Naval convoys, operational research and stuff: Part 1/2; World wars period

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(A new naval affairs-related blog post of mine, for a change. )
Disclaimer: Naval affairs aren't even close to being my speciality. Don't expect the same quality in posts tagged "navy" as in others, please. 

Naval convoys are an interesting organisational answer to the problem of how to secure thousands of ships against attacks while using only hundreds of warships for the job. Convoys are so interesting because of unintentional side effects.

One such side effect is inefficiency in regard to time in harbour (for loading or unloading). A convoy only leaves the harbour when its last ship has completed loading. This means that other, already loaded ships are required to idle. This alone already yields a considerable loss of productivity for the merchant marine involved.

A similar and on long travels or with large harbours more important inefficiency is caused by cruise speeds: A convoy of any kind only stays coherent if it doesn't cruise faster than the lowest cruise speed of all ships involved.

These two effects mean that the mere accomplishment of forcing an opposing power to employ a convoy system already reduces its merchant marine capacity a lot. Strangely, this effect was not to be found in any work that covers either a Battle of the Atlantic or other convoy regimes that I've ever read (= several ones).

There is another, operational research-driven, detail about convoys: Western Allies' operational research calculated with really simple math that it's a more efficient use of escorts to form a huge convoy than multiple small ones. The reason for this is that the escorts basically had to guard the circumference of the convoy. Both square and circle-shaped convoys grow quicker in area (size) than in circumference. Twice as many escorts in a convoy were able to escort more than twice as many freighters.

 
This efficiency is an efficiency in regard to the use of escorts, of course. It further adds to the freighter-related inefficiencies mentioned before. The optimal convoy size did thus only in part depend on the scarcity of escorts - it is always a compromise.

Another interesting detail is that there's a threshold speed that allows for a dramatic drop in required escorts. German World War 2 subs had a surface top speed of about 18-19 kts, while some Japanese ones had a few kts more. Fast freighters made an attack approach from behind largely impractical, as a single escort was able to secure even a really big convoy's rear.

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WW2 convoy protection had furthermore interesting parallels to other increasingly sophisticated tactics of warfare from other domains.

It became increasingly a combined arms effort by '42. CVEs (escort carriers) were added to large convoys and provided near-constant aerial daylight support. The aircraft were able to spot and attack submarines on the surface. The spotting alone was already bad enough for the subs; it was asserted that no ship was sunk on Caribbean convoys that were escorted by a blimp (which did only spot, not destroy).

HMS Audacity, a CVE from WW2

Convoys furthermore at times received ships meant for search and rescue of the sailors of sunk ships, and ships with primary or secondary purpose of refuelling the escorts on the high seas.

Sub hunter escorts also began to employ hunter-killer tactics, since it was difficult to close in for the kill without losing sonar contact.

Another interesting convoy parallel to another sophisticated domain of warfare was that the fight against submarines became an area effort.
The defenders did not wait for subs at the convoys any more, but were increasingly organised into sub hunter groups that patrolled on sub travel routes. Land-based long-range aircraft patrolled the Northern Atlantic (with a quite small gap in the north central region). In the end, bombing runs against submarine bases and aerial naval mine-laying in submarine training waters were done with quite substantial effort and in the latter case also substantial success.

The interesting analogy is there the analogy with fighters protecting bombers: As early as 1940 it was well-known that 'freie Jagd' (freely roaming combat air patrols) was much more worthwhile than close escort of bomber formations - although just as in case of naval convoys, a certain amount of the latter was found to be quite indispensable.

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Modern naval convoys appear to be still quite similar to WW2. The so-called anti-submarine aircraft are now more often called maritime patrol aircraft since their effectiveness against submerged subs is small. Helicopters based on carriers AND on escorts (frigates, destroyers) have largely replaced the naval fixed wing ASW aircraft and their mission is more the identification and engagement of contacts  (suspected, but probably false detections of subs)

Naval convoys are an interesting matter in my opinion, and I am preparing a 2nd part of this post with some analysis (or speculation). As usual, it will conclude with some remarks that are quite critical of current budget priorities.

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Edit: Changed the diagrams for more intuitive reading (same math).

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