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I am curious about any reference in the books. Is there any suggestion in any canon or semi-canon sources about how long it takes to reach destination B from destination A on a dragon's back?

I am also curious about how long can a dragon keep flying, if it is referred to in the canon and semi-canon sources.

EDIT: I am actually more interested in the sprint speed of dragons. Here we see Drogon causes a very high pressure underneath.

Drogon

I think we can get the sprint speed using water viscosity, water depth and wavelength of water. However, I am not well versed with fluid dynamics, so I wanted to start from here.

Möoz
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    Dry weight vs. full fuel tanks; drag coefficients; light reflection; etc. – Gallifreyan Aug 09 '17 at 14:31
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    @PaulD.Waite also, what is the stall speed of a non-flapping dragon? –  Aug 09 '17 at 14:49
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    If evidence from the TV show is acceptable (S07E04) then Drogon easily outpaced galloping horses (~30 mph). A maximum speed of 60-70 mph doesn't seem unreasonable. – TheMathemagician Aug 09 '17 at 15:02
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    @TheMathemagician You gave me a brilliant idea! We can measure distance from the hills that Lannisters forgot to leave a patrol even though they were afraid of possible ambushes to the army lines by the time it takes for horsemen to reach and assuming a full gallop speed of 50-60 km/h.. Drogon also appeared pretty much at the very top of that hill for the first time. We can just divide the distance by the time in the show. Not canon enough but still better than nothing :) –  Aug 09 '17 at 15:11
  • @TheMathemagician It takes about 86 seconds for horsemen to reach the gap drogon caused in Lannister lines. Drogon takes 18 seconds to take and burn the lines. This makes drogon around 240 km/h if horse gallop speed is 50 km/h. I don't think the water ripples were that realistic if the rest of the laws of physics hold. Cheers! –  Aug 09 '17 at 15:21
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    Westeros or Essos? (I don't know. AAAAAGGGGGGHHHHH!) – gowenfawr Aug 09 '17 at 15:37
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    I remember a 'So Spake Martin' where he mentions that once you start going into details about 'how fast can a dragon fly' etc, then you've gone too far! Can't find it though... – Möoz Aug 10 '17 at 05:51
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    GRRM is deliberately vague on such details to minimize the risk of someone discovering an error in his story. There is one indicator that Princess Rhaenyra and Prince Daemon used to race their dragons every day to Dragonstone and back. Dragonstone is approx 200-300 miles away from KL. Take it from there. So at the minimum, Dragons can fly 200-300 miles in one go and take the same trip back in that very day. There is no indication in the books about that and nor will there ever be as GRRM avoids such details. So that makes it POB – Aegon Aug 10 '17 at 07:44
  • @Aegon I read this question after I asked mine. Had I read it before, I might not have asked this question. Although they are not the same questions, the relevance is a lot and available information seem little. So thank you. I am actually content with the answer I reached with the suggestion of TheMathemagician. It is semi-canon but holds some meaning :) –  Aug 10 '17 at 23:27

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Intentionally unspecified

The author, George R. R. Martin, has stated in the past that:

If I start worrying about Brienne's chromosomes, the next step is trying to figure out the aerodynamic properties of dragons, and then the whole thing falls apart.
-So Spake Martin - Entry 1147

He has left these things vague and unspecified on purpose so that it doesn't detract from the real story:

The reason I am never specific about dates and distances is precisely so that people won't sit down and do this sort of thing.

My suggestion would be to put away the ruler and the stopwatch, and just enjoy the story.
-So Spake Martin - Entry 1198

Now there are many references you can make, and calculate some sort of an answer, he even suggests a starting point:

However, if you really must know, you can figure out the distances for yourself. The Wall is a hundred leagues long. A league is three miles. Go from there.

But if you turn up any mistakes in travel times by using that measure, let it be your secret.
-So Spake Martin - Entry 2787

You could calculate the amount of time it took for Drogon to carry Dany from the Fighting Pits (Daznak's Pit) to the Dothraki Sea or even the amount of time it took for Good Queen Alysanne to fly from Winterfell to the Wall (Queensgate, formerly known as Snowgate); but I would suggest you don't go down that road.

Möoz
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