How does air density affect take-off performance?

I've been reading about density altitude and I'm a bit confused about how it all ties together. On a hot day at a high-elevation aerodrome, should I expect a longer or shorter ground roll? And does humidity play into it as well?

Great question. Higher temperature, higher elevation, and higher humidity all reduce air density. Lower air density means the engine produces less power and the wings generate less lift at any given indicated airspeed. The practical result is a longer take-off roll and a reduced rate of climb. Always check the performance charts in your POH for the actual conditions — don't just guess.

That makes sense. So density altitude is basically a way of expressing the effective air density as an equivalent altitude in the standard atmosphere?

Exactly. If the density altitude is 5000 ft, your aircraft will perform as though it's at 5000 ft in the ISA, regardless of your actual elevation. It's a critical concept for flight planning, especially at aerodromes that are already at a high elevation or during summer operations.