Humans have wing envy. For thousands of years, we’ve been dreaming up hare-brained schemes to fly like birds. The ancient Greeks conjured up Icarus and Daedalus, who made wings from bird feathers, strings and wax. Leonardo da Vinci put a little more thought into it, drafting plans for a mechanical winged contraption known as the ornithopter.

While 20th-century humans are perfectly capable of taking to the skies, there’s something intrinsically unsatisfying about doing so in an aluminum behemoth. We still want to fly like birds — taking off under our own power and gliding effortlessly once we’re airborne. There’s even a $250,000 prize for the first human-powered helicopter that can stay airborne for 60 seconds, although no one has come close to achieving that objective since the initial offer was made more than 30 years ago.

Why, after at least two millennia of thoughtful engineering, are humans still trying to figure out individual flight? Why can’t we strap on a set of wings and take off? What about us is so unsuited to soaring?

“Our muscles are too weak. Our wings are too short. And we weigh too much,” explains Jim Usherwood, who studies the biomechanics of animal flight at the Royal Veterinary College in London.

Okay. That’s a start. But there’s a lot more to say about this. The three problems that Usherwood identifies are related. To understand why, consider the physics of liftoff.

The Martin Jetpack flies above Canterbury, New Zealand, last month. The flight, which used a weighted dummy rather than a pilot, lasted about nine minutes and reached an altitude of 5,000 feet. The craft — essentially a helicopter backback — landed with the help of a parachute. (Courtesy Martin Jetpack)

In order to leave the ground, the forces driving a body upward must overcome the downward force of the body’s weight. You can see this in action during a jump. When you push your feet down into the ground, Earth provides an equal and opposite reaction, forcing the body upward.

You can’t rely on the ground when trying to achieve sustained flight, since the whole point is to uncouple yourself from Earth. So flying creatures and machines have to push air down into the ground, instead of pushing on the ground itself.

There are two ways to manage the problem of pushing down enough air to achieve liftoff. You can accelerate a small amount of air downward very quickly, as a hummingbird does. That takes incredible power, and none of the muscles in the human body muscles can even come close to accelerating air that quickly.

Alternatively, you can accelerate a large amount of air more slowly, which is the more efficient technique, especially for heavier fliers. (That’s why a pelican’s wings don’t flap as fast as that of a sparrow or hummingbird.) You might think, then, that we could just build really, really large wings and flap them quite slowly.

But there’s a problem here, too. Bigger wings, and the muscle required to move them, add weight to the equation. The amount of power required to take off increases by the square of the additional weight. So a doubling of weight requires a fourfold increase in power output. Unfortunately, our arm and back muscles just aren’t that strong.

Our more powerful quadriceps and gluteal muscles, stretching from our thighs up, however, can almost do the job. Last year, a team of students at the University of Toronto built a machine loosely based on da Vinci’s ornithopter sketches. The bicycle-powered, wing-flapping contraption couldn’t achieve liftoff, but it could maintain its altitude for 19 seconds once towed into an airborne position. Last month, a group of students from the University of Maryland managed to lift a human-powered helicopter off the ground and stay aloft for four seconds.

Neither of these achievements would be considered flight by the average dreamer, but they suggest leg-powered flight is possible with some tweaking and improvements in materials. It’s a long way off, though. And don’t expect to commute to work in your bike-powered flyer. The current versions can only fly in ideal conditions, since winds would upend the device and destroy the feather-light wings.

According to Usherwood, for a human to take flight on flapping wings, “your body would have to be made almost entirely of muscle.” In other words, humans make terrible hummingbirds.

With flapping and spinning apparently non-starters, a couple of options remain. Some birds, including albatrosses, take to the air by riding thermal updrafts. They coast between the rising and falling air currents to manage their trajectory and execute a landing. It’s a phenomenon similar to hang-gliding. But the whole process is totally dependent on the right wind conditions — and many scientists think albatrosses can’t fly on a still day, and therefore consider the birds technically flightless.

We could attempt fixed, airfoil-shaped wings, as we use in airplanes. When a plane gets going fast enough, the air moving over the top of the wing is at a slightly lower pressure than the air underneath, creating the phenomenon known as lift. The problem is that you have to get going far faster than your legs can carry you.

The frustrating physical reality seems to be that, unless we can lose a lot of weight without losing any strength, humans simply aren’t destined to fly any significant distances under their own power.

But there is a happy ending, of sorts, to this story. The jet pack, probably the closest thing a human will ever get to flying like a hummingbird, is right around the corner. A New Zealand-based company has developed the Martin Jetpack, essentially a helicopter backpack.

“I figured since age 5 that jet packs would be a better way to walk to school,” says founder Glenn Martin.

Working with the same basic problem that faces human-powered flight — power requirements increase at the square of added weight — Martin developed a rotary wing system with the lightest engine capable of turning the rotors. What he ended up with was an automobile-style piston engine. It’s lightweight, and it forces far more air through the rotors than it uses to combust the gasoline that powers the engine.

Martin has interest from both government and private buyers. He expects to have the first models roll off the assembly line within the next 18 months. Your personal joystick-controlled jet pack will run around $100,000, but you will probably be able to take a rented model for a spin for just a few hundred bucks. Under U.S. government rules, the private packs will be limited to 30 minutes of flying time and a range of around 30 miles.

While it’s not exactly soaring like a majestic bird, it’ll save you the hard work of flapping your way up there.