I was holding on for dear life in the passenger seat of a Toyota van as it careened across Queen Elizabeth National Park in southwestern Uganda. In the dry grasslands of the Kasenyi Plains, my driver was chasing two SUVs raising clouds of choking dust. I kept both hands on the grab handle just in case we hit one of the ruts hard enough to catapult me out of my seat.

We passed warthogs, waterbuck, herds of Uganda kob, but they were a blur. My driver didn't slow down to let me look, because he had bigger game in mind, and didn't mind driving like a maniac to find it.

For all my terror, I was glad to be on a relatively low ground, racing across the plains on an accidental safari.

Two days earlier, stricken with altitude sickness, I had cut short what was supposed to be an eight-day trek in the Rwenzori Mountains, which straddle the border of Uganda and the Democratic Republic of Congo. I took refuge in the comfortable Ihamba Safari Lodge, which overlooks a lagoon of Lake George. Still, I had three days before my hiking companion was supposed to emerge from the mountains, and after a day of recovery, I was getting tired of sipping Tusker Beer and listening to grunts of unseen hippos in the papyrus swamp.

Spreading over a half-million acres in southwest Uganda, Queen Elizabeth National Park lies within the Albertine Rift, a geological zone that spans a chain of lakes in five countries. Thanks in part to its sharp variations in elevation and climate, it's one of the most biodiverse areas in Africa, according to the Wildlife Conservation Society. Designated a UNESCO Biosphere Reserve in 1979, the park offers a remarkable variety of landscapes in a small area. In a matter of hours, a visitor can pass through a classic East African savanna, beside wildlife-rich swamps and crater lakes and a thick jungle seldom visited by humans. While mountain gorillas, Uganda's best-known tourist attraction, don't live here, I was impressed with what does.

Encountering elephants

On the road through the Maramagambo Forest, I came across huge troops of baboons that blocked the road, and watched black-and-white colobus monkeys high in the trees. I knew that chimpanzees lived here, too, though they tend to stay far from humans. From the Mweya Peninsula, which juts into Lake Edward, I took a cruise down the Kazinga Channel to gape at elephants, hippos, African buffalo, warthogs and Nile crocodiles crowding the banks. Storks, pelicans, egrets, sacred ibis, ducks, geese, cormorants and hundreds of other birds lingered on a sandbar near one of the fishing villages that the Uganda government allows to remain within the park's boundaries.

I didn't have high hopes for the more conventional game drive in the northern reaches of the park. The Kasenyi Plains are mostly open grassland, dotted with euphorbia, a cactus-like tree. This place resembles the better known savannas of northern Tanzania, and my safaris there earlier in the trip had spoiled me with their abundance of charismatic megafauna. Still, once I had come into the presence of such tremendous beasts, I had a very hard time saying goodbye. So I booked a last-minute game drive through my trekking outfitter.

My driver, whose name was Muwamba, picked me up at my lodge before sunrise. We headed south, away from the mining town of Kasese, and soon we crossed the equator, which is marked with a circular monument on both sides of the road. A sign at a turnoff to the right indicated that was the way to Congo. We kept going and drove through the park gate.

I paid my park entrance fee of about $40, and we were off into the bush. The sun was a big red ball rising through the clouds. Within minutes, off to the right I saw the familiar shape of an elephant moving parallel to the road, then another, and another, maybe 20 in all, a procession of elephants young and old, oblivious to us. They seemed to be heading for a water hole, where some very tasty bushes were growing that they ripped down effortlessly with their trunks. Muwamba was surprised to see them here, so he took that as a good sign for what we would encounter deeper in the park.

Joining a lion chase

Being a good safari guide, like so many things these days, is about who you know, not what you know. Muwamba did not know much about wildlife, and he wasn't an especially keen spotter, either. He did know how to work his connections. Shortly after we arrived, he glommed onto two private-drive SUVs whose drivers knew what was where and when. We lingered to watch some buffalo, who watched us back. We stopped for coffee at the market that overlooks a crater lake. The shallow lake appeared to be divided into segments, like an immense white pizza. Muwamba pointed out the villagers working all over it, mining it for salt.

When the two SUVs left, so did Muwamba. After meandering a bit through the plains, the lead SUV did a sudden U-turn and took off at high speed past us. Muwamba spun the wheel and followed. My safari was suddenly a car chase, on roads so pitted and gouged that I thought the crowns would pop off my teeth. I had visions of hitting a buffalo. I did not want to be responsible for roadkill in a national park that's the pride of Uganda. Then again, fully grown buffalo can tip the scales at a ton. Two of them might be able to match our Toyota van, when it came to sheer weight.

The buffalo and every other animal stayed out of our way, fortunately, as we zigged and zagged through the dusty grass. After about 15 minutes, we saw the cluster of safari vehicles and mercifully came to a stop. I put my binoculars to my grit-covered face and trained them on a hilltop. A female lion lay in a clump of brush. She was doing what lions usually do in the wild, which is a lot of nothing. She lifted her massive head and looked around. Then she got up. Then another got up. And a third. They all walked slowly away. No more lions.

"Now we'll go see a leopard," he said, with a suspicious amount of confidence.

We took off again, with the two SUVs leading the way. Seven minutes later, we joined a smaller group of vehicles beside a large euphorbia tree. It took me a few minutes of scanning with my binoculars to see the unmistakable swatch of spotted fur on one branch. It took me the longest time to figure out which way the cat was facing. It dropped a big paw, which helped. We drove up a bit, and I could see the top of the leopard's head through my binoculars. Again, it was the portrait of feline inertia. I was happy anyway. The hunt was over. We had spotted four of Africa's big five — lion, leopard, elephant, buffalo and rhino — in a matter of hours. All creatures, native and visitor, had survived to tell the tale.

One of the main roads out of Queen Elizabeth National Park passes through the Ishasha Plains. They're famous for tree-climbing lions, which loll about in the branches of fig trees. When we went that way, I suppose we could have rattled over the plains in search of a big cat in a tree. I wanted to keep going. There were gorillas waiting for me down the road.