4827 



HYDROGRAPHIC MANUAL 



Page 428 



Method of use. — Speed scales of both types are used in the same manner. To find 

 the speed of a vessel the only information required is the elapsed time between two fixed 

 positions and the distance between, which is taken from the boat sheet or smooth sheet 

 by dividers. This distance is applied directly to the speed scale, parallel to the appro- 

 priate axis, and the speed to tenths of knots is found by interpolation. The reverse 

 problem, when the speed is known and the time required to cover a given distance is 

 desired, or vice versa, is solved with equal facility. The speed at any moment is 

 obtained from the two preceding plotted positions, and with that speed the moment 

 when the vessel will be at a certain position is easily determined. 



4827. Log-factor Scale 



The log factor, expressed as a ratio which is the true distance divided by the log 

 distance, may be quickly determined from a log-factor scale, which is simply a propor- 

 tional diagram constructed for the scale of the survey sheet. This type of scale is used 

 extensively in plotting dead reckoning during hydrographic surveys controlled by 

 R.A.R. or astronomic observations. It is also used in making the dead-reckoning plots 

 used in plotting R.A.R. smooth sheets. (For calibration of logs, see 4454.) 



Construction . — To construct a log-factor scale draw two lines at right angles to each other and let the horizontal line represent a log 

 factor of 1.0, the vertical line being merely a construction line. Draw other equally spaced horizontal lines, parallel to the first, to rep- 

 resent the probable range of factors to be used, as in figure 95 from 0.7 to 1.2. The spacing should be sufficient, about three-fourths of an 

 inch, so that hundredths may be easily interpolated. On the horizontal line first drawn, representing a log factor of 1.0 lay off to the 

 right and left of the vertical line distances of 5.5 miles at the scale of the survey. Subdivide the total distance into 11 equal parts, each 

 equal to 1 mile. The upper and lower horizontal lines are similarly subdivided except that the equal intervals are miles multiphed by 

 the respective factors; in the figure each subdivision on the lower line is equal to 1.2 nautical miles and each on the upper is equal to 0.7 

 nautical mile. 



NAUTICAL MILES 



Figure 95.— Log-factor scale. 



The corresponding points on the upper and lower horizontal lines are connected by diagonal lines which should pass through the 

 corresponding points on the horizontal line representing a 1.0 log factor. Leaving the diagonal line farthest to the left unnumbered, 

 the remaining lines are numbered toward the right from to 10. The interval to the left of the zero line is subdivided into 10 equal 

 parts to represent tenths, and from this hundredths can be interpolated. 



The scale is constructed in a fan shape to avoid acute intersections with the horizontal lines. 



Method of use. — To find the log factor at any time the true distance between two 

 fixed positions is taken oft" the survey sheet with dividers. This interval on the dividers, 

 held parallel to the horizontal lines, is fitted to the scale where it corresponds to the 

 distance measured by log between the two fixed positions. Where it fits, the log factor 

 is read by interpolating to hundredths. After the log factor is known, log distances 

 may be scaled with dividers from the horizontal scale corresponding to the factor deter- 

 mined, and plotted directly on the survey sheet. 



When the speed of the vessel is at a constant rate through the water, time intervals 

 are frequently used for the same purpose as log distances, and a time-distance scale 



