The answer to LTT-14 is two supply ships are needed to support the main cable laying ship.
The main cable laying ship (M), and two supply ships (S1 & S2) all leave Porthcurno at the same time, with full tanks of fuel. At the 1/6 way point on the circumference of the Globe, S1 refuels M with a 1/3 of its fuel, so it has just enough fuel to return back to Porthcurno. Meanwhile M and S2 continue until they reach the 1/4 way point of the circumference of the Globe. At this point, S2 refuels M, so it has a full tank of fuel and can sling shot around the Globe from 1/4 to 3/4 way point. S2 then turns around and heads back towards Porthcurno, and refuels with S1 at the 1/12 way point. Both S1 and S2 have enough fuel to head back together towards Porthcurno, where they both refuel and then head out in the opposite direction towards the 3/4 way point to rendezvous with M. At the 5/6 way point, S1 refuels S2, so it has a full tank of fuel to continue towards the 3/4 way point to meet up with M, while S1 returns to Porthcurno to refuel. S2 continues on and meets M at the 3/4 way point and refuels it, so M can return back to Porthcurno. S1 returns to the 11/12 way point and refuels S2, which now has more than enough (surplus) fuel to return back to Porthcurno.
As an additional part to the question, how much further could the main supply ship travel after the last rendezvous? After S1 & S2 have refuelled at 11/12 way point, there is half a tank of surplus fuel left or enough to travel 1/4 circumference around the globe.
Congratulations to Derek Burgess for providing the winning answer. Educated at Cambridge University in the UK, Derek is a software engineer specializing in embedded systems in the digital broadcasting arena, having dabbled in telephony based speech recognition systems en route.
Derek will receive a copy of our book, Revenue Assurance: Expert Opinions for Communications Providers.
Thank you for a fine quiz and my hats off to Derek Burgess for a job well done. I racked my brain for a couple hours on this one, came close, but missed some important details.
I have zero understanding of logistics, however, I know a lot about supply ships having served as an Ensign about the USS Tolovana AO-64, an oil tanker of the U.S. Pacific Fleet, a vessel that has long since been decommissioned and turned into scrap — God rest the poor soul.
For the most part, my tour aboard the Tolovana was a rather boring one at sea. The Pacific Ocean looks remarkably similar once you get “below the kirk, below the hill, below the lighthouse top.” However, I remember the magnificent sight of coming alongside the aircraft carrier, USS Enterprise, to fill it with jet fuel. And I also remember the time Tolovana’s engines failed when we were refueling and the rubber refueling hose stetched like a huge rubber band until the safety release gave way.
But for sheer excitement, being an industry analyst also has its moments :- )
It would be interested to hear how Derek, yourself, or anyone should framed the LTT- 14 problem. What’s the best way to attack a problem like this? It certainly was a challenging but interesting one to work on.
I did something like this.
Flatten the globe into a circle and picture it as a clock face. We start and end at 12 o’clock.
The main ship can travel alone for half the circumference, which by symmetry means it will have to start with a full tank at 9, travel through 6 and on to the 3 o’clock position, where it will stop empty.
Then apply trial and error to see how to get it to 9 o’clock, and use the same approach to rescue it later at the 3 o’clock.
If we have a single support vessel travelling with the main ship from 12 to 9, it would have enough fuel to refill the main ship but would be left with an empty tank, so would not be able to get home.
OK, so let’s see if we can do it with 2 support ships… by now the method is becoming clearer. One ship travels so far and refuels the other 2 and goes back; the other 2 press on. And so on.
(Similarly for the rescue)
Fortunately 2 support ships were sufficient, so trial and error proved sufficient.
Dan, I’m glad you enjoyed this one. You were not alone however, several persons contacted me wanting to be put out of their misery ;o). I think Derek sums up well the thought process behind it. Start with one supply ship and by working through trial and error you get to the answer. Some people got the number of supply ships correct i.e. 2, but their refueling strategy was not optimal. The key part to the question is, “you work in the cost control and operational efficiency department”, so the locations of the refueling points would have an impact on the project costs as well.