NavList:

I am researching the sinking of the RMS Rangitane in WW2 300 miles off New Zealand on her way to the UK via Panama. I have established that she was about 50nm off a whole circle course after about 45 hours having sailed 420nm of the 1500nm to her first pre-arranged waypoint. I am trying to establish whether being off course could have been the result of normal navigation error.

I know that the weather at the time was not good - overcast skies and rain for much of the time. I have learnt a little bit about old fashioned (pre-GPS) navigation and would like to test out some conclusions on you learned guys.

1. I have been advised that under normal wartime conditions of radio silence and out of sight of land an accuracy of about 2 arc minutes or 2 nm was routinely achievable with celestial navigation on a large ship. But with constant cloud cover, I assume that a position could only be estimated from bearing, log, knowledge of currents and leeway.
2. Compass error could be as much as one degree - about 7nm in 420nm from poor steering and calibration.
3. Errors from a poorly calibrated log could be as much as 5% - 23nm after 45 hours.
4. Errors from a mid ocean 1kt current could be as much as 42nm but I understand that this would have been automatically compensated for by the navigator.
5. I do not know how much windage would have affected a 16,000 ton ship.

If all these factors were cumulative then I assume that 50nm deviation after 45 hours might have been possible, yet many people have told me that it is highly unlikely. But I need to explore one further possibility but my maths isn't up to it:
I understand that there are two fundamental ways to navigate between two points - whole circle and Mercator and I think I understand the relative benefits. But how do I calculate the difference in track after 45 hours using the two different methods? Can anybody point me to some software which might help?

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