In the middle and late 1990s, I optimistically assumed that a lot of previous researchers had placed birds in Calorimeter Rooms, which accurately measure the exact amounts of heat released by any object. Around 1977, I had built a Calorimeter Room in my factory to be able to measure and track the performance of the advanced woodstove that I had invented and was manufacturing. Many energy-related products are subjected to such testing. The concept is actually quite simple. The amount of wood placed in the woodstove was accurately weighed. Since each pound of wood contains a consistent amount of chemical energy in it, that provided the AVAILABLE CHEMICAL ENERGY. The calorimeter room accurately measured the amount of heat in the smoke which left up the chimney, the amount of radiant energy and the amount of convective energy transferred to the air in the room, which all MUST total the same as the available energy (less certain losses, such as ash that did not burn and particulate matter in the smoke that also did not burn). A basic Law of science, the Conservation of Energy, requires that no energy just disappear! Comparing the different values then provided the ACTUAL OVERALL EFFICIENCY of the product.
I had assumed that the same analysis had been done many times regarding birds flying! The amount of food provided to and eaten by a bird establishes the available chemical energy. The calorimeter room would measure the amount of heat given off from the bird. Much of that heat is given off due to the skin temperature being above the ambient temperature of the surrounding air. When the bird would simply sit still for an extended time, the calorimeter room would accurately determine that heat loss, due to the basal metabolism of the bird.
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This indicates that such simple tests inside calorimeter rooms should accurately have established the energy efficiency of bird flight. However, as near as I can tell, NO ONE has ever done those simple experiments!
For a couple years, I concentrated on an assortment of thousands of OBSERVATIONAL studies of bird behaviors. Researchers would tend to watch what a bird colony or individual ate and estimate how much is eaten in each meal. They have discovered many wonderful new insights, particularly regarding females eating habits during pregnancy and after and the growth rates of birds of different ages. However, no such studies that I could ever find ever directly addressed the situation of flying. Only anecdotal comments regarding eating more food related to greater amounts of flying, without any accurate data numbers, seemed to be available.
Recently (Nov 2007) I have discovered some VERY old research which IS very helpful. The researchers took a wonderfully creative approach to obtaining information! The research was done in 1958, 1959 and 1960, all near Champaign, Illinois. The researchers had been frustrated in trying to study migration behaviors of birds for several years, until they discovered / realized something very useful. Many species of birds only migrate at night. The thought is that it is such a stressful activity that the daytime higher temperatures and sunlight would probably cause much greater loss of body water through evaporation and transpiration. Even in night migrations, some species of birds appear to average a loss of HALF their body weight in a 10 hour migratory flight!
The researchers had learned that Swanson's Thrushes nearly always begin their migration right at sunset, and fly through the night, for about an 11 hour migration (of around 350 miles). Apparently, normally, that flight goes well. However, when it is heavily overcast or foggy, those migrations sometimes would unfortunately pass through the location where the WCIA TV transmitting tower happens to stand. The result was a total of 469 birds that had collided with the tower and been killed. On the night of Sept 16-17, 1958, they seem to have collided with the tower during the entire night. On the night of Sept 28-29, 1959, most collided with the tower around 1 am, meaning after about seven hours of their flight. On the night of Sept 18-19, 1960, most collided with the tower around 5 am, meaning after about 11 hours of their flight.
The researchers performed full dissections of each bird. One of the findings that is important here was that the birds which collided after seven hours of flight were significantly heavier than those that collided after eleven hours of flight. Statistical analysis was done regarding that data, which gave the conclusion that some of those birds had an average weight of 31.4 grams after 7 hours of flight and 29.4 grams after 11 hours of flight. The researchers examined many more birds and concluded that the birds lost around 2.6% to 4.4% of their body weight per hour of their migration. They also examined a substantial number of slightly larger birds, Gray-Cheeked Thrushes with similar results.
They acknowledged that these findings were not in good agreement with the calculations of Salt and Zeuthen (1960) who calculated a weight loss of 5.5% per hour at a flight speed of 31 mph. (That rate would have resulted in a weight loss of around 1.8 gm/hr, well more than these experiments seemed to suggest.)
THIS is the data that I needed for the energy rate analysis regarding flight!
The statistical averaged results were that 0.8 to 1.4 grams of body mass was consumed every hour of the migration flight, for birds that flew at around 31 mph and which weighed an average of around 33 grams each.
Some of that body weight loss was certainly due to evaporative loss of water during the flight. The actual amount of this loss is not easy to precisely calculate. For the reasons of this discussion, we will neglect that factor completely, and therefore derive a figure for a MAXIMUM POSSIBLE CHEMICAL ENERGY available.
We know that one mole of bodyfat materials contains around 690 kilo-calories of chemical energy in it. One point one gram (the average of the 0.8 and 1.4 figures above) is around 0.006 gram-mole. That means that the maximum amount of bodyfat consumed per hour contains a total amount of available chemical energy of 4.22 kilo-calories or 4220 (small) calories. This is the same as about 4.5 Watt-hours of maximum available chemical power used up each hour.
That in itself is pretty impressive. For a (small) bird to fly and only use up a maximum of around 4 Watts of power seems rather astounding. But the migration research certainly establishes this as being true.
Aerodynamic equations provide a way to analyze the power needed
to supply flight. The first applicable equation is:
D = Cd * S * 0.5 * ρ * V2,
where D is the aerodynamic drag (in newtons); Cd is a factor regarding how streamlined the shape of the object is; S is the frontal area (in square meters); ρ is the density of air (which is 1.2 kilograms per cubic meter for the conditions of the flights); and V is the flight speed (14 meters per second).
The frontal area constantly changes during the wing flaps. There are times when it is as small as about .003 square meters, but it is also sometimes around three times that large. For these calculations, we will take an average of those two values, .006 square meters.
There is no easy way to establish what the coefficient of drag is. Again, during the wing flaps, it must certainly vary between around 0.2 to 0.6, both simply estimates. In any case, we will assume that the AVERAGE Cd = .4.
The aerodynamic drag is therefore about 0.4 * 0.006 * 0.5 * 1.2 * 196 kilogram-meters per second squared, or 0.28 newton. That means that the bird must produce exactly the same amount of Thrust to maintain constant speed flight.
If this drag force is multiplied by the speed (14 meters/sec), we get 3.9 newton-meters/second or 3.9 Watts as the rate of power needed to propel that bird at that speed of flight.
There are two of these factors, the frontal area and the coefficient of drag, which may be incorrect. However, this rate of power usage to enable the flight at that speed (3.9 watts) seems to be in general line with the maximum amount of chemical energy available from the conversion of bodyfat estimated by those migration studied of 50 years ago (4.5 watts). If these numbers are accurate, it implies that birds are extremely efficient at using the available energy to fly in migration.
At takeoff, the 747-100 can have 36,000 gallons of fuel in its fuel tanks, which is enough for about a ten-hour flight (or around 5700 miles). The later and larger 747-400 can have 57,000 gallons of fuel, which is enough for about a maximum trip of 8,290 miles. These both mean that very close to one gallon of fuel is burned every second. Boeing data confirms this rough value. At cruising speed, the 747 consumes about five gallons of fuel per mile of flight. When takeoff and landing is included, this rises to around 6.5 gallons of fuel per average mile for a whole trip.
Roughly 1/3 of the takeoff weight of the 747 is that fuel, not too different from the Thrush ending up weighing half as much after a 10-hour migration. We know the chemical energy in a gallon of Jet-A fuel is 18,300 Btu/pound, which is about 32 kWh per gallon. Since we have one gallon being consumed every second, that is 32,000 Watt-hours per second, which is 115 million Watt-hours per hour or 115 million Watts. This can be compared to the 4.5 Watts of power used by the Thrush!
The number is surprisingly not terribly out of line! We humans weigh around 3,000 times as much as a Thrush, and a 747 can carry more than 500 of us at a time. We might say that would suggest that if we were birds, then 500 of us would collectively use up around 6 million Watts of power (to fly at 31 mph). The airliner travels at around 16 times faster. However, it flies at extremely high altitude where there is far less air resistance (and drag). When the aerodynamic aspects of the different speeds and air densities are taken into account, the total amount of energy and fuel used up by a 747 is really not that different (ballpark) from what would be needed by us if we were birds!
The total drag of a 747 is a combination of the drag of the fuselage, wings, tail, and other structures. Boeing does not seem interested in divulging that exact number, but adding up the aerodynamic drags for the different components of that size suggests that the total drag must be about 24,000 newtons (or 56,000 pounds). NASA published a document that indicates that a 747 requires 55,145 pounds of thrust at its maximum cruising speed of 871 ft/sec or 265 meters/sec or 593 mph. (They generally fly at around 525 mph).
The actual required thrust changes significantly during a long flight. At the beginning of a flight, there can be over 300,000 pounds of fuel being carried (out of around 800,000 pounds of total aircraft weight). This requires much more aerodynamic lift, which therefore requires the aircraft to be oriented with the nose much higher, that is a greater Angle Of Attack (AOA). This emphasizes the type of aerodynamic lift called Reaction Lift, which is very inefficient as it causes massive turbulence in the air. As that fuel is consumed during the flight, the aircraft total weight drops to around 2/3 as much, which allows a much lower AOA, which also reduces the turbulence created and therefore the drag, and therefore the required thrust. I have never gotten any commercial pilot to confirm this, but it is certain that on long flights, the engine power must gradually get cut back and the AOA reduced, for these reasons.
This all confirms the drag number, which must be the same as the thrust for constant velocity. This 24,000 newtons of drag force can be multiplied by the velocity of 265 m/s to get a (maximum) actual power consumption of 65.1 million Watts. (at the common cruising speed of 525 mph, this is less, at around 45 million Watts.) One can see WHY they generally fly at the lower 525 mph speed, to only require about 2/3 the power and the fuel!
Depending on how precisely accurate all these numbers are, this seems to imply that the 125 million Watts of chemical energy consumed is converted into about 45 million Watts of energy that works at moving the aircraft. Regarding this part of the operation, the efficiency seems to be around 35%, which is fairly decent.
C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago