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In a recent game I sent several TFs to Cape Town over the course of 3 days. One contained a major warship which had suffered some damage but was still capable of 20 kts. All of the others contained auxiliaries or merchant ships whose top speeds varied between 18 and 12 kts. Some days later several of these TFs entered the off map track to Cape Town in roughly the same area. All ships in every case are travelling at mission speed. Now I see the following:

TF1 containing an 18 kt oiler will arrive in Cape Town in 5 days
TF2 containing a 12 kt freighter will arrive in Cape Town in 6 days
TF3 containing a damaged 20 kt warship will arrive in Cape Town in 16 days

Since the damaged warship is still faster, even though damaged, than the freighter and the oiler how come the warship is going to take 10 days longer to travel roughly the same distance?

It's the cruise speed that matters, not the top speed. I don't know if that answers your question but it's the place to start.

That is true. Once I had a destroyer escort the QE. And discovered that the cruise speed of the destroyer was much lower than the QE so the TF was moving slower than expected. Now I just send the QE on her own and pray she will out run torpedoes. She as so far.

This thread sounds familiar. I sent the Brit carriers to Cape Town to use the shipyard but I discovered they had all ran out of fuel. when they intially entered off map area they were due in Cape Town in 6 days. I checked back 2 days later and the whole task force was out of fuel and taking damage and it would take 60 days. By that time they all would have sunk due to damage. I had to back the game up 3 days and NOT send them to Cape Town. I withdrew the all the Brit carries except Hermes, it's May of 42. Historically they hide in Madagascar anyway.

I checked the cruise speeds of the various TFs:

The damaged warship's cruise speed is 9 kts.
The freighter's speed is 10 kts or 11 kts (I couldn't decide which of two possibilities it was)
The oiler's TF speed was 14 kts (or roughly 1 and 1/2 times the damaged warships speed).

So why does the damaged warship take 3 times as long to reach Cape Town rather than 1.5 times as long?

Just a thought, but check the endurance of the ships in the various TFs. If a TF must slow to refuel some ships, will that not effect their over-all speed?