Why do the flames from rockets seem to be proportionally as large as the rocket itself?

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I’m a big rocket nerd and have watched a lot of launches and every time I see one, the flames produced by the engines seem to be just as large as the size of the rocket. Is this simply a coincidence or is there a reason behind it?

In: Engineering

A larger rocket is usually heavier. A heavier object needs more thrust to reach escape velocity. More thrust means the engine outputs more power. That usually manifests as a larger flame!

Most rockets launch with a thrust to weight slightly over 1, because the engines are the most expensive part of the rocket, it’s usually most cost effective to add fuel until you can barely lift off. As most of the rocket is fuel, more thrust = bigger rocket, and more thrust also tends to mean a bigger flame. It’s not quite that simple because different fuels result in more or less visible exhaust. Hydrogen for example is nearly invisible, while solid rocket motors are very visible. The space shuttle has both, so you can get a pretty dramatic comparison.

Ambient air pressure also matters, at higher altitude the exhaust expands and cools off much faster, making it less visible.

The flames are the *result* of rockets needing a large thrust, therefore its sizes are not coincidental but rather another outcome

Either I am misunderstanding your question or all the other commentators are.
Of course a bigger rocket makes a bigger flame. But why is the flame the same size as the rocket? Why not 50% of the size, or 150%?
That is how I understand OP’s question.
Personally I have no idea, and from watching rocket launches myself I think the length of the flame varies a lot depending on where they are in the burn (altitude etc), but I have also noticed that they are about the same length fairly frequently.
Here is a picture of the Falcon X to demonstrate.

https://spaceflight101.com/falcon-9-orbcomm-flight2/wp-content/uploads/sites/57/2015/12/16698990295_88e932fafb_k.jpg

I don’t think they are. Obviously, bigger rockets need more thrust and more powerful engines, so the flame is bigger, but it’s not specifically as large as the rocket.

The size varies a lot depending on fuel type as well as where the rocket is. (At higher altitudes the flame spreads out, looking almost umbrella-like, and on the moon it was basically invisible)

If you compare (most) American rockets to Russian ones, the former generate what look like huge explosions, while the latter produce something more like a thin, precise stream behind them, because they use different types of fuel.

If you look at videos of the Shuttle launches, the flame was probably 3-4 times longer than the Shuttle or its booster. Looking at the SpaceX Starship test launches, the flame looks significantly shorter than the length of the rocket.

There’s a lot of variance, but I think the bottom line is that if you’re hurling tons of superheated gases out every second at high speeds, they’ll be able to produce a visible flame behind you for about 50-60 meters or so, before either spreading out or cooling down too much to be visible, which is in the same ballpark as the height of most rockets.