The vehicle SpaceX lost the other day has been described as a Falcon IX R with three engines. It is a bit intriguing to speculate on the purpose of three engines as opposed to the nine of the full up stage, or the one of the Grasshopper I.
The first and most likely thought is that more than one and less than nine are needed for the test flight profile. So three are required to do the job, but there is no financial sense in tying up, and possibly losing, six additional engines that are not required for this particular test program. The problem with that explanation for us in the peanut gallery is that it is boring and gives us nothing to speculate about.
An explanation that I find more fun and interesting is that there might be a financial and technical case for a three engine Falcon. A shortening of the stack for the lighter vehicle would produce a lower profile for a possible reusable version. Landing on a barge at sea would be with a vehicle with far less bending moments that a full Falcon IX stage. It seems possible that such a vehicle could land (barge) in a much heavier sea state than the larger vehicle. If that is a actual possibility, then Falcon III boosters could be attached to a Falcon IX stack with very low costs per mission if the mini boosters could be reused quickly and often.
Even a first take on such an arrangement yields some suggestive possibilities. A 66% increase in take off thrust would allow as much as 66% more take off mass and slightly more than that increase in payload with the additional staging event. With cross-feed, the Falcon III stages would drop off at under a minute and a half, barely supersonic, and fairly close to the launch site for a quick booster RTLS. The fully fueled Falcon IX would be in near vacuum conditions by that time with the considerable gain in Isp compared to a ground launch. A payload gain of over 2/3 for minimal cost could not be ignored if technically feasible.
For flights where the basic Falcon IX has enough performance to do the primary mission, but not enough for any recovery options, the Falcon III boosters could up the propellant reserve to allow core stage recovery. Small, quick turn around boosters enabling the recovery of a core for certain missions would be a nearly slam dunk decision if technically feasible.
For some Falcon IX missions, a Falcon III heavy could possibly deliver a bit more payload with the same number of engines. The engines being one of the major expense items could make not requiring more of them a sound business decision if the staging events become safe and routine enough. The extra payload would come from the same nine engines powering the stack for the first couple of minute as the normal Falcon IX, after which the two boosters drop off with the consequent dead mass reduction for the remaining stage. The remaining Falcon III would have the same velocity and remaining propellant as the base Falcon IX at this point, but would be boosting 1/3 of the engine and tank mass along with the upper stage and payload.
Last thought is on the difficulty of RTLS of stages entering from far down range. A barge landing is often mentioned, virtually always coupled with the words “good sea state” in some manner. This means that barge recovery is permanently dependent on the sea not being too rough. Some missions could be delayed by days or weeks to let the waves subside from a previous storm. Some whole seasons could be off limits if the recovery is sensitive enough.
The helicopter recovery I suggested a couple of years back might bear revisiting for lighter stages. The major objection to snagging a Falcon IX core in the air with a helicopter and flying it back to launch site was the excessive weight of the stage. A Falcon III stage might be air recoverable in a way the the Falcon IX stage could not be.