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Based on a recent discussion of fuel usage rates at Cruise and Full speed, I did some testing of ships, starting with Post 10 of this thread: Fuel Tests in the War Room. One thing I discovered is that ships set to patrol a single hex use no fuel, whether at a base or in the open sea. I would assume they should use at least one hex worth of fuel. Ships with Remain on Station orders do seem to use one hex worth of fuel (40 endurance) per turn, but ships on Patrol orders, but with a single patrol point, do not.

Is this a bug or WAD?

Here's the text and data from the relevant test:

Turn 3 Patrol Tests
While I was testing, I decided to test fuel usage when patrolling. As I expected, ships used the normal cruise rate of endurance to get to their patrol points. And they appeared to use the normal cruise rate between patrol points, over a couple turns. The 3 DDs in the first 3 TFs were set with patrol zones at different distances. The DD patrolling a 2-hex range seemed to move 4 hexes every turn, once between each point. The DD with a 4-hex range varied, it went to the first point the first turn, hit both points the second turn, and stayed at the second point the third turn (using appropriate fuel for 4 or 8 hexes, respectively).

What surprised me, though, was ships set to patrol a single hex. The manual states:
Each ship in a TF that is not docked also expends a small amount of Endurance every turn equal to 40 times the ship’s cruising speed in hexes (i.e. it is assumed they are constantly moving at cruising speed even if they aren’t moving to other hexes).

That implies that the ships would use a normal turn’s fuel for a full cruise range. However, I have noticed before that stationary ships don’t use much, I expected it to use one hex worth of fuel. This was true for ships ordered to remain on station, they used ~40 endurance total, not 40 per cruise hex range. Ships ordered to patrol a single hex, however, did not burn any fuel. Ships remaining in port (no destination) also did not burn fuel, nor did the DD assigned to patrol the port hex. (I set both ships to Do Not Refuel, and checked the fuel level at the port, to ensure they weren’t getting refueled in the background).

What version are you using? I recall fixing up some issues where the fuel got rounded down 0 and thus did not come off the ship.

The latest official version: 1.7.11.24, dated 24DEC14.

Okay, I'll check it. I would have thought a patrol mission would be using same endurance expenditure.

Yes, it does seem that same hex patrol is not getting to the fuel expenditure section due to thinking it has already reached its destination. Will look into.
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Have made it so it will use a random endurance up to the normal day expenditure.
Included in latest beta

Thanks Michael!!!

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Michael, thanks for your continued support for all of us!