The reason why trains are expensive are that the cost to maintain miles of track is a lot. Roads have the advantage that with roads one has many many vehicles passing over them daily so the costs are shared. I am not saying aircraft are cheap as they are certainly not, but they dont have to maintain miles of steel rails... So though there is great maintenence costs and flying costs associated with the aircraft themselves, the actual running costs bring them close to rail travel.
Railways (I know far more about this from the UK perspective) really thrive when one needs to transport freight in bulk, especially when all the items are of the same type and are going to the same place. The history of railways in Britain stems from the transportation of various goods from minerals to perishables and in the past livestock (Livestock by rail was banned in the UK in 1958 due to fly shunting and hump shunting techniques used by staff who didn't care much for the wealfare of the animals which led to a protest).
Anyway... Nearly all passenger lines failed to make money even though ticket prices seemed to be high. The cash was generated from bulk transport of the freight industry. Origionally passengers would sit on top of the goods being transported or with the occasionalmpassenger only train, the convayence of passengers was more to promote the idea of railed transport then to actually carry passengers as a service.
Right round Britain throughout its history few lines were able to survive under their own merit if they were passenger carrying lines. The only real exceprion to this were railway companies that concentrated on running teains in and out of London, as London has so many people so most trains rarely run empty, so they can make a profit. The main issue being for the rest of the UK is that most of the time of the day trains run only about a quarter or a third full at best. Peak time trains are only a small portion of a much longer journey. I will give an example. Lets say I will run a typical train service from one point to another through many towns and villagss over a few hundred miles. Peak time of this service will be something like half an hour of its whole run. Due to peak time does rhe company run a longer train to cope, but the rest of the service runs at a big loss due to the extra costs involved in running such a long train, or does one run short trains that can make a small profit and leave many peak time passengers behind? And keeping extra trains running just to cope with peak times is very uneconomical, especially in todays marketplace where few train companies own their own trains.
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