mid-15c., gadden, "go quickly, hurry," of uncertain origin, perhaps from gad (n.) "sharp stick for driving oxen" on the notion of moving as animals do when being driven by a gad. There also was a Middle English gadeling (Old English gædeling) "kinsman, companion in arms; fellow, man," but which had a deteriorated sense of "person of low birth, rogue, vagabond" by c. 1300 (it also had a meaning "wandering," but this is attested only from 16c.). Related: Gadding.
c. 1300, "a goad, sharp pointed stick to drive oxen, etc.;" c. 1400, "sharp-pointed metal spike," from Old Norse gaddr "spike, nail," from Proto-Germanic *gadaz "pointed stick" (see yard (n.2)). Attested earlier as "metal bar or rod, ingot" (mid-13c.) hence also in Middle English a unit of length in land-measure, varying from 10 to 16 feet. Not related to goad (n.), but perhaps influenced by it in sense.