Running Broad Reach is defined as a heading of about 22.5° either to the left or to the right of the direction in which the wind is blowing.
Running Broad Reach can be used to describe the heading of a ship - I.E. the ship is heading ~22.5° off to either side of the wind's direction.
It can also be used to describe the position of an object relative to the ship. For example, if an enemy ship is at Running Broad Reach, we must turn ~22.5° off the wind's direction in order to head directly towards it.
If the wind is blowing from east to west, as occurs often in the Caribbean, Running Broad Reach would be both West North West (WNW) and West South West (WSW). Of course, since wind direction tends to change, the direction of Running Broad Reach changes with it. It will always be 22.5° off the wind's current direction, whereever the wind is heading at the time.
The vast majority of Ship Types will sail very well when at Running Broad Reach. This is because the wind is pushing the ship almost directly from behind, and most sails are designed to catch wind entering them from such a direction.
Square Rigged ships make the best use of this sort of wind. At this heading, the conditions are perfectly balanced between the wind's push against the sails, and its contact with as many sails as possible all at once. In fact, it is better than the wind coming directly from behind the ship, in which case it'll push very powerfully against the sails, but only against the rear-most set, after which the wind loses its potency by the time it reaches the main sails or fore sails. At Running Broad Reach, it is coming at a sufficient angle to hit all sails, thus creating a greater push on the entire rigging set. In fact, the more Square Riggings a ship has (and the larger they are), the faster it will sail at this heading.
Fore-And-Aft Rigged ships gain less of a benefit from this wind heading. Their sails are designed to catch wind coming at a more acute angle, and so this is not their Best Point Of Sailing. Nonetheless, due to the wind coming a bit to the side but primarily from behind, the push against the ship is sufficient to keep it moving forward at quite a reasonable speed - these ships are by no means slow at Running Broad Reach, just not as fast as they can be.
In the original game, the rule of thumb is that the larger the ship, the faster it will sail at Broad Beam Reach (where size is a factor of Cargo Capacity, as it is everywhere else in the game).
Therefore, the ships sailing fastest at this heading are the War Galleon, Fast Galleon and Frigate. Oddly, the Galleon, the largest ship in the game, actually sails better at the slightly wider angle of Broad Reach, though the game does not explain why this is so.
Additionally, in very strong winds, the War Galleon becomes the fastest ship in the game when sailing at Running Broad Reach. In these conditions it can achieve 15 leagues, a feat only matched by the Galleon at Broad Reach. The Frigate and Fast Galleon also do well here, clocking 12 leagues (again, in strong winds). However, remember that these large vessels are still relatively slow when winds are light, clocking no more than 7 leagues even at this heading.
Conversely, smaller ships do not sail optimally at Running Broad Reach. The smaller the ship, the wider an angle it needs to achieve its top velocity. Nonetheless, small ships are less affected by wind speed and direction, meaning that most smaller vessels will still sail fairly well, at around 5-8 leagues, at Running Broad Reach.
Sid Meier's Pirates! (2004)Edit
In Sid Meier's Pirates! (2004), Running Broad Reach is by far the domain of the largest vessels in the game, while being far less than optimal for all smaller ships.
This is most easily visible in the Frigate Class ships: they become the fastest ships in the game when heading at Running Broad Reach, observed clocking up to 25 knots in stormy conditions, and pulling upwards of 15 even in poor conditions. The Combat Galleon Class is a very close second, with similar results. Even Merchant Galleon Class ships, normally considered pitifully slow, can make excellent speeds at this heading (though they are reported to be even faster at Before The Wind).
Once again, as we go down the size chart to the realm of smaller ships, especially the Fore-And-Aft Rigged classes, Running Broad Reach becomes less and less of an optimal course.
Merchantman Class and Fluyt Class ships do get their best speed at this heading, but it is certainly not an impressive top speed. Sloop Class and Brig Class ships can maintain some speed at this heading, but for them most headings are equally fine, and battle is all about turning and turning anyway.
The two "true" Fore-And-Aft Rigged vessels, the Barque Class and Pinnace Class prefer completely different angles, even going so far as to sail Close-Hauled when necessary since no other ship can match their performance at that heading, and Running Broad Reach is therefore not in their repertoire. This is especially true for Pinnaces, whose real potential comes from being able to utilize Beam Reach to extreme effectiveness, and will lose too much of their advantage (and speed) by turning to Running Broad Reach.