One of the first things you learn as a pilot is that certain documents are required to be aboard the airplane. The nemonic is ARROW—Airworthiness Certificate, Registration, Radio License (now required only if flying out of the country), Operating Limitations, Weight and Balance.
An FAA approved Flight Manual (AFM) is required to be in the aircraft for all aircraft over 6,000 lbs and for aircraft manufactured after March 1, 1979. This manual, along with panel markings and AFM supplements for additional equipment, constitute the Operating Limitations documents that are required to be in the aircraft. Prior to 1979 aircraft came with “Operations Manuals”, “Owner’s Manuals”, or “Operator’s Handbooks”. These aren’t required to be in the airplane, but since they have information like takeoff distances and moments, it’s hard to imagine flying without them. Due to quirks in the copyright laws, the older ones are in the public domain. Here are a few that I use.
Operation Manual-Cessna 170 Series 13MB pdf.
Cherokee 140 Owner’s Handbook 42MB pdf.
Cessna 152 Information Manual – 1980 9MB pdf.