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Prisoners of The Sun: Could Tintin really survive the jump from the bridge?

jock123
Moderator
#1 · Posted: 23 Apr 2013 14:13 · Edited by: jock123
Following an observation made by mct16 in this thread, rather than digress too much from that topic, I thought I better break off a new thread, get out the back of an envelope, and do some physics...!
mct16:
when Tintin jumps into the river, the height from which he goes from and the shallowness of the water would have meant him hitting the bottom and quite likely being seriously injured on impact.

Agreed - but I'm not even certain that the water being shallow would have been an issue - from the height from which he jumped, and the very poor position in which he falls, he'd probably have been fatally injured, if not killed outright, on impact with the surface of the water, given that water is quite dense, and thus without need of rocks under the surface. He'd certainly have been knocked unconcious (again!), and in all probability drowned, if the impact hadn't killed him first, rocks or not.

Anyway, let's look at the physics...
Say the bridge is 45m (approx 150ft) from the river; Tintin would take 3 seconds to fall from the trestle to the water (I'm not allowing for additonal momentum imparted from the train, which may have some small bearing on the matter). He'd be travelling at over 29m/s, or in the region of 65 miles per hour when he struck the surface. If the bridge was 60m (c. 200ft) high, he'd fall for 3.5 seconds, and be heading towards 80 mile per hour - ouch!

His posture is undoubtedly very poor - without going into too much detail here, you don't want to be in a sitting position like that, because, apart from shattering and compacting his spine (nasty!), at high speed water will be forced into the body cavity through a part of the anatomy which definitely won't benefit from a high speed inrush from a cold mountain river... So if the crash didn't get him, the internal shock might just do it!
To reduce this problem, he should have straightened up, clenched his nether regions (to be fair, a fall from a train off a high bridge might have this effect anyway... Swings and roundabouts, I suppose), and tried to make his body as aero/ aqua-dyamic as he could, to slice into the water.

It has been suggested, I think, that throwing something into the water to break up the surface might have a cushioning effect to the blow - however, even if his reflexes had been up to it in the short time available, Tintin's options in this matter are limited to what he happens to be carrying, which in this case would almost certainly not be in Snowy's favour... ;-)

Good thing they live in a world of cartoon physics!

There is also a thread from the past dealing with the possibility that Tintin is in fact more than he seems: Tintin: Is he super-human?, which might have some bearing on the matter of how he survives the drop...


Update: Having just checked the scene in the Ellipse-Nelvana cartoon, the jump takes aroung 6 seconds! A body in free-fall under gravity on earth would cover 577 feet, or 177.5 meters in that time, and attain a velocity of over 131 miles per hour - the outcome would not be pretty!

Erratum: Should have remembered about terminal velocity - the figures I find for a falling human in a random posture (as opposed to adapting one's body posture like a free-fall parachutist to increase or decrease drag) come between 117 and 125 miles per hour, so the height of the bridge suggested above should be reduce a bit as Tintin wasn't falling as fast as I thought.

He'd still more than likely die...
Emdy
Member
#2 · Posted: 24 Apr 2013 01:22
jock123:
I’m not allowing for additonal momentum imparted from the train, which may have some small bearing on the matter

In fact, the momentum would probably have made him miss the river and smash into the rocks. Also, it's been proven that dropping something else into the water in front of you won't lessen the impact.
jock123
Moderator
#3 · Posted: 24 Apr 2013 07:50
Emdy:
the momentum would probably have made him miss the river and smash into the rocks.

Good thing that the wind-speed must have counter-acted the train’s momentum, and steered him away from the cliffs…! ;-)
Emdy:
dropping something else into the water in front of you won't lessen the impact.

It was a long shot, but Snowy is grateful he won’t be used as a missile for such purposes!
mondrian
Member
#4 · Posted: 4 May 2013 19:46
jock123:
Should have remembered about terminal velocity - the figures I find for a falling human in a random posture (as opposed to adapting one’s body posture like a free-fall parachutist to increase or decrease drag) come between 117 and 125 miles per hour, so the height of the bridge suggested above should be reduce a bit as Tintin wasn’t falling as fast as I thought.

Actually 50meters/s (rougly 125 mph)is the terminal velocity for a human freefalling in the standard x-position used in skydiving. If an experienced skydiver is able to fall feet- or headfirst (and counter-intuitively, such position is very difficult to maintain in freefall), much higher speeds (I believe 80m/s is quite usual) are possible.

That said, wind resistance etc. slow down the acceleration, which means that even 50m/s (125 mph) takes much longer to achieve than simple calculations based only on laws of gravity would imply.

All of the above is from memory from my skydiving days, so I hope you allow slight inaccuracies. My school days are even further away, so can't calculate physics behind it either...

Either way, collision onto anything on such speeds would be rather dangerous.
Emdy
Member
#5 · Posted: 23 May 2013 00:44
Actually, I just remembered that a strong wind can dramatically slow a person's descent. There was one teenager who jumped off the Golden Gate Bridge, but because it was so windy, he got away with nothing more serious than bruises. If the wind was strong enough to keep Tintin from smashing into the wall, it almost certainly would have been strong enough to stop him from breaking all his bones on impact.
jock123
Moderator
#6 · Posted: 23 May 2013 08:27 · Edited by: jock123
Emdy:
If the wind was strong enough to keep Tintin from smashing into the wall, it almost certainly would have been strong enough to stop him from breaking all his bones on impact.

That would have to fall into the category of freakish, highly unlikely (although not entirely impossible) scenarios (which under the circumstances is what the book deals with - however, we’re looking at Tintin’s chances under “real-world” conditions).

I think you must be referring to an incident in 2011 when not one but two people separately survived falls from the bridge.

One, a young girl, was injured and hospitalized; the other, a teenage boy, apparently was more or less unhurt, which may have been due to the wind cushioning his fall, as you say.

However, this is well outside the norm: the fall from the bridge is almost always fatal (indeed notices actually on the bridge itself are not in any way equivocal, and state: “The consequences of jumping from this bridge are fatal and tragic.”), and we should therefore assume that the wind is, on median average, not going to support you, and on modal average not any help at all in offering support.
You still would be buffeted by it, causing lateral movement; this may or may not cause Tintin to avoid the sides (he may just have been lucky!) - but whatever happens, he definitely is going to hit the water at the bottom…!
calculite
Member
#7 · Posted: 24 Jul 2013 12:59
I don't know if the air would be thick enough to cushion Tintin.
We should take into account that Tintin is in Peru. Correct me if I am wrong, but Peru is a pretty mountainous country.

On page 13 or 14, Tintin says that the train climbs up 15,865 feet. I don't know if this 15,865 feet above sea level or 15,865 feet above the station from which Tintin and Haddock get on the train, but let's assume it is above sea level.
Here is a conversion chart for the height:

Feet: 15865
Miles: 3
Meters: 4835

So the railway climbs to about 3 miles above sea level. Now, the train achieves that height after going 108 miles. The train has been travelling several hours before Tintin jumps. Prisoners of the Sun was published in 1949. According to my sources, passenger trains outside of the U.S. in 1950 usually went at least 100 miles per hour. So, technically, in only about one hour, the train would be at 3 miles above sea level. Even at 50 miles an hour, fairly slow for a passenger train in the 1950s, the train would reach 3 miles in about 2 hours. We could consider this slow speed accurate because a train conductor would want a slower speed to stay safe, as he is going up a mountain.

With this conclusion, I would say that when Tintin jumps, he is at an elevation of a little less than 3 miles above sea level.

Now I will relate all these calculations to wind and air:
Air pressure becomes lower as you reach higher elevations. Oxygen levels deplete, which is why mountain climbers have oxygen tanks. Essentially, the higher you go, the thinner the atmosphere gets. Three miles above sea level is a formidable height. 15, 865 feet is 4,835 meters. Using this graph, the air pressure from where Tintin is jumping is about 50% of the air pressure at sea level. 50% is a big difference.

It is highly unlikely there would be enough air to save Tintin's life even in sea level conditions. Add to that the fact that air is 50% thinner than normal where Tintin is jumping, and you have a recipe for disaster. At that height, the air would be too thin to cushion Tintin's fall.

So air resistance saving Tintin's life is out of the question. Anyone have any other ideas?
jock123
Moderator
#8 · Posted: 24 Jul 2013 22:10 · Edited by: jock123
calculite:
let's assume it is above sea level.

Agreed - I think that's what was meant; it agrees with the information I can find about the line between Lima and Huancayo (which is the high point you mention), on the service called the Tren de la Sierra.

The height is such that people often succumb to altitude sickness on the way, and in modern times there is a law that requires trains on the line to carry a nurse and oxygen, to care to for flagging travellers.

calculite:
According to my sources, passenger trains outside of the U.S. in 1950 usually went at least 100 miles per hour.

Nothing like, I'm afraid. For one thing, it would have been impractical for most services - 100mph/ 160kmph is fine for long-haul, intercity trains under good conditions; wholly impractical for the majority of "stopping" trains, where stations may only be a few miles apart. And there is also the not inconsiderable matter of the terrain the train must travel over...
So the notion that the minimum rate of travel anywhere in the world was ever "at least 100 miles per hour" (my emphasis) seems to be highly doubtful, and not even practical as an average, when you consider that the The Mallard, which set the high speed steam record reached just a fraction over 125mph (just over 200kmph), and that was under specific "racing" conditions, not as part of a regular service.

calculite:
We could consider this slow speed accurate because a train conductor would want a slower speed to stay safe, as he is going up a mountain.

However, the biggest misconception you have, I feel, is that a train - and a steam-train at that - could ascend three miles, on highly meandering track, through tunnels and over trestles at such speed: it assumes a prodigious effort on a virtually continual gradient, and that's before working in the effects of altitude on combustion and water-boiling. Even today the diesel-pulled trains take 12 to 14 hours to cover the 108 miles.

I couldn't find a reference to it for the Lima line, but in looking for information I did see a mention to the effect that in Argetina, on one of the mountain lines there, progress by the train is so slow at times due to the geography, that passengers can safely get off and walk along-side the train to stretch their legs!

There is a clue in the text: if they had been on the train for "several hours" - which is a term for more than a "couple of hours" (which would be two) - and they still hadn't reached the terminus, which would be the highest point, then the train is indeed going slower than even your lower estimate.

This also means that even after "several hours", the Captain and Tintin have not reached the full three miles high, so you are quite right to point out that the air will be thinner, but perhaps not as attenuated as you first thought?
There's nothing to say that the incline between point A and point B on the line is a straight graph, but if we imagine it is, and say that the train has been under-way for perhaps four hours out of twelve, they are only a third of the way there, so approximately a mile high?

calculite:
Using this graph, the air pressure from where Tintin is jumping is about 50% of the air pressure at sea level.

I'm not sure of what that graph is showing me, to be honest, or exactly how to read the scales.
However, a mile high is the about same altitude as Denver, Colorado, and the atmospheric pressure there is said to be about 50% of sea-level atmospheric pressure in the literature I can find, so we can agree on the figure, if not exactly how it was derived!

calculite:
At that height, the air would be too thin to cushion Tintin's fall.

I think it's fair to say that, even at sea-level, air resistance would have very little effect on Tintin, at least in terms of being great enough to ensure his safe passage to the ground - so at altitude, under "ideal" conditions (still air, no wind, no buffeting from surroundings, etc.), it would have even less effect.
However you might need to factor in prevailing conditions at Tintin's location - such as the effect of wind in an enclosed environment like the ravine into which he's jumping, which might increase pressure above that of standing air at a similar altitude; can't say I think that the outcome would be much different (i.e. pretty disastrous for our boy reporter and his dog), but in the interest of completeness we should at least consider it... ;-)
blisteringbarnacle
Member
#9 · Posted: 22 Oct 2013 06:08
Calculite,

Many American Streamliners did come close to 100 mph, in 1950, but surpassing such a speed is rare.

By this time almost all railroads had their top of the line trains diesel powered, the main exception being the Norfolk & Western.

However to compare to the service of American Streamliners like the New York Central's 20th Century Limited or the Santa Fe's Super Chief to this train would be false equivalency.

In 1950, American railroads were prosperous, they had mainlines in excellent condition and the most modern up-to-date equipment of that time.

The railway in Peru has a terrible route to start with and considering Peru is a poor country, I doubt it or the equipment is in excellent condition.

Climbing this line at 100 mph, which would not be a good idea even with excellent equipment and track would be suicide, if the locomotive was even capable of reaching such a speed.

Unfortunately, Hergé didn't draw trains with the same detail as he did with automobiles (think of the European trains in Tintin in America), so the train in Prisoners of the Sun is not an accurate depiction of a Peruvian train at the time.

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