I wonder…

I’m sure everybody who has watched HTTYD remembers Hiccup and Toothless’ first test flight.  And nobody can forget that memorable music written by John Powell, Test Drive.

Well, doesn’t everybody want to ruin the amazing scene with physics?  Because I do.

Exactly how high up in the atmosphere were Hiccup and Toothless?   It can be figured out, with our frenemy physics.

Click the read more to find out.

First, we must not account for air resistance.  As far as I know, no one has yet created a life size 3D model of Toothless and put it into a wind tunnel, so it is easier to just not bother with it.

When there is no air resistance, all objects near the surface of the Earth (somewhere in the homosphere)  fall at the same speed.

If we do not account for air resistance, we can calculate how fast the pair fell with this formula.

Distance = 1/2 x (acceleration) x (time) squared.

In other words, to find the distance they free fell solely under the influence of gravity,  multiply 1/2 times acceleration times the time it took to fall squared.

The acceleration for objects free-falling is constant, meaning that they accelerate at a constant speed.

The acceleration due to gravity for any object is 9.8 meters/second in metric units and 32 ft./second in English units.

Since I live in a country where confusing English units are used, I will use English units.  But, for those who use the metric system (which really is simpler) I will also use metric units.

So, Distance = 1/2 x (32 ft./second) x (time) squared, or Distance = 1/2 x (9.8 meters/second) x (time) squared.

Now, we need to find out how long it took them to fall.  I went back to watch the movie again, and there are two places to choose from when they stopped falling.  They either stopped falling when they began to weave through the rock stacks, or when Toothless spread out his wings.  I’m going to choose the former, because we’re not accounting for air resistance.

It took them 36.53 seconds to fall from high up in the clouds to where the rock stacks are.  We insert that into the formula.  I’m using English units right now, but the same applies to metric units.

Distance = 1/2 x (32 ft./second) x (36.53 seconds) squared.  After working that out, I got that they fell 21, 351.0544 ft, (6,538.76041 meters).  I’m going to convert those numbers into miles  and kilometers.  Toothless and Hiccup fell 4.0437603 miles (6.53876041 kilometers).  The troposphere is about 7 miles high (11 kilometers) so they were about halfway up into the troposphere.

That’s still plausible.  Normally, skydivers jump from 12,500 ft (about two miles, or 3.8 kilometers) but Hiccup and Toothless fell from roughly 21,000 ft.  Luckily, Felix Baumgartner, an Australian skydiver, jumped from 128,000 ft (39,000 meters) (which would be in the stratosphere) without supplemental oxygen and survived (although he did have a special suit on), so I don’t think we have to worry about Hiccup and Toothless dying.  I believe that they would live!



Image credits:
Screenshot by Olivia Asis.  While searching for images, I found her Physics blog.  If you want to read about how HTTYD broke a few of Newton’s laws, click the link.
Other image: Hiccup and Toothless by Hawkeyewong









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