Yes, flying really feels like that.

High Flight

Oh, I have slipped the surly bonds of earth
And danced the skies on laughter-silvered wings;

Sunward I've climbed, and joined the tumbling mirth
Of sun-split clouds -- and done a hundred things

You have not dreamed of -- wheeled and soared and swung
High in the sunlit silence. Hovering there,

I've chased the shouting wind along, and flung
My eager craft through footless halls of air.

Up, up the long, delirious, burning blue
I've topped the windswept heights with easy grace

Where never lark, or even eagle flew.
And, while with silent, lifting mind I've trod

The high untrespassed sanctity of space,
Put out my hand, and touched the face of God.