I find it very ironic that some of the very things done to safeguard the safety and well-being of aircraft passengers so often winds up scaring the crap out of them.
I’ve ridden out a number of go-arounds in commercial jets, and done my fair share of them in small airplanes.
In the small airplanes, with non-pilot passengers, I tell them of the possibility (among a few other things) even before we take off, usually phrasing it as something like “When we come in for a landing, if things aren’t exactly right in the last couple hundred feet I might choose to go back up and come around again, rather than take an unnecessary risk. If we do that, it’s not that something is wrong, I’m just doing my best to avoid trouble”. Then again, they’re usually sitting right next to me so if something does happen - deer on the runway, someone pulling onto the runway in front of us, whatever - they can see what’s happening and don’t really require an explantion.
I think the most “violent” go around (which was violent at all to my perception, but many of my fellow passengers disagreed) was going into Midway airport in Chicago about six years ago now. We were coming in for what seemed to be a very routine landing. The man in the seat next me stated as how happy he’d be to be on the ground again. Right then, as if on cue, the engines spool up and all the frou-frou on the wings (spoilers, slats, slits, flaps, winkerdoodles, etc.) start moving around again, and a glance out the window showed stuff retracting into the wing. I said we weren’t landing just yet, we’d be going back up, making a big circle, and coming back. My seat mate was basically telling me I was nuts when the airplane did one of the abrupt changes of direction, people yelped and squealed, and I tried very hard not to have a smug “I told you so” smile on my face.
From my viewpoint, the manuver wasn’t extreme at all - very smooth, in fact. And sure enough, once we were up and leveled off again one of the pilots came on the PA, explained a construction truck had pulled out onto the runway in front of us and we’d be landing just as soon as we circled around and lined up on the runway again.
Well, the gentleman sitting next to me was looking at me sort of peculiar, as if the cute little lady next to him has spoken of being Kareen Abdul Jabar prior “the operation”. And he asked me how I knew what was going to happen. I said that I was a pilot and recognized some of the stuff the pilot was doing as the start of a go-around before the non-pilots became aware of the manuver.
“You — you don’t look like a pilot —”
(Yes, I get that a lot. For some reason.)
Anyhow, I’ve no doubt that some of my fellow passengers thought what happened to be quite frightening, but really it was pretty tame compared to some of the things I did to myself in training. It’s just that the average passenger is exepecting to be upright and level as much as possible with no abrupt changes of any sort. The average person also doesn’t have any idea of what airplanes are really capable of (and capable of withstanding), or what’s safe and what isn’t. Same thing for the emergency descents - oh, yeah, they’re LOTS faster that the norm, but they’re not unsafe, just different.
Doing a go-around is equivalent to swerving your car to avoid an obstacle. In some cases, it’s pretty much a non-event (like altering course so you don’t re-run over the dunk skunk in the road) and in others it’s a hair-raising accident-avoidance thing, and mostly it’s somewhere in between.
As for the fire-trucks and what not - one little “Mayday” over the radio brings out the calvary. Yeah, the first time it looks scary, but now I find it reassuring that if I feel a need to yell for help someone really will show up and do all they can to render asssitance. Sometimes more folks than you really need, but having spoken to those guys they’d rather show up a hundred times and not be needed than fail to show up the one time they are needed.