Bagnold developed his formula for bedload transport over several decades, w
ith the final form of the relation given in his 1980 paper. In this formula
, bedload transport rate is a function of stream power above some threshold
value, depth and grain size. In 1986, he presented a graph which illustrat
ed the strength of his relation. A double-log graph of bedload transport ra
te, adjusted for depth and grain size, versus excess stream power was shown
to collapse along a line having a slope of 1.5. However, Bagnold based his
analyses on limited data. In this paper, the formula is re-examined using
a large data set in order to define the most consistent empirical represent
ation, and dimensional analysis is performed to seek a rationalization of t
he formula.
Functional analysis is performed for the final version of the equation defi
ned by Bagnold to determine if the slope of 1.5 is preserved and to assess
the strength of the relation. Finally, relations between excess stream powe
r and bedload transport are examined for a fixed slope of 1.5 to assess the
performance of various depth and grain size adjustment factors. The ration
al scaling is found to provide the best result. Copyright (C) 2000 John Wil
ey & Sons, Ltd.