For ideal measurements a ROAB acoustic receiver would be mounted at the bow. From a practical perspective though, that is not going to work. It is though very practical for a ROAB unit on the boat to be attached at or near the stern. This has the added advantages of placing the rest of the ROAB unit near the cockpit crew and also allowing the boat behind an easier view of the ROAB on the stern of the boat ahead.
When a boat is pointed straight at the mark and its bow crosses into the zone the stern of the boat is the zone length plus one boat length (zone+1BL) away from the mark. However, as any good hand on the helm knows, the boat is not driven straight into the mark. Due to simple geometry, shown in the figure next to this paragraph, as the boat approaches the mark on a parallel path farther away from the lay line, the farther the bow is away from the zone circle when the stern crosses the zone+1BL circle. This extra distance would seem to create a small problem for using a ROAB at the stern to indicate when the bow enters the zone.
The good news is that this theoretical issue is truly just a small problem, and the way to see this is to calculate how long it takes for the boat to travel this extra distance, the 'addendum', from when the stern crosses the zone+1BL point to when the bow crosses into the zone. Based on the simple geometry of the situation, the length of the addendum can easily be calculated. Once that distance is known, a table can be constructred for how long it takes to transit the addendum depending on the boat's speed. As the below tables show, under most normal conditions the extra time caused by the addendum is generally less than a second.
NOTE: The discussion on this page is for a stern mounted ROAB acoustic receiver, which is the worst case addendum scenario. For a ROAB installation with the acoustic receiver forward from the stern, like on the keel, the boat unit would need to be programmed accordingly, the adendum would be smaller and thus the extra time would be smaller as well.
The first column on the left of the table is labeled "BL's off lay line." This is the offset in terms of boat lengths for how far away the approaching boat is from the lay line straight into the mark. The next column labeled "addendum as %BL" is the straight ahead distance, in boat lengths, from the bow of the boat to the zone when the stern crosses the zone+1BL point. For example, when a boat is coming in half a boat length off the lay line, 0.5 BL's, the addendum is 1.1% of the boat's length. To convert that into an actual distance a boat length needs to specified, which is what the third column, labeled "BL=". The three tables below show data for boat lengths of 10', 30', and 50' respectively.
The next nine columns are for speeds of 2 to 10 knots, as labeled at the top of each column. The cells on the table are how long, in seconds, it takes to cover the addendum distance on that row for the speed indicated at the top of that column. The region of the table where the time is between a half and one second (0.5 to 1.0 sec.) has been indicated by color inverted characters. NOTE: Rounding of numbers is why some cells say 0.5 and are not inverted, while other 0.5 cells are inverted.
In light wind conditions boats are going to be coming in on parallel path closer to the lay line. In heavy wind conditions boats may be coming in farther from the lay line but they are also going to be coming in faster. As the below tables show, under most normal conditions the time to transit the addendum is less than a second.
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