================================================================ KAYAK RACE [Kaypro version] Game and text are copyright (c) 1986 by Peter Donnelly and may not be distributed for gain ================================================================ THE FILES The complete game comprises the following files: KAYAK.COM - the command file. Adjusts automatically for graphics and non-graphics Kaypros. KAYAK.HLP - instructions called from KAYAK; also TYPEable. KAYAK.ARL - optional title page. If you have a non-graphics Kaypro, hide (rename) or delete this file. KAYAK.DOC - TYPEable to screen or printer. TIDAL CURRENTS The rate of current for each turn is calculated according to a formula taken from "Chapman Piloting." This formula reveals that the rate of increase and decrease is not arithmetical but sinus- oidal, the result being that the average flow is high - about 63% of maximum - while periods of relatively slack water are minimal. The following graph illustrates a typical curve of rates in a narrow passage subject to swift currents, on a day when the maximum flood occurs two hours after the first slack and three and a half hours before the second one. Time Rate (knots) (h) 1 2 3 4 5 Notes 0 | . . . . . |**** . . . . <-- The current rises to 1 kn in |******** . . . the first quarter-hour... |*********** . . <-- ...and reaches over half its 1 |************** . . maximum after only 45 minutes. |***************** . |****************** . |******************** 2 |******************** <-- The rate is within .2 kn of its |******************** maximum for more than an hour. |******************* |******************* 3 |****************** . |***************** . |**************** . |************** . . 4 |************ . . <-- Two hours after maximum, the |*********** . . current is still at 62% of full. |********* . . . |******* . . . 5 |**** . . . . |** . . . . . 5.5| . . . . . An excellent introduction to the factors influencing tidal streams in straits and sounds, along with much other lore of interest to kayakers and other mariners, is to be found in Richard E. Thomson's "Oceanography of the British Columbia Coast," published by the Canadian Department of Fisheries and Oceans. CORRECTING FOR CURRENT The calculation of what course to steer in order to exactly offset a current flowing at right angles to the desired direction of travel depends on the solution of a right-angled triangle ABC, where the known quantities are AC, the speed of the boat through the water, and CB, the speed of the current. C . _ . | /| . | Paddling . | Current speed . | | . | | . | V . | A ._______________| B Speed over ground --> We desire to know the angle BAC. The necessary trigonometrical formula is: sin BAC = BC/AC The length of AB in the triangle indicates how much progress the boat will make toward its destination in 1 hour. The value can be calculated using the Pythagorean theorem: the square of AC equals the square of AB plus the square of BC. If the application of the triangle is not clear to you, first consider a situation where there is no current, and look at the triangle as a map whose sides are measures of distance rather than speed. (It comes to the same thing: AC is the distance the boat travels through the water in one hour.) Say the line AB runs from west to east. If the paddler sets off from A and paddles directly to C, he travels eastward the length of AB and north- ward the length of BC. Now add the effect of a current running from north to south. The paddler's direction and distance travelled through the water are the same, but now the whole body of water has moved to the south. Thus if the paddler has moved northward 1 mile, while the current has been flowing southward at 1 knot, his net progress on the north-south axis is nil and he ends up at B. The simplest way for the paddler "in the field" to find the angle of correction and resulting speed over ground is to construct the above triangle with pencil, paper, and the ruler and protractor on a transparent compass. First draw CB to scale for the speed of the current. Then draw a long baseline at right angles from B. Now lay the ruler so that the zero mark is at C and the mark for paddling speed touches the baseline, forming the line AC. The following table shows the necessary angle of correction and resultant speed over ground at various current speeds, always supposing a paddling speed of 3 knots. Current Angle Ground speed o .25 kn 5 2.99 kn .5 10 2.96 .75 14 2.9 1.0 19 2.8 1.25 25 2.7 1.5 30 2.6 1.75 36 2.4 2.0 42 2.2 2.25 49 2.0 2.5 56 1.7 2.75 66 1.2 3.0 90 0.0 The surprising thing that emerges from the table is how little effect a correction against the current has on forward progress; even when the current is running at two-thirds of the speed of the boat, the speed over ground is diminished by only 27 %. However, ground speed diminishes more rapidly as the angle of correction increases - again following a sine curve. The appli- cation of this phenomenon in the game, as on the water, is that the paddler must overcorrect when the current is weak so that he can undercorrect when it is strong. Consider the case of two racers who paddle at 3 knots from point A toward point B for two hours. For the sake of simplicity, let the current through the first hour flow at 1 knot, and through the second hour at 2 knots. Going by the table above, the first paddler steers 19 degrees against the current in the first hour and 42 degrees in the second, staying on course the whole time and covering a total of 5 miles over ground: 2.8 miles in the first hour and 2.2 in the second. Meanwhile the second paddler keeps a steady bearing of 30 degrees. In the first hour he covers 2.6 miles in the direction of AB (a bit more over ground, since he is deviating from the line) and moves 1.5 miles against the current, ending up 0.5 mile off course in the upstream direction. In the second hour he again moves 1.5 miles against the current, which now at 2 knots pushes him back the half-mile he has gained, so that he is once more on course; meanwhile he has moved another 2.6 miles along AB, for a total of 5.2, and is a fifth of a mile ahead of his opponent. What has happened in this race becomes even clearer if you draw another triangle in which BC is the total drift of the current, 3 miles, and the base AB is the distance toward the goal, 5.2 miles, covered by the second paddler in two hours by paddling straight along AC, which is 6 miles long. Since the first paddler has zig-zagged through the water, his line from A to C will have an elbow in it, and in fact will not reach C; thus he must paddle further in order to make the same distance AB. Evidently, then, the ideal strategy in KAYAK RACE (as much as it is permitted by other considerations such as winds and hazards) is to keep to a single heading throughout the race, bearing upstream in weak currents, even steering with the current at times, rather than attempting to stay always close to the centre. To determine the correct bearing, of course, you must estimate the average or net effect of the current over the whole game - something that is by no means easy to do. CORRECTING FOR WIND Since the effects of moderate and strong winds in the game are known constants, they can simply be added to or subtracted from the current rate. Only the easterly or westerly push is signifi- cant to the necessary angle of correction in a given turn, but the north-south component will affect the boats' speed toward the goal and hence the net effect of the current over the whole game. For example, an outlook for strong southerlies would give greater weight to the currents later in the day. When the wind is not blowing from one of the cardinal points, its effect on the east-west movement of the boats will be about 70% of its total effect (again using the Pythagorean theorem; the east-west co-ordinate is one short side of a right-angled triangle). So a strong wind from the NW, for example, would add 0.7 knots to the effect of a westerly current. Peter Donnelly 964 Heywood Ave., Apt. 220 Victoria, B.C. Canada V8V 2Y5 ================================================================