Throughout this book, something bothered me: given the apparent population of Canticle, the amount of sunhearts used seems to be highly unsustainable.
On Canticle, each family seems to have their own ship. This is implied by the general descriptions, the fact that Elegy had a ship to herself, etc. It's also confirmed by the "flying over the mountains" sequence: When Beacon really squeezes, they fit a population of 135 (and essential infrastructure) onto eight ships, but it's a much tighter squeeze than normal. Thus each ship is normally occupied by significantly fewer than 135/8~=18 people.
How frequently do you have to sacrifice someone to run a ship? Well, Rebeke's mother sacrificed herself only two weeks ago (page 117) to power a single ship. By the time of the story, Beacon has essentially run out of fuel - they don't have enough to complete one more rotation around the planet. The Beaconites know that sunhearts can be split, so this implies (in particular) that Rebeke's mother's sunheart didn't have enough fuel left to get every ship around the planet once. Even assuming that there was one ship for every Beaconite, then, Rebeke's mother's sunheart doesn't have enough fuel left for 150 rotations. This means that a full sunheart, running a single ship, would last a maximum of 2 weeks and 150 rotations. Maybe a little more if it's just flying around the planet at a steady speed instead of being used for missions. Assuming the weeks on Canticle are actually somewhere around the 7-10 figure we see elsewhere in the Cosmere, that means each ship needs a new sunheart every 200 rotations maximum.
This is also confirmed by the fact that Beacon stopped the sacrifices less than two weeks ago (unless Rebeke's mother disobeyed orders) and is already running out, which indicates an even shorter figure. The fact that the Cinder King demanded a daily sacrifice from each of his vassal towns, and seems to need that many sunhearts to run the city (page 312: the workers are worried he'll start sacrificing them once he runs out of captives), also supports the idea.
So even with the most generous estimates possible, for every 18 people in your settlement you need to sacrifice someone (or steal a sacrifice from somewhere else) every 200 rotations. Which is way too fast to be sustainable. Unless you have all the women get pregnant as much as possible and sacrifice all their babies to the sun, but (thankfully) there's no indication that anyone has tried to implement that horrible idea.
