Giant Eagles: Flying Capabilities: 1. Giant Eagles: Flying Capabilities

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1. Giant Eagles: Flying Capabilities

This article is for those who wondered what the flying speed of a giant eagle would be, and if it could carry a person.

Right off, I have to point out that, there is an inherent limit in scaling up animals, which is the reason we don't face 17 ton cockroaches that stomp us when we enter “their” kitchen. A given design only is feasible within a range of sizes. Eagles are already the largest birds of prey and likely that is because nature has already discovered the limit, but this is fiction, so what the heck.

OK, assuming that an eagle would scale well, here is what I get. It would have to be a big eagle for people to ride them. I figured that it would have to weigh as much as a horse. I took 1000 lbs. (450kg) as the weight of a riding horse. Just a guess, don't all the horsians (This word should indicate my level of horse knowledge, i.e., they are big and I have seen a lot of them in cowboy movies) or whatever you call yourselves throw things at me. If it is a different number, the eagle scales accordingly. If you take a large eagle of 15 lb. and 8 foot span and scale it to 1000 lb., you end up with a bird that has a span of about 32 feet (9.7 M) and stands about 15 feet (4.6M) tall. Roughly four times as large in all dimensions.

A thought occurs, if the brain also scales up it now has a brain as large as ours. It might be real smart and intelligent speech may not be all that farfetched. Well, it is farfetched, but hey, this is fiction. It makes more sense than smart talking crows that know how many years they have been alive.

I don't believe an eagle would travel the way a duck does, laboring along the path, flapping all day. Eagles are soaring birds and would travel great distances the way a sailplane does. They would travel by day and look for updrafts caused by the temperature differences of different types of terrain. They are always there and are one of the causes of turbulence at low altitudes. You have to experience the power of an updraft to believe it. One day, while taking a flight lesson, I was discussing the topic with my instructor who was also a sailplane racer. He gave me a demonstration. He spotted a nice thermal over a freshly plowed field and made for it. As we got there, he cut the throttle to idle, so we were only relying on heat to raise us and banked our small craft into a very sharp turn which held us in a tight 75 mph (120 km/h) circle, which he quite skillfully kept centered over the lift. It was like being lifted by the hand of God. Our little trainer, which normally couldn't climb much faster than 700 feet or 200 meters per minute was going up at several thousand feet (1 Km) per minute. Enough that the rate of climb indicator was pegged. In a few minutes, we had made it to 10,000 feet (3 km), a task that would have taken 20 minutes or more on a hot summer day using motor with two on board. The method of travel would be to find a thermal. Use it to climb as high as it would take you and then glide along your course looking for the next big thermal and repeating the process.

Sailplane racers use this method to travel amazing distances. A typical race is a triangle shaped course about 100 miles on a side using airports as checkpoints where you have to fly over low and have your number identified by the spotters. Winning speeds on a sunny day can reach 70 mph and maximum straight line speeds of the planes is in the area of 150 mph or 250 km/h, although the most efficient straight line speed is more like 60 to 100 mph (100 - 160 km/h). This is done with no expenditure of energy other than a tow to 1000 feet.

Climbing in a thermal is intense. The fastest rising air column is narrow, and you need to maintain a tight turn to stay in it. That means large g loadings, i.e. your weight would increase dramatically. There is also the disorientation of rapid turns. A high performance sports car like a Porsche 911 will turn at about 1 g. Most of us, Porsche owners included, never experience even that level of turning performance. A 1 g turn at 60 mph would be about a 550 foot (160M) in diameter circle. An eagle doing a 3 g turn will make that 180 feet, (50M) at the same speed. Instead of 18 seconds for a full 360 degrees, it's more like 6 seconds. High g turns are a “where's that barf bag” experience to the uninitiated.

Also, the flyer sees a tilted world in a big turn. It feels like the horizon is tilted 60 or 70 degrees and is swirling around you at breakneck pace in an intense turn. When you fly and can look forward, it feels like you are upright at all times and the world tilts as you turn.

A second type of lift is wave lift. If you had a mountain range and a steady wind was blowing at it sideways, the air would turn up hill as it crossed the range. Since there is now a constant current of uphill air, you could cruise down the length of the range, travelling downhill in an upward flow of air, much the way a surfer rides the slope of a wave.

Thermalling only really works well during daylight hours. At night thermals are much weaker. Wave lift works whenever there is wind over hills, but the wave is the strongest close to the mountain and for people the risk of flying into the ground at high speed makes it an unacceptable risk to travel at night. Who knows what the eagles of Arda could accomplish?

Perhaps they can see in the night.

I learned reading a Scientific American article on predatory dinosaurs that an animal’s rate of locomotion varies at the square root of leg length, all else being equal. It turns out that this applies to flying animals as well. All air vehicles have the equivalent of gates, i.e. speeds where they do various things best. These speeds are defined by the angle of attack. They change from vehicle to vehicle due to geeky sounding items like coefficient of drag and aspect ratio, but for similar vehicles, they would remain the same. Angle of attack (AOA) is the angle at which the wing strikes the air. If you drew a line from the leading edge of a wing to the trailing edge, the difference between that line and the true direction of airflow is AOA. Lift varies directly with AOA, up to the point where airflow breaks down across the top surface of the wing, due to too high an angle of attack, a state called stall. If the AOA which gives the best cross country performance for a real eagle is say 4 degrees, then it would still be 4 degrees if you scaled that eagle up to a larger size. The best speed would increase, but the AOA would remain the same. Here is why. If you double the size of an eagle, the wing area would increase by 4 times, twice as much, length and width (2*2). However, its weight would increase 8 times, twice as much length, width and height (2*2*2). This means there is now 8 times as much eagle being supported by 4 times as much wing. I.e. wing loading has doubled. Wing loading is equal to weight divided by wing area. With twice as much weight for each square unit of wing to support in the air, the air vehicle must now travel fast enough to generate twice as much dynamic pressure. (Dynamic pressure = the force you feel when you hold your hand out the window in a fast moving car) Dynamic pressure varies at the square of velocity. I.e., go twice as fast get four times the dynamic pressure. So if you double span and get double the wing loading, requiring double the dynamic pressure to support the air vehicle, you need a speed increase equal to the square root of 2, since dynamic pressure varies wit the square of speed, proving that the square root law applies.

Well you say, that's all fine and dandy Mike, but you lost me back at AOA, or as Kirk once said to Spock, “please, just push the right button”. So here's the Cliff Notes version. If the eagle is 4 times as big, as an American bald eagle, all it's flying speeds double. I found on a web page that their speeds were, typical gliding speed 65 mph (105 km/h), max dive speeds 150 - 200 mph (250 - 320 km/h). That means the giant eagles of Arda will cruise cross country at 130 mph (210 km/h) during glides, but trip speed will be reduced to more like 100 mph (160 km/h) or 33 l/h (leagues per hour) because of the need to climb in thermals 25% of the time. What does this mean to a rider? Well, for one, he/she is in for a bad hair day. 130-mph wind will set your hair in such bad tangles it will all get pulled out when brushing it. Perhaps a scarf, maybe super-glued to their head would be in order, or better yet a helmet. Goggles would be nice. Also, anything they want to have with them when they arrive better be firmly lashed to their body. We are talking hurricane force winds here. Don't even consider a high speed dive at 300 to 400 mph (500 - 640 km/h). They would be blown off. At 300 mph, dynamic pressure is 225 lb. per square foot, meaning areo forces would rip them from the eagle's back unless they were firmly attached.

If you are considering having your eagle simply fly slower, think again. Devices that fly have a characteristic unfamiliar to those who use road vehicles. It takes more power to travel slow than fast, up to a point. This is because they are subject to two types of drag. We are quite familiar with what is called parasite drag, the drag of the air catching on the body of a vehicle moving through it. Overcoming parasite drag is the largest use of energy in most vehicles. A winged flying vehicle also has induced drag to deal with. That is the drag caused by the wings as they generate lift. It works exactly opposite parasite drag. Whereas parasite drag goes up at the square of velocity, induced drag goes up in a square function as speed decreases. When you combine the two and show it on a graph plotting drag vs. speed, you get a u shaped curve. The low point of this curve is the most efficient flying speed, where the least work is required to stay aloft. If the eagle slows down dramatically, it would be working so hard it would soon tire. The low speed portion of its flight envelope would only be useful for takeoffs and landings.

Hopefully this will be useful to those who want to have a giant eagle in their story. It is derived from a series of e-mails on Henneth-Annûn to help Isabeau with a Captain My Captain chapter. If you have further questions, I would be happy to answer what I can or render an opinion as to the feasibility of any eagle action in a story.

Fëadan

This is a work of fan fiction, written because the author has an abiding love for the works of J R R Tolkien. The characters, settings, places, and languages used in this work are the property of the Tolkien Estate, Tolkien Enterprises, and possibly New Line Cinema, except for certain original characters who belong to the author of the said work. The author will not receive any money or other remuneration for presenting the work on this archive site. The work is the intellectual property of the author, is available solely for the enjoyment of Henneth Annûn Story Archive readers, and may not be copied or redistributed by any means without the explicit written consent of the author.

Story Information

Author: Fëadan

Status: General

Completion: Complete

Era: Other

Genre: Research Article

Rating: General

Last Updated: 09/20/03

Original Post: 10/10/02

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