Watched an Apollo Saturn launch. Why is a stage allowed to separate/drop with residual fuel?

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Watched the Apollo 11 famous footage of the launch and the camera perspective was from the ground focused on the ascending rocket. When it came time for staging and dropping the first stage, we can clearly see cutoff of rocket motors, separation and ignition of the second stage.

One thing that puzzled me always was the first stage as it falls away is seen trailing vapor, residue from its shut off engines. This reasonably has to be residual unburned oxidizer/propellant. its enough of a plume to be visible even 30+ seconds later it is still leaking away as the second stage carries the rocket further away and away.

Im asking bc every ounce, every bit of weight is calculated for and certainly fuel is no exception. Why lug the fuel up there just to shut the engines off presumably early and not burn it. Any reason for this inefficiency?

EDIT: Including link to video. [https://www.youtube.com/watch?v=dhTvadtW2dc](https://www.youtube.com/watch?v=dhTvadtW2dc) Begin watching at time 36:38

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Anonymous 0 Comments

For a variety of reasons, if you achieve your desired velocity by a desired altitude EARLY, you’re gonna shut down EARLY. Who knows- wind, humidity, design error, this batch of oxidizer is extra oxidizery who knows. But you still shut off when you need to because your payload has no means of “coming back” if you overshoot its target orbit/trajectory. Oh and to that end, what if there’s a problem with one of your engines on that stage. Like what we saw with several of the Raptor engines on the Starship booster (it lost 3? 4? – literally exploded) – so the remaining engines may have to burn longer to achieve the same delta-v, and <something something rocket equation> fewer engines burning for longer may NOT use the same qty fuel as more engines burning for less time. So, when the stage drops, it may have extra fuel. And a bit extra in general for contingencies. But not much.

– not an expert or anything just armchair rocket fan.

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