[Problem E | 1995 ACM finals problem set | My ACM problem archive | my home page]

Sail Race

A race course is defined by marks with up to 10 marks per race
course. A sailboat must sail to all marks in the specified order. The
marks are identified as *x*- and *y*-coordinates on a
hypothetical grid with a single unit equal to one nautical mile
(nm). The positive *y*-axis is oriented due north and the
positive *x*-axis is oriented due east. The race course is in
open waters without any navigational limitations.

For purposes of this planning tool, the only driving force controlling a sailboat is the wind. The wind determines the sailboat's speed of advance and limits its direction of travel. The wind is constant for the duration of each race and is specified in terms of the direction from which the wind is blowing and its speed in nautical miles per hour (kts). Wind direction is specified as a compass bearing in degrees measured clockwise from 000.0° as north.

Sailboats cannot steer any closer to the wind than a given "point angle" off the wind direction. In order to make progress closer to the wind direction, the sailboat must tack back and forth across the wind, steering no closer to the wind than its point angle. Each time the sailboat tacks or passes a mark it incurs a tack penalty. For this simulation, each sailboat will travel each leg of a race (the portion of a race between successive marks) with the minimum number of tacks and the minimum possible distance. Courses and directions are specified as compass bearings in degrees measured clockwise from 000.0° as north.

The speed of a sailboat is determined by the sailboat design, wind speed, and direction steered relative to the wind. In the figure, the wind direction is 45° and the point angle is 40°. This means then that this sailboat cannot steer between 5° and 85° because it cannot point that closely into the wind.

Sailboat traveling from P in this
direction moves at point speed ratio times wind speed

Sailboat traveling from P in this
direction moves at reach speed ratio times wind speed

Sailboat traveling from P in this
direction moves at downwind speed ratio times wind.

Point angle is 40°

Reach angle is 60°

downwind angle is 145°

Each angle is measured as the smallest angle between the direction of travel of the saiboat and the direction from which the wind is blowing.

For this problem, the ratio of sailboat speed to wind speed is one of three ratios, selected as shown in the table below according to the angle off the wind :

Angle off wind Applicable ratio ----------------------------------- -------------------- >= point angle and < reach angle point speed ratio >= reach angle and < downwind angle reach speed ratio >= downwind angle downwind speed ratio

For instance, if the boat is steering at an angle off the wind which is between the reach angle and downwind angle then

boat speed = reach speed ratio × wind speed

The subsequent *n* lines of the data set represent the n race
marks in the order in which they must be reached. Each line begins
with a 2-character mark id followed by the *x*-coordinate then
*y*-coordinate of the mark.

The end of input is denoted by a line of four 0's.

Output for each race begins with a header containing the number of the data set (1 for the first, 2 for the second, etc.) and the number of legs. The next line is the total length of the race course, measured as the sum of distances between successive marks.Courses, tacks, directions 0.1 degree Distance 0.01 nm Speed 0.1 kts Time 0.01 hours

For each leg of the course, the leg number, beginning and ending mark id's, course from the beginning to end marks of the leg, and the leg distance is presented. This is followed by a listing of the tacks necessary to complete the leg. The tacks for each race are numbered sequentially, with tack numbers beginning with 1 for each race. For each tack, the tack number, the projected sailboat speed, the course steered, and the length of that tack are presented.

The summary output for each data set includes the total number of tacks, the total distance traveled for the race, the estimated race duration, and the total tack penalty time incurred by the sailboat after leaving the first mark.

The exact format of the output is not specified, but all output should be organized so that it is in the specified order, appropriately labeled and follows given numeric specifications.

45 10 .1 6 45 0.5 90 0.75 135 0.67 M1 15 10 M2 25 20 M3 22 30 M4 5 25 M5 10 15 M6 10 10 0 0 0 0

Race 1 has 5 legs The race layout is 58.48 nm long ----------------------------- Leg 1 from Mark M1 to M2 == > Direction: 45.0 Distance: 14.14 nm Tack 1 ==> Speed: 5.0 Direction: 90.0 Distance: 10.00 nm Tack 2 ==> Speed: 5.0 Direction: 0.0 Distance: 10.00 nm Leg 2 from Mark M2 to M3 == > Direction: 343.3 Distance: 10.44 nm Tack 3 ==> Speed: 5.0 Direction: 343.3 Distance: 10.44 nm Leg 3 from Mark M3 to M4 == > Direction: 253.6 Distance: 17.72 nm Tack 4 ==> Speed: 6.7 Direction: 253.6 Distance: 17.72 nm Leg 4 from Mark M4 to M5 == > Direction: 153.4 Distance: 11.18 nm Tack 5 ==> Speed: 7.5 Direction: 153.4 Distance: 11.18 nm Leg 5 from Mark M5 to M6 == > Direction: 180.0 Distance: 5.00 nm Tack 6 ==> Speed: 6.7 Direction: 180.0 Distance: 5.00 nm -------------------------------- Race 1 was 64.34 nm long with 6 tack legs Estimated Race Duration is 11.47 hours with 0.50 hours of Tack Penalty

This page maintained by Ed Karrels.

Last updated September 20, 1999