It's kind of funny; when you think of Shinkansen, you think of the Tokaido Shinkansen, which runs from Tokyo to Osaka, but it turns out that since the Tokaido is the oldest line (first opened in 1964!) it's also the slowest. The segment I'm talking about is part of the Sanyo Shinkansen, which runs between Osaka and Hakata/Fukuoka. The segment in question, which opened for business in 1975, includes a trip through the 18km long Shinkanmon tunnel between the main island Honshu and the western island Kyushu.
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There are four basic services on the Sanyo Shinkansen: Kodama, Hikari, Hikari Rail Star, and Nozomi.
Nozomi are the super limited express shinkansen trains, stopping in cities of 1 million people or more. The trains are long (16 cars), new, clean, popular, and tend to be crowded. If you ride with an unreserved seat at rush hour, expect to stand for the first part of your ride.
Hikari and Hikari Rail Star are the middle ground. They make less than half as many stops as Kodama does, but they do stop at every significant metro area along the way. A "Hikari" is a train that runs on both the Tokaido and Sanyo Shinkansen; the "Hikari Rail Star" runs only to the west of Osaka, on the Sanyo Shinkansen.
The Kodama trains are the "locals." They make every stop on the line and tend to dwell for ~10 minutes or so at smaller stations while they wait for another train on a faster schedule to pass by. They are also generally run with older, steel frame, 6-car equipment, so in spite of the fact that they stop more often, they take longer to get back up to speed. The train that takes 89 minutes to go from Hiroshima to Kokura is a Kodama. Kodamas never make Tokyo -> Hakata runs from end to end, since that would take far too long. Instead, they run on smaller segments of the route, connecting with the faster trains to provide continuing service to stations not served by the more limited trains.
Between Tokyo and Osaka, Nozomis make up about 60% of the traffic on the Sanyo line, with the Hikari and Kodama comprising 20% each. However, on the Hiroshima -> Kokura run, the traffic is almost evenly balanced: 33% Nozomi, 33% Hikari, and 33% Kodama. Something that foreign tourists should take note of, is that the "all you can ride" Japan Rail Pass does not work on the Nozomi, so you miss out on the very fastest of the fast. Oh well.
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Of course, there are heaps of conventional trains as well. There's the Local (futsuu), Rapid (kaisoku) and Super Rapid (shin-kaisoku) which all charge the base fare. Locals make every stop, while the Rapids and Super Rapids skip the smaller stations. These trains always have commuter-like accomodations. Then there are Express (Kyuukou) and Limited Express (Tokkyuu) trains, which bear the most resemblance to Amtrak in this country. Most sleeper trains in Japan are classified as Express or Limited Express. They sometimes have lounges, or at least vending machines or airline-style foodservice. The Express trains are more expensive, and you generally don't find any express service except for sleeper trains in areas served by the Shinkansen.
Nearly all service (including the shinkansen) is run with EMUs or DMUs. I prefer the US in that respect, since older MUs can be extremely noisy. Conventional lines in Japan are on a 1067mm narrow gauge, but the Shinkansen is standard, 1435mm gauge track. The trains themselves are wider than most standard-gauge equipment, and comfortably seat 5 people abreast with an aisle wide enough to fit large suitcases (there is no checked baggage on the Shinkansen.)
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While I was in Hiroshima, I did ride the shinkansen through Kokura on two occasions, although I've never had the opportunity to make the 44 minute run. While the Hikari and Kodama both cost the same, the Nozomi is a little more expensive. Needless to say, I took the Hikari both times, and I continued on to the end of the line in Hakata both times as well. Even the Hikari sometimes makes only one stop on the way, in Yamaguchi or Tokuyama - other than that, it just goes. And boy does it go! It probably takes about 5 minutes to get up to top speed. The gearing is different, so it's 0-100kph time is way slower than the local trains on the conventional lines, but it just keeps going. The train spends perhaps 90% of its route either on an elevated viaduct or in a tunnel, so the view is frequently obstructed, but you can still see a lot of stuff go whizzing by really fast. The ride is extremely smooth, although there is definitely a sense of motion. It's kind of disorienting when you travel through the comfort spiral before a curve - the same sort of dizzy feeling you get when an airplane is banking into a turn.
You can bet just about anything that if the shinkansen schedule says it takes 44 minutes, it takes 44 minutes to make the trip. Barring some sort of equipment failure (so rare it makes the national news when it happens) you WILL arrive within 1 minute of the schedule, with a slightly early arrival being the rule. Arriving even 1 minute late is considered absolutely unacceptable, because trains sometimes run on 3 minute headways, and even the slightest delay would cause a ripple effect through the entire system. You'd think that with a schedule this packed, the system would fall apart regularly but it doesn't. If you're watching the seconds tick by on a cell phone that synchronizes its clock from the tower, a departure scheduled at 8:20am departs at 8:20:00am.
It's a truly amazing system, dare I say it unmatched even in Europe, but you pay for it. Even with the enormous economies of scale, a four hour trip with a reserved seat from Hiroshima to Tokyo can cost you nearly $200. If you don't have a reserved seat, you'll can get stuck standing for at least part of your journey at rush hour - and remember, most of these trains seat more than 1300.