Copyright 2016 Robert Clark
On the blog page "Altitude compensation attachments for standard rocket engines, and applications", I suggested various methods to accomplish altitude compensation with already existing engines. One method was a sort-of "inverted aerospike". It consisted of a movable spike pointed inward, rather than pointing outward as with the standard aerospike:
There are two disadvantages to this method. First the spike has to be movable so that adds mechanical complexity. Secondly, the size of the outer, fixed nozzle in order to achieve high Isp at high altitude has to be large. But this nozzle will be used all the way from the ground, so this will induce high drag at low altitude.
The reason why this nozzle has to be large is because you are not really using the altitude compensating capacity of a shaped spike on exit from the nozzle. The only purpose of the movable spike is to vary the size of the exit plane of the nozzle, to provide a variable area ratio.
But could we use a fixed nozzle and the usual outward-pointing aerospike? This would have the advantages that we could use the altitude compensating capacity of the usual aerospike, so we could use a shorter nozzle, and also have a fixed spike, reducing mechanical complexity.
The problem with this with a usual engine is you would need to change to a toroidal combustion chamber, an expensive change to an engine. So instead of this, we will also use an inward pointing spike so that the exit of the nozzle has a toroidal shape:
This now has two advantages. We will be using this as an attachment to a usual ground-firing engine and nozzle. Since these already expand the exit gases to a certain extent, you would need a much shorter, slimmer and lighter outward-pointing spike to accomplish the rest of the expansion at high altitudes. The usual aerospike has to accomplish the full expansion from ca. 100 bar combustion chamber pressures to near vacuum pressures at high altitude, requiring a large and heavy spike.
Another advantage is that nozzles for sea-level-firing engines actually overexpand the exit gases at sea level. This is because you want a longer nozzle to achieve at least moderate performance also at high altitude. But now, with the addition of the inward-pointing spike you can reduce the pressure at exit of the nozzle to that of sea level by reduction of the exit plane area. This will also improve the performance at sea level.