single-handedly vs under one's own steam

single-handedly

adv
  • Alone; without assistance; by oneself. 

under one's own steam

prep
  • At one's own initiative; of one's own accord, unbidden, unprompted. 

  • Using one's own resources; independently, unaided. 

  • Of the movement of a locomotive or a watercraft: by means of the power of its own engines (originally steam engines), rather than pulled or pushed by another vehicle. 

How often have the words single-handedly and under one's own steam occurred in a corpus of books? (source: Google Ngram Viewer )