Dan Dailey, World's Champion All-Around Cowboy (saddle bronc, bareback and bull-riding; calf roping and steer wrestling), never takes off the hat. He wears it in the atrium of Children's Hospital while he's standing around tight-mouthed (that wad-of-snuff-under-the-lower-lip look) listening to the Riata Ranch Cowboys (that's the band for the World's Toughest Rodeo, opening Thursday at the Capital Centre) sing to the kids on stretchers, in wheelchairs, kids with bottles draining into their arms who look up at Dan Dailey in his eel-skin boots, and the gold-and-rubies belt buckle the size of a hubcap, and The Hat, a black Stetson with a five, count 'em, five-inch brim . . . "I can't take hospitals, I got a weak stomach," he says, meaning he feels sad about, say, the kid lying on the stretcher next to him. "That'n there got hit by a truck, he's paralyzed, he can't breathe by'm self, makes you see how lucky you are . . ." Dan Dailey with legs broken three times (three screws and a plate in one of them when he hung up on a bull in Pontiac, Mich., couldn't get his hand out from under the strap and it hooked him and stomped him) a couple of broken wrists, a cracked neck, three teeth knocked out, what you get from going down the road, rodeoing, winning four all-around championships in the last five years, so he deserves, by God, to wear a hat this big, and being a cowboy he never takes it off, not even at lunch, sitting down in a motel restaurant to eat a club sandwich and a Coke, and trying to explain about the ways a bull can move:

"There's no way you can grab hold of that bull and out-strong him, it's 16 to 2100 pounds, (Dan Dailey is 5 feet 11 inches, tips the Toledos at 169-172, never more or less) and you got to be loose on that bull. Bull jumps way up high, he'll throw you out the back end, is what we say, so you got to lean way forward, but you draw a bull that spins sideways, you have to lean back to keep from going out the back end. Then you get a down-draft horse, you got to brace on that arm holding the strap when he hits the ground, we call it push; then you get a bull that wells, when he comes down you can't just push because he drops one shoulder, so you got to be leaning to the other side . . . " And those blue eyes hiding under that black hat, and behind a dry fan of wrinkles at the corners . . . those eyes look wary and adamant, then puzzled, then discouraged, then despairing of ever explaining it to somebody who didn't grow up with it, as he did, on a ranch in eastern Oregon, then Buckley, Wash., where his father still runs some horses on a little place he's got. The secrets: Do rodeo cowboys give each other the lowdown on all the animals on the circuit?

"I wouldn't like you if you wouldn't tell me," he says, with a smile that reminds you that you should be smiling too. "Cowboys all help each other. Of all the sports I believe it's the honestest and fairest sport; I don't know a cowboy who wouldn't tell another cowboy about an animal." . . . downdraft, welling, the back end . . . Then there's a horse called L-75 (all the rodeo stock are known by numbers) also called Phoenix, "she jumps four or five times then she'll whirl around and come back on you -- that horse has hurt a lot of cowboys. I can tell you every move she makes, except some days she don't do it.

"Most of your injuries are people who enter, they never rode before, or not much. But when I'm in trouble, say on bareback, I'll double-grab and declare myself, put both hands on that strap before the eight-second buzzer and be disqualified because I know I won't get no points if I stay on, anyway. I broke two bones in my foot one year, got the cast put on on a Friday, I was supposed to ride on a Sunday. So I cut my boot down the side and put laces in it like a work boot, and cut the cast off, I get on that horse from crutches. The only problem was I couldn't walk, so in the bull-riding if I drew a bull that would hook you, go after you with his horns when you're thrown, I wouldn't ride because I couldn't run, but otherwise I'd ride."

That's how you get to wear a black Stetson with a five-inch brim and not have people start fights with you; that kind of style, going down the road, as they say (and mean it -- 110, 120,000 miles of driving every year) making $30,000 in the first half of this year, which is okay money, but there's more: "It gets in your blood, you got to really love it. If I'm home (a ranch he's building in Florida, cowboy style, putting up the barns and arena first, the house last) for a few days, let's say I messed up with my bulldogging, I'm not shaping my steer right, I'll practice, I got my own stock to practice on."

And more: the letters he gets from kids asking him how to get started, the endorsement deal with Stetson, which had to custom-make that hat, they didn't have a hat with a five-inch brim, but then they didn't have Dan Dailey, either, with his jaw you could drive railroad spikes with, and those eyes with that blue glare of thousand-yard stare in the twilight under that brim . . . and there are the moments, the perfect moments when the whole madness of men trying to ride animals that cannot be ridden . . . well, moments: "When you draw one of the top horses and you're tapped off with that horse right out of the gate, you're just right with him -- when that eight-second buzzer sounds you just wish you could ride longer."

And out at the Capital Centre, where the World's Toughest Rodeo crew is covering the floor with six to eight inches of dirt for Dan Dailey to fall on (he competed yesterday and will again Sunday) he says: "I'd like it for a lot of people to remember me, that I was the greatest."

He is walking up the ramp they lead the horses down. Somebody asks him if he ever takes off that Stetson, and it's hard to tell what he's thinking, his mouth has that country-cautious and one-up set to it from the load of Copenhagen snuff under his lower lip (he has this way of spitting so gently it's like he's tossing a dime on the ground) but what he says, after a while (he says everything after a while) is: "Oh, sometimes." Is he laughing? Would you ever know if he was? He walks up the ramp, his hat rising into profile against the sky at the end, and the sound of cars on the highway on the other side of the woods, going down the road.