### Tide Predicting Machines

#### Tide-Predicting Machine No. 1

The first tide-predicting machine was designed by Sir William Thomson (afterwards Lord Kelvin) and was made in 1873 under the auspices of the British Association for the Advancement of Science. This was an integrating machine designed to compute the height of the tide in accordance with formula #1 below.

(1) h = Ho + Sum{ƒH cos[at + (Vo+u) - K]}

The terms of the equation, h = Ho + Sum{ƒH cos[at + (Vo+u) - K]} , are defined as follows:

h = height of tide at any time t.
Ho = mean height of water level above datum used for prediction.
H = mean amplitude of any constituent A.
ƒ = factor for reducing mean amplitude H to year of prediction.
a = speed of constituent A.
t = time reckoned from some initial epoch such as beginning of year of predictions.
(Vo+u) = value of equilibrium argument of constituent A when t = 0.
K = epoch of constituent A.

It provided for the summation of 10 of the principal constituents, and the resulting predicted heights were registered by a curve automatically traced by the machine. This machine is described in part I of Thomson and Tait's Natural Philosophy, edition of 1879. Several other tide-predicting machines designed upon the same principles but providing for an increased number of constituents were afterwards constructed.

The first tide-predicting machine used in the United States was designed by William Ferrel, of the U.S. Coast and Geodetic Survey. This machine, which was completed in 1882, was based upon modified formulas and differed somewhat in design from any other machine that has ever been constructed. No curve was traced, but both the times and heights of the high and low waters were indicated directly by scales on the machine. The intermediate heights of the tide could be obtained only indirectly. A description of this machine is given in the report of the Coast and Geodetic Survey for the year 1883.

#### Tide-Predicting Machine No. 2

The first machine made to compute simultaneously the height of the tide and the times of high and low waters as represented by formulas #1 above and formula #2 which follows.

(2) dh/dt = - Sum{aƒH sin[at + (Vo+u) - K]} = 0

It was designed and constructed in the office of the Coast and Geodetic Survey. It was completed in 1910 and is known as the United States Coast and Geodetic Survey tide-predicting machine No. 2. The machine sums simultaneously the terms of formulas #1 and #2 and registers successive heights of the tide by the movement of a pointer over a dial and also graphically by a curve automatically traced on a moving strip of paper. The times of high and low waters determined by the values of t which satisfy formula #2 are indicated both by an automatic stopping of the machine and also by check marks on the graphic record.

The general appearance of the machine is illustrated by the accompanying figures. It is about 11 feet long, 2 feet wide, and 6 feet high, and weighs approximately 2,500 pounds. The principal features are: first, the supporting framework; second, a system of gearing by means of which shafts representing the different constituents are made to rotate with angular speeds proportional to the actual speeds of the constituents; third, a system of cranks and sliding frames for obtaining harmonic motion; fourth, summation chains connecting the individual constituents elements, by means of which the sums of the harmonic terms of formulas #1 and #2 are transmitted to the recording devices; fifth, a system of dials and pointers for indicating in a convenient manner the height of the tide for successive instants of time and also the time of the high and low waters; sixth, a tide curve or graphic representation of the tide automatically constructed by the machine. The machine is designed to take account of 37 constituents, including 32 short-period and 5 long-period constituents. The most important of the 37 constituents are defined in the Tide and Current Glossary. The 37 constituents are: J1, K1, K2, L2, M1, M2, M3, M4, M6, M8, N2, 2N, O1, OO, P1, Q1, 2Q, R2, S1, S2, S4, S6, T2, lambda2, µ2, nu2, rho1, MK, 2MK, MN, MS, 2SM, Mf, MSf, Mm, Sa, Ssa.

The heavy case-iron base of the machine, which includes the operator's desk, has an extreme length of 11 feet and is 2 feet wide. This forms a very substantial foundation for the superstructure, increasing its stability and thereby diminishing errors that might result from a lack of rigidity in the fixed parts. On the left side of the desk is located the hand crank for applying the power, and under the desk are primary gears for setting in motion the various parts of the machine. The superstructure is in three sections, each consisting of parallel hard-rolled brass plates held from 6 to 7 inches apart by brass bolts. Between these plates are located the shafts and gears that govern the motion of the different parts of the machine.

The front section, or dial case, rests upon the desk facing the operator and contains the apparatus for indicating and registering the results obtained by the machine. The middle section rests upon a depression in the base and contains the mechanism for the harmonic motions for the principal constituents M2, S2, K1, O1, N2 and M4. The rear section contains the mechanism for the harmonic motions for the remaining 31 constituents which the machine provides.

#### Predicting Tidal Currents by Machine

Since the tidal current velocities in any locality may be expressed by the sum of a series of harmonic terms involving the same periodic constituents that are found in the tides, the tide-predicting machine may be used for their prediction. The harmonic constants for the prediction of current velocities are derived from current observations by an analysis similar to that used in obtaining the harmonic constants from tide observations. For the currents, however, consideration must be given to the direction of flow, and in the use of the machine some particular direction must be assumed. The machine can be used for the prediction of reversing currents in which the direction of the flood current is taken as positive and the maximum velocity in this direction corresponds to the high water of the predicted tide. The ebb current is then considered as having a negative velocity with its maximum corresponding to the low water of the predicted tide. Rotary currents may be predicted by taking the north and east components separately but the labor of obtaining the resultant velocities and directions from these components would be very great without a machine especially designed for the purpose. Predictions can, however, be made along the main axis of a rotary movement without serious difficulties.

#### Predicting Machines from Other Countries

A Number of countries with a seafaring heritage have found it advantageous to be able to generate their own tidal predictions for local ports as well as ports frequently visited by their merchant marine fleets. The tide-predicting machines once used by Brazil and Germany are pictured here.

#### Prediction with Electronic Computers

Since 1966, predictions in the U.S. have been made by electronic computer, initially these were large "mainframe" computers running tide prediction software written in FORTRAN. Despite the advent of electronic computers, the annual creation and publication of the U.S. Tide and Tidal Current Prediction Tables remained a rather labor intensive and exacting process.

In 1965 the Table master pages were hand typed each year. In 1973 predictions were done on a CDC6600® which produced a closet sized room of 80-column computer punch cards. These were "feed" into an IBM360® to generate another closet sized room of punch cards representing "near" master Tide Table pages. After extensive hand sorting these were reassembled into card decks to produce individual master pages on a WANG® computer-driven printer. Interactive telephone dial-up access to a UNIVAC® computer replaced the CDC and IBM machines in 1979 and a Diablo® 1640 printer replaced the WANG. Personal Computers became the prediction and production engines in 1987, and by 1990 the PCs were on a Local Area Network driving a high density (1200x1200 dots per inch) Printware® Model 720 PostScript® printer. Successive generations of personal computers and peripherals have come and gone. Today, the official publication of the Tide and Tidal Current Prediction Tables is no longer in the form of a book. All seven volumes fit on one CD-ROM.