push the envelope

This is an aviation term. It means to fly an aircraft beyond the limits it was designed for, especially in the context of flight testing. Envelope has several secondary definitions in mathematical and engineering jargon referring to the area covered by a series of curves. So in the world of aeronautical engineering the envelope is the collection of curves that describe the maximum performance of an aircraft. To push the envelope is to take the aircraft to the edge of what it was designed to do and try and take it beyond.

The mathematical sense of envelope dates to the 19th century. Isaac Todhunter’s 1871 Differential Calculus:

The locus of the ultimate intersections of a series of curves is called the envelop [sic] of the series of curves.

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