Back in college I spent a summer in Berkeley CA (1990) and went to the San Francisco zoo one day. They had (and still do) a building where they brought all the big cats (lions and tigers) into for feeding. This was before they had their "incidents" and you could get fairly close to the cages (between 6 and 8 feet away if memory serves), the floors of which were raised a foot or two compared to where I was standing. So the cats' heads were about chest height. They closed the doors and brought out fresh meat. The sound of the roars was deafening in the enclosed space and you could feel the bass in your bones. One of the few times in my life I've experienced something akin to primal terror--a momentary feeling where time slowed and I was acutely aware of everything going on around me. And my own insignificant place in the universe.
Obviously not the same as being outside with them sans bars or cages. But I kind of get what you were experiencing. They are awesome creatures (in the truest sense of the word--literally inspiring awe).
That sounds amazing. There was an American lady killed in SA 2 years ago. There are signs everywhere saying close windows. She and her husband ignored it .wound the windows down and proceeded to drive into the park. Then stopped next to lions, turned off engine, so electrics were off i.e. no way to get windows up. Anyway, a lioness ultimately managed to pull her out of the car and kill her. Scary stuff and yes that primal fear kicked in.
I think I am happy to be home to nextdoors tabby cat and our Sister in laws Bichon dog. They are wild enough for a while ...