I was intrigued by the invitation from an old friend whose family owns a lodge in central Namibia. "Come and track cheetahs," said Donna Hanssen in her email. "You’ll love it."

That evening, I told my wife, Brenda, that I was going to take us deep into a neighbouring country where we would get out of the car and stalk predators with razor sharp teeth and claws – animals that are capable of outrunning any other on earth. She was less than enchanted.

"That sounds horribly dangerous," she said. I laughed nonchalantly and gave her my great white hunter look. "Don’t worry. I know how to deal with cheetahs."

A week later (it takes Brenda that long to pack) we crossed the Orange River and entered the primordial nothingness that is southern Namibia. The stifling desert heat turned the inside of the car into an oven and Brenda into a carping harridan. "Didn’t you say you were going to get aircon put into this car?"

Stopping over for the night in Keetmanshoop, I made the mistake of trying to rehydrate with Windhoek Lager instead of water and had to go to bed early.

In the morning, Brenda insisted on driving the last 500kms to the capital. That was fine by me. I have driven that road before. It is so straight and uneventful that if you wedged a brick on the accelerator and tied the steering wheel to the wing mirror, you could put your feet up and read a book for most of the way.

Heading north through Windhoek and onto a road that eventually ends where Angola begins, I kept a sharp eye out for game. In these parts, kudu and warthog are famous for making sudden headlong dashes from one side of the road to the other. Luckily, the only animal to cross our path was a tortoise. I stopped and took him back into the bush, pointed him in the direction of Botswana and sent him on his way.

We reached the turnoff to Okonjima, the Hanssen family’s lodge, a few kilometres south of the town of Otjiwarongo. After bouncing along a dirt road, we found Donna waiting for us in her 4x4. Tall, blonde and beautiful, Donna looks a little out of place in this harsh landscape of thorn trees and dry river beds. But she wouldn’t exchange her life for anything.

"Follow me," she shouted, taking off in a cloud of red dust. A few minutes later, we pulled up outside the villa. We had the place to ourselves. Impressed by the level of luxury, Brenda was rendered speechless when Donna casually said, "Brad Pitt and Angelina Jolie stayed here not too long ago. You can have their bedroom."

That night, I pretended to be Brad but eventually gave up holding my stomach in and went back to being me. Brenda seemed disappointed.

The next morning, a guide picked us up in open-topped Land Rover. A tracker wearing headphones sat on the bonnet listening for signals from the radio collars worn by four cheetahs in the enormous rehabilitation camp operated by Africat, another Hanssen family project.

When we ran out of road, we all piled out and ploughed through the bush. The beeping got louder, then petered out. We kept on walking. And walking. Suddenly the signal grew stronger and the tracker raised his hand. There, perfectly camouflaged, was a fully-grown male cheetah watching us from 10 metres away. Then it was gone.

Brenda was beside herself with excitement. I was terrified. "That was fantastic," I said to the guide. "Can we go now, please?"