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I will be in Barcelona soon and would like to try out the high speed rail. I don't want to go farther than necessary (e.g. to Madrid), but I would also like to avoid short segments where the trains don't accelerate to full speed (310km/h according to Wiki).

So what is the shortest train ride I can take out of Barcelona that would satisfy the requirements?

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    If you are looking for top sensations, you'd better go for a rollercoaster :) Because you won't really feel the speed in the high speed train. – Olielo Oct 17 '16 at 14:28
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    Maybe up to Zaragoza ? as Olielo wrote, don't waste your money on that. – Max Oct 17 '16 at 14:38
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    Having done it myself (not in Spain), it was certainly an interesting experience to go that fast in a train. Often things that are "boring" to those who routinely experience them will be interesting to a tourist. – user35890 Oct 17 '16 at 16:04
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    (+1) It's difficult to find comprehensive info but this article from 2011 and some other more recent sources suggest that it might only be on the section between Lleida and Madrid that trains truly reach 310 km/h. – Relaxed Oct 17 '16 at 16:26
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    Make sure to take an AVE on your barcelona/Lleida or Lleida/Madrid trip, Alvias use 200-250kmh-only locomotives and Avants use 200kmh-only locomotives as far as i know, that's why they are cheaper ( it takes 5-10 more minutes to get to tarragona and up to 15 minutes more to get to barcelona with an avant than with a Ave, both stopping only at tarragona). – CptEric Oct 18 '16 at 11:45
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Trains (especially trains designed with that in mind) don't need that long to accelerate, this document from Siemens states that it takes 148 seconds (a little more than 2 min) for the Velaro trainsets used in China to reach 200 km/h. The Velaro trains used by RENFE are not exactly identical and it would take even longer to reach 300 but they could still easily manage 200+ on relatively short segments.

But they can only do so if the design of the railway line allows it (and it is deemed economical to go that fast). From Barcelona, there are only two high-speed lines: the one to France and the one to Madrid. Wikipedia suggests the whole Barcelona-Madrid line is operated at 300 km/h. Only the section between Lleida and Madrid is planned for 310 km/h (this article is a bit old already but it does not seem to have changed).

Looking at the schedule, the closest stop from Barcelona in either direction is Camp de Tarragona. It takes AVE trains 30 min to reach it, for a distance a little over 100 km. That's 200 km/h from station to station so, assuming it takes a few minutes to leave the city center and reach the top speed, I would expect the train to reach at least 250 or more at some point along the way.

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    Last friday it took less than 24min from Tarragona to Lleida in an AVE ( for the "mere" cost of 19€). so it might go at 300km/h at some points, atleast the morning service. – CptEric Oct 18 '16 at 11:54

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