The world may chide America for its supersized ways, but when it comes to the Grand Canyon, the more-is-better approach is clearly the right way to go. Just take a peek over the edge. The canyon captivates because of its immensity. It is a tableau that reveals the earth’s history, layer by dramatic layer.

Most visitors experience the canyon from the rim, others hike within, but there are three other adventurous options.

White-water rafting
Rafting the Colorado is an epic, adrenaline pumping adventure. The canyon’s true grandeur is best grasped by looking up from the river, not down from the rim. Its human history comes alive in ruins, wrecks and rock art. You can hike to mystical grottos and waterfalls, explore ethereally lit slot canyons and view wildlife in its native habitat.

Commercial trips vary in length, from three days to three weeks. Motorized pontoon rafts are the most stable option. Oar boats are more exciting and common. A fun alternative is to float in a river dory, a small, elegant hard-shelled rowboat for four passengers. Still, if you are after thrills, book a trip in an inflatable raft, which has you, your shipmates and a guide paddling all at once.

At night you will be camping under stars on sandy beaches (gear provided). It is not as primitive as it sounds – guides are legendary not only for their white-water acumen but also for their culinary skills.

Veteran river guides suggest you plan a trip in April or between mid-September and mid-October, when air temperatures are mild and rafters can tackle day hikes not possible in summer. Drawbacks of a spring or fall excursion include occasional storms, headwinds and shorter daylight hours. It takes about two or three weeks to raft the entire 279 miles of river through the canyon. Shorter sections of around 100 miles take four to nine days.

Mule rides
If you want to see the inner canyon from the backside of a mule, you have to commit to an overnight trip to the bottom. Otherwise there is a three-hour ride from Grand Canyon Village to the Abyss Overlook, the site of a 3,000ft vertical drop beside Hermit Road.

Rides depart daily from the stone corral west of Bright Angel Lodge and wind over a mule trail through ponderosas, junipers and piñons. Overnight trips head 10 miles down via the Bright Angel Trail to Phantom Ranch and up eight miles on the South Kaibab Trail.

Riders must be at least 4ft 7in tall, speak fluent English and weigh 200 pounds or less (225 pounds for a day trip). Wranglers will not let you saddle up unless you wear a hat tied to your head (April to October), a long-sleeved shirt and long pants.

To book a mule trip (more than 24 hours and up to 13 months in advance), contact Xanterra. If you get to the park without a reservation, stop by the Bright Angel Lodge transportation desk and see what there is available. If it is all booked, sign the waiting list, show up at 6:15am the following day and hope for a cancellation. Or make tracks to the other side of the canyon: mule rides on the North Rim are usually available the day before the trip.

Mountain biking
Mountain bikers have limited options inside the park, as bicycles are only allowed on roads and the Greenway Trail. Hermit Road offers a scenic ride west to Hermits Rest, about 16 miles round-trip from the village. Keep in mind that shuttles ply this road every 10 to 15 minutes between March and November. They are not permitted to pass bicyclists, so you will have to pull over each time one drives by. The rest of the year, traffic is minimal, making this a very pleasant ride.

Grand Canyon shuttle buses have racks that can hold up to three bikes. Alternatively, you could ride out to the East Entrance along Desert View Drive, a 50-mile round-trip from the village. The route is largely shuttle-free but sees a lot of car traffic in summer.

Just off Desert View Drive, the one-mile dirt road to Shoshone Point is an easy, nearly level ride that ends at this secluded panoramic vista, one of the few places to escape South Rim crowds. The Greenway Trail, running between Canyon View Information Plaza and Grand Canyon Village, is open to cyclists but is shared with pedestrians and wheelchairs. Bright Angel Bicycle Rentals began renting bikes inside the park in 2010.

The article 'Three alternative ways to see the Grand Canyon' was published in partnership with Lonely Planet.