chainline adjustment for running a triple crank as a double
 

I'm a tall guy, and use 180mm cranks when I'm able.

I plan to use a Shimano "deerhead" triple crank (FC-6206) as a compact double. I am trying to calculate how much shorter a bottom bracket spindle I should use to get proper chainline. I calculate 8mm (4mm shorter on each side). Can anyone verify?

My calculation (assuming 130mm rear spacing for 8-11 speed road drivetrains):
Triple crank chainline is 45mm, measured to the center of the middle chainring.
Double crank chainline is 43.5mm, measured to the midpoint between the two chainrings.
Chainring spacing is approximately 5mm.

Moving from 45 to 43.5mm subtracts 1.5mm from the drive side
Moving the measuring spot from the middle ring to the midpoint of middle and outer ring subtracts another 2.5mm from the drive side.
To keep equidistant pedal spacing, 4mm should also be removed from the non-drive side.
Hence 8mm shorter BB spindle. (any asymmetry in the original spindle would still apply)

Let me know if my math/reasoning is off.

That sounds about right. It's not life-or-death precision, and it wouldn't hurt to measure your current chainline to see if it's even close to Sheldon's ideal before ordering parts. ;)

Another option would be to use the middle and granny rings as an "ultra compact" double, in which case you're already so close it wouldn't be worth changing the BB.

That's a lot of math with no basis in fact if you don't have the triple crank mounted on the bike with the chainline set and the length of the bottom bracket yielding the chainline known.

Do you have a square taper bottom bracket that you can install on the bike so you can mount the crankset with the two rings you are planning on using so you can check the chainstay clearance (to the smaller chainring) and the chainline? There are often differences between the calculated crank spindle length and the actual need spindle length.

When I'm changing bottom brackets, I find it easier just throw the parts together, and check the clearances. Then, I can decide if I need to increase or decrease the chainstay clearance or the spindle length to alter the chainline (taking note of the length of the test spindle that I installed, as well as whether it's symmetrical), and then calculate the bottom bracket spindle length needed. .

I use a fair bit of trial and error.
But if I need to buy a new bottom bracket, and the original intended spindle length for the crank (for proper chainline when used as a triple) is known, it seems like this basic arithmetic should be useful.

You are going to take the granny ring off, right?

Your guess looks good. On a Shimano triple I measured, the chain ring spacing is closer to 6mm with calipers.

You'll be within 1/2 mm.

Sounds like you have the crank on hand already. If so, you can determine where the square tapers of the BB spindle should end. It will be at the bottom of the recess for the crank bolt, or very close to that point.

You also know that the center cog of your cassette will determine distance of chain line from the center of your hub (midpoint of over-lock-nut distance of your rear axle). On a triple, the middle ring of the crank should be the same distance from the center of the BB shell. All of these measurements can be taken from the bike and the crank, so there is no guessing needed.

Once you know the length of the BB spindle from the center of the BB shell, double that distance to get the overall spindle length of a symmetrical BB.

To avoid confusion, I make a simple top-view diagram of the drive train and label the distances.

[Edit: Since you are converting your triple crank to a double, the manufacturer's recommended BB length is irrelevant. You must measure CL from the space between the rings to the midpoint of the BB shell after you reconfigure the crank. Add to the CL the distance to the bottom of the bolt recess. Double that total to get BB spindle length.]

I'd mount it and check how much room there is between the crankarm tips and the chain stay, the old granny mounting tabs and frame and inner chainring and chainstay. Then decide on chainline.