Curiosity got the better of me, so I decided to work out how much the top of a seatpost would deflect vertically if a 200 lb sack of potato sits on the saddle.
For the base case, I assume:
Seat tube angle of 73 degrees
Young's Modulus of 22,000,000 psi (approx. for carbon, Ti is ~16,000,000, aluminium is ~10,000,000)
Seatpost outside diameter 27.2mm, wall thickness 2.5mm (based on my Campag Record carbon post)
I calculated vertical deflection due to bending as well as compression. Contribution from the latter is always small compared to the former, and is ignored for this discussion.
The answer I found, is 0.04mm for a 6" exposed post, but 0.32mm for a 12" exposed post - deflection is proportional to the exposed length's power of 3.
In relation to the motions and deflections of tyres/wheels/forks/frame/saddle we experience trundling down the road, I doubt this level of deflection can be detected in a blind test.
Finally, I found the nearest alloy post at hand to have the same wall thickness - being less stiff, it should be more compliant.
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For those who would like to check my calculation, for 12" exposed post:
Second moment of inertia: 0.036 in^4
Bending load: 58 lbs
Bending deflection: 0.043" or 1.08mm based on
this formula