I’ve been fascinated by self-erecting cranes for some time. These work by having a cage which can move up or down the column of previously built units (blue). When it stops, the bottom part of the cage engages with a unit and pushes upwards off its roof, lifting all those units above one unit higher.
If you want to build a tower by this method, the fastest approach is a)
keep the cage at the bottom and keep injecting units without waiting for them to be lifted any higher. If, however, you want to minimise the stresses on the cage, then b) is a better option ie insert units at the top.
If you wanted to build a towerblock in which each unit was a floor of the building, b) would be used. A novel, ‘instant’ fire escape would need to operate in a) mode.
Today’s invention is a simple algorithm for building such towers.
Knowing the maximum safe load for the cage, inject from the bottom for maximum speed of construction until this load is reached.
Then, move the cage up one unit and inject at this new level. Repeat this last step until building is complete.