Elon Musk was presenting plans for Mars trips at a space industry conference on September 29th, when he returned to one of his favourite subjects: slow traveling between points on Earth. Details were light, but he showed a pretty video of the concept of one of SpaceX’s BFR* systems launching from a harbour and landing on the other side of the world. (*BFR = Big Falcon Rocket)
Counter-intuitively, based on my calculations, the BFR model would likely see about 40% of the carbon footprint of passenger jet travel on a per passenger basis before inevitable secondary and tertiary effects kicked in, or up to a less likely 240% of the carbon footprint.
Suborbital travel between cities has been a staple of science fiction for decades, but science fact has been in short supply. Musk’s latest insertion into the travel industry is in line with The Boring Company and Hyperloop in that it’s wildly different than the status quo and also deeply unlikely to turn into anything real.
Others have already dealt with the rather absurd elements of the solution, including crushing G forces, radiation exposure, launching and landing very large rockets next to major urban centres, and the not so farfetched problem of explosive failure.
But what about carbon footprint? Would it be worse than passenger jet travel today? Someone on the “March for Science” Facebook site asked this, so I decided it was time for some napkin math. As always, the fine strangers over at Quora did a good job of keeping my math honest on things like this, allowing me to present numbers with some degree of confidence.
The SpaceX BFR was originally envisioned as a liquid oxygen (LOX) and liquid hydrogen (LH2) rocket but shifted in 2012 to methane (CH4) and LOX. It’s straightforward to create LH2 and LOX in an environmentally friendly way using wind and solar electricity and water, an idea I explored for Space Shuttle flights in one of the reference links, but most hydrogen is created from natural gas. Similarly, methane is almost entirely derived from natural gas, as it represents 88–92% of the naturally occurring gas. Biomethane is created in much larger volumes than carbon neutral hydrogen today and has seen decreasing carbon footprints as well. Methane is 25 to 86 times more potent as a greenhouse gas than CO2, so leaks (which will occur) are a concern, but when burned, it creates a lot of CO2. The primary point of this is that there are lower-carbon forms of rocket fuel available, but the assessment will use normal carbon fuels to compare rockets to jet fuel trips.
There are a few assumptions and range boundaries to set:
- 16,000 kilometer travel distance.
- Suborbital vs full orbital values to provide a lower and upper range.
- Straight CO2 emissions vs well-to-rocket emissions.
- Comparison is to a Boeing 747 with 876m3 of pressurized volume and 660 passengers in one-class configuration. Two-class or three-class configurations have lower passengers, but Musk’s statement was about economy class airplane travel.
- The BFR is projected to have 825m3 of pressurized volume, and the ratio suggests around 620 passengers as possible for economy cost travel.
Assuming full fuelling, the BFR will produce about 4,400 tons of CO2 per launch and landing based on combining the 240 tons of CH4 and 860 tons O2 of fuel in Stage 2 plus the fuel in the booster. That gives about 7.2 tons per passenger per trip for the BFR for just the base fuel use. The well-to-rocket emissions are 40% higher assuming equivalent for CNG cars, so it’s actually closer to 10 tons per passenger trip. Note that the majority of the extra 40% is compression and cooling, which is also amenable to low-carbon electricity and so could be reduced.
However, it likely won’t be fully fuelled because suborbital is much easier than orbital. The maximum payload to orbit for BFR is intended to be 151,000 kg. Assuming 620 people with seats, luggage, their body mass, oxygen, and water, it’s probably in the range of 230 kg per passenger all in for a total mass of about 143,000 kg, within the total limit. It’s a bit of a rounding error actually with this level of napkin math, so I won’t adjust for that.
I will adjust for the suborbital vs orbital fuel requirement. Per the source found with a minimum of searching, that’s a ratio of 4 to 5 times the mass to fuel change. That source is a debunking of a common rule of thumb of a 64 times factor, but it’s conservative for this purpose. As a result, instead of 4,400 tons of CO2, it’s likely in the range of 1,100 tons of CO2, or about 1.4 tons of CO2 per passenger for the base fuel use. Adding the 40% gives potentially 2 tons per passenger.
747s produce the equivalent of 0.25 tons of CO2 per hour of flying well-to-wings per passenger including takeoff, landing and cruising at altitude. Assuming 16,000 miles flight at 920 km/h, you are in the range of 17.5 hours flying time, so you’d be seeing roughly 4.4 tons of CO2 per passenger.
Assuming these bounds, it appears as if the BFR will likely have lower CO2 emissions per passenger than a 747 flying the same distance, somewhere from 40% of the carbon footprint up to the unlikely upper bound of 240% of the total. Different planes have different emission profiles of course, and planes have biofuel choices today. Emerging hybrid electric planes and other emerging lower carbon choices will also lower air travel emissions. And note that another answer to the same Quora question suggested higher carbon emissions using different assumptions, including 200 passengers.
While biomethane is a very accessible alternative fuel today, it’s also about 19% more expensive according to one data point that seems reasonable. Given the already lower carbon footprint and the intended economy class model, it’s questionable whether biomethane would be sourced. Given that SpaceX isn’t using carbon-neutral fuels today, it’s unlikely to do so tomorrow.
Note also that another assessment with different assumptions suggested 7–10 times more CO2 per passenger. It’s worth checking out that Quora answer. I like my numbers, but theirs are compelling as well.
Musk might have something that would make the world even smaller and be more carbon neutral. The price and logistics might kill it, but not the speed and probably not the carbon footprint. Of course, if it took off and more people hopped to the other side of the world than do today, the net result would still be more greenhouse gases. Having traveled across the equator and international dateline several times, I can assert that the duration of travel is as much an inhibitor as the cost.
- BFR (rocket) — Wikipedia
- Extreme Engineering: The Boeing 747
- Aviation sources
- Michael Barnard’s answer to Are we capable of making rocket fuel out of completely renewable fuel sources?
- Suborbital VS Orbital
- Using natural gas for vehicles: three comparisons
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