Please post links to the whitepapers you have found, it's hard for the rest of us to discuss this w/o the same background info. you have available. My memory of my research into this subject says that your: "I suppose that a number of sectors on each side of each plate in HDD is approximately the same." is an acceptable simplification.
There are 2 things are wrong w/ your method:
- I have taken drives apart & measured, reality is: r2 ~= 2.71*r1 (see below)
- You do not follow through to find "r50", the median radius -- the one at which S2-S50 == S50-S1
I have an actual platter in my hand as write. There are 2 (inner & outer) unwritten-on bands between the physical edges (of the bearing & platter), & the edges of the magnetic info. These are necessary because the drive's heads can't go all the way to the physical edges of the platter or bearing. These bands seem to be 1/16" wide, changing any diameters by 1/8". That's 2 more radii or diameters to consider. Altogether:
dalek is probably right -- just buy more RAM.
Dh (bearing) == 1-3/16" == 1.1875" == 3.01625 cm
D1 (info. 1) ~= 1-5/16" == 1.3125" == 3.33375 cm
D2 (info. 2) ~= 3-9/16" == 3.5625" == 9.04875 cm
Dp (platter) == 3-11/16" == 3.6875" == 9.36625 cm
However, the fact is that info. transfers are ~2.7 times faster from the outer sectors of a drive than from the inner sectors of a drive, & this will remain true for as long as we continue to use drives w/ platters. I think that balancing the speed of transfer against against head movement time is an interesting intellectual -- but not practical -- problem. My seat of the pants guess is that the optimum place for swap is near R75. I usually implement this on a single drive system by making it the 3rd primary partition, just before the extended partition.
If you're not going to buy more RAM, then put your swap on the outer sectors of a separate spindle. If you want to get really fanatical about it, track down an obsolete SCSI drive, cable, & card that will give you reasonable speed. See this chart of Parallel SCSI
interfaces. Ultra2 SCSI, aka Fast-40, or better would probably do the trick.