Response to “Comment on ‘An accurate determination of the acceleration of gravity for lecture hall demonstration,’” [Am. J. Phys. 82, 803–804 (2014)]

In our original paper, we integrated the variable drag coefficient over the total time interval of the fall to obtain an “effective” C_D of 0.42 and pointed out that this value is a factor of 1½ times larger than that determined by the experiment—a rather surprising difference. We argued that the difference might be attributed to the phenomenon known as drag crisis, but that further experimentation was needed to support that claim.

I would like to thank Rod Cross¹ for discovering the real reason for the discrepancy. We indeed had (incorrectly) assumed that the expression v/t yields the same average acceleration as the expression 2H/t². Since g₂ − g = 2(g₁ − g) for small kt, C_D (obtained from the slope of the line in our Fig. 2) will be a factor of two...