# "One of the girls was thrown hundreds of yards by the impact of the train."

This is from the recent BBC article “Girls killed by train at crossing”

From this website let’s assume a 14 year old girl weighs 100 pounds and is standing directly in the middle of the tracks and is not moving. From this website lets assume a train weighs 150,000 pounds.

How fast would a train have to be moving to throw her say, 200 yards?

There is a detailed Wikipedia article on the type of train, so I should modify the numbers. It is a British Rail Class 158 with a maximum speed of 90 mph. Not sure on how much it weighs.

You need the trajectory angle to solve that.
Assuming she attains the same speed as the train, and is launched at 45°, a few rounds with this handy trajectory calculator, gives an initial speed of 43 meters per second;154.8 km/h or 96.2 mph. For lower or higher angles, the train would have to be going faster.

Not sure the train weight would matter because any train of this type would so out-weigh her that the inertia generated by varying weights of the trains would be irrelavant.

I’m wondering why it didn’t just squish her.

Squink, does your calculations take into account the absorbed inertia of her soft body?

It could also be that the fellow from the Essex Ambulance Service was talking out of his hat, and she was actually thrown several hundred feet.

Nope, it’s a simple calculation of how fast she’d have to be going to get tossed 200 yards.

Got it, sorry. I read your post too fast. I was still thinking of the OP’s question of how fast the train would have to be moving.

My guess is that the body was found a long way from the initiol point of impact. Not telling how much of the distance was a result of being dragged or carried by the train.

One report saying the train was travelling at about [urlhttp://www.timesonline.co.uk/article/0,2087-1903307,00.html]70mph.

Ah. Google ads. Sometimes the match is so scary it’s funny. I can’t even figure out which search fodder it fixated on, unless it was “ambulance”.

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I agree with Eve… the distance was likely feet, not yards, as was reported.

Still, I’d be interested in the answer to this interesting, if not grim, physics problem.

If she would have to be traveling 96.2 MPH and the train was estimated to have been travelling at 70 MPH it’s doubtful she was thrown that distance.

In Soviet Union, train catches you.

At 70mph, neither the train nor the body will behave as rigid objects. If the body was pinned to the moving train for one second, that’s already carried it over thirty yards. As the front of these trains are lightweight aluminium panels, isn’t it the case that they could act as a spring and release the body faster than the train was travelling? (Not to mention the flexibility of a human body). Say 50m/s launch speed, and a realistic launch angle of 10 degrees, and the trajectory calculator is putting it at around 87 metres. Just about enough for the reporter to get away with describing it as ‘hundreds of yards’, meaning one hundred.

Oh, and FWIW it’s not a Class 158 train, but a Class 170. The bulbous front panel is about four feet off the ground, positioning it to directly propel the torso of the body.

It’s not correct that you can assume that the woman would simply be thrown at the speed the train was moving.

The piece missing is how much the train was slowed by the impact. Of course it would be an imperceptible amount, but when we’re talking about a train this massive, even a tiny fraction of speed loss would matter.

I saw a video once of a woman being hit by a train, and I can tell you that she was going a lot faster than the train was after the impact. If she wasn’t, she would have just stuck to the train and eventually been run over by it. Instead, she went rocketing past the camera’s field of view in a flash. I’d guess she was going at least twice the speed of that train.

Think of a baseball being hit by a bat. After the collision, the baseball’s going a lot faster than the bat was, even if you start with a stationary baseball on a tee. Conservation of momentum at work.

She could go 2x the speed of the train with a perfect bounce. Velocities are relavent. The train was moving at 0mph (relitave to the train), she was moving towards the train at 70mph (or whatever). When she hits the train at that speed, some of her will absorb the impact, the rest will bounce off.

She could have also rolled after she landed which would give you a few extra yards

Slightly off-topic, but there are many stations in Great Britain where passengers must cross at track level as at Elsenham, where the problem is exacerbated because passengers in one direction are obliged cross the track twice in order to buy a ticket before they board - which they must do because they would incur a “penalty fare” if they bought their ticket from the conductor aboard the train - because there is only one ticket office.

This problem would appear to be easy to solve: either provide a second ticket office or a self-service ticket machine on the other platform, or just build a footbridge.

But new footbridges must conform to a set of standards originally laid down by the Rail Regulator in 1995 (revised by the Strategic Rail Authority in 2002 and now the responsibility of the Department for Transport) in order to be fully accessible under the terms of the Disability Discrimination Act 1995. That means that they must incorporate (a) ramps, whose gradient should ideally be 1 in 12 and certainly no worse than 1 in 20, and which must have a level landing every 6 metres, making them expensive, impractically long and possibly requiring Network Rail to acquire additional land adjacent to the station [which they probably used to own themselves but flogged off to a property developer for a whacking great profit] on which to build them, or (b) lifts, at a capital cost of about £250,000 apiece plus the attendant longer-term repair/maintenance/renewal costs.

Before they became a not-for-profit organisation, Network Rail would have had their shareholders’ interests in mind when considering a solution and probably been happiest if the station operator (Central Trains, I think) just splashed out a few thousand quid on a ticket machine. But now they can happily blame the Government/Office of Rail Regulation for not giving them enough funding for stuff like this.

What a way to run a railway!