I know that max-q normally occurs around 11-15km (based on observations of watching falcon 9 launches and this). Furthermore, I know that the fuel usage for each rocket would vary a lot (which I assume is because of weight differences of different rockets). However, what percentage of the overall fuel (fuel for both stages) is used up by max-q for a rocket like a falcon-9? Furthermore, would the percentages of fuels for different rockets at max-q vary?
would the percentages of fuels for different rockets at max-q vary?
Yes, it will certainly vary with different rocket designs, and even for a given launcher with different payloads and trajectories.
what percentage of the overall fuel (fuel for both stages) is used up by max-q for a rocket like a falcon-9?
Flightclub.io's simulation of the CRS-15 Falcon 9 mission shows max Q at 66 seconds, with about 350 tons of first and second stage propellant remaining out of an initial quantity of 509 tons, so about 31% of fuel has been used.
Looking at a different rocket, Braeunig's simulation of Apollo 11 (archive.org link) gives max Q at 83.7 seconds into flight and 13.8km altitude, with 1,553,418 kg of propellant remaining from an initial 2,656,755 kg -- about 41.5% of total propellant used. Considering that the total fuel includes that required to go from LEO to the moon, the higher usage might seem surprising, but the upper stages of the Saturn V have much better specific impulse than the Falcon 9 second stage, and the first stage slightly poorer, so in the early part of flight it is expending fuel mass at a disproportionately steep rate.