Archive for the ‘Great Circle’ Category

… and Real Sizes

One other effect that the distortion in Mercator Projection maps introduces is that land areas closer to the poles appear, on the map, to be bigger – sometimes much bigger – than similarly-sized land areas closer to the equator. Have you ever looked at Greenland on a ‘normal’ map and wondered at how big it looks? Or Alaska? We all know that Alaska is the biggest State in the Union, but is it really half the size of continental USA? No, it’s not. The image above shows how it compares when the distortion is removed and it’s placed alongside the other 48 continental States. Yes, it’s still big but not as big as it appeared.

There’s a website (as there always is) that allows you to select individual countries and then moving them around the map. Great fun, but also instructive. Here’s the link: https://www.thetruesize.com. Start by clicking on ‘Clear the Map’ – that will deselect the countries selected by default when you first access the map – then type the name of the country you want in the box – that will highlight that country. You can then select the country and drag it around the map, resize the map, etc.

The images below show some other interesting comparisons: India placed over Europe – when seen at the same scale as Europe it stretches from northern Norway to the toe of Italy, and from London to east of Moscow; the UK on top of Australia – actually, on top of less than half of just one State; and especially for my sister, Turkey (she lives there) lying on top of Europe, with London and Istanbul just about contiguous.


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Great Circles….

In my last post, ‘Travels of a Laptop‘, I briefly mentioned that on its journey from South  Korea to Germany, the package that contained my new laptop followed a Great Circle Route. I didn’t however explain what they are, and why they’re significant.

For most of us, the usual map of the world that we look at is based on the Mercator Projection. This preserves accurate latitude distances – that is, North/South distances – but distorts Longitude. 1˚ of Latitude is always the same distance, both on the map and on the actual globe, but 1˚ of Longitude will vary on the globe depending on your latitude. We all know that there are 360˚ in a circle, which means that at the equator the length of 1˚ of longitude will be the circumference of the earth at the equator (about 24,900 miles) divided by 360, or just over 69 miles. But at a latitude of 45˚ (North or South) the circumference of the earth is only about 17,637 miles. Therefore at that latitude, 1˚ of Longitude is 17637 miles/360, which is about 49 miles – less than it is at the equator. Unfortunately the Mercator Projection doesn’t show this at all, and therefore the further away from there equator, the more the map distorts reality. This has two distinct effects on what we see on the map and possibly on how we think.

The first relates to distances and directions. As I mentioned in that earlier post, one stage in my laptop’s journey was from Anchorage, Alaska to Cologne in Germany. The image below shows the route you might expect it to take between those two points. I’ve created as near a straight lines as I could on the Google Maps image, and that route works out at 6,410 miles.

In fact the route taken was very different, and below are two images showing that route. First is how it looks on a standard Mercator map:

That looks truly odd; why would it take that strange curving route instead of the straight line? Well, actually it was a straight line, as this third image shows.

That’s the Great Circle route – the shortest route around the curvature of the globe – and you can see that it is in fact pretty close to a straight line. Furthermore it’s shorter than the first route I traced out – 4,600 miles as against 6,400 miles, or 1,800 miles shorter. That’s more than three hours’ flying time, and a whole lot of fuel.

In the next post I’ll show you how the Mercator Project distorts the size of countries, and makes those closer to the either pole look much bigger than they actually are. In the meantime here’s a link to the website (greatcirclemap.com) from where I got the two images above. You can make your own maps – just enter the starting and finishing airports, and use the buttons over on the r/hand side to see the difference between the great circle route and the apparent route on a Mercator map.

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Yes, that’s right – Travels OF a Laptop, not Travels WITH a Laptop. Let me explain.

Apple recently released a new version of one of their best-selling computers, the MacBook Pro 13″, and I was immediately tempted. I’ve been without a laptop for almost a year. I used to have a 2014 MacBook Pro which I mainly used for travel – quite apart from the whole browsing & email thing, it was good to be able to do some initial processing of images while I was still on a trip, and of course I was also able to write blog articles (both here and in the Cruise blog). However, when the time came to replace the old laptop I was seduced by the idea of using an iPad as a laptop replacement, and so I bought an 11″ iPad Pro, a Smart Folio keyboard, and an Apple Pencil. (I also part-exchanged the old laptop.)

In the event the “iPad as laptop replacement” idea didn’t work for me. Well, it worked, insofar as I was able to use it, but I didn’t get on with the key piece of software that I had to use, Lightroom Mobile. So I had been thinking of going back to a laptop anyway, and when Apple announced the 2020 13″ MacBook Pro I was interested.

Apple has improved the base specification of the new laptop over last year’s model in some areas – double the storage and an improved keyboard, for example – and for the same starting price, but I decided to enhance the spec by going for a further optional upgrade, an extra 8Gb of memory making a total of 16Gb. I knew that this was not a standard build and that therefore delivery would be slightly delayed, but I had expected that it would still come from Apple UK – my assumption was that Apple themselves must order small numbers of the various optional configurations for onward supply to customers. Not so in the case of mine!

In addition to the usual deluge of order confirmation, etc, emails that I got from Apple, I was surprised to receive a tracking notification email from UPS showing “the package” (my new laptop) starting in China – “Label created” was the first entry in the list, on 29 May. “The package” spent the rest of that day and a couple of following days in China. The first entry just said ‘China’ but subsequent ones said ‘Shanghai’. Here are steps “the package” went through:

  • 29/5 to 31/5: Order Processed in China, then customs clearance and various scans in Shanghai (presumably, this location refers to a UPS facility in Shanghai);
  • 1 June: a Departure Scan 😁 at Shanghai at 3am, followed by an Arrival scan at Incheon, South Korea at 5am on the same day;
  • 1 June: more progress! At 7:30am there was a Departure scan at Incheon, followed by an Arrival scan at Anchorage, Alaska, at 9:25pm – date 31 May. This was initially confusing – had “the package” travelled back in time? could this be how UPS meets its deadlines? – but then I realised that the journey from South Korea to Alaska would have taken it across the International Date Line, and that’s what caused the date reversal;
  • It didn’t stay long in Alaska – less than two hours later, at 11:17pm, still on 31 May, there was a departure scan from Anchorage;
  • Next was was an arrival scan at Koeln (Cologne) in Germany, at 18:15pm on 1 June (again….). There’s a 9 hour time difference between Alaska and Germany, so actually it arrived in Germany just 8 or 9 hours after leaving Alaska. Interestingly, the Great Circle route between Anchorage and Cologne passes across the Arctic, so “the package” went close by the North Pole, albeit at 35,000 ft or so;
  • It had an overnight stay in Germany before having an Exit scan from Koeln at 4:48am on 2 June, followed by a Departure scan at Stanford-Le-Hope at 8:48pm the same day. Stanford-Le-Hope? Well it turns out there’s a huge UPS facility near to St-L-Hope which I believe handles packages arriving both by sea at the new London Gateway container port, and by air at Stansted airport;
  • After Stanford-Le-Hope came an Arrival scan at Tamworth late on 2 June followed by an Arrival scan at Sheffield early on 3 June….
  • ….and finally “The Package” was delivered to me at home just before 1pm on 3 June.

So my laptop entered 5 different countries – China, South Korea, the USA, Germany and the UK – passed over several more (the Great Circle route from Alaska to Germany would include Canada, Greenland, Norway, and maybe Denmark), crossed an ocean, a pole, and the International Date Line. Not a bad trip! – I wish I’d been with it.

I found this to be an interesting insight into the world of global logistics. I was surprised that my order was being handled as a separate, discrete package, on its own – clearly, it wasn’t in a container with thousands of other Apple laptops. I discovered that the facilities at Incheon, Anchorage and Cologne are mega-hubs for their continent, and that it’s normal for packages to be routed from one such hub to another if their journey requires it; my little laptop would never have been sent from Shanghai direct to the UK. I can only imagine the cost of doing this – while I’m sure that Apple doesn’t pay the rate I would to send a 2.9kg package half-way round the world, there must have been some cost. (Which I didn’t see, btw – my order included free delivery.)

And thereby hangs a bit of a tale, perhaps. A couple of days after I’d ordered my new laptop, and had the order accepted, Apple doubled the price of the memory upgrade that I’d included, from $/£100 to $/£200. There’s no official reason for this, although it is suggested that the lower price was a mistake. Really? By Apple, the most price- and market-conscious corporation on the planet? Well, perhaps; but is it also possible that one month into the new product’s life they were finding that there were so few orders for that particular upgrade that they were having to be handled as one-offs? Increasing the price would have two effects, perhaps: a) it would increase the revenue from orders for that configuration and thus meet the shipping costs, and b) it would narrow the price difference gap between that bespoke configuration and the next standard configuration up, and thus encourage customers to order the higher-priced standard config which would always be shipped in bulk. But we’ll never know the truth.

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