The following is an approximate solution for the amount of resistance opposed by a bilge keel to isochronous rolling of a ship in still water.
The following quotations give the most valuable and conclusive testimony as to the value of bilge keels:
Effect on English Troop Ships, 1871. Committee on Design, App. p. 330. " Serapis. Since fitting the bilge keels the maximum roll in a heavy Atlantic beam sea was reduced to 23° leeward, 14° windward, a reduction of 10° each way. Other captains reported that the speed was not influenced, and that the bilge keels acted beneficially."
These keels were 27 inches deep.
Admiral Ryder, p. 286, vol. 13, Inst. Nav. Architects. After alluding to the favorable effect of bilge keels on the troop ships he says : " In the report which was sent to the Admiralty as to the effect on the turning power of the ship after the bilge keels had been put on, it was said that not the slightest difference could be detected ; and as to the effect upon the speed, a measured mile had been run, both before and afterwards, and not the slightest loss could be detected in that respect either."