Calculating the Great 🦅Eagles' Power

[Thorin]

But I realised right away that it is no good to use the same ratio for weight as wingspan. For instance 100 feet and 175 pounds is a remarkably lightweight eagle.

The bigger the eagle, the less length he will have per pound.

After further consideraton and consultation, I believe that my calculations are not really accurate. After presenting this to a few of my grade 11 students who take Physics, the impression they said was that you couldn't take a normal ratio between weight and wingspan. The weight would be well over a 1000 lbs One student believe that the ratio would need to be cubed. If the wingspan was 30 times greater, then the weight would need to be 30 cubed. However, we realized that this would be true for a fully solid, 3D object, and that you would end up with some ridiculous number.

We came to the conclusion that the height of the body needs to be taken into consideration as well.

So...
The average height of a bald eagle is about 3ft with a 7 foot wingspan*
*
Something I knew but forgot to factor in is that the females are the bigger birds. The males average around 9 lbs as opposed to the female 14.

So Thorondor and Gwahir at least we know were males.

So here are the facts:

Male bald eagle
Height - 3 ft
Wingspan - 7 ft
Weight - 9 lbs


Thorondor

Height -
Wingspan - 180 ft
Weight -

So what is the proper way to calculate the proper ratio between these three criteria to determine Thorondor's height and weight?

Where the heck are all the Physics majors in this forum??

 

[Gothmog]

If we used the base numbers to assume for that of Gwahir and the rest of the eagles in LoTR, then they would have a wing span of about 100 feet and a weight of about 175 pounds. I'm not sure if the difference between Thorondor and Gwahir would have been that significant though, do you?

There may well have been less difference between Gwahir and Throndor than 80 feet of wing-span, I agree. But using the 100 ft. as a 'reasonable' figure was looking at a minimum size for the eagles of LotR. Since I doubt that all the great eagles were the same size, perhaps it would be better to give a range of 100 - 140 foot Wing-span.

 

[Thorin]

There may well have been less difference between Gwahir and Throndor than 80 feet of wing-span, I agree. But using the 100 ft. as a 'reasonable' figure was looking at a minimum size for the eagles of LotR. Since I doubt that all the great eagles were the same size, perhaps it would be better to give a range of 100 - 140 foot Wing-span.

I edited my previous post, Goth. Maybe go back and read it and see what else you could contribute to my changes.

I agree that closer to 120-140 feet are probably a better comparison from Gwa to Thor.

 

[Confusticated]

Eagles are so odd shaped I can't figure out how to calculate it. Baragund is a civil engineer, so he'll know physics more than most. Maybe we PM him with an invitation if he doesn't turn up here any time soon?

 

[Thorin]

Okay...I consulted with our math teacher here and she confirmed my initial results.

According to the facts of a regular male bald eagle, Thorondor would have been:

77 feet in height
180 ft wingspan
225 pounds

I know some said that this would be way to light for a bird that size but when we really look at th ratio of wingspan to weight of a regular eagle, that would still seem a bit far fetched..but it is how it is. They are mostly air!

Perhaps simple math can't solve this, so I will consult with the physics teacher as well....

Someone else want to get an expert opinion on the matter?

 

[YayGollum]

And I am fairly certain that I read someplace that Thorondor was of a type of giant eagle that was some kind of larger than the Misty Mountains breed. Did I make that up, is it merely a general (and decent) theory that everyone obtained via the aether, or does some book actually give the information? Also, Garn, I didn't think that this question was that interesting.

 

[Gothmog]

Thorin, I read back over your post. I could not think of anything to add.

I don't think there is any reason to be concerned about the weight issue, it may not be completely accurate but is probably not far out. In most animals, a large part of the weight is due to Bone. In birds the bones form in a way that reduces weight while retaining strength for what they need.

The 'Light-weight' eagles we have in this world certainly do not suffer from being short a few pounds. They are still very powerful birds.

 

[Confusticated]

Thorin, it looks like you used the same ratio to figure the weight and height as you have for the wingspan?


This question will demonstrate what I have been trying to say about the length per pound decreasing as the eagle size increases. I have been taking height into consideration and height is why the pound per length changes with the bird's size. Only if a giant eagle were still the same height as a bald eagle would the weight per length remain the same.

A bald eagle can lift at most half its own weight. Would a 225 pound giant eagle be able to lift Gandalf?

 

[Confusticated]

I just attempted to verify how you got those numbers Thorin, because it looks like the weight is slightly different ratio that the height and length. It uses 25 while he others are at 25.7. Did you just round it off for simplicity or is something fancy going on?

 

[Confusticated]

Lets use a simple example.

If you have a block of 1 cubic inch weighing 5 grams, and you make it twice as long, tall, and deep... you then have 8 cubic inches... which weighs a lot more than twice what it originally did. Weight does not increase at the same ratio as the individual size dimensions. It would be 40 grams, not 10. Same with the eagle but the calculations are more complex.

 

[Confusticated]

Geometry is what is needed. Someone to break down the eagle into shapes like spheres and cones and such and calculate its volume, then maybe we can get the weight. There might be another way of doing it too, but I don't know what that would be.

Thorin - get back here!

 

[Thorin]

Yes, Nom, I rounded it up from 25.7 to 26.

I just checked with our Physics teacher and he agrees that the weight would be considerably more and Nom, you are on the right track, he said that we would need to determine the volume of the body of the regular eagle to get a better idea of what Thor's weight would be.

I realize now that increase of size wouldn't be simple ratio calculations. If a man was twice our height (let's say 12 feet tall) it would make no sense to say that he would be twice our weight (maybe 400 pounds). Shaquille O'Neill is 6'8 and over 300 lbs if I'm not mistaken..and he ain't fat.

So we have to figure out the density of his body mass in volume.

Jeez what did I get myself into...I'm a French/Music teacher..I didn't even make it past grade 10 in physics.

 

[Confusticated]

I am trying to find some detailed measurements online. Chest and head circumference for instance. Wing depth, things not so easily found as the body length and wingspan. Then we can break the bird down into geometrical shapes and find the corresponding formulas online. It would be easier to measure the dimensions of an eagle without wings expanded though, then maybe figure wing length separate?

 

[Firawyn]

A gullible Dwarf!

Yeah, and Dwarves got slaughtered by a freakin' Belrog. They're smart.

 

[YayGollum]

Argh. More elves, on the whole, as well as as far as I can tell, were slaughtered by Balrogs. That method of death said little for their levels of intelligence. Of course, how the method came about does. Dwarves, just doing how they do, digging up some mithril, accidentally waking some irritable Ainur up versus elves spotting a Balrog and yelling, "Charge!" Ah, anyways, Yay giant eagles! From what has been written, I was apparently correct in making my giant eagle R. P. G. character around ten or eleven feet tall, since he's supposed to be pathetic compared to most.

 

[Thorin]

Yay giant eagles! From what has been written, I was apparently correct in making my giant eagle R. P. G. character around ten or eleven feet tall, since he's supposed to be pathetic compared to most.

Umm..I think even Gwahir would be much taller than 11 feet tall but not everything is conclusive yet.

 

[YayGollum]

Right. Which is why I am presuming myself correct when it comes to making a giant eagle character that was meant to be smaller than most of them.

 

[Confusticated]

If a bald eagle with its wings in and head down is shaped something like a football then using a 34 inch long eagle that is 8 inches across the body and 14 lbs, and if a giant eagle is 600 lbs (which I think is in the reasonable neighborhood) then the giant eagle @ .0122877 pound per cubic inch (like the bald eagle) would be around 4 feet across the chest and have a body length of 20 feet. Wingspan in the neighborhood of 50 feet.

 

[Firawyn]

Now that's starting to sound a bit more realistic. I think we may be getting a bit closer to an answer.

Yay for math wizzes! (not me!)

 

[Thorin]

If a bald eagle with its wings in and head down is shaped something like a football then using a 34 inch long eagle that is 8 inches across the body and 14 lbs, and if a giant eagle is 600 lbs (which I think is in the reasonable neighborhood) then the giant eagle @ .0122877 cubic inches per pound (like the bald eagle) would be around 4 feet across the chest and have a body length of 20 feet. Wingspan in the neighborhood of 50 feet.

So is it safe to do a ratio with these calculations for a 180 foot wingspan?
That would put Thorondor at about 72 feet high which was close to my initial appoximations. I'm not sure how you calculated the 20 feet and 4 foot chest...Could you use these numbers to determine the width and weight of Thorondor?

Good night! I'm looking 20 feet up and 50 feet across and that is huge in itself. Thorondor is sounding like a monster! He could eat Godzilla for breakfast and King Kong for lunch.