It took the
Eagles at least an hour to get to
Sam and
Frodo.
So the eagles flew a little faster than 100 mph (161-162 kmh), which is a reasonable "giant eagle speed" in a fantasy setting... 200 mph would beggar disbelief even in ME (imo). Despite ME being "the land of faerie" within his subcreation
Tolkien still strove to maintain plausibility.
And how did I arrive at these numbers? (asks
@Aethelwulf in utter confusion, dismay and indignation).
Right away dismiss all images in your head from the movie scene; Sam and Frodo did
not dash from the Sammath Naur (S-N) and leap onto the ash hill right across from it. That makes for good action drama but, again, go
ad fontem (read the book!) for the real story.
The ash hill was a good ways distant from the S-N doorway.
N.B.: I'm using Fonstad's ME Atlas for all distances and locations.
1) The
Nazgul did not immediately fly off to Mount Doom when Frodo "put on
the Ring and claimed it for his own".
"At his [Sauron's] summons, wheeling with a rending cry, in a last desperate race there flew, faster than the winds, the Nazgûl....southwards to Mount Doom."
Also:
"But the Nazgûl turned and fled,...hearing a sudden terrible call out of the Dark Tower."
(Mount Doom is a little over 100 miles---straight line-- from where the Forces of the West stood on the two slag heaps)
2) At the same time (1) was happening Sam "got up, dazed" from being clobbered with a rock by
Gollum.
There now ensues the fight between the unseen Frodo and Gollum: to and fro, falling to ground, rising again, teetering on the brink of Crack. finally Gollum biting off Frodo's finger and doing his "happy dance", losing his balance, falling and being consumed by the fires.
(3) The Eagles had already arrived by the time of (1) because they "bore down" on the Nazgûl even as they were were wheeling away at
Sauron's call.
(4) Meanwhile, back at the ranch, Sam picks up Frodo, carries him outside and stands there and watches the fall of
Barad-dûr which, big as it is, takes some time to occur; it didn't just collapse like a house of cards. Right after that, Frodo and Sam have a convo about Frodo's hand, the Ring, Gollum's part etc.
(5) At Sam's (imminently sensible) suggestion, they leave the dangerous S-N and "
went slowly down the winding road... and passed toward the Mountain's quaking feet....[and]
reached a low ashen hill at the Mountain's foot."
If you look at Fonstad's
map you'll see the Ashen Hill is at least 2 miles, if not closer to 3 miles (on foot) from the S-N doorway.
Add that to the Mountain quaking, there is debris falling from the skies, rock and shale slides, and they are now off the road (which was tumbled rock even when they first climbed it), Sam and Frodo would be lucky to traverse that distance at even 2 mph; by way of comparison 2mph is a leisurely strolling pace.
Also, Mount Doom didn't suddenly explode like Mount St Helens; it erupted, extremely violently to be sure, but it didn't "blow up".
And all that, "rending and vomiting" Tolkien describes took some time.
(For a great simulation of what it was like for the Pompeii-nians when Mt Vesuvias erupted in 79AD.....
Destruction of Pompeii)
So from the time Frodo put on the Ring, to the time the Three Eagles arrived to rescue them, was at least an hour if not longer.
Therefore they flew at no more than 100 mph, probably slower. The Nazgûl would be slower still.
(And Watson, I hope you are duly chastened at having made an ill considered estimate 🙄... I expected so much better of you 😉)
