From: http://www.rationalistjudaism.com/2016/02/on-eagles-wings.html
One ornithologist writes:
"Many ornithologists have thought that the Bible picture of an eagle carrying her young was merely figurative, but in recent years
certain reliable observers have actually seen a parent bird let its
young rest for a moment on the feathered back - especially when there
was no other roosting place in sight. When an eagle nests on the ledge
of a sheer-walled canyon, many feet above the earth, with no jutting
tree or protruding rock to break the fall, the quick movement of a
mother bird to offer her own back to a frightened fledgling may be the
only way to let it live to try its wings again." (V.C. Holmgren, Bird
Walk Through The Bible [New York: Dover Publications 1988] p. 98)
One report of this behavior is as follows:
"Our guide was one of the small company who have seen the golden eagle teaching the young to fly. He could support the belief that the
parent birds, after urging and sometimes shoving the youngster into
the air, will swoop underneath and rest the struggler for a moment on
their wings and back. ... Our guide, when questioned, said that every
phrase of the verse [Deut. xxxii, I I] (which was new to him) was
accurate, save the first; he had seen it all except the stirring up of
the nest." (W.B. Thomas, Yeoman's England [1934], pp. 135-6)
Another report concerning the golden eagle comes from Arthur Cleveland
Bent, one of America's greatest ornithologists, on the authority of
Dr. L. Miller:
"The mother started from the nest in the crags and, roughly hand-ling the youngster, she allowed him to drop, I should say, about
ninety feet; then she would swoop down under him, wings spread, and he
would alight on her back. She would soar to the top of the range with
him and repeat the process. Once perhaps she waited fifteen minutes
between flights. I should say the farthest she let him fall was a
hundred and fifty feet. My father and I watched him, spellbound, for
over an hour." (A. C. Bent, Bulletin of the Smithsonian Institution
CLXVII [1937], 302)
Sefer Ha-Itur, Chizkuni and Yalkut Me'am Loez
). Read the articles in full for more detail. See also this article.