The Sioux arrows that you find in museums were mainly for buffalo hunting....so they are made in one piece from flexible shoots. The thick end was toward the nock. The shaftment, where the fletchings were placed, was tapered and the nock was bulbous with a V-type notch cut in. The widest part of the shaft was at the nock. The next widest part was about in the middle. The nock could be up to 1/2" diameter and the middle of the shaft could be up to 3/8" diameter. The thickness depended on the material used and the spine required. Arrows made from red osier tended to be thick and those made from dogwoods were thinner.
The poundage of the bows was usually about 50lb but could go as high as 80lb or as low as 40lb.
The tips of the shafts were tapered to about 1/4" dia. in the area where the arrowhead was attached.
Almost all Sioux arrows had 3 wavy, shallow, shaft grooves running up and down the shafts between the arrowhead wrapping and the forward fletch wrapping. The forward fletch wrapping was usually a single, wide strand of sinew laid down in a spiral similar to a "candy cane" stripe. This left gaps in the wrapping about as wide as the strand of sinew.
The shaftment was painted with bands of water-based paint or stained. The fletching raged from 5-1/2" long to 9" long and laid on straight... with wrapping on the ends and not glued down in the middle. Sometimes the feathers were painted or stained as well. Raptor feathers were preferred. Sometimes the rear of the fletchings extended past the nock. The average length of fletchings was about 6".