In a previous issue we looked at how the moon and sun caused the rise and fall of the tides. It turns out that all this rise and fall translates into a flow of water called a tidal current. Coastal navigators need to be aware of tidal flows if they are to avoid unnecessary delays, or even worse, putting their vessel aground.
In order to describe a current, it is necessary to know both its direction of movement and its speed. The direction that a current flows toward is called its set. This differs from wind direction which is described by the direction from which it comes. The speed of current is its drift and is commonly measured in knots. Set and drift of a current may be shown as a vector (typically depicted as an arrow) where the length of the vector is drift and the direction of the vector is set. A longer arrow representing the current means that drift is greater. A vector pointing in a direction of 135 degrees shows a current moving from northwest to southeast and would be said to have a set of 135 degrees.
Change in current is affected by the state of tide. While tide is rising on shore, current is flooding (moving toward land). Similarly, when tide falls, the current ebbs taking water away from land. Lacking any information about tidal current, but with a knowledge of tides, it is a good guess that the two will roughly correspond. However, due to the vagaries of topography, sometimes the two do not neatly correspond.
This ebb and flood description implies a bi-directional current, either flowing toward land or away from it. Currents are rarely that simple, however. The vast majority of tidal currents can be described as rotary currents. Currents are full vectors. The vectors clock around as a function of time,andquot; says Jim Mays, president of Micronautics, a leading producer of tidal current prediction software. In many places this takes the form of an elongated ellipse. In some locations, the short axis of the ellipse is minimum or missing. In this last case, the current would conform to a simple bi-directional model.
A simplistic model of Earth, where there were no land masses or sun to confuse tidal forces, would have a wave of high and low tides moving steadily with the moon in its orbit. High tides on Earth would occur either under the moon or on the side of Earth opposite the moon. Interspersed between these two highs would be two lows. In this scenario, currents would set only east and west as they followed the high and low water marks around.
Earth is not smooth, of course, and its topography is a critical factor for determining current. While moon and sun create the major tidal forces or “signals” different topographical configurations amplify specific aspects of these signals. This leads to differing tidal current patterns depending on bottom characteristics.
Discovering and quantifying the wide range of factors affecting tides and current was one of the great successes of nineteenth-century science. In the latter part of the century, British and American hydrographers, working separately, were able to isolate the rhythmic cycles of astronomical movements. Using historical records of tidal measurements these scientists determined the varying effects of each of these cycles (or constituents, in hydrographic parlance) on tides and currents in different locations. In 1906, the Coast and Geodetic Survey produced Tide Prediction Machine No. 2 – a mechanical computer of such excellence that it continued as the source of all U.S. tide predictions well into the electronic age. Even after its retirement, hydrographers refer to it with an awed affection typically reserved for war heroes. Old No. 2 combined 37 constituents into each prediction.
These same 37 constituents are still used by NOAA when making its current predictions today. In many areas, the most significant constituent is the semi-diurnal lunar tide already described. Other first-order constituents include the varying distance between Earth and the moon, the sun’s semi-diurnal tide (far smaller than the moon’s), declination of the moon and declination of the sun. Second-order constituents have relatively little effect on most currents, but may resonate with certain topography, creating a significant current component. One second-order constituent is the effect on the orbit of the moon caused by the position of the sun.
Depending on local topography, some unusual currents can occur. For example, an agger is a double current. This describes a flood (or ebb) current that reaches its maximum speed; has that speed diminish; then increase to a new maximum without ever changing to the opposite direction.
Rivers can produce odd effects as their downstream current interacts with tidal currents. At some point in the river, the height of the river will be above sea level at high tide. This location is typically the farthest upriver that tidal current is experienced. Due to the volume of water moving downstream, tidal currents are often partially negated and the cycle may include more hours of ebb and/or a greater drift rate during ebb to account for this excess freshwater volume. It is also possible that surface water may move downstream while, along the bottom, water from the ocean moves upstream.
The Delaware Bay/River system shows one example of the ability of a river to contort tidal current. The time that the current changes is progressively later as one moves up the bay and river. For example, if the flood starts at 0628 at the Delaware Bay entrance buoy, it starts at 0851 near Arnold Pt, which is approximately 40 miles up the bay. At Marcus Hook (just south of Philadelphia and another 32 miles up the Delaware River) the flood starts at 1127 and at Bristol, PA (roughly 37 miles upriver from Marcus Hook) the flood does not start until 1324 – about one hour after ebb started 110 miles away at the mouth of the bay. The reason that current change varies so substantially over this distance is that the tidal wave continues upstream almost with a life of its own. “The wave has its own needs,” says Mays. “Remember that this wave (representing the tides) has both a high and a low.” A wave slows down proportionally with the square root of the depth, so the shallow water of the bay and river (compared to the water depth in the ocean or continental shelf) retards the progress of the tidal wave.
The state of tidal prediction has not stood still since the nineteenth century. An increasing body of knowledge has been gathered about the effects of shallow water on currents. This has led to the development of many shallow water constituents for tide and current predictions in both Canada and Great Britain. The Canadians analyze 45 fundamental constituents and 101 shallow water constituents for current predictions.
This added analysis should eliminate some disparity between predictions and reality. Because the waves created in the oceans by tides are so large (semi-diurnal tides caused by the moon have a length of more than half the circumference of Earth), they come in contact with the sea bottom even in the deep ocean. Shallow water constituents try to account for the frictional forces of the bottom on various small astronomical effects as current waves pass onto the continental shelf and then into shallower bays and harbors. Shallow water constituents are not new – there are some mingled in with the 37 constituents used by NOAA – but modern computers have allowed the assessment of many more of them.
One example in U.S. waters where shallow water constituents are critical is in Anchorage, Alaska. NOAA now uses 99 constituents to predict tide there because the topography of that region produces effects that have minimal significance elsewhere. One of these, for example, is an effect caused by the moon where 14 tiny tides are superimposed on top of “normal” tides each month.
Although many hydrographers argue that more constituents are better, Jim Mays notes that the random effects of weather and runoff may dominate the predicted tide or current. A prolonged, powerful wind can change the direction of a current. Even under less extreme circumstances, weather may alter set and drift of current substantially. And, while the orbit of the moon may be predicted with good accuracy, wind speed and direction on any day cannot be predicted. In this sense, the weather has a random effect on currents. One reason tide and current predictions are notoriously poor in Florida Bay is that wind can stack water up against the keys, overwhelming astronomical effects on tide and current.
A hydraulic current is an example of a non-rotary current. It typically occurs in a natural channel or canal connecting two bodies of water. The current is hydraulic because it acts to equalize the water level at each end of the canal. One example of this is the Cape Cod Canal in Massachusetts that connects Cape Cod Bay with Buzzards Bay. Current ebbs or floods in the canal, not because of tide rising or falling in the canal, but rather to account for the different tide levels at its opposite ends (see figure 2). Unlike most tidal currents, which slowly increase their flow from a minimum (or slack), hydraulic currents have a relatively short slack and reach speeds close to maximum fairly quickly.
Even without a current table, it is possible to make a fairly accurate assessment of hydraulic currents by noting the state and height of tides at each end of a canal. Figure 2 shows that the minimum current in the canal occurs when the height of tide at each end is similar. The maximum flow occurs near the time that the tidal difference is greatest.
Tidal current information is available from a number of sources. Areas with extreme currents may have arrows printed on charts with maximum current listed next to the arrow. Arrows with feathered tails show flood set and those with no feathers show ebb. Most printed tables and computer programs are based on government data. The advantage of current prediction programs is that the current is graphically displayed for all times in the tide cycle. This makes it much easier for a navigator to determine the current set and drift at any given time.
Current tables are used like tide tables in that there are reference stations along the coast that are typically important ports. Many subordinate stations are listed separately with corrections based on nearby reference stations. Typically, a reference station will list time of maximum flood and ebb current with the maximum drift achieved as well as the time of minimum current flow between each. This assumes that currents are basically bi-directional.
Subordinate stations provide time corrections to each of four events: maximum ebb, maximum flood and the two minimum flows when current changes direction. Also listed are two factors to be applied to drift rate for ebb and flood at the reference station. These factors are multiplied by the listed drift at the reference station to give the maximum drift at the subordinate station. Each subordinate station also lists the set of current during flood and ebb.
A navigator using current tables is capable of determining the time of each change of current as well as set and maximum drift. Intermediate times and drift require interpolation. While double currents are clearly shown in graphical representations of current speed, current tables display this phenomenon by three consecutive entries in the column for flood or ebb.
Some stations have rotary currents that are so pronounced they must be expressed as such. On some charts these will be printed as current roses showing vectors for each hour of the current. For example, the vector numbered “4” would show the set and drift four hours after a specific current change at a reference station. The length of the vector corresponds to drift and its direction to set. There is usually a special scale on the chart for measuring drift. In areas where the tide has a diurnal inequality (like much of the West Coast), rotary currents will also show an inequality and 25 vectors may be displayed. Rotary current information may also be found in a printed table with the set and drift listed hour by hour for each station.
Lacking a current table, or if transiting an area where there is no station listed, it is possible to estimate the current by looking at the effect on a buoy, or other object moored to the bottom. The set is fairly easy to determine; current is flowing in the same direction as the buoy’s wake. Drift is much harder to estimate. It takes some practice, or a good teacher, to correlate the size of the current’s wake on a buoy to drift. A good estimate based on these observations is often a starting point for determining currents.
A better method for determining set and drift while underway is to start with a fix of the vessel’s position. As the vessel continues on, plot a DR position at the time of the next fix. The DR position is where the vessel should actually be if there were no current pushing it off course. If the second fix does not coincide with the DR position then there is current. (This assumes other factors like leeway, compass, log, and helmsman error have been accounted for.)
This current may be quantified by the distance and direction from the DR to the fix. The current has pushed the vessel from the DR toward the fix, so the direction from DR to fix is set. The distance from DR to fix is the distance that the current pushed the vessel between fixes. The formula for determining speed is: speed = distance anddivide; time. If there was one hour between fixes then drift (speed) is the same as distance. For example, if the distance from DR to fix is one mile then the drift is one knot. If there was only one-half hour between fixes, then speed = 1 mile anddivide; .5 = 2 knots.
While knowledge of current set and drift is, by itself, edifying to some, it is only a tool for the navigator. Like any tool, it must be used to be effective. With a known current, a navigator needs to determine what course to steer given a known set and drift to stay on a rhumbline. This may be accomplished using any compass rose and scale; a maneuvering board is, perhaps, ideal for the task.
Start by plotting the rhumbline course from the center of the compass rose. Next plot the current vector: first draw a line from the center of the compass rose in the direction of set; measure a distance equal to drift from center of compass rose out along set line. This point may be called the current point. Next, set a pair of dividers to equal boat speed through the water. Place one point on the current point and swing dividers until the other point rests on rhumbline course line. Mark that point as the boat point. The direction from current point to boat point is course to steer. The direction from center of the rose to boat point is course made good, which corresponds to rhumbline course. Distance from center to boat point is speed made good.