OK, here's something that roughly fits the criteria of the original post: early sceptical attitudes to the safety of rail travel.
Early trains could travel at around 25 mph (40 kph) and this was considered to be dangerously fast. There were fears that being shaken about and travelling at that speed could cause nerve damage.
An average saddle horse can gallop at around 25 – 30 mph and a thoroughbred somewhat faster (a quick search suggested 40 – 45 mph).
So for centuries, some people had been shaken about at speeds in excess of 25 mph. This was clear evidence that flew in the face of the idea that 25 mph in a train was "dangerously fast" but people were still afraid of travelling that fast in trains.
Of course, there were other considerations, such as the quality of brakes, the stability of the rails, the integrity of the companies running the trains, and the simple discomfort of being in an open carriage at that speed. However, the simple idea that rattling along that fast would cause nerve damage was contrary to a large body of evidence from horse riding.
I found some interesting discussion of an actual phenomenon known as "railway madmen". There were several instances of individual passengers becoming violent while the train was in motion, but calm while it was stationary. Whether this was "escaped lunatics" using the rail system, or some form of fashionable hysteria, or just individuals behaving badly, or some combination of factors is unclear.
Here's a link to an interesting article I found while checking this before posting.
Edited extracts from the article linked above:
The most common danger on Victorian trains was the threat of attack by “railway madmen”. Many of these individuals seemed like ordinary passengers upon boarding the train, however, began lashing out when the train was in motion. As an attempt to curtail these attacks, the railway carriages were fitted with enclosed sections with a locked door...
It is believed that this insanity was due to the noise and rocking of the train carriages, as when a train reached the next station, the insane individual would be calm until the train was once again set into motion. Many medical professions during this time also held the belief that the rocking and jolts of the train shattered nerves in the brain, leading to uncontrollable behaviour ... Many professionals believe that these episodes were due to passengers experiencing “mania”, which included mind-racing, quickly speaking, and feeling empowered.
An illustration was published in Punch ... of railway tracks, with a final destination leading to a mental institution. This is due to the fact that patients in these institutions who escaped, sought freedom on the rails, and terrorized travelers on board.
Oddly enough, towards the end of the 19th century, and as railways became more commonplace, attacks on board trains subsided substantially.
Below: various images relating to "Railway Madmen" including the Punch cartoon mentioned above.
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