A couple of suggestions for the reusable version of the Falcon 9. First, model it on the DC-X. In the SpaceX video of the proposed reusable launcher the first and second stages have the same straight sides of the expendable versions. But having sloping sides helps to protect the sides of the vehicle during reentry as well as increasing aerodynamic stability during reentry.
Note that as long as the cross-section remains circular for a conical shaped stage you should still get the high tankage ratio that obtains for cylindrical tanks:
Space Access Update #91 2/7/00.
The Last Five Years: NASA Gets Handed The Ball, And Drops It.
"...part of L-M X-33's weight growth was the "multi-
lobed" propellant tanks growing considerably heavier than promised.
Neither Rockwell nor McDonnell-Douglas bid these; both used proven
circular-section tanks. X-33's graphite-epoxy "multi-lobed" liquid
hydrogen tanks have ended up over twice as heavy relative to the
weight of propellant carried as the Shuttle's 70's vintage aluminum
circular-section tanks - yet an X-33 tank still split open in test
last fall. Going over to aluminum will make the problem worse; X-
33's aluminum multi-lobed liquid oxygen tank is nearly four times as
heavy relative to the weight of propellant carried as Shuttle's
aluminum circular-section equivalent."
http://www.space-access.org/updates/sau91.html
The McDonnell-Douglas version mentioned there was the scaled up DC-X.
There are a couple of ways this DC-X styled Falcon 9 could be implemented. As this is to be a multi-stage launcher, you could have each stage have the same sloping sides as the DC-C. Then each stage would have the shape of a truncated cone, a frustum, and when stacked one on top another the vehicle would have the shape of a single cone.
However, I prefer another method. It is known that you can increase your payload using parallel staging with cross-feed fueling. Indeed SpaceX intends to increase the payload of its Falcon Heavy launcher using this method. Then another method for this reusable Falcon 9 would have each stage in the shape of a full cone, but the second stage instead of being placed on top of the first stage would be placed along side of it in parallel fashion.
In addition to increasing the payload this would have an another key advantage. The high mass ratio of the Falcon 9 first stage, above 20 to 1, means that if it had high efficiency engines such as the NK-33 or RD-180 instead of the rather low efficiency Merlin 1C it would have SSTO capability. However, because of the high investment of SpaceX in the Merlin engines they no doubt are committed to its use.
But a key fact is that IF you have altitude compensation then even a low efficiency, i.e., low chamber pressure, engine can achieve high vacuum Isp while still providing good performance at sea level. Methods of altitude compensation such as the aerospike have been studied since the 60's. Then SpaceX could provide their DC-X styled Falcon 9 stages with altitude compensation to give their stages SSTO capability while still using the Merlin engines.
Then these SSTO stages could serve as low cost launchers for smaller payloads, including being used for private, manned orbital vehicles.
The second model for the reusable Falcon 9 stages would be on the ESA's proposed Intermediate eXperimental Vehicle (IXV):
Article:
Europe Aims to Launch Robotic Mini-Shuttle By 2020.
Rob Coppinger, SPACE.com ContributorDate: 13 June 2011 Time: 02:58 PM ET
http://www.space.com/11948-robot-space-plane-europe-ixv-launching-2020.html
This does not use the powered landing of the DC-X but rather uses a glided landing via its lifting body shape. SpaceX does not like the use of wings for landing because of the extra weight. But this design would not have wings. It would have larger thermal protection weight because the horizontal underside would have to be covered, whereas in the DC-X mode only the base has to be covered. However, it would make up for this in not requiring fuel for the powered landing.
In this case because the stages would have to maintain the aerodynamic shape, they could not be stacked as for serial staging. Parallel staging would have to be used. Once again this means the separate stages could be used as SSTO's.
Bob Clark