turned signal is 
fe (eae) (1) 
x e+ vy 
where fy. is the frequency of the volume re- 
verberation signal at the receiver, vy is the 
velocity of flow along the axis of the trans- 
ducer-pair, c is the speed of sound in the 
medium, and f is the transmitting frequency. 
The velocity Vy, is considered positive in the 
direction the transmitted wave is projected. 
The received signal beats with the transmitted 
tone, the beat frequency being the Doppler 
frequency. The Doppler frequency is given by 
Af=f- fy. =fe- (c = Ms def 
"4 
= 2Vy 
Cc + Vx 
(2) 
Since the speed of flow is small compared to 
c, the Doppler shift may be approximated by 
afte “xe, 
(3) 
It is convenient to use the quantity 
~ = = x 10°, (4) 
the normalized sensitivity for Doppler-shift 
devices, which has the units cps mce/m/sece 
The normalized sensitivity for sea water is 
about 1300 cps/mc/m/sec. Rewriting (3), we 
have 
Af=Yv, f', (5) 
where f' is the transmitting frequency in 
megacycles. It is desirable to have f' as 
large as possible for good resolution. The 
normalized sensitivity, Y= Ye), is dependent 
on the speed of sound in the water; therefore, 
if very accurate measurements of flow rates 
(less than +5% error) are to be made, it 
would be necessary to determine or estimate 
the speed of sound at the point of measure- 
ment. Although the speed of sound varies 
widely in the ocean, it is possible to estin- 
ate the speed of sound at a point of measure- 
195 
ment closely enough to ensure satisfactory flow- 
rate determinations. 
The sensitivity at 10 mc is about 13,000 
cps/m/sec, making practical an instrument with 
a working range of 1 mm/sec to 10 m/sec. If it 
is desired, the range can be extended to higher 
and lower flow rates with little additional 
efforte 
The transmitting frequency must be held em- 
stant for accurate measurements to be made. 
Errors can be caused by short=- or long-term in- 
stability in the transmitting frequency. dZrrors 
due to short-term instability occur when changes 
in frequency occur during the time it takes a 
transmitted wave to return to the receiver. 
This round-trip time is om the order of one 
millisecond; hence, the frequency drift rate 
would have to be extremely high to introduce any 
appreciable error. Long-term drift of the oscil- 
lator frequency produces an error in the Doppler 
signal that is proportional to the error in the 
transmitting frequency. 
A change in the sense of v, results only in 
a 180° phase change in Af; therefore, if the 
instrument is to determine sense as well as 
speed, it is necessary to beat the returning 
signal with a reference signal differing in fre- 
quency from the transmitted wave by more than 
the maximum Doppler frequency to be measured. 
Sf = (te - £) + Bee (6) 
Here f# is the reference frequency (assumed 
greater than f for this discussion) and §f is 
the new difference frequency. For zero flow, 
the difference frequency is not zero, but is the 
offset frequency f* - f. When 6f is less than 
the offset frequency, this corresponds to a 
negative vy, or flow toward the transducer-pair. 
If f* is assumed to be less than f, similar re- 
sults are obtained. If the current meter is 
oriented facing the current by a vane arrmge- 
ment, the sense information would not be re- 
quired. 
One further advantage was gained by using 
a transmitting frequency of 10 mc, that being 
the control over the region in which the current 
is to be measured. Attenuation at 10 mc is 
about 20 db/m, which effectively limits the dis- 
tance the instrument "sees". There is an area 
immediately in front of the transducer-pair 
which gives no return, because the transducers 
are spaced a small distance apart. The beam 
width of the transducers is narrow, so the 
lateral area covered is small. Because of these 
conditions, the region of observation is limited 
to a narrow volume extending fram about 0 to 
