

61 

55

45 

53

48

36

22

49

CO cm

1

 

65

50

2

65

65 

42

....

Recommended 

overall 

field 

sampling 

efficiency, 

in percent

70 

65

45

} 40 1 60

Hydraulic 

efficiency, 

in percent

.

f 161

1=S
24 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

In addition to the information given in table 2, Novak also concluded 

from the sampler tests:

1. With a uniform size of bedload and with samplers that have thin 

lower front edges, the efficiency increases only slightly, if at all, as 

the particle size increases.

2. The VUV, wire-mesh, and Karolyi samplers retain particle-size 

distributions that agree, in general, with the distribution of the 

actual bedload, except for the sizes smaller than the mesh of the 

wire-mesh sampler and except for Karolyi samplers having blunt 

lower front edges.

3. For samplers having a thin lower front edge, efficiencies may increase slightly as velocity increases.

4. The height of the lower front edge of the sampler affects the efficiency materially, particularly for the particle sizes smaller than 

the height of the edge. The lower inlet edge should be sharp and 

gently sloping.

5. Hydraulic efficiency is only a qualitative index to sampling

efficiency.

Uppal and Gupta (1958) have described two pressure-difference 

samplers that have been developed and tested at the Irrigation and 

Power Research Institute, Punjab. One of these samplers, sampler 

B, (fig. 17) has a horizontal curved wall, slotted at the rear, that 

divides the inside of the sampler into an upper part and a lower part 

in a manner similar to that of the Karolyi and VUV samplers. The 

other sampler, sampler A, has a rapidly expanding cross section and 

one vertical and one canted baffle for retaining the sediment. Laboratory tests of both of these samplers show sampling efficiencies of about 

90 percent at stream velocities of 0.38 to 2.03 feet per second. The 

laboratory studies were made by comparing the weight of material 

collected in the 4-inch-wide sampler models with that collected in a 

7-inch-wide box at the lower end of the flume; efficiencies were determined by assuming that the load did not vary with the width. The 

efficiency of the prototype of sampler B was concluded to be the same 

as the efficiency of the model after tests in a canal showed that the ratio 

of weight of material collected in the prototype to that in the model 

was 2.7, whereas the scale ratio was 2.5. Information is not available 

on the efficiencies by size ranges nor on the hydraulic efficiency. Also, 

information is not given as to whether the models were tested on a 

solid or movable bed.

Hiranandani (1943) described a proposed sampler that operates on 

a pumping principle. The sampler (fig. 18) consists of a nozzle attached to the suction side of a pump. Attached to the nozzle are two 

Pitot tubes, one of which is about 2 inches from the outside wall of
RECENT BEDLOAD-MEASURING APPARATUS 25

FIGURE 17. Sampler B of the Irrigation and Power Research Institute, Punjab (from

Uppal and Gupta, 1958).

the nozzle and one of which is on the inside and at the center of the 

nozzle. Each Pitot tube is connected to one side of a manometer so 

that the liquid levels in the manometer are equal when the velocities 

are equal. The pump discharge is regulated to attain the equal velocities. The sampler is intended as a point-integrating sampler for 

suspended sediment as well as a bedload sampler. Information is not 

available on whether or not such a sampler was ever constructed. Presumably, the sampler is limited in application to the measurement of 

the discharge of sands.

V. C. Kennedy (written communication, 1959) has suggested a 

magnetic bedload sampler for collecting particles from about 0.05 to 

5.0 mm that are composed wholly or partly of magnetic minerals. 

The proposed sampler would consist of a series of electromagnets in 

the form of parallel vanes either completely or partially encased in a 

housing similar to that of a pan or pressure-difference sampler. The 

sampler and method are based on the assumption that the total bedload 

discharge can be computed from the discharge of magnetic-mineral 

particles that have the same size and shape and that behave in substantially the same way as nonmagnetic particles. Magnetic minerals 

have specific gravities as high as 5.2; therefore, the specific gravity a
26 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

I I M 1,111 !

'!

Rotary pump

Suction pipePitot tubes

Manometer

-Pitot tube inside suction pipe 

Pitot tube outside suction pipe

~ FIGURE 18. Suction-type sampler proposed by Hiranandani (fromi Hiranandani,

1943).

particle must have before its behavior is significantly different from 

the majority of nonmagnetic particles of the same size should be considered in the method. Tentatively, Kennedy has assumed that magnetic particles have a specific gravity of less than 2.90 can be used for 

determining the bedload discharge. The bedload discharge would be 

computed for each size range by dividing the collected weight of par-
RECENT BEDLOAD-MEASURING APPARATUS 27

tides having a specific gravity of less than 2.90 by the fraction of such 

particles in the bed material; the total bedload discharge would be the 

sum of the individual discharges from each size range.

Because the number of particles that will be collected by the sampler 

depends on the attractive forces of the electromagnets and on the 

forces that act on the particles, the sampler will have to be calibrated 

for different flow conditions, rates of bedload movement, gradations 

of particle size, and particle density. Herein lies a primary difficulty 

with the method. Also, particles must be separated according to 

specific gravity. However, Kennedy has suggested and used the simple 

heavy-liquid flotation method of separation.

Kennedy made preliminary studies of several streams and found 

sufficient quantities of light magnetic-mineral particles to make the 

method feasible. In addition, Mundorff (written communication, 

1955), who also conceived a magnetic sampler, made similar studies 

of several Nebraska sandhill streams in 1954, and found significant 

amounts of magnetic particles.

INDIRECT-MEASURING APPARATUS

Of the indirect-measuring apparatus recently developed, several 

are acoustic instruments, one is an ultrasonic sampler, and one is a 

tiltmeter. All the acoustic instruments and the ultrasonic sampler 

have transducers, which convert acoustical energy to mechanical 

energy, or vice versa. The acoustic instruments are designed to pick 

up the sounds produced by interparticle or particle-instrument collisions and convert them to a variable electric current that is amplified 

and reproduced as sound or some other sensible phenomenon. The 

ultrasonic sampler is designed to give the bedload discharge by 

measuring the flow velocity and the sediment concentration through 

the sampler; the concentration is determined from the absorption 

of ultrasonic energy. The tiltmeter, the only nonelectric apparatus, 

is designed to give the total sediment discharge by measuring the 

ground tilt that results from the passage of sediment loads.

ACOUSTIC INSTRUMENTS

Acoustic apparatus have been used in sediment investigations for 

some time. As early as 1936 a microphone placed close to the water 

surface was used to listen to the sediment movement during the 

formation and passage of large-scale boils (Reitz, 1936), and in 1942 

a hydrophonic detector was constructed at Grenoble. France (Braudeau, 1951).

The Beauvert Laboratory hydrophonic detector, which is a modification of the original Grenoble instrument, was adopted and
28 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

somewhat altered by Braudeau (1951) and others at the Service des 

Etudes et Recherches Hydrauliques, d'Electricite de France. The 

Beauvert Laboratory detector consists of a triangular base plate of 

brass (75 cm on a side), which rests on the bed; a watertight case, 

which is supported 15 cm above the base by three acoustically insulated 

uprights; and a microphone, which is housed in the case and is actuated 

by a plate spring attached to the base. Braudeau's apparatus (fig. 

19) is the same as the Beauvert Laboratory detector except that the

FIGURE 19. Hydrophonic detector of Electricity de France (from "Detecteur Hydroiphonique," Electricity de France, Direction des Etudes et Recherches, Departement 

Essais, written communication, 1960).

microphone rests directly against the base plate and is housed in a 

small watertight, streamlined cupola. In both instruments, the sound 

of the interparticle collisions and of the particle impact on the base 

plate is picked up by the microphone, amplified, and transmitted to 

headphones or a magnetic tape recorder.

Braudeau (1951) states that during tests on the Isere River when 

the flow was regulated to give an increase and then a decrease in the 

bedload discharge
RECENT BEDLOAD-MEASURING APPARATUS 29

The phenomena could be "heard" with an accuracy comparable to that of purely 

visual sensations. Each sound could be distinguished: at the outset, the murmuring of the water, the impacts and the sliding of individual grains of sand; 

then, the progressive arrival of pebbles of different sizes, their rolling or their 

repeated impacts on the plate; finally, as the discharge slowly decreased, the 

more and more frequent sliding of the pebbles and the very gradual return to 

the initial condition.

Juniet (1952) has commented that instruments such as the hydrophonic detector give good results in streams having coarse bed material. However, in streams having fine bed material, the sound level 

is weak, and the presence of a relatively large instrument may disturb 

the flow sufficiently to alter materially the local bedload transport. 

Juniet has developed a much smaller instrument for monitoring 

the bedload movement. The instrument, called L'Arenaphone, (figs. 

20, 21) consists of a rod, which is about 20 cm long and is forkshaped 

at the lower end; a transducer of some piezoelectric material, to which 

the rod is attached; a cylindrical housing for the transducer, sealed 

at the lower end by a watertight membrance through which the rod 

passes and at the upper end by a cap through which an insulated cable 

passes; a tripod, which is fitted with stability discs; and a regulator, 

which is fixed at the top of the tripod and adjusts the vertical position 

of the cylinder and rod. During sediment movement, particles collide 

with each other and with the fork-shaped part of the rod, which is inserted a few centimeters into the bed. The vibrations engendered by 

the collisions are transmitted by the rod to the transducer, which is 

stressed and thereby produces a variable electric current that is 

selectively amplified to filter out the bass frequencies created by the 

interparticle collisions. The amplifier has outputs for headphone, 

oscilloscope, and magnetic tape recorder.

Ivicsics (1956) has presented an acoustic instrument that is somewhat different from the other acoustic instruments already described. 

This instrument, which was developed at Epitoipari Es Kozlekedesi 

Miiszak Egyetem, measures the intensity of sound of only the interparticle collisions. Its unique feature is that it can be suspended 

several meters above the bed; thus, it does not influence the bedload 

movement. The instrument (fig. 22) consists of a streamlined torpedo-shaped body, which is made of 3.5-mm iron plate and weighted 

at the front and rear with lead ballast, and a TO-mm crystal microphone, which is housed in the body. The microphone (see fig. 22B) 

faces downward, and a 0.3-mm brass plate seals the microphone cavity 

at the bottom wall of the instrnument. Because the microphone is 

insulated on the sides and above by felt and cotton batting, only 

sound originating directly below the instrument is picked up. The 

sound, in turn, is amplified, and its intensity is registered on an am-
30 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

FIGURE 20. L'Ar naphone (from Juniet, 1952) : Operating 

.position.

meter. The sound can also be transmitted to headphones. The intensity of sound does not change significantly when the instrument is 

raised or lowered within a 5-meter interval because the microphone is 

extremely sensitive.

The instrument is used to determine the relative sediment transport 

in cross sections and the relative variation of transport with time. 

Also, the instrument is used to determine the location and number of 

verticals to be used in bedload sampling with bedload samplers of the 

trap type. Field studies indicate that the relative difference in bedload discharge from one place to another as measured with samplers 

of the trap type sometimes differs greatly from the relative difference
RECENT BEDLOAD-MEASURING APPARATUS 31

FIGURE 21. I/ArSnaphone (from Juniet, 

1952) : Fork and transducer.

as measured with the instrument. (See fig. 23.) The discrepancies 

are assumed to be caused by inaccuracies in the samplers.

ULTRASONIC BEDLOAD SAMPLER

Smoltczyk (1955) has commented in detail on various existing 

methods for measuring the bedload discharge and has experimented 

with several different electronic methods for measuring sediment concentration. The experiments were made as a prelude to the development of a device for measuring the bedload discharge of streams that 

have bed material of fine sand. One method for determining concentration was based on the measurement of the electrical resistance
32 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

B Arnyekolf kiibel 46mm

A tnikrofontortb hosszmetszete

Sargarezmemtiran /]. &0

Figure 22. Ivicsics' acoustic bedload recorder (from Ivicsics, 1956) : 

A, Operating position; B, Plan view.

of water-sediment mixtures. However, this method was rejected because the resistance varied with the particle size and because impurities in the water caused a polarization effect that hindered the 

reproducibility of the results. Measurement of concentration by high 

frequency (ultrasonic) sound waves proved to be very satisfactory and 

was employed in the design of a bedload sampler. Smoltczyk intimates that some experiments were performed with a sampler, but he 

presents no results.

The basis for the ultrasonic method is that different amounts of 

transmitted acoustic energy are absorbed by transmitting mediums 

of different sediment concentrations. Thus, by measuring the degree 

of absorption in a medium of unknown concentration relative to that
RECENT BEDLOAD-MEASURING APPARATUS 33

FIGURE 23. Variation of acoustic energy and sampled bedloati discharge, Rajka gaging 

section (from Ivicsics, 1956).

in a medium of known concentration, the unknown concentration can 

be determined. 

Absorption phenomena are characterized by the function

ti iJoe~a3e 

where

y is the magnitude of a quantity after absorption.

yo is the magnitude of the quantity at some initial condition.

e is the natural logarithm base.

a is the absorption coefficient.

x is the independent variable (such as time, distance, concentration).

For the change in sound-wave amplitude with concentration,

or

where

In A/A0= aCI

A is the amplitude. 

Cp is the concentration.

Smoltczyk, by measuring sediment of different sizes and concentrations, determined that the absorption coefficient was a constant for
34 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

any given size but that it varied from size to size. From measurements, Smoltczyk also determined that the relation between particle 

size and absorption coefficient l was given by

a=pd2m + q

where

p and q are constants for the particular sediment and frequency. 

dm is the characteristic particle size of the size range.

Thus, for any particular kind and size of sediment

or

E=E e~ 

where

E is the sound energy, which is proportional to the square of the amplitude.

Because

E1 =Eoe-> 

and

#2 =#1<r2(1)<

for a mixture of k different particle-size ranges

ET T7T -2Cp (pSjCd2 + )

-Cf fc=.Cro6 m

where

Ek is the- energy received after the sound waves pass through a mixture 

that contains k different size ranges, each of which has a concentration Cpj, Cp2 , . . . Cvk.

CPt is the total concentration and equals CPl +CP2 + . . . +Cpft . 

dm is the characteristic particle size for each size range. 

C is the fraction, for each size range, that the concentration of the 

range is of the total concentration (CVJ = C\CP ^).

Smoltezyk's sampler (fig. 24) is virtually an open-end rectangular 

tube whose interior walls and top are convex toward the inside. The 

convexity causes an increase in the flow velocity and provides side 

walls thick enough to accommodate, on opposite sides, a reflector and 

a quartz crystal transducer, which transmits and receives high frequency sound waves. In addition, one wall of the tube contains a 

control crystal that is near the floor of the instrument and that indicates when the floor is covered with an appreciable amount of sediment. 

Also, Smoltczyk describes, but does not show in the figure, a flow1 Studies made as a part of the research project, "Methods used in measurements and analysis of sediment 

loads in streams," of the Federal Inter-Agency Committee on Water Resources (written communication) 

indicate that this equation is valid for only a limited range of particle sizes and frequencies.
RECENT BEDLOAD-MEASURING APPARATUS 35

tangMctmitt fame Seitenruder und (Inter) QueruMtt

ffbb.36: (MnschaQsande or fanaeschietKmeswng.

(M. 1:2, 1:*»

FIGURE 24. Smoltczyk's ultrasonic bedload sampler (from Smoltczyk, 1955).

velocity measuring apparatus consisting of two transducers which are 

fixed at opposite ends of the tube in such a way that each receives the 

signals transmitted by the other. The basis of operation for this velocity apparatus is that sound waves traveling downstream will have a 

velocity of Fs +Ff, and those traveling upstream will have a velocity 

of Vs Vf ; thus, Vf = Vs (tu fa) / (fa+1»), where Vs and Vt are the 

velocities of sound and flow, respectively, and tu and fa are the times 

required for a sound wave to pass between the transducers in an upstream and downstream direction, respectively.

The sampler measures continuously the parameters required for the 

determination of the flow velocity and the amplitudes of the reflected 

sound waves. By installing modulating and integrating elements into 

the electronic system, the logarithms of the amplitudes are electronically determined and converted to concentrations, the flow velocity 

is determined, and these data are combined to give a continuous record 

of accumulated weight with time.

The method, of course, cannot be applied without a knowledge of 

the size distribution of the load. Smoltczyk states that the sensitivity 

of the sonic measurements is sufficient for predicting accurate loads 

only at concentrations greater than about 1 percent and that, for 

streambeds composed of fine sand, such concentrations reflect a condition of the movement of all particle sizes in the bed. As a result, 

Smoltczyk assumes that the particle-size distribution of the bed material is equal to the size distribution of the bedload and that the size
36 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

distribution of the bed material, therefore, can be used in determining 

the concentration.

In addition to the assumption that the size distribution of the load 

is the same as that of the bed material, several other important assumptions seem to be inherent in the method: All particles are transported 

at the velocity of flow; the load passing through the sampler can be 

determined from the product of the mean concentration and the mean 

velocity (that no velocity and concentration gradients exist); the bedload is transported for some distance above the bed; the suspended 

sediment that enters the sampler does not change the absorption or 

the absorption coefficient; and the instrument has hydraulic and sampling efficiencies very close to 100 percent.

TII/TMETER

Taniguchi (1958) has developed a method for computing the total 

sediment load by using a tiltmeter, which measures the variations in 

ground tilt near the channel that result from the passage of different 

weights of water and sediment through the channel. The tiltmeter 

consists of a Zollner pendulum suspension and asociated recording 

equipment. The Zollner pendulum suspension (fig. 25) is a bar, 

weighted at one end, that is supported by a 30-micron-diameter superinvar thread attached near the center of the bar and held in a 

horizontal position by another similar thread attached at the end of 

the bar opposite the weight. The upper or supporting thread is attached to an inverted J-shaped vertical support, and the lower or 

counterbalancing thread is attached to the base into which the vertical 

support is fixed. If the vertical support (and base) is tilted parallel 

to a plane that is perpendicular to the horizontal bar, the bar rotates 

in approximately a horizontal plane. Very small tilting angles produce relatively large turning angles. In the tiltmeter, a mirror, which 

is attached to the horizontal bar, reflects light from an electric bulb in 

a small collimated beam so that the beam strikes photographic paper 

and produces a continuous record of turning angle with time. An 

electric water-stage recorder and thermograph are also arranged to 

record on the same photographic paper.

According to Taniguchi, if the titlting angle, which can be computed from the turning angle, is plotted against the stage, a curve 

similar to OB in figure 26 will result from a sediment-laden flow. 

Also, Taniguchi states that a straight line (see OA in fig. 26) must 

result from a sediment-free flow. Thus, the sediment load at any 

stage is the weight that will produce a tilting angle equal to the difference between the curve and the straight line at that stage.

Taniguchi has reported on two different field measurements with 

the tiltmeter. In both these measurements, two tiltmeters were used
RECENT BEDLOAD-MEASURING APPARATUS 

20mm

37

Base

FIGURE 25. Diagram of Zollner pendulum suspension (from TanigucM, 1958).

(not to scale.

Drawing

and placed so that they were perpendicular to each other. In the first 

measurement, the tilting angles registered by the two meters were 

greater after the subsidence of a high flow than they were prior to 

the flow. The difference in tilting angle was attributed principally 

to sediment deposition in the channel and somewhat to a decrease in 

ground resistance as a result of bank saturation. Subsequent computations showed that the depth of deposit required to cause the difference in tilt was about the same as the measured depth of deposit 

in the channel. In the second measurement, a power failure and equip-
38 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

WATER LEVEL

Figure 26. iRelation between water level and tilting 

angle (from Taniguchi, 1958).

ment damage limited the data; however, the information plotted in 

figure 27 was obtained. The tilt angle and stage curves in figure 27

150

100

Tilting angle

12:00 12:00

1.00 

U 

UJ 

CO

Z 

0.4<

12,'QO

 September 27- September

FIGDRE 27. Tiltmeter chart, Kokidaira in Tone River System, September 27-28 (from

CTaniguchi, 1958).

are combined in figure 28 to show the tilt-stage relation. The dashed 

straight line is the presumed relation between tilting angle and sediment-free flow stage. The conclusion from this second measurement
SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 39 

0.3 (/)

o

2 

O 

O 

LU

? 0.2

uT

o

z

< O.I

o

Presumed sediment-free relation

o 50 100 

WATER LEVEL, IN CENTIMETERS

FIGURE 28. Relation between water level and tilting angle, Kokidaira in Tone River System, September 27-28 (from Taniguchi, 1958).

was that the variation in tilting angle was influenced by something 

besides the flow and the sediment load.

One of several vague points about the tiltmeter method is the use 

of a linear relation between tilting angle and stage for sediment-free 

flow. Taniguchi has not discussed this point except to say that the 

relation must be linear. Because the weight distributions in alluvial 

channels are variable with time, because the bank stability probably 

varies with the degree of saturation, and because channels are usually 

not rectangular, the linear relation between tilting angle and stage 

seems questionable. Another vague point is the determination of the 

sediment discharge from the weight at a given stage. Regardless of 

how the discharge is determined, the accuracy would seem to depend 

on the degree to which the velocity of the sediment particles approaches 

the velocity of the flow.

Probably, the tiltmeter method is applicable only to streams that 

have relatively large variations in sediment discharges and that flow 

through unconsolidated materials.

SOME NEW POSSIBLE APPARATUS AND METHODS 

FOR MEASURING BEDLOAD

None of the recently developed apparatus seem to be completely 

adequate for measuring bedload discharge or total sediment discharge 

accurately. Therefore, some new apparatus and methods have been 

investigated insofar as possible. These apparatus and methods include 

a portable pit sampler; photography; tracking of dune movement,
40 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

particularly by ultrasonic sounding; pressure transducers; and ultrasonic sounding of large particles.

PORTABLE PIT SAMPLER

The most accurate of all the retaining-type bedload samplers is the 

slot or pit sampler. Some preliminary investigations were made on 

possible designs for a small portable pit sampler. The most practical 

design seems to be for one that is modeled after Einstein's Mountain 

Creek sampler, which was semiportable and consisted mainly of a 

hopper and a pumping unit. The sampler, however, would be considerably smaller than the Mountain Creek sampler and would have 

the additional features of portability and automatic placement by 

dredging. Figure 29 shows the contemplated design. The essential 

features are as follows: A hopper that can slide vertically along the 

suction pipe and can be dropped and locked in position after the suction pipe has been inserted into the bed a distance sufficient to offer 

horizontal support against the drag force on the hopper; a small 

motor-pump unit; an automatic valve that closes the lower end of the 

suction pipe after dredging is completed; an automatic valve that 

opens the sides of the suction pipe at the bottom of the hopper so that 

the accumulated bedload can be continuously removed by pumping; 

and a fixed rim at the top of the hopper to insure that the hopper rests 

flush with the bed surface. The practicability and efficiency of such 

a sampler, of course, are subject to question; and the sampler could 

be used only in streams that have predominantly sand beds and low 

velocities, unless stay lines are used. Figures 30 and 31 show that 

if slurry (bed material and water) concentrations of about 100,000 

parts per million were pumped during placement, a hopper with a 

volume of 2.0 cubic feet could be placed into the bed in about 5 minutes 

with a 2-inch pump that discharges 50 gallons per minute and a motor 

that delivers about 3 horsepower (30-foot head).

PHOTOGRAPHY

Motion pictures of bedload movement in several different streams 

and in one canal have been taken to determine if it is possible to estimate the bedload discharge by counting the number and measuring 

the nominal diameter of particles as they move downstream into or 

out of the field of view. Unfortunately, neither an industrial highspeed camera nor a projector that could be used to show individual 

frames at a manually operated speed was available. However, exploratory films, which were taken through a glass-bottom box that was 

fixed to a tripod (see fig. 32), were viewed at one-sixth normal motion 

(64 frames per sec exposure speed and 10.7 frames per sec projection
SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 41
42 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

500,000

z 

o

_l -J

5

CL 

UJ 

Q.

££

<.

Z

z"

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5cr

HUJ

0

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£

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X '

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N

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N

\

s

\

\

\

k

\

N 

\

x

\

-\

s

s

s

\

\

 ^

^ \

-V

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1.0

X;

\

N

N

N

N

s k

s

fc

^

^

X

S

f>

i

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X

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\

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3

N

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: <? '^<0~

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 ^ Ok ^

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k

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S L\

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\

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*s

^

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V 

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1C

TIME, IN MINUTES, TO PUMP ONE CUBIC FOOT OF BED MATERIAL

FIGURE 30. Time required to pump material from the bed at different 

slurry concentrations and pumping rates. Based on a specific weight 

for bed material of 103 pounds per cubic foot.

speed). At this speed, particles larger than about pea size can be 

readily counted if the field of view is divided into lateral segments 

and if the film is projected repeatedly; however, particle diameters 

can be measured only if the motion is further reduced.

In addition to motion reduction, one of the major problems connected with photography is visibility. In order to prevent any disturbance to the bed and bedload movement, the photographic equipment must be placed about 2 feet from the bed. However, limited 

field experience indicates that at a distance of 2 feet, the visibility 

is poor, with concentrations as low as 600 ppm (parts per million) 

of suspended sand; it is probably even poorer with silt and clay suspensions. As a result, the use of photography for estimating bedload discharge is limited to streams having low suspended-sediment 

concentrations and transporting particles about pea size or larger. 

Also, because of the enormous amount of film that would be required 

if bedload movement were photographed for a reasonably long time, 

the method seems generally impractical.

TRACKING OF DUNE MOVEMENT, PARTICULARLY BY 

ULTRASONIC SOUNDING

In 1894, Deacon (Goncharov, 1929) observed in the laboratory that 

the discharge of sediment along the streambed could be determined
SPEED, REVOLUTIONS PUMP INERMINUTE CO 

Or\> 

B o

ra_o o

NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD

-40 ft

20 ft

40 ft

-20 ft

- - 

- 

 - -

~- --

-^ "-

^-

^^

^^

^

^

^--

eed

.

^JsS^""^

x

X

^^

f/

/

ft 5 o 

WBRAKE HORSEPOWER 

D 100 500

PUMP DISCHARGE, IN GALLONS PER MINUTE

FIGURE 31. Relation of pump speed and brake horsepower to the discharge of a 2-inch pump for 20- and 40-foot heads.

from the volume of the sand waves and their crest velocities if the 

stream velocity was less than some critical value. Benedict, Albertson, and Matejka (1955) applied this idea in the field and computed 

the bedload discharge of a sand-bed stream from the average dune 

height and the average dune velocity. In the comp'utation, the dune 

height and velocity were determined from maps of the streamfoed that 

had been defined by 1-hour interval soundings over a short reach of 

the stream. However, the soundings were difficult to obtain and only 

fairly accurate because they had to be made manually. Richardson, 

Simons, and Posakony (1961) developed the following equation for 

the bedload discharge from a differential equation by assuming a 

constant dune shape :

where 

QB is the volume of bedload discharge per unit of width per unit of time. 

X is the porosity of the 'bed material. 

V is the average velocity of dune crests determined by timing the movement of individual crests for a known distance. 

h is the average of individual dune heights determined by measuring the

difference in elevation 'between the crests of individual dunes and the

adjacent downstream troughs. 

G is a constant of integration that, according to the boundary conditions,

is equal to zero.
44 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

FIGURE 32. .Motion-picture apparatus.

Computation of the bedload discharge from dune movement has 

been deterred in the past by an inability to obtain accurate data. Recently, however, studies (op. cit.) made as a part of a research project 

by the U.S. Geological Survey on channel roughness at Colorado 

State University, Fort Collins, Colo., indicate that very accurate and 

meaningful records of dune shape and movement can be obtained with 

ultrasonic sounders (Richardson, Simons, and Posakony, 1961).

Ultrasonic sounders operate by means of a transducer, placed under 

the water surface, which transmits short bursts of ultrasonic energy 

at a constant frequency. The energy travels through the water and 

is reflected back to the transducer by the streambed. The electronic 

system measures the time interval, which is proportional to the depth, 

between the transmission and receipt of the energy and converts the 

time into a voltage that is graphed by a strip recorder as depth.

In the movement of bedload, particles are alternately eroded and 

deposited. Because the erosion and deposition have unequal rates
SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 45

over the bed area, bed configurations develop and continuously change 

their absolute position. Thus, the erosion and deposition determine 

the character and magnitude of the bedload movement and also the 

specific form and rate of movement of the bed configuration. In 

the tranquil-flow regime, erosion predominates on the upstream side 

of the bed forms, and deposition predominates on the downstream 

side; consequently, the bed forms move in the direction of flow.

In natural streams, generally, the bed profile along any longitudinal 

line lacks symmetry and shows no consistent dune shape. Also, the 

dunes differ radically in height and probably differ in velocity. 

Therefore, a relation between the bedload discharge and dune movement would seem to be the most realistic if dune shape and average 

heights and velocities are not critical parameters. Some simplified 

examples of dune movement will serve to explain the development of 

a relation that uses as the critical parameter the volume of material 

presumed to pass through an incremental width in a total time.

For the first example, consider the idealized longitudinal profile 

of a thin increment of the width, die, shown in figure 33. During the 

time period t2 ~t^ volume (abcd)dw progresses the distance ab and, 

in doing so, moves volume (abc)dw past line X-X'. The movement 

is accomplished through the erosion of particles from (abc)dw and 

the deposition of the particles on the downstream side of (adc)dw. 

During the time t3 tz^ particles are similarly eroded from (efg)dw 

and deposited on the downstream side of (ebf)dw so that the volume 

(ebf)dw passes line X-X', Thus, during the total time required to 

move one dune length, t3 t1 =t^ volumes (abc)dw and (ebf)dw pass 

line X-X'. Inasmuch as the bedload moved only in this manner, 

the bedload discharge in the incremental width, die, that passed 

line X-X', or any other line, can be expressed by

or

where 

&= v(al)Cd), '-Aw 

P

=vH Aw

6 is the volume rate of bedload discharge in the incremental width.

v is the dune velocity (v=p/t).

p is the dune length M.

H is the mean height of the dune and is computed so that Hp= (abed) .

However, bedload does not necessarily move according to the above 

concept. Some particles probably are eroded from one dune and 

are not deposited until they reach some other downstream dune.
46 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

/A
SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 47

Consider the simplified example of this phenomenon as shown in 

figure 34. In this figure, the assumption is made that for every three 

particles eroded from a dime, only one is deposted on the downstream 

side of the same dune and the other two pass to the next dune. (This 

assumption probably does not reflect a natural condition, but it does 

facilitate the explanation.) During the time t2 ~t^ the dune progresses the distance ab and, in doing so, moves the volume (abc)dw 

past line X-X'. However, for every particle in (abc)dw^ two others 

also pass line X-X'. Thus, the total volume passing line X-X' in 

time£2 £1 is (abc)dw+2(abc)dw=3(abc)dw. During the time t3 tz, 

volume (ebf}dw passes line X-X' ; but, again, for every particle in 

(e&/)dio, two others also pass line X-X' so that the total volume is 

(ebf)dw+2(ebf)dw = S(ebf)dw. Hence, in time £, volumes 3(abc) 

dio and 3 (ebf) dw pass line X-X'. Because ebf equals adc, the volume 

rate of bedload discharge is expressed by

&=3- _ (abed)  - -

or

In nature, the ratio of the number of particles eroded from the 

upstream side of a dune to those deposited on the downstream side is 

probably not extremely variable. However, the following equation 

should be applicable :

= KvHdw

where

K is a variable coefficient that probably is very close to unity, except 

possibly at times when the bedload discharge is high or when 

the bed relief is low.

For the entire stream width

B-r*X<^>d» (1) 

Jo *

or

B

rw

= KvHdw (2) Jo

However, because the variations in K and (abcd}/t (or vH) between 

elemental widths are indeterminant, equations 1 and 2 must be approximated. These equations probably can best be approximated 

by using a K that is an average for all dunes and all parts of dunes 

within some width interval and by summing into one total area, J., 

all the dbcd-Y&e, areas that pass a representative point within the
Time /,

Time /.

Time

FIGURE 34. Idealized diagram of dune movement if only one of every three particles 

side of the same dune and the other two pass on to 
SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 49

width interval in a reasonably long time, T. For these approximations

where

B'=Z^A (3) 

or

(4) 

in which

Aw is the width interval.

K is the average K for all dunes and all parts of dunes within Aw. 

v is the mean velocity of the part of the dunes that passes the

representative point (v='2p/T=pN/T) . 

~H is the mean height of the part of the dunes that passes the

representative point (H=A/'2p=A/pN). 

p is the mean dune length. 

N is the number of dunes that passes the point in time, T.

If the bedload discharge is expressed as a weight rate rather than a 

volume rate, the foregoing equations become :

QB=^(l-\}y,K^w (5)

or

QB=^l (l-\)v a 'KvTI&w (6)

where

QB is the weight rate of bedload discharge for the entire width of the

stream. 

y, is the specific weight of solid sediment without voids.

Equations 5 and 6, which apply only if the bed is formed of ripples 

and dunes, can be solved if data within each width interval are 

available on the shape of a representative longitudinal profile and 

on the change in bed elevation with time at a representative point. 

The first kind of data is required so that a relation can be established 

between the height of the dunes along the line and the associated 

vertical areas that are subject to movement (the abcd-\ike areas). 

The second kind of data is required so that the total time, T, for a 

number of dunes to move past the point can be determined and so 

that the height of the dunes that actually move past a point can be 

measured and converted to vertical areas with the height- area relation. 

Three different computations of bedload discharge have been made 

from field data by using equation 5. In these computations, the relation between the dune height and vertical dune area was established
50 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

by defining the vertical area as the area that would move if the entire 

profile were to progress downstream without changing its shape and 

by defining the height of the dune as the maximum height associated 

with the area. Thus, the vertical area for any single dune was taken 

as the area bounded by the bed surface and a line, called the dune 

base, that was parallel to the water surface (assuming uniform flow) 

and that passed through the lowest point on the upstream face of 

the dune. Correspondingly, the dune height was taken as the distance, 

perpendicular to the dune base, between the highest point on the surface of the dune and the dune base. (Bed elevations were measured 

relative to the water surface so that the dune baselines are drawn in 

subsequent figures as horizontal.) If the total configuration of a 

large dune appeared to be several dunes, one on top of the other, 

only the uppermost apparent dune was considered as a separate dune 

and all lower parts were considered to be one lower dune. The vertical areas that were presumed to have actually moved were determined 

by converting the dune heights, which were measured on the graphs 

of change in elevation with time, to areas by using the height-area 

relation. Separate dunes were distinguished on the graphs of elevation change with time in the same manner as they were on the profiles, 

and their heights were determined by measuring the distance that 

the bed elevation dropped with the passage of the dune. Whenever 

the drop in bed elevation was irregular so that some parts of the graph 

were horizontal, the configuration was considered to be a dune on 

top of a dune, the uppermost drop was considered to be the height of 

the uppermost dune, and the total of all lower drops was considered 

to be the height of the lower dune. The total time that was used in 

each computation started when the first completely defined dune 

began to pass the sounding point and ended when the last completely 

defined dune had just passed the point. However, in some graphs this 

rule was waived and the time was started with the first sounding 

even though part of the downstream side of the dune did not appear 

on the time graph; the rule was waived in order to extend the total 

time period, but only if the missing time appeared to be insignificant. 

The value of K was necessarily assumed to be equal to 1.0 for all 

computations.

The first computation was made for a part of the width of the 

Little Blue River near Fairbury, Nebr. Data for the computation 

were collected by sounding manually with wading rods in a grid system 25 feet long and 12 feet wide. The sounder always stood at least 

1.5 feet from the point of measurement so that the bed was not disturbed any more than necessary. Sufficient soundings were made to 

define the bed contours (see fig. 35) and the change in bed elevation 

with time at five points on each of five different longitudinal lines.
SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 51

t

«

3NH yO '133d Nl 'H1QIM
52 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

O.I

0.01

o.c

>- x',^^

^

o

/

s

/

/fy

^

/

'

/

o

?2o

o

1 O.I 1.0 1C

VERTICAL DUNE AREA, IN SQUARE FEET

FIGURE 36. Relation between the dune height and the vertical dune area, Little Blue 

River near Fairbury, Nebr., May 28, 1958.

The height-area relation (see fig. 36) was defined by means of dune 

heights and areas that were computed from six profile lines (see fig. 

37) that had been determined from the contour map. Dune heights 

were determined from each of the 25 graphs of elevation change with 

time (see fig. 38) and converted into areas by using the height-area 

relation. The,areas were summed, multiplied by the width interval 

and K, and divided by the total time. The resulting B' values from 

each station on a common line were then averaged. The averages 

were summed to give the total volume discharge, which was converted 

to a weight discharge in tons per day with the factor 74.16 ton minutes per cubic foot day (based on yg = 166 Ibs per cu ft and A=0.38). 

The computation is shown in table 3 together with a comparable bedload discharge computed with the Meyer-Peter and Miiller equation 

(1948).

The second and third computations were made for the Middle Loup 

River at Dunning, Nebr., on August 7 and 8, 1958, at a section about 

300 feet upstream from the turbulence flume (Benedict, Albertson, 

and Matejka, 1955). Manual soundings were made to define the bed 

profiles along five longitudinal lines which were 50 feet long and 

spaced approximately according to water discharge across the entire 

width of the channel. Soundings were also made at a single point 

on each line periodically for about 3 hours. Graphs of some of the 

data from these measurements are given in figures 39 to 44. The
SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 53

to

LJ

Z 

_J

-- 

 -

r

\

sT

Jl

+

10

\

V

^- 

^

\

I

\

^

i

r

\

^

-^

 ?

X

^J

\

/

]/

>

1

\

\

-""

7

\

\

wniva xavanaaw aAoav 'i33d NI '
TABLE 3. Computation of bedload discharge by the dune-tracking method, Little Blu

[Height and measured vertical area used to define height-ar

Dune No.

0-1. ...

0-2 

0-3 

2-1. --

2-2 

2-3 

2-4- 

2-5 

2-6 

2-7 

4-1 

4-2. 

Height 

(ft)

0.20

.15

.05

.20

.05

.05

.05

.30

.05

.15

.25

.20

Measured 

vertical 

area 

(sq ft)

1.05

.45

.25

.54

.02

.10

.05

1.10

.10

.54

1.35

.30

Dune No.

4-3 

4-4- 

6-1 

6-2- 

6-3--- _ -

6-4 - 

6-5 

6-6 

8-1 

8-2_ 

8-3 

8-4 

Height 

(ft)

0.35

.10

.10

.10

.15

.05

.25

.30

.05

.05

.30

.05

Measured 

vertical 

area 

(sq ft)

0.88

.20

.08

.48

.83

.04

.50

.93

.02

.09

.74

.10

Dune 

8-5 

8-6 

10-1 

10-2 _ 

10-3 

10-4 

10-5 -

12-1 

12-2..

12-3.-

12-4 

[Point-time data from graphs of the change in bed elevation with time. Vertica

Station No.

1 .

TotaL 

7 ......... _.

Total- ...

LineO

Point-time data

Dune

No.

0- 1-1 

2 

3

7-1 

2 

3

Height

(ft)

0.10 

.10 

.05

0.05 

.05 

.05

Time 

(min)

114

100

Vertical 

area 

(sq ft)

0.26

.26

.10

0.62

0.10

.10

.10

0.30

Width 

(ft)

1.0

1.0

K

1.0

1.0

B'

(cfm)

0. 00544

0. 00300

Line 2

Point-tune data

Dune

No.

2- 1-1 

2 

3

7-1 

2 

3 

4

Height

(ft)

0.05 

.20 

.10

0.10 

.05 

.05 

.10

Time 

(min)

143

153

Vertical 

area 

(sq ft)

0.10

.62

.26

0.98

0.26

.10

.10

.26

0.72

Width 

(ft)

3.0

3.0

1

1
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SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 57

80 100 

TIME, IN MINUTES

FIGURE 38. Change in bed elevation with time at stations along line O, Little Blue River 

near Fairbury, Nebr., May 28, 1958. Vertical arrows indicate the height of the numbered dune.

computations, which are identical in basic method to the Little Blue 

computation, are shown in tables 4 and 5. Also included in the tables 

are unmeasured sediment discharges that were determined as the difference between the total load measured at the turbulence flume and 

the suspended-sediment discharge measured at the sounding section. 

The computed bedload discharge for August 7 seems to be slightly 

low in comparison with the unmeasured sediment discharge, and the 

discharge for August 8 seems to be too high. Both of these computations have time-sounding periods that were too short; consequently, 

many of the major dune forms were undefined. On August 8 especially, the time period was so short that the soundings reflected mostly 

a lowering of the bed elevation.

In addition to the field computations, three computations have been 

made using data from ultrasonic soundings made by D. B. Simons 

and E. V. Richardson of the U.S. Geological Survey in a flume at 

Fort Collins, Colo. The procedure and the assumptions of these 

computations were the same as those for the field computations except 

that A. was assumed to be equal to 0.35. Table 6 shows the computed
58 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

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VERTICAL DUNE AREA, IN SQUARE FEET

FIGURE 40. Relation between the dune height and the vertical dune area, Middle Loup 

River at Dunning, Nebr., August 7, 1958.

TIME, IN MINUTES

FIGURE 41. Change in bed elevation with time at single points, Middle Loup River at 

Dunning, Nebr., August 7, 1958. Vertical arrows indicate the height of the numbered 

dunes.
60 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

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SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 61

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VERTICAL DUNE AREA, IN SQUARE FEET

FIGURE 43. Relation between the dune height and the vertical dune area, Middle Loup 

River at Dunning, Nebr., August 8, 1958.

LINE 2

8O IOO 120 140 I6O ISO 

TIME, IN MINUTES

FIGURE 44. Change in bed elevation with time at single points, Middle Loup River at 

Dunning, Nebr., August 8, 1958. Vertical arrows indicate the height of the numbered 

dunes.
62 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

TABLE 4. Computation of bedload discharge by the dune-tracking method, Middle 

Loup River at Dunning, Nebr., August 7,1958

[Longitudinal-profile data used to establish height-area relation. Point-time data from graphs of the change 

in bed elevation with time. Vertical area from height-area relation]

Longitudinal-profile data

Dune No.

Bl-l._-..._ 

2...... ......

3... .........

4............

5............

6............

B2-1 ..... .

2..... ....

B3-1 

2....... ..

3............

4............

B4-1-... .......

2__.._ .......

3............

4... ______.._

5............

B5-1- ...... ..

o

3............

4... .........

5 ... 

6............

7... ...... ...

8... .... ..

9............

Al-1 

2 ._ . 

3......... ...

4............

5.... ........

A2-1- -

2 

3... -.-_-...

4............

A3-1... ..-.. -

3 

4............

5............

A 4 1

2............

3 .... 

4_______.___-

6... __.... 

A >i_1

2............

4_.... ......

Height 

(ft)

0.15 

.05 

.05 

.35 

.45 

.50

.05 

.10 

.95

.05 

.30 

.05 

.50

.10 

.05 

.20 

.20 

.85

.15 

.05 

.25 

.10 

.10 

.10 

.80 

.05 

.70

.45 

.50 

.10 

.10 

.10

.65 

.30 

.05 

.10

.05 

.30 

.30 

.20 

.10

.30 

.30 

.15 

.70 

.15 

.35

.10 

.05 

.20 

.20

Vertical 

area 

(sq ft)

0.56 

.18 

.47 

7.17 

6.80 

4.99

.21 

.42

15.81

.17 

1.00 

.29 

6.93

.41 

.10 

.62 

1.47 

21.40

.32 

.27 

1.18 

.17 

.12 

.20 

16.14 

.12 

7.35

1.53 

2.95 

.29 

.13 

.47

3.04

2.85 

.26 

.26

.06 

2.53 

3.32 

1.26 

.15

2.80 

.89 

.79 

14.05 

.44 

.60

.27 

.08 

.75 

.37

Point-time data

Dune 

No.

1-1 

2 

3 

4

5 

6

7

2-1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12

3-1 

2 

3 

4

5 

6 

7 

8 

9 

10

4-1

2 

3

4 

5 

6

7 

8

5-1 

2 

3

Height 

(ft)

0.15 

.25 

.20 

.10 

.15 

.30 

.25

.10 

.15 

.10 

.15 

.10 

.05 

.15 

.05 

.10 

.20 

.05 

.10

.35 

.05 

.05 

.15 

.05 

.45 

.05 

.20 

.15 

.15

.05 

.05 

.10 

.20 

.20 

.05 

.05 

.05

.20 

.35 

.05

Time 

(min)

167

156

171

125

143

Vertical 

area 

(sq ft)

0.47

1.12

.75

.25

.47

1.61

1.12

5.79

0.25

.47

.25

.47

.25

.09

.47

.09

.25

.75

.09

.25

3.68

2.18

.09

.09

.47

.09

3.70

.09

.75

.47

.47

8.40

0.09 

.09

.25

.75

.75

.09

.09

.09

2.20

0.75

2.18

.09

3.02

Width 

(ft)

15.0

15.0

16.0

15.0

15.0

K

1.0

1.0

1.0

1.0

1.0

B'

(cfm)

0.520

.354

.786

.264

.317

2.241

Computed bedload discharge (74.16)(2.241)_...________________________ 166 tons per day 

Unmeasured sediment discharge...___.__________________ __ 461 tons per day
SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 63

TABLE 5. Computation of bedload discharge by the dune-tracking method, Middle 

Loup River at Dunning, Nebr., August 8, 1958

[Longitudinal-profile data used to establish height-area relation. Point-time data from graphs of the 

change in bed elevation with time. Vertical area from height-area relationl

Longitudinal-profile data

Dune No.

1-1.... .......

2....... _ ....

4. 

5.... .......

2-1 

2. 

3...... ... .....

4 _ ........ ..

3-1 

2 -

3_ 

4 - 

5 -. 

6... -

4-1 

2.. .......

5-1.... 

3.. . ...

4-_ ... -

Height 

(ft)

0.35 

.30 

.20 

.45 

.05

.45 

.30 

.10 

.05

.35 

.10 

.05 

.05 

.15 

.85

.30 

.05

.10 

.15 

.10 

.35

Vertical 

area 

(sq ft)

2.60 

1.56 

.62 

3.86 

.04

2.50 

1.31 

.07 

.06

1.12 

.16 

.17 

.16 

.35 

12.59

.63 

.03

.11 

.33 

.09 

3.64

Point-time data

Dune 

No.

1-1 

1-2

2-1

3-1 

3-2 

3-3 

3-4 

3-5 

3-6 

3-7 

3-8 

3-9

4-1 

4-2 

4-3 

4-4

4-5 

4-6

5-1 

5-2 

5-3 

5-4

5-5

Height 

(ft)

0.15 

.85

.70

.10 

.30 

.15 

.50 

.20 

.05 

.15 

.20 

.15

.05 

.05 

.80 

.45 

.15 

.10

.05 

.15 

.50 

.60 

.05

Time 

(min)

92

70

174

172

158

Vertical 

area 

(sq ft)

0.33

13.00

13.33

8.50

.16

1.30

.33

4.00

.56

.05

.33

.56

.33

7.62

.05

.05

11.60

3.16

.33

.16

15.35

ni

.33

4.00

6.00 

.05

10.43

Width 

(ft)

15.0

15.0

16.0

15.0

15.0

K

1.0

1.0

1.0

1.0

1.0

B'

(cfm)

2.17

1.82

.70

1.34

.99

7.02

Computed bedload discharge (74.16) (7.02). 

Unmeasured sediment discharge_____

521 tons per day 

222 tons per day

discharges and data for comparison, including bed-material discharges, which were measured at the end of the flume, and bedload discharges, which were estimated from suspended-sediment sampling to 

be one-half of _the bed-material discharges. Also given in the table are 

the values of K required to give the measured bed-material discharge 

and the estimated bedload discharge. In each computation, the computed discharge was_greater than the bed-material discharge; and the 

required values of K, which would be expected to be about equal or 

greater than 1.0, were less than 1.0.

Computations with the flume data have also been made by using 

equation 6 (p. 49). For these computations, the mean dune velocity 

was determined by dividing the mean dune length (obtained from the 

longitudinal profile) by the total time and then multiplying the quo-
64 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

TABLE 6. Bedload discharges computed by the dune-tracking method from flume data

Discharge (Ib per sec per ft)

Computed

0.0637 

.0792 

.1220

Measured bedmaterial

0. 0273 

.0423 

.0715

Estimated 

bedload

0. 0136 

.0212 

.0358

Computed discharge 

as percentage of 

Measured bedmaterial 

discharge

233

187 

171

Estimated 

bedload 

discharge

467 

375 

342

Required K for 

Measured bedmaterial 

discharge

0.428 

.534 

.587

Estimated 

bedload 

discharge

0.214 

.267 

.293

tient by the number of dunes that passed the measuring point in the 

total time, and the mean height was determined by dividing the area 

subject to movement (obtained from the longitudinal profile) by its 

corresponding length. By using equation 6, the height-area relation 

is eliminated, but the results were less accurate than those listed in 

table 6 in two out of three computations.

Although the results of the computations are inaccurate, they do 

not necessarily reflect adversely on the procedures nor on equations 5 

and 6. The inaccuracies could have resulted from inaccuracies in the 

estimates of the vertical areas and in the values used for porosity and 

specific weight of dune material. One important assumption in the 

computations with equations 5 and 6 is that the area that is actually 

eroded is equal to the area that would have to be eroded if the profile 

were to move downstream without changing form. This assumption, 

which inherently includes as load all the material that lies above the 

elevation of the lowest upstream trough, apparently is invalid. If the 

material that lies beneath discernible dunes is ignored, as it can be by 

any of the many different arbitrary means, the computed bedload discharges will agree much more closely with the measured discharges. 

However, the arbitrary selection of area seemed unwarranted at this 

point in the project, particularly because so few data are available. 

Only after special studies have been made on the nature of dune movement can any realistic conclusion be made on the specific areas that 

should be treated or, for that matter, on the suitability of the area 

concept.

The principal attributes of dune-tracking methods for computing 

bedload discharge are that the flow is not disturbed and that the statistically distributed short-term variations in discharge are ignored. 

On the other hand, an important shortcoming of the methods is the 

requirement of sounding for relatively long periods of time in order 

to obtain representative data. This requirement somewhat limits the 

application of the methods because constant flow conditions usually 

persist only at times of normal flow. In addition, application of any 

method, at least for the present, is limited to the tranquil-flow regime.
SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 65 

PRESSURE TRANSDUCERS

Pressure transducers, which generally operate with strain gages, 

may be an aid in determining bedload discharge by measuring dune 

movement (change in bed elevation at a point with time). Although 

no actual measurements have been made, the application of pressure 

transducers can be visualized. By placing transducers beneath the 

bed surface, the variations in weight above the transducers could be 

measured and recorded. If a dual transducer having one strain gage 

to measure the total weight above the transducer (combined weight 

of the flowing water-sediment mixture, the pore water, and the bed 

material) and another gage to measure only the weight of the watersediment mixture and the pore water was used; then, a continuous 

record of the difference between the weights registered by the two 

strain gages would define the weight, hence the height, of bed material 

above the unit.

One possible design for a dual transducer is shown diagrammatically in figure 45. In this design, the pressure-sensitive section of the 

transducer is divided into two parts so that each part actuates a 

separate strain gage. One of the parts is covered with a mesh capable 

of supporting the bed material; this part is sensitive only to the 

weight of the water-sediment mixture and the pore-space water. Such 

a design is somewhat similar to one used by Bagnold (1955) for 

measuring the weight of sediment in suspension.

By using several pressure transducers to measure dune movement 

simultaneously at different places in a cross section and by using a 

portable ultrasonic sounder for measuring the bed configuration, the 

time required for collecting the data necessary for a bedload computation would be substantially less than the time required for collecting 

all the data by using only an ultrasonic sounder. However, at least 

two factors hinder the use of the pressure transducers for measuring 

dune movement. The installation of the transducers would be difficult, particularly in deep water, and would probably have to be 

permanent because the transducers would have to be placed below the 

lowest elevation of scour. Also, the electrical leads would have to 

be buried the distance from the transducer to the bank unless a vertical 

support sufficiently strong to withstand ice, flood, and debris was 

provided.

ULTRASONIC SOUNDING OF LARGE PARTICLES

Ultrasonic depth sounders, in addition to being able to define dune 

movement, may provide a means for determining the discharge of 

bedload particles that are about 3 inches or larger in diameter. However, for the measurement of large particles, certain modifications
66 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

Pressure-sensitive 

section

TOP VIEW

Mesh 

covering

Pressure plate of strain gage

Strain gage 

SECTIONAL VIEW

FIGURE 45. Diagrammatic sketch of a dual pressure transducer.

must be made to the ultrasonic sounders available at present. These 

modifications consist of providing one rapid-scanning transducer, at 

least two stationary transducers, and some sort of distributor system,
SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 67

which would allow a single electronic unit to operate all the transducers and a multiple-channel recorder.

The theory of measurement with this system is based on the idea 

that the scanning transducer will define the shape of the particles, the 

stationary transducers will define the particle velocities, and information from both types of transducers can be used to determine the particle dimensions. Consider a transducer that scans back and forth in 

a plane and a particle that is moving in a direction pependicular to 

the scan. As the particle passes beneath the transducer, the ultrasonic 

sounder will measure and record the elevation of the upper part of 

the particle along some line that is defined by the intersection of the 

particle and a vertical plane. Thus, the recorder trace of each particle, 

particularly if it includes several scans across the particle, will define 

reasonably well the shape of the particle. However, the scanning 

record alone will not be a measure of the particle size because the scan 

lines across the particle are vector resultants that are neither parallel 

to each other nor perpendicular to the direction of particle movement. 

The particle size can only be determined by knowing Vp, the particle 

velocity, Vt, the scanning velocity, and Z, the scan distance. Both 

Vt and L can be predetermined and fixed, but Vv must be determined 

for each particle. Vp can be determined by measuring the time required for the particle to move between stationary transducers that 

are arranged a known distance apart along the line of particle movement. With a knowledge of Vp, Vt, L, and 0, which is the angle between the scan line across a particle and a perpendicular to the direction of particle motion (0=arctan Vp/Vt), some particle dimensions 

can be determined. The particle dimensions and the estimate of shape 

can then be converted to an estimated particle volume. By computing 

the total volume of all particles passing in a given time, the bedload 

discharge is established.

For spherical particles, only one scan across each particle is necessary for determining the particle volume. Consider a spherical 

particle moving on a flat bed. The recorder trace would show the 

elevation of the flat bed until the transducer started to scan across 

the particle, at which time the upper half of an ellipse whose minor 

axis equals d cos 0 (where d is the diameter of some circle of the sphere) 

would be recorded. By finding d and then the center of the circle of 

the sphere, the center of the spherical particle is established; the distance from this center to the bed is the radius of the particle. (See 

fig. 46^4.) For spherical particles moving on an irregular bed, the 

computation is the same as that for the flat bed except that the radius 

of each particle is determined from the points of support on the bed
68 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

Scon line

a-d cos 0

Radius of 

sphere

Radius of circle 

of sphere

Projected area 

of sphere

Time scale converted to absolute 

distance

A. Flat bed

Scan line

a- d cos 0

Estimated rodius 

of sphere

Projected orea 

of sphere

Radius of circle 

of sphere

Support points

Previously defined 

bed surface

Event marks to indicate reversal ofsconning direction

Time scale converted to absolute « 

distance

B. Irregular bed

FIGURE 46. Determination of radius of spherical particle from a recorder trace by ultrasonic sounding.

which would have been recorded at a time when no particles were 

passing through the scanning distance. (See fig. 465.)

For particles of a nonspherical shape, the computation of the volume 

of an individual particle is considerably more tedious and less accurate 

because the particle volume must be determined from estimates of the 

projected and cross-sectional areas of the particle.

For particles that have a high degree of sphericity, regardless of 

the mode of movement, the scanning method for computing bedload 

discharge seems plausible and should give reasonably accurate results. 

However, for particles that have a low degree of sphericity and that 

move by rolling or skipping, rather than by sliding, the recorder trace 

would not indicate the true cross-sectional shape of the particle. Con-
SOME NEW POSSIBLE APPARATUS FOR MEASURING BEDLOAD 69

sequently, computed particle volumes would be inaccurate unless some 

characteristic of the recorder trace would indicate the mode of movement and furnish information from which volume corrections could be 

made.

For nonspherical particles, the accuracy of the computation depends 

to a large extent on the number of scans across each particle. Figure 

47 shows the minimum number of times a spherical particle will be

\

L/D

\

\

\

H

FIGUEE 47. Minimum number of times a spherical particle will be scanned. Whenever 

Li ID for a given VP/Vt is less than that shown by the curves, a spherical particle will 

be scanned at least the indicated number of times.

scanned for different ratios of Vp/Vt and Z/Z>, where D is the sphere 

diameter. In order to use the graph for nonspherical particles, substitute for D the particle dimension in the direction of particle movement. The graph shows that for a reasonable number of scans at 

large L/D ratios, Vt must be large in relation to Vp. Herein lies one 

of the shortcomings in present instrumentation. According to the 

manufacturer of ultrasonic sounders available at present (oral communication), scanning velocities could not exceed about 1.5 feet per 

second and still maintain an accurate record. Thus, even at the maximum scanning velocity, particles that have velocities as high as about 

1.0 foot per second will be scanned only about once when the L/D 

ratio is greater than 1.0.
70 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

CONCLUSIONS

The bedload discharge at any given point varies in an oscillatory 

manner with time. Thus, a bedload discharge defined by a single 

short-term measurement is not necessarily representative of the mean 

bedload discharge, and the discharge through an entire stream cross 

section can be determined only by measuring many times at each of 

several points.

Any bedload apparatus in which sediment accumulates or through 

which sediment passes must be calibrated to determine its efficiency for 

a given condition.

The efficiency of a bedload sampler is difficult to determine and only 

fairly reliable because samplers can be calibrated only in laboratory 

flumes by using sampler models, which are not likely to be hydraulically similar to the prototype sampler in the field.

The efficiency of apparatus that trap and accumulate sediment, 

except pit samplers, varies widely with different velocities, particle 

sizes, bedload magnitudes, degrees of filling, and bed configuration. 

The effect of bed configuration on efficiency is superimposed on the 

other factors by affecting sampler orientation and stability. Probably, efficiencies are least variable when the bed relief is low except 

when the velocity is sufficiently high to make the sampler unstable.

Efficiencies average about 45 percent for basket and pan samplers 

and about 65 percent for pressure-difference samplers. In general, 

efficiencies of pressure-difference samplers vary less than those of 

basket or pan samplers. Pit samplers have high and relatively constant efficiencies. However, they have limited application because 

they must be placed into the stream-bed.

Because samplers usually have high hydraulic resistances and because sampler orientation and stability are important to efficient 

operation, sampler suspensions and placement are paramount 

considerations.

The total sediment discharge is not necessarily the simple summation 

of the measured suspended-sediment discharge and the discharge 

from a bedload measuring apparatus. The expression for determining 

the total sediment discharge depends on the particle size, the sediment 

distribution, and the kind of discharge measured by the apparatus. 

For any given set of conditions, the determination is easiest if the 

apparatus measures only the bedload discharge.

The Sphinx and VUV samplers probably represent the most advanced accumulating-type apparatus for determining the discharge 

of material that moves close to the streambed. The efficiency of the 

Sphinx, which is designed to measure fine sand, has not been determined exactly; however, it probably remains fairly constant and aver-
CONCLUSIONS 71

ages about 80 percent. The efficiency of the VUV sampler, which is 

designed to measure sediments from 1.0 to 100 mm, averages about 

70 percent. The principal advantage of the VUV sampler is that it 

usually gives a good representation of the actual bedload size 

distribution.

The magnetic bedload sampler proposed by Kennedy has not been 

constructed and tested. The sampler and the method may have merit.

Acoustic apparatus that record the sound engendered by interparticle or particle-instrument collisions measure the relative bedload 

discharge and not the actual bedload discharge; therefore, they are 

valuable only as an aid in certain kinds of studies or in association with 

other apparatus. . Ivicsics' apparatus is the only device of this type 

that operates in a suspended position above the bed.

Taniguchi's tiltmeter method, which is intended to give the total 

sediment discharge from measurements of the ground tilt, may prove 

to be useful for some kinds of river studies; however, in its present 

state of development, it does not seem to be satisfactory for determining sediment discharge.

Smoltczyk's ultrasonic instrument for determining concentration 

and the associated instrumentation and procedures for determining 

bedload discharge do not seem to be sufficiently developed for practical 

field application. However, with modifications and improvements, the 

method might provide an acceptable means for determining the discharge of sediment that moves close to the bed of streams transporting 

fine sand. The present instrumentation incorporates some of the objectionable characteristics of samplers that accumulate sediment, and 

the bedload discharge cannot be determined unless several unverified 

assumptions are made.

Although substantial advances have been made in the design of 

direct-measuring apparatus and although some of the indirect-measuring apparatus are based in ingenious ideas, no completely satisfactory 

apparatus exists at this time for measuring the bedload or total sediment discharge of coarse sediments.

A suggested portable pit sampler may provide an acceptable means 

for determining bedload discharge. However, its application is limited to shallow sand-bearing streams that have velocities less than 

about 4 feet per second.

The discharge of particles larger than about pea size probably can 

be determined by using motion-reduction photographic techniques 

provided the flow is clear. However, photography is generally not 

practical.

Eecently developed ultrasonic sounders provide a means of obtaining accurate and meaningful records of bed configuration and dune
72 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

movement for use in mapping the streambed and computing bedload 

discharge.

A proposed method for computing bedload discharge from bed 

configuration and dune movement is based on equations in which the 

product of A (the summation of vertical areas presumed to move in 

a long time), dw (an incremental width), and the reciprocal of T 

(a long time) is a critical parameter. Although the method nullifies 

the effects of the oscillatory variation of bedload discharge with time, 

soundings must be made for relatively long times in order to provide 

adequate information. Several actual computations with the method 

were inaccurate, possibly because of inaccurate values for porosity and 

specific weight and very probably because of inaccurate estimates of 

the vertical areas. Much additional laboratory and field study is 

required before any method can be selected as the most valid and practical for determining the bedload discharge from dune movement.

A dual pressure transducer for measuring the weight of bed material 

above a point in the bed may provide an acceptable means for determining dune movement. However, the installation of such a transducer would be difficult and would probably have to be permanent. 

If several transducers are used simultaneously to measure dune movement at several places in a cross section and a portable ultrasonic 

sounder is used to define the bed configuration, the data necessary 

for bedload computations could be collected in substantially less time 

than if an ultrasonic sounder is used to collect all the data.

A proposed modified ultrasonic sounder, which contains one rapidscanning transducer and two stationary transducers, and a proposed 

computational method might provide a means for determining the 

discharge of particles larger than about 3 inches in diameter. The 

method seems to be plausible for particles having a high degree of 

sphericity; however, it probably is unsuitable for particles having 

a low degree of sphericity.

Of the new possible apparatus and methods for determining bedload discharge, dune tracking with ultrasonic sounders seems to offer 

the greatest potential for general application; and the portable pit 

sampler, photography, the dual pressure transducer, and ultrasonic 

sounding of large particles seem most suited for special applications.

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Benedict, P. C., Albertson, M. L., and Matejka, D. Q., 1955, Total sediment load

measured in turbulence flume: Am. Soc. Civil Engineers Trans., v. 120,

p. 457-489.
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74 APPARATUS AND TECHNIQUES FOR MEASURING BEDLOAD

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 &U.S. GOVERNMENT PRINTING OFFICE: 1967 O 258-134