How big would a bird have to be to carry a human if gravity were halved?

How large would a bird have to be to still be able to fly, while carrying a human, specifically if gravity is half as strong as it is on Earth?

Most riders would be less than 140 pounds and under 5'10. They live mostly in the desert and would often have favorable wind conditions with few clouds. The composition of the atmosphere is essentially the same as Earth's, and the atmospheric pressure is also the same as Earth's.

The birds need to be able to both take off and effectively fly while carrying their rider. They also need to be able to reach a height of 2000 feet above the ground and maintain it for at least 1 hour while carrying the rider. Manuverability, combat ability, and speed are not the main focus, but would be nice advantages.

The birds primarily glide and soar while in the air, like most raptors. The birds have a body structure similar to that of a Bald Eagle and their bones are also just as heavy and strong as an eagle's. Otherwise they might be strained under the additional weight of a rider.

I'd prefer it if magic was not taken into account much, and answers tried to be realistic as possible. The one main exception would be to possibly ignore the square-cube law, which almost nobody in the fantasy genre seems to care much about anyways, and would likely make this creature impossible.

Okay - so let us start with some Baselines:

According to Google - the most weight lifted by a Bird is apparently 18 Kg, lifted by the Harpy Eagle. Halving the gravity gives us a weight of 36 Kg - which is a bit light, considering your goal weight is just over 60 Kg.

However, in terms of Wingspan, they are not as big as say an Albatross or Condor - so this suggests that the relationship between the size of bird and absolute lifting power is not strictly linear.

But for the sake of argument, let us say it is, they have a current wingspan of about 2 metres, so doubling that - 4 metres. Something Something Cube Law something - we will need to increase this again, I CBF doing the maths - but let us consider that to accomodate the musculature to power such an impressive wingspan that it is cubed - so 8 metres.

Interestingly enough - that is approaching the size of a small light aircraft wingspan (The humble Cessna clocking in at 11 metres)

So - an Eagly like bird of Prey - with an 8 metre wingspan is my answer.

For bonus worldbuilding points - If you have the animal primarily feeding on something like Baby Camels (which weigh in at over 30 Kg at Birth) and have its hunting method effectively Boom-and-Zoom (Swoop in, grab the Baby Camel, carry it off to eat) - then you can probably get close enough to justify carrying a human.

While some birds like the Harpy Eagle can lift a lot of weight for short periods of time by beating their wings really hard, if you want to be able to maintain flight for an hour or more, you will need to find a body plan that will work off of the bird's gliding power, not just a maximum lift.

To figure this out, you need to consult the lift formula:

Lift = 0.5 * AirDensity * Velocity^2 * WingArea * CoEffOfLift * sin(AngleOfAttack)

For a bird body plan, we will want a large bird that has a reasonably high cruise speed, good endurance, and a high wing area to weight ratio and scale it up from there. For this I will be using a California Condor which has a cruise speed of 25m/s, a wing area of about 2.23 square meters, a lift coefficient of about 1.0 (this is just average for birds, I don't know about the condor specifically), and a weight of 10kg. I will also assume your bird needs to be able to manage some kind of upwards vector; so, I'll also assume it can climb at an angle of 30 degrees without stalling, and I'll use an air density of 1.087kg/m^3 based on your 2000ft altitude with a temperate Earth like atmosphere. Keep in mind that Condors can fly much higher than this on Earth; so, its wings are way over-engineered to be able to carry itself at these altitudes even before we cut gravity in half.

It gets a bit more complicated because the human will add drag to the bird. If your rider were to lean flat against the back of the bird, this will approximately double your drag reducing your cruising speed down to about 17.5m/s, but if you were to sit up right on it, you could be looking at 4-6 times the drag reducing your speed to 10-12.5m/s

We can from here simplify the formula to Lift = 0.478 * WingArea * Velocity^2 which for a normal sized condor moving under ideal drag at 17.5m/s is 334 Newtons of lift. Which means that a Condor at 1/2 Earth's Gravity could glide (with the extra drag) at a total weight of 68kg. Since a condor only weighs 10kg, that gives you about 58kg of carry capacity which is not quite your goal, but it is enough to carry a particularly small person... except that the condors are not actually big enough for a human to lay flat against, and if you had to dangle or sit up right it would multiply your drag so high that your bird would slow down well below stalling speed.

So instead of worrying about simple lift equations, you also need to consider the literal size of the bird, and if you can lay down on it. If you instead made it about 1.5 times the size of a condor, you'd see a lot of factors compound to increase your weight capacity. You'd have more room for a small rider to be able to lay down on its back reducing his drag. The rider is proportionally smaller which also decreases relative drag, which together would work to get you moving much closer to the cruising speed of the bird, etc. So if you assume a condor that is 1.5 times bigger (4.4m wing span), you'd see a cruise speed close to 20m/s meaning a total lift capacity of 200kg for a bird that only weighs 34kg. While it seems counterintuitive for your lift to weight ratio to go up as the bird gets bigger because of the square cube law, relative drag reduction will play a larger role in increasing your max carry capacity than the square cube law will work against you (in this weight range) because speed is so critical to lift.

EDIT NOTE: I've removed my comments about take-off speeds because many birds can flap to produce even greater lift at a near standstills than they have in gliding lift at cruising speeds.