At what altitude does one have to be to notice the curvature of earth?

Because even in high altitude weather balloon footage (100,000+ feet) that doesn't use a fish eye lens no curvature can be seen:

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Can someone make a model or do the math?

Do you mean 10,000 feet or 100,000 feet?

Hmmm... Technically I would say that you could see the curvature by just standing on the ground. A property of a ball is that it looks like a circle from every perspective, as long as you are not inside of it. Take a ball in your hand, and you see the curvature in the sence that you see a circle. If you would look from the perspective of the "north pole" of the ball, you will never be able to see the "equator" of the ball, no matter how far away you are. But the closer your eye is to that ball, the further the distance is away from that equator. So technically, you can never see more than a hemisphere of a ball. 

But no matter how close you are to that ball, you will always see a circle, and that circle IS the curvature of the ball. If you'd make a camera the size of an ant, and you place it on the ball, you'd see the "horizon" of the ball. And that horizon surounds you as a circle. That circle IS the curvature of the ball.

The same applies to the earth. The horizon IS the curvature. The horizon is that circle. And no matter how high you go up, you can never so more than a hemisphere at the same time. The fact that you cannot see beyond the horizon, is evidence for a spherical earth. It's as easy as that...

Fixed.

I could distinguish the curve from a plane flying at roughly 10,000 meters. But only just. And as geodetective wrote, the curve is more a circle around you than a hill-like shape in front of you. I was lucky that it was clear then, so the vision was great. It was also over an extremely smooth area in china, with very few mountains or hills.

And what you can see on these high-altitude cameras is not only the vague curve but also that the landscape further away from the camera seems to angle away:

Picture from 101,000 feet.
You can see a slight curve, and you can see slightly how the landscape closer to the horizon seems to curve away from the camera. And I noticed something lucky as well: Above the horizon you can see clouds dead from the side. You don't see the top of them, but you see them from the side. The clouds are roughly on the same flat plane as the camera, despite the camera being higher up. That can only happen if the earth is curved.

I'm sure that I can find curvature in those videos, and I will do that when I get home to my PC.  Calculating the amount of curvature is hard mostly because it's hard to figure out what units to use to measure it.  I could do some precise calculations that can be compared with the videos if I knew the exact focal length of the camera used but without that my calculations would be pointless.

If you have a wide angle lens (Fisheye) you can see the curve. You just need to make sure the left and right side of the horizon is vertically centered and the lens is level.