Rules of the Road, rule 5, states "Every vessel shall at all times maintain a proper lookout by sight and hearing as well as by all available means appropriate in the prevailing circumstances and conditions so as to make a full appraisal of the situation and of the risk of collision."
Believe it or not, this rule does not require a look-out to be topside 24/7 making continuous visual sweeps. However, it also does not abdicate a sailor from keeping a proper lookout simply because he has radar
and AIS installed. I would like to share a technique of maintaining a proper lookout that I have not seen discussed in any bookstore available books on seamanship.
My discussion will be addressed towards open ocean sailing with excellent visibility (but the technique can be adapted as necessary for other conditions). On the open ocean, we can expect displacement-hull vessels to be operating and as such, the longer of them are the faster. Therefore, one collision risk at sea is with a large ocean going tanker. Of this class of ships, we can estimate a masthead height of 120ft and a cruising speed of 12kts (distance to horizon for 120ft is 13.4 nautical miles).
Let's suppose that we are cruising along at 6 knots and from the cockpit our height of eye to scan the horizon is at 8ft above sealevel (distance to horizon for 8ft is 3.5 nautical miles).
Visibility supporting, we should be able to gain first sight of this large tanker at a distance of 16.9 nautical miles, 10ft of its mast at a range of 16.4nm, and 50% of its height at 13nm.
Now, lets talking about collision. The worst case risk of collision is if this tanker is headed directly towards us and we are heading directly towards them. With our combined speeds, that would put our worst case closing rate at 18kts (12kts(theirs)+6kts(ours)). If our look-out goes below and takes his eyes off the horizon the moment that a tanker appears on the horizon and we are both closing one another at 18kts then it would take just over 56 minutes for us to collide (16.9nm / 18kts = 56.3 min). Obviously, collision is not acceptable so 56 minutes is too long for a look-out to take his eyes off the horizon. Lets pick a minimum safe range of, say, 1nm. To ensure that is maintained, our lookout cannot go below for longer than 53 minutes (15.9nm / 18kts = 53 minutes). 53 minutes is an odd interval to maintain a lookout on so ... lets make it 45 minutes. At a 45 minute 'look interval', we ensure a worst case warning of 3.4nm. The look interval is the time required between a look-out performing subsequent full 360-degree scans of the horizon.
Now that we have come topside with a large tanker heading directly towards us with 3.4nm of warning, we turn off our current course by 90 degrees. The time required for the tanker to close that last 3.4nm is roughly 11 minutes. In that eleven minutes, our new course will carry us 1.1nm away from the tankers path when he crosses behind us.
In this case, worst case collision course, maintaining a 45 minute 'look interval' will provide a CPA of roughly 1nm from this hypothetical tanker.
Another collision possibility, lets suppose, is another sailboat just like ours who is not maintaining a proper look-out. Let's take a Beneteau First 36.7 (masthead height 55.75', hull speed 7.7kts). To maintain a CPA of 1nm after avoidance from this contact would require a 'look interval' of 48 minutes (the math on this case is up to you). Since 45 minutes is the shorter of the two calculated look intervals then it will keep us safe from collision for both.
This sort of technique to maintain a proper lookout is used widely and is sufficient to 'maintain a proper lookout' as is required and prudent. The method to calculate a look interval can be modified to account for lowered visibility (if visibility range is less than the combined distance to horizon) by replacing the 16.9nm range from above with the visibility range in the calculations. Coastal traffic can be compensated for by assuming collision with a different class of vessel (for example, a coastal tanker or small freighter when nearshore) and making appropriate assumptions of likely cruising speed and masthead height. Our actual vessel speed, being known, should be substituted for the 6kts used in the above examples.
This method can even be used for extreme navigation conditions such as heavy fog. You might find, given heavily reduced visibility, that your safe look interval comes out to be a matter of seconds and that safe CPAs can't be maintained any less than visibility range itself. Of course, if CPA can't be maintained less than 20ft (because visibility is 20ft) and your look interval comes out as 2 seconds ... you should probably be anchored out of the channel anyway.