Weighing global matter over lunch

Here’s an interesting example of the power of estimation.

Anyone can calculate the Earth’s weight, approximately, sitting in a chair without recourse to a computer, or even paper. It’s a good lunchtime exercise. We just need a few rough facts: the volume of a sphere is about 4 times its radius cubed; the Earth’s diameter is about 8000 miles; a cubic metre of water weighs a tonne.

So – that’s a radius of 4*10^3 miles (half the diameter). Cubing gives 64*10^9 cubic miles. Multiplying by 4 gives 256*10^9. There are 1.6 kilometres in a mile, so about 4 cubic kilometres in a cubic mile. Hence the Earth’s volume is around 1000*10^9, or 1*10^12, cubic kilometres. The Earth’s interior is fairly liquid apparently – all that molten rock – so let’s crudely assume it’s as dense as water. There are 1000 metres in a kilometre, hence 10^9 cubic metres in a cubic kilometre, hence 10^9 tonnes. So overall the weight of the Earth is 10^21 tonnes.

The right answer is roughly 6*10^21 tonnes, according to Google. The main error in the above calculation is that the Earth’s density is nearly six times that of water. But it’s an interesting example of the power of estimation – that most of us are capable via a little mental arithmetic of estimating the Earth’s weight to within one order of magnitude (power of ten).

Estimating the impact of a vegan land release

Emboldened, we could apply the power of estimation to a recent broadcast about the vegan diet.

In New Year Solutions on BBC Radio 4, Jo Fidgen has been exploring everyday solutions to the climate crisis. One of the solutions is to go vegan (or, at least, to cut out most meat and dairy consumption). Apparently about 40% of the land on our planet is now devoted to meat and dairy farming. That’s about 60 million square kilometres. If we go vegan, we could free up much of that land for planting trees – say half of it for the sake of argument, an area equal to the US, Europe and China combined. What does that mean for our carbon emissions?

The best plants in Europe capture carbon at a rate of roughly 15 tonnes of CO2 per hectare per year (Mackay 2009). Given that the best plants might have to be supported by the second-best plants, let’s say vegan-supported tree-planting captures an average of 10 tonnes of CO2 per hectare over 30 million squre kilometres. There are 100 hectares in a square kilometre. So that’s a capture of 100 * 10 * 30 million = 30 billion tonnes of CO2 per annum. The UN projects a population of around 10 billion people by 2050 (Rosling 2018). That’s an extra allowance of 3 tonnes of CO2 per person per annum, freed up by the vegan transformation.

A flying comparison

Let’s put this in context with the example of international aviation. A return flight across an ocean has a carbon footprint – per passenger – of anywhere between 2 tonnes of CO2 equivalent for London to New York and 6 tonnes for London to Sydney. Assuming, that is, economy travel and using Defra’s carbon coefficients, including their figure for radiative forcing (Defra 2018). On average, let’s say a return trans-oceanic flight equates to 3 tonnes per passenger.

Conclusion? If we all became vegan and geo-engineered the world so that we covered an area equal in size to the US, Europe and China combined with carbon-capturing plants – an area that is currently devoted to livestock farming and is hence treeless – then, as a result, we might all be able to have one extra return flight (across an ocean) per annum. By all, I’m including the majority of the world’s population who currently never fly.

There’s also the direct GHG benefit of the change in diet to veganism, which is usually estimated to be circa 1-2 tonnes per person per annum, perhaps more if one gives greater weight to methane emissions (the standard international convention is to calculate the global warming potential of each greenhouse gas, including methane and CO2, over a period of 100 years: if a shorter period is used, then the relative importance of methane compared with CO2, and hence the relative impact of beef-farming versus energy-related activities, is increased).

I don’t know about you, but for me this type of calculation just reinforces the view that either the climate scientists are wrong, or we need to do something major about flying. The 7 billion who don’t fly want to catch up with the 1 billion who do. The physics of flight are not going to change. Battery-powered flying, for long-haul flights, seems unlikely. (The weight of the best batteries is around 100 times that of the equivalent amount of jet kerosene in terms of energy storage. It’s hard to see how a battery-powered plane taking off to cross an ocean would get off the runway.) Biofuels emit CO2. Perhaps future planes will run on hydrogen – but where will the energy come from to produce it?

Flying under the radar

Part of the reason why I go on about flying is that others don’t. Country statistics generally ignore international aviation. It does not feature in the Paris agreement. The EU only tracks emissions in European airspace for its emissions trading scheme. We are told that flying only accounts for a few percent of emissions, when the UK Dept of Transport has published a detailed study (DofT, 2017) showing the figure is at least 10% for the UK – and double that if radiative forcing is taken into account. Other sectors are showing some signs of falling emissions, whilst those from aviation are rising strongly.

Schools encourage foreign trips. Young people love to travel. Business people think face-to-face meetings with partners around the world are essential.

We rich Westerners may have to travel less in the future, not more. When we do travel, perhaps we could train-it rather than plane-it over land. (Cars are no help really: the energy consumption per person is similar for a car and a plane, assuming there are circa 2 people per car.) Crossing bodies of water is hard to do without using lots of energy. Whilst transporting bananas over the sea is surprisingly energy-efficient, most of us don’t want to be stacked like bananas when we travel; and passenger ships to date are no better than planes. Maybe nuclear-powered ships will feature in years to come. Or maybe, if we insist on air travel, we could learn to do so in helium-filled airships and accept the longer time it takes.