# 1bn Hiroshimas = 1 (Isle of Wight) × 20 (speeding bullets)

## July 2013

I think one of the problems with science journalism is that before a science story can be reported in the news media, someone has to convert everything from metric to journalist units. But some recent work may allow us to do science directly in journalist units, thereby making scientific papers immediately understandable to laypeople. According to a throwaway letter in the Guardian

1 billion Hiroshimas = 1 Isle of Wight × 20 speeding bullets

This is based on a G2 article about the asteroid that wiped out the dinosaurs that described the asteroid’s mass, energy and speed in those terms.

Unfortunately, the equation is wrong, as you can’t multiply speed by islands to get explosions. But it’s not far off. In fact, kinetic energy K = ½*mv*^{2}, where *m* is mass and *v* is speed – so actually

1 Chicxulub asteroid strike = 10^{9} Hiroshimas = ½ Isle of Wight × (20 × speeding bullet)^{2}

I’ll forgive the correspondent the factor of 2, but he should have known that the speed needed squaring given that the only other sentence in his letter was “Who needs E=mc^{2}?” Honestly, it’s as if some people have no grasp of dimensional analysis at all.

In fact, this is also wrong, because the Isle of Wight is more correctly a unit of *area*, not mass, so to use standard journalism units, we should really write

1 Chicxulub = 10^{9} Hiroshimas = ½ (Isle of Wight^{³⁄₂} *ρ*_{rock}) × (20 × speeding bullet)^{2}

Better still, that should be

1 Chicxulub = 10^{9} Hiroshimas = ½ (Isle of Wight^{³⁄₂} *ρ*_{rock}) × (21 × speeding bullet)^{2}

as the rock hit 20 times *faster than* a bullet, not 20 times as fast as one.

And we can test this hypothesis simply by typing “(1/2) * (density of rock * (isle of wight area)^(3/2)) * (21 * speed of bullet)^2” into Wolfram|Alpha. It returns the figure 5.023×10^{23}J, and if you click on that figure, it rephrases it to “≈ 1.005 × estimated energy released by the Chicxulub meteor impact”.

Let’s just bask in the impressiveness of that for a moment.

Done basking? Then it’s time to admit there are a few problems with this. Alpha cites this as 8 billion Hiroshimas, not one billion. Alpha also takes ‘a bullet’ to be a rimfire .22LR usually deployed against small pests and tin cans, whereas Dr Collins appears to favour the somewhat meatier M16 assault rifle. Maybe that’s standard for a *speeding* bullet. Also I assumed the asteroid was a sphere that would cover an area of land equal to one Isle of Wight. In fact the Isle of Wight is long and thin so if we spun it around its major axis it would be a bit lighter than this; equally we could attempt to estimate the mass of the Isle of Wight and that could go either way.

The point is that you absolutely can do science in these units. They totally work. We use metric instead only because the numbers are easier – 1 Joule is 1 kilogram metre per second squared, avoiding having the annoying factor of 21 kicking around that the journalism units version above does. (I’m not going to quibble about the billions, though, as you only need to define the ‘gigashima’ to make that go away.)

To make life easier for anyone choosing to do science in journalism units, I have identified some relationships that may prove useful:

- 1 coal-fired power station ≈ 1 Hiroshima per day
- 1 thickness of human hair ≈ 1000 Olympic swimming pools per area the size of Wales
- 1 weight of a double-decker bus ≈ 1 Hiroshima per distance to the moon and back

All of these are approximate, but they’re all exactly true for at least one combination of reasonable guesses, so all we have to do is identify a mutually-convenient set of plausible values, then agree to use it forever. We can’t really fiddle with

- 1 Isle of Wight = 381km
^{2} - 1 distance to the moon and back = 3.85×10
^{8}m - 1 Wales = 20,779km
^{2}

and we know that defining

- 1 speeding bullet = 340ms
^{−1} - density of rock = 2.65g/cm
^{3} - 1 Chicxulub asteroid strike = 5.023×10
^{23}J

gives us one neat relationship. Let’s add to that

- 1 Hiroshima = 1 Chicxulub ÷ 8 billion = 6.27875×10
^{13}J - 1 coal-fired power station = 1 Hiroshima ÷ 24h = 726.7MW
- 1 double-decker bus = 1 Hiroshima ÷ 1 moon and back = 8.416 tons
- 1 Olympic-size swimming pool = 2,500m
^{3} - 1 thickness of a human hair = 1000 Olympic pool ÷ 1 Wales = 120.3μm

Now all our relationships are spot on, and we can hopefully get on with doing some science with journalism units. At least, science that involves using coal to power buses to the moon.

Ie, the best science.