We’re kicking things off in Dubai today,
home to the world’s tallest building, the
Burj Khalifa.
You’ve just enjoyed the view from the observation
deck on the 148th floor, about 555m up the
829.8m building.
And, quite sensibly, you decide that taking
over 2,000 steps to the ground floor is too
much effort.
So, you hop in to one of the elevators, and
start making your way back down.
Suddenly... SNAP!!
You’re hurtling towards the ground! Things
don’t look good.
What do you do?
Your life starts flashing before your eyes,
when you realize, wait a minute!?
You’ll just jump a split second before the
elevator hits the ground,
taking yourself out of the equation during
the moment of impact and you’ll be OK.
But, is this actually possible, and what other
options do you have?
I’m Stu this is Debunked and we’re here
to sort the truths from the myths, and the
facts from the misconceptions.
Most us won’t have the opportunity to journey
up the world’s tallest building, but, more
and more of us are living in high-rise apartments.
Now, I’m willing to bet I’m not the only
one to have stepped through those sliding
doors and thought it could turn into a giant
metal coffin.
After all, the only thing separating you from
a meeting with the grim reaper are a few cables.
If they snap, then surviving the fall seems
pretty unlikely.
Unless, you can time that last second jump,
just right.
_It seems to make sense, just before the elevator
hits the ground,
you jump and you’ll be suspended in mid-air
taking your body out of the equation at the
moment of impact.
Then, when you land, it’ll be as soft as
if you were jumping normally.
Time to bust out some physics, and a few hypothetical
situations, to see whether this is actually
true or not.
So, if you’re riding that elevator in a
Skyscraper, it means it must be at least one
hundred meters high -
as that’s the widely accepted definition
for a Skyscraper.
Our fictional Debunked Towers is one hundred
meters.
So you’re getting the elevator down from
the roof, one hundred and fifty meters up,
when all the cables snap! And the brakes fail.
Now, most other articles you’ll come across
will assume the elevator and its occupant
are now in free fall, this is incorrect,
unless you were in a vacuum, and then the
lack of air may be your bigger concern than
the falling elevator. Plus if you were in
free fall,
you would feel weightless and end up jumping
like you were on a spacewalk.
But, in fact the effect air resistance would
have on the elevator carriage,
will increase as it plummets faster towards
it’s doom, and it would be too great to
completely disregard it.
So, we consulted a physics boffin from the
University of Cambridge, to help us out.
What we are going to assume in our calculations:
- is that the elevator carriage is a perfect
rectangular box.
- It falls straight down, meaning it isn’t
slowed by breaks or scraping along the edge
of the shaft,
- and that all factors that affect air resistance,
other than its speed, stay constant.
These are things like, the air density, and
the air flow patterns around our elevator.
Now, that our conditions are established we
can get on with the fun stuff,
and see how fast you are going to be travelling
before you hit the bottom.
Well gravity, will be exerting an accelerating
force of 9.81 newtons per kilogram,
which converts to an acceleration of 9.81
meters per second every second.
When you take into account the air resistance
the carriage will experience as it hurtles
down,
it means that after just five seconds, the
elevator will already be traveling at 37.5
meters per second, which is a whooping 83.9
miles per hour.
Now you’re probably starting to panic at
this point.
In fact, we’ve calculated the elevator to
reach terminal velocity at just over 49 meters
per second,
but unfortunately, you won’t reach that
because just 1.1 seconds later you will smash
in to the ground…
...at 41.3 meters per second or 92.4 miles
per hour.
The entire one hundred and fifty meter fall
will have lasted just 6.1 seconds.
So, you’ve got just over 6 seconds to realise
what’s going on and launch yourself from
the elevator floor before it crashes in the
bottom of the elevator shaft.
Now, the common misconception is thinking
that you would change direction when you jump.
‘Of course you would!’ I hear you cry!
‘You’re falling DOWN and then you’re
jumping UP!’
I mean, it seems logical to think it would
work that way, because if you were stood in
a stationary elevator and jumped,
you would go up and the elevator would stay
where it was.
But when you’re plummeting towards the ground
inside the elevator, both you and the elevator
are falling downwards at high speed,
so all you would be doing when you jump is
leaving the elevator floor and reducing your
body’s falling speed, to, hopefully, a less
lethal rate.
But, what could you hope to reduce your falling
speed to?
Using data from the SMU Locomoter Performance
Laboratory, an athlete can jump with a vertical
velocity of 2.45 meters per second.
So let’s say that you’re impending doom
makes you bring your A-Game,
and you manage to propel yourself with the
power of an athlete.
If we assume, when a person bends their legs
to jump,
the process of pushing themselves off the
ground takes 0.4 seconds and the average mass
of a human is taken to be 75kg.
Using Newton’s second law, we can calculate
that the average force you exert on the ground
is about 460 Newtons. Making your athletic
jump achievable.
But, jumping whilst falling changes everything.
When the floor you are standing on is static,
it will react to any force that you apply
to it,
by applying an equal and opposite force back
on you.
This is a consequence of newton’s third
law.
To put this in context, imagine you are standing
in a room, your weight, pushes your feet downwards
onto the floor.
So the floor pushes back upwards to your feet,
by the same amount.
These two forces cancel each other out, and
you remain stationary.
You then use your muscles to push down on
the floor more (using the 460 newtons we calculated
earlier),
and the floor pushes back up on you more,
and so, lifts you into the air.
The problem is, in a falling elevator, only
70% of your body weight, is being used to
keep your feet on the floor.
The other 30% is being used to accelerate
you earthwards.
This means, the amount of force the ground
pushes back up on you will also be less,
as it only needs to counter your weight. at
this point you remain stationary.
To put this into context, if you were standing
on a set of scales, you would seem to be 30%
lighter,
as your feet aren't pushing down towards the
ground as hard.
So then, when you try to jump, you will be
applying the same extra force from your muscles
as before (the 460 newtons),
plus what is now only 70% of your weight,
or gravitational acceleration.
so now you have less upwards force for your
jump, meaning it will be slower and you won’t
jump as high.
In a room you might have been able to jump
to athletic speeds of 2.45 meters per second,
but now in an elevator where the cables have
snapped,
and it’s accelerating downwards, your jump
will only get you to about 1.3 meters per
second.
So with all of this taken into account, will
your new found athleticism help you, as you
time your jump to perfection?
No…
with your now pathetic jumping speed of 1.3
meters per second,
and with the elevator impacting with the ground
at a staggering forty one point three meters
per second…
the math is simple.
You will be traveling at the same velocity
of the elevator
Minus your jumping velocity,
which means you’ll smash in to the bottom
of the shaft at 40 meters per seconds,
that’s a pretty fatal...
89.5 miles per hour.
Now, if jumping won’t help you, what’s
the best thing you can do?
You might think bending your knees to absorb
some of the impact may help,
but according to Dr Eliot H. Frank, a research
engineer at M.I.T...
“THE IMPACT OF THE ELEVATOR AT THE BOTTOM
OF THE SHAFT WOULD SUBJECT YOU TO EXTREME
GRAVITATIONAL ACCELERATION”
“[AND] AT HIGH G-FORCES YOUR LEGS WOULD
SIMPLY NOT BE ABLE TO SUPPORT THE WEIGHT OF
YOUR BODY,”
ELIOT H. FRANK | RESEARCH ENGINEER
CENTER FOR BIOMEDICAL ENGINEERING | MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
In fact, according to our calculations, the
force of the impact would be around 6 million
newtons,
but if you do bend your knees, by around 50
cm, then you would, decrease this force to
about 120,000 Newtons.
If you consider your tibia bones, in your
legs, will break at about one hundred thousand
Newtons of vertical force,
then your legs will be crushed,
but this could potentially absorb enough of
the impact, to preserve your more vital organs,
but you’re just as likely to be dead.
There are other schools of thought that suggest
placing all your luggage on the floor to help
soften the impact, but that’s not much USE,
unless your on your way to the airport with
2 weeks worth of suitcases.
STU STOOD IN THE LIFT. SUITCASES PILE UP UNDERNEATH
HIM.
Dr frank, suggests laying on the floor as
flat as you can.
“THIS WILL DISTRIBUTE THE FORCE OF IMPACT
OVER THE GREATEST AREA OF YOUR BODY SO THAT
NO PARTICULAR PART OF YOUR BODY IS SUBJECTED
TO THE WEIGHT OF ANY OTHER PART OF YOUR BODY,”
But to be honest, you’re unlikely to ever
be in this situation,
as there numerous safety features built into
all modern elevators.
Each individual cable, holding the elevator
carriage, can support the elevators weight
on its own.
And, if a freak accident caused all the cables
to snap, then there are automatic braking
systems that are backed up by electromagnetic
brakes.
And finally if everything else fails, there’s
a shock absorber system at the bottom of the
shaft,
that is designed to save passengers lives,
by absorbing the impact.
In fact against popular belief, although around
18 billion passenger trips are made every
year in elevators,
they are actually safer than taking the stairs,
or an escalator.
With elevators causing only 27 deaths per
year.
This means the odds of an elevator trip causing
your death is a miniscule zero point zero
zero zero zero zero zero one five percent.
