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The type of body you're looking for and the sort of flying your character will be doing have a significant bearing on what sort of wings they'll need. The "ideal" bodytype would perhaps be harpy-like, without unaerodynamic things like clothes or extra limbs (which would also be dead-weight when flying). Deep chest with massive muscles. Much more lightweight bones. Probably a pointier head. Much less weight and muscle in the legs and buttocks (again, deadweight, no good for flying). Actually, lets just cut to the chase... the ideal shape is "a bird". Every deviation from the basic bird bodyplan will probably lead to a heavier and less aerodynamic body which will need bigger wings to stay aloft and stronger muscles to take off.

The type of flying you intend to do also has a big impact on wing shape, and one which I'm not going to go into detail on here

So, in the absence of more information, lets consider one of the largest known flying birds, Pelagornis sandersi. Upper weight limit was about 40kg, conveniently about the weight of your guy. Wingspan was over 6m.

Remember this is a bird, so was optimised for life on the wing, not tottering around on the ground, holding tools, chatting with other beings, wearing clothes, etc etc. I believe this species was assumed to be a seabird, and those very long slender wings certainly look quite albatross-like, optimised for long efficient glides over great distances and extended times.

A much heavier bird (up to 70kg or so), Argentavis magnificens, had a similar wingspan, but much deeper wings (there's probably a better term in the aviation or ornithology worlds, but I'm not aware of it) to support that extra weight. Again, bird, optimised for flying (or at least soaring), none of the other people things you might be interested in.

The condor also in this picture weighs up to about 15kg and has a wingspan of over 3m. This should probably tell you that you can't just give your dude big fat condor-style wings and have him fit in a confined space... there's not too much chance you'll get away with wings under 4m, though it is tough to provide a more realistic minimum for you.

These should give you some idea of the sheer size needed, even if they don't give you a good idea of how radically different the body plan of a flyer is compared to a human (apparently a tree-dwelling ape who took up endurance running and burning things). Trying to combine the two bodyplans will be tricky, to say the least, but there are pages and threads and questions out there ad nauseam about anatomically plausible flying humans.

For a more unusual bodyplan, consider a pterosaur:

Frustratingly, no-one seems quite sure about how much those things actually weighed. Early estimates were ludicrously low. That Quetzalcoatlus sp. probably weighed at least as much as an adult human, with a 6m wingspan. Smaller pterosaurs obviously existed, but no-one knows how much they weighed either, but the possibility exists that with pterosaur style wings you might be able to give your guy a wingspan as low as 4m. Positively petite!

As a closing note, consider the attempts to make mere humans fly under their own power. Paragliders, outstretched wingspan of 8.4m. Hang-gliders 9m. Both are for adults, and both add 20-40kg, but they only scale down so far and only allow unpowered takeoff. Ornithopter... 32m, still needed an assisted takeoff. Pedal-powered propeller... 34m. Both of those needed olympic-class athletes to operate, which should give you some idea as to the athleticism and stamina your character needs to have in order to fly.

You could model your flyer on Argentavis. It weighed about 80 kg. It had wings 9 meters wide.

https://en.wikipedia.org/wiki/Argentavis

Prior published weights gave Argentavis a body mass of 80 kg (180 lb) but more refined techniques show a more typical mass would've likely been 70 to 72 kg (154 to 159 lb), although weights could've varied depending on conditions.[8][4][9] Argentavis retains the title of the heaviest flying bird known still by a considerable margin, for example Pelagornis weighed no more than 22 to 40 kg (49 to 88 lb).[6] For comparison, the living bird with the largest wingspan is the wandering albatross, averaging 3 m (9 ft 10 in) and spanning up to 3.7 m (12 ft 2 in). Since A. magnificens is known to have been a land bird, another good point of comparison is the Andean condor, the largest extant land bird going on average wing spread and weight, with a wingspan of up to 3.3 m (10 ft 10 in). This condor can weigh up to 15 kg (33 lb).

9 meter wide wings will make it tough to dance. Might I suggest you give your flyer a preternaturally slim, elfin build. Taking his weight down from 80 to 30 pounds will let him have 9 foot condor wings.

It greatly depends on flight conditions.

Paragliders has wingspawn about 8-12 meters (4-6 half-wing). It is able to takoff from ground and land more o less safely. Jet wing had only 2.5 meters wingspawn, but needs a "drop down" takeoff.

Both support much more weight, than 30 kg (about 90-120). But wingspawn depends on weight more like sqrt(x). It means you can divide this values by 2 at max. It means 2-3 meters for takeoff and hardish landing from/to ground for wery thin bat-like unnaturaly strong wings

It's not just a question of wingspan. Most birds have (sort of) hollow bones, which helps to keep weight down. And that's really important.

Additionally, actually getting into the air requires speed, and powerful muscles to flap the wings to achieve lift.

Another consideration is the weight of the wings themselves, and the strain placed upon the spine by them. Bigger means more weight, and more weight means more strain. If big enough, the kid could be a cripple by 20.

In order for your character to be able to get into the air and fly, it would need:

1. Powerful legs to build speed for lift.
2. To rely on wind,or high drop offs to build enough speed for lift.
3. Powerful chest and shoulders to flap for extended periods to brute force it into the air.
4. Any combination of the above.

Muscles are dense, no matter where on the body they are, and that adds weight. In order to protect the spine, said child would need to have well developed chest, shoulder and back muscles, and be extremely lean. Bones would have to be, as previously mentioned, hollow-ish(think of a honey-comb structure), which makes them less resistant to breakages, and has a lower hard limit on how much weight they can sustain before breaking.

Nature imposes these limits on us all the time. We are the size we are, because anything bigger tends not to survive (giants have heart attacks, and skeletal problems due to weight).

So let's assume a wingspan of 10 feet on the child. By the time that child is 20, that wingspan will need to increase, and as such will also increase in weight.

Eventually, the muscle mass required to even move the wings would put enormous strain on the heart and skeleton(because humanoids have a leverage based skeletal/muscle structure), so flapping to generate lift would necessarily give way to soaring and taking advantage of thermal updrafts later in life. There is a reason that large birds tend to live in aeries: So they can jump out and build up enough speed to glide and soar. It's actually very difficult(and energy intensive) for them to get off the ground without strong wind. This means your flying child would have to have incredibly powerful legs, so that he could either jump VERY high in the air, or run REALLY fast to generate enough speed for the wings to generate lift efficiently.

The reality of your character is that even at 11 years old, he would look like a miniature body builder, and would be an athlete rivaling Olympic medal winners. And even whilst folded, those wings would reach well above his head, and would drag along the ground when he walked.