8, U. S. COAST AND GEODETIC SURVEY 



It may be noted that the formula made use of in the preceding cal- 

 culation can give only approximate results. For not only is the 

 average current derived through the cosine relationship approximate, 

 but what may be even more serious is the fact that in the formula 

 it is assumed that the floating object during the various stages of its 

 journey will experience the changes in velocity which occur at the 

 point where it started. Where more exact results are desired, correc- 

 tions to the above approximate results can be applied. 



If the durations of flood and ebb are equal, and also the strengths of 

 the flood and ebb currents, a floating object would be carried a given 

 distance downstream and a lilve distance upstream. The presence of 

 fresh water in tidal waterways, however, makes both the strength and 

 duration of the ebb greater than the flood, and therefore floating 

 objects tend to be carried out to sea. 



DURATION OF SLACK 



In the change of direction of flow from flood to ebb, and vice versa, 

 the reversing tidal current goes through a period of slack water or 

 zero velocity. Obviously, this period of slack is but momentary, and 

 graphically it is represented by the instant when the current curve 

 cuts the zero line of velocities. For a brief period each side of slack 

 water, however, the current is very weak, and in ordinary usage 

 "slack water" denotes not only the instant of zero velocity but also 

 the period of weak current. The question is therefore frequently 

 raised, How long does slack water last? 



To give slack water in its ordinary usage a definite meaning, we 

 may define it to be the period during which the velocity of the current 

 is less than one-tenth of a knot. Velocities less than one-tenth of 

 a knot may generally be disregarded for practical purposes, and such 

 velocities are, moreover, difficult to measure either with float or with 

 current meter. For any given current it is now a simple matter to 

 determine the duration of slack water, the current curve furnishing a 

 ready means for this determination. 



In general, regarding the current curve as approximately a sine or 

 cosine curve, the duration of slack water is a function of the strength 

 of current — the stronger the current the less the duration of slack — 

 and from the equation of the sine curve we may easily compute the 

 duration of slack water for currents of various strengths. For the 

 normal flood or ebb cycle of 6^ 12.6™ we may write the equation of 

 the current curve y=A sin OASSlt, m which A is the velocity of the 

 current in knots at time of strength, 0.4831 the angular velocity in 

 degrees per minute, and t is the time m minutes from the instant of 

 zero velocity. Setting y=0.1 and solving for t (this value of t giving 

 half the duration of slack) we get for the duration of slack the follow- 

 ing values: For a current with a strength of 1 knot, slack water is 24 

 minutes; for currents of 2 knots strength, 12 minutes; 3 knots, 8 

 minutes; 4 knots, 6 minutes; 5 knots, 5 minutes; 6 knots, 4 minutes; 

 8 knots, 3 minutes; 10 knots, 2}^ minutes. For the daily type of cur- 

 rent with a given strength, the duration of slack is obviously twice 

 that of a semidaily current with like strength. 



VELOCITY OF CURRENT AND PROGRESSION OF TIDE 



In the tidal movement of the water it is necessary to distinguish 

 clearly between the velocity of the current and the progression or 



