98 Lecture 5 
TABLE 5.1]. Calibration of Field Velocimeters 
Instrument TR-2, No. 2 TR-2, No. 3 
4/5/61 | 4/25/61 | 4/5/61 | 4/25/61 
No. of points 12 12 12 12 
Temp. extremes, °C 11035 1 to 35 1to 35 || 1 to 35 
Effective length, 1 
Value, cm 20.6141 | 20.6032 | 20.5820 | 20.5897 
Std. dev., cm 0.0112 0.0106 0.0062 0.0059 
Time delay, t, 
Value, psec 0.1760 0.2628 0.2785 0.2311 
Std. dev., p sec 0.0771 0.0731 0.0430 0.0403 
Std. dev. of 1/f data 
psec 0.0068 0.0064 0.0038 0.0036 
ppm 48 46 27 26 
Std. dev. of prediction, 
ppm 14 13 7.8 7.5 
This computation yields the time delay t, and the effective path length /. (If the 
path is not of low-expansion material, the length | in Eq. (1) should be replaced 
by/,[1+ @(T — T)], where I) is the lengthattemperature T), T is the temperature, 
and a the coefficient of thermal expansion.) Table 5.1 shows the results for two 
instruments made at NBS. Again, the oldinstrument is much superior to the new, 
but the new one is sufficiently accurate for the field use for which it is intended. 
It should be borne in mind that the uncertainty in f due to the inherent +1 counter 
error is +10 ppm for the tube model and +13 ppm for the transistor model, and 
that at the low temperatures, an uncertainty of 0.01°C corresponds to an error of 
30 ppm inf. 
Some interesting calibration data are available fortwotransistorized instru- 
ments made by NBSandinconstant use for more than two years by the U.S. Naval 
Electronics Laboratory in San Diego. Mr. K. V. Mackenzie of NEL kindly made 
available to us some calibration data taken before and after a cruise during which 
the instruments were subjected to severe treatment in a storm so violent that it 
was barely possible for the crew to work. The results are given in Table 5.II. 
Note that these instruments are roughly equivalent to the TR-2 instrument used 
only in the laboratory. The differences in 7 and +, barely exceed the standard 
deviations and are probably not highly significant. For these calibrations the 
counter errors and the errors in temperature measurement are probably 
insignificant. 
5.5. HISTORY AND DISTRIBUTION 
The earliest mention we have found of the sing-around principle is in the US 
patent [3] filed in 1937 and granted in 1943 to F.H. Shepard, Jr., of RCA. As 
mentioned in a FIAT review [11], Freund and Hiedemann filed a German patent 
application in 1940. Shortly thereafter, in 1941, W. Kock, then of the Baldwin 
