Why did the framers include the Chief Justice in Impeachment Trials?

Maybe the drafters were tired by then. Was any mention made in the Federalist Papers of impeaching VPs? IANAL but I’d guess the Senate is left to draft rules of VP trials. A kinky Senate might have the impeached (indicted) VP preside over their OWN trial. No satirical reporting would be possible; IRL absurdity would trump any parody. The accused = the judge = a jury member whose vote would break ties. Sacre bleu!