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Among two animals and nine machines:

- In terms of mass⋅distance/energy, the most efficient animal was 2-8x more efficient than the most efficient machine. All entries fell within two orders of magnitude.
- In terms of distance/energy, the most efficient animal was 3,000-20,000x more efficient than the most efficient machine. Both animals were more efficient than all machines. Entries ranged over more than eight orders of magnitude.

This case study is part of research that intends to compare the performance of human engineers and natural evolution on problems where both have developed solutions. The goal of this is to inform our expectations about the performance of future artificial intelligence relative to biological minds.

We consider two metrics:

- Distance per energy used (meters / kilojoule).
- Mass times distance per energy used (kilograms⋅meters / joule).

These operationalize the problem of flight into two more specific problems. There are many other aspects of flight performance that one could measure, such as energy efficiency of acceleration in a straight line, turning, hovering, vertical acceleration, vertical distance, landing, taking off, time flying per energy, and our same measures with fewer or further restrictions on acceptable entries. For instance, we might look at the problem of flying with flapping wings, or without the restriction that the solutions we consider are heavier than air and self powered.

We did not require that the flight of an entry be constantly powered. Solutions that spend some time gliding as well as some time using powered flight were allowed. Both albatrosses and butterflies use air currents to fly further.^{1} The energy gains from these techniques were not included in the final score, and entries were not penalized for spending a larger fraction of time gliding. It seems likely that paramotor pilots use similar techniques, since paramotors are well suited to gliding (being paragliders with propeller motors strapped to the backs of their pilots). Our energy efficiency estimate for the paramotor came from a record breaking distance flight in which the quantity of available fuel was limited, and so it is likely that some gliding was used to increase the distance traveled as much as possible.

When multiple input values could have been used, such as the takeoff weight and the landing weight, or different estimates for the energetic costs of different kinds of flight for the Monarch butterfly, we generally calculated a high and a low estimate, taking the most optimistic and pessimistic inputs respectively. In all cases, the resulting best and worst estimates differed by less than a factor of ten.

We selected case studies informally, according to judgments about possible high energy efficiencies, and with an eye to exploring a wider range of case studies.

We started by looking at the Boeing 747-400 plane, the Wandering Albatross, and the Monarch Butterfly. We chose the animals for both being known for their abilities to fly long distances, and for both having fairly different body plans.

All three scored surprisingly similarly on distance times weight per energy (details below). This prompted us to look for engineered solutions that were optimized for fuel efficiency. To that end, we looked at paramotors and record breaking flying machines. In the latter category, we found the MacCready Gassomer Albatross, which was a human powered flying device that crossed the English Channel, and the Spirit of Butts’ Farm, which was a model airplane that crossed the Atlantic on one gallon of gasoline.

For reasons that are now obscure, we also included a number of different planes.

We would have liked to include microdrones, since they are different enough from other entries that they might be unusually efficient. However we did not find data on them.

These are the full articles calculating the efficiencies of different flying machines and animals:

- Wright Flyer
- Wright model B
- Vickers Vimy
- North American P-51 Mustang
- Paramotors
- The Spirit of Butt’s Farm
- Monarch butterfly
- MacCready Gossamer Albatross
- Airbus A-320
- Boeing 747-400
- Wandering albatross

Results are available in Table 1 below, and in this spreadsheet. Figures 1 and 2 below illustrate the equivalent questions of how far each of these animals and machines can fly, given either the same amount of fuel energy, or fuel energy proportional to their body mass.

Name | natural or human-engineered | kg⋅m/J | m/kJ | ||||||
---|---|---|---|---|---|---|---|---|---|

worst | mean | best | worst | mean | best | ||||

Monarch Butterfly | natural | 0.065 | 0.21 | 0.36 | 100000 | 350000 | 600000 | ||

Wandering Albatross | natural | 1.4 | 2.2 | 3 | 240 | 240 | 240 | ||

The Spirit of Butt’s Farm | human-engineered | 0.086 | 0.12 | 0.16 | 32 | 32 | 32 | ||

MacGready Gossamer Albatross | human-engineered | 0.19 | 0.32 | 0.46 | 2 | 3.3 | 4.6 | ||

Paramotor | human-engineered | 0.058 | 0.079 | 0.1 | 0.36 | 0.36 | 0.36 | ||

Wright model B | human-engineered | 0.036 | 0.078 | 0.12 | 0.1 | 0.16 | 0.21 | ||

Wright Flyer | human-engineered | 0.022 | 0.042 | 0.061 | 0.080 | 0.13 | 0.18 | ||

North American P-51 Mustang | human-engineered | 0.25 | 0.38 | 0.5 | 0.073 | 0.083 | 0.092 | ||

Vickers Vimy | human-engineered | 0.081 | 0.17 | 0.25 | 0.025 | 0.038 | 0.05 | ||

Airbus A320 | human-engineered | 0.33 | 0.47 | 0.61 | 0.0078 | 0.0078 | 0.0078 | ||

Boeing 747-400 | human-engineered | 0.39 | 0.61 | 0.83 | 0.0021 | 0.0021 | 0.0021 |

**Table 1: Energy efficiency of flight for a variety of natural and man-made flying entities.**

On mass⋅distance/energy, evolution beats engineers, but they are relatively evenly matched: the albatross (1.4-3.0 kg.m/J) and the Boeing 747-400 (0.39-0.83 kg.m/J) are the best in the natural and engineered classes respectively. Thus the best natural solution we found was roughly 2x-8x more efficient than the human-engineered one.^{2} We found several flying machines more efficient on this metric than the monarch butterfly.

On distance/energy, the natural solutions have a much larger advantage. Both are better than all man-made solutions we considered. The best natural and engineered solutions respectively are the monarch butterfly (100,000-600,000 m/kJ) and the Spirit of Butts’ Farm (32 m/kJ), for roughly a 3,000x to 20,000x advantage to natural evolution.

We take this as weak evidence about the best possible distance/energy and distance.mass/energy measures achievable by human engineers or natural evolution. One reason for this is that this is a small set of examples. Another is that none of these animals or machines were optimized purely for either of these flight metrics—they all had other constraints or more complex goals. For instance, the paramotor was competing for a record in which a paramotor had to be used, specifically. For the longest human flight, the flying machine had to be capable of carrying a human. The albatross’ body has many functions. Thus it seems plausible that either engineers or natural evolution could reach solutions far better on our metrics than those recorded here if they were directly aiming for those metrics.

The measurements for distance.mass/energy covered a much narrower band than those for distance/energy: a factor of under two orders of magnitude versus around eight. Comparing best scores between evolution and engineering, the gap is also much smaller, as noted above (a factor of less than one order of magnitude versus three orders of magnitude). This seems like some evidence that that band of performance is natural for some reason, and so that more pointed efforts to do better on these metrics would not readily lead to much higher performance.

*Primary author: Ronny Fernandez*

According to very rough estimates, the monarch butterfly:

- can fly around 100,000-600,000 m/kJ
- and move mass at around 0.065-0.36 kg⋅m/J

The **Monarch Butterfly **is a butterfly known for its migration across North America.^{1}

The average mass of a monarch butterfly prior to its annual migration has been estimated to be 600mg^{2}

The following table gives some very rough estimates of energy expenditures, speeds and distances for several modes of flight, based on confusing information from a small number of papers (see footnotes for details).

Activity | Description | Energy expenditure per mass ( J/g⋅hr) | Energy expenditure for 600mg butterfly (J/s) | Speed (m/s) | distance/energy (m/J) |

Soaring/gliding | Unpowered flight, including gradual decline and ascent via air currents | 8-33^{3} | ~0.0014 – 0.0056^{4} | Very roughly 2.5-3.6 on average^{5} | 446- 2571^{6} |

Cruising | Low speed powered flight | Very roughly 209^{7} | 0.035^{8} | Maximum: >5^{9} | Maximum: >143^{10} |

Sustained flapping | High speed powered flight | Very roughly 837^{11} | ~0.14^{12} | Maximum: >13.9^{13} | Maximum: >99^{14} |

Soaring is estimated to be potentially very energy efficient (see Table 1), since it mostly makes use of air currents for energy. It seems likely that at least a small amount of powered flight is needed for getting into the air, however monarch butterflies can apparently fly for hundreds of kilometers in a day^{15}, so supposing that they don’t stop many times in a day, taking off seems likely a negligible part of the flight.^{16}

This would require ideal wind conditions, and our impression is that in practice, butterflies do not often fly very long distances without using at least a small amount of powered flight.^{17}

There is stronger evidence that monarch butterflies can realistically soar around 85% of the time, from Gibo & Pallett, who report their observations of butterflies under relatively good conditions.^{18} So as a high estimate, we use this fraction of the time for soaring, and suppose that the remaining time is the relatively energy-efficient cruising, and take the optimistic end of all ranges. This gives us:

One second of flight = 0.15 seconds cruising + 0.85 seconds soaring

________________= 0.15s * 5 m/s cruising + 0.85s * 3.6m/s soaring

________________= 0.75m cruising + 3.06m soaring

________________= 3.81m total

This also gives us:

= 0.75m / 143 m/J cruising + 3.06m / 2571 m/J soaring

= 0.0064 J total

Thus we have:

distance/energy = 3.81m/0.0064 J = 595 m/J

For a low estimate of efficiency, we will assume that all of the powered flight is the most energetic flight, that powered flight is required half the time on average, and that the energy cost of gliding is twice that of resting. This gives us:

Energy efficiency = (50% * soaring distance + 50% * powered distance) / (50% * soaring energy + 50% * powered energy)

= (50% * soaring distance/time + 50% * powered distance/time) / (50% * soaring energy/time + 50% * powered energy/time)

= (0.5 * 2.5m/s + 0.5 * 13.9m/s) / (0.5 * (0.0056 * 2) J/s + 0.5 * 0.14 J/s)

= 108 m/J

Thus we have, very roughly:

distance/energy = 100,000-600,000 m/kJ

For concreteness, a kJ is the energy in around a quarter of a raspberry. ^{19}

As noted earlier, the average mass of a monarch butterfly prior to its annual migration has been estimated to be 600mg^{20}

Thus we have:

mass*distance/energy = 0.0006 kg * 108 — 0.0006 kg * 595 m/J

= 0.065 — 0.36 kg⋅m/J

*Primary author: Ronny Fernandez*

The wandering albatross:

- can fly around 240m/kJ
- and move mass at around 1.4—3.0kg.m/J

The wandering albatross is a very large seabird that flies long distances on wings with the largest span of any bird.^{1}

In a study of wandering albatrosses flying in various wind speeds and directions, average ground speed was 12 m/s, though the fastest ground speed measured appears to be around 24m/s, ^{2} We use average ground speed for this estimate because we only have data on average energy expenditure, though it is likely that higher ground speeds involve more energy efficient flight, since albatross flight speed is dependent on wind and it appears that higher speeds are substantially due to favorable winds.^{3}

One study produced an estimate that when flying, albatrosses use 2.35 times their basal metabolic rate^{4} which same paper implies is around 1,833 kJ/bird.day.^{5}

That gives us a flight cost for flying of 0.050 kJ/second.^{6}

This gives us a distance per energy score of:

distance/energy

= 12 m/s / 0.050 kJ/s

= 240m/kJ

Albatrosses weigh 5.9 to 12.7 kg.^{7}

Thus we can estimate:

mass.distance/Joule

= 5.9kg * 240 m/kJ to 12.7kg*240 m/kJ

= 1.4—3.0kg.m/J

*Primary author: Ronny Fernandez*

We estimate that a record-breaking two-person paramotor:

- covered around = 0.36 m/kJ
- and moved mass at around 0.058 – 0.10 kg⋅m/J

Paramotors are powered parachutes that allow the operator to steer.^{1}

The Fédération Aéronautique Internationale (FAI) maintains records for a number of classes of paramotor contest. We look at subclass RPF2T—(Paramotors : Paraglider Control / Foot-launched / Flown with two persons / Thermal Engine)—which is appears to be the most recent paramotor record for ‘Distance in a straight line with limited fuel’.^{2}

The record distance was 123.18 km.^{3} The FAI rules state that no more than 7.5 kg of fuel may be used.^{4} We will assume that in the process of breaking this record, all of the available fuel was used. We will also assume that regular gasoline was used. Gasoline has an energy density of 45 MJ/kg.^{5}

Distance per energy = 123.18 km / (7.5 kg * 45 MJ/kg)

= 0.36 m/kJ

The weight of an entire paramotoring apparatus appears to be the weights of the passengers plus motor plus wing plus clothing and incidentals, based on forum posts.^{6} These posts put clothing and incidentals at around 8kg, but are estimates for single person flying, whereas this record was a two person flight. We guess that two people need around 1.5x as much additional weight, for 12kg.

Wikipedia says that the weight of a paramotor varies from 18kg to 34 kg.^{7} However it is unclear whether this means the motor itself, or all of the equipment involved.

The glider used appears to be MagMax brand, a typical example of which weighs around 8kg, though this may have been different in 2013, or they may have used a different specific glider.^{8} To account for this uncertainty, we shall add the glider weight to the high estimate, and so estimate the weight of the glider and motor together at 18-42kg.

We will assume that the apparently male pilots weighed between 65 and 115 kgs each, based on normal male weights^{9}.

Thus we have:

weight = motor + wing + people + clothing and incidentals

weight (low estimate) = 18 + 65*2 + 12 = 160kg

weight (high estimate) = 42 + 115*2 + 12 = 284kg

High efficiency estimate:

284kg * 0.36 m/kJ = 0.10 kg⋅m/J

Low efficiency estimate:

160kg * 0.36 m/kJ = .058 kg⋅m/J

This gives us a range of 0.058 – 0.10 kg⋅m/J

*Primary author: Ronny Fernandez*

The Spirit of Butt's Farm:

- covered around 31.67 m/kJ
- and moved mass at around 0.16 – 0.086 kg.m/J

The Spirit of Butt’s Farm:

- covered around 31.67 m/kJ
- and moved mass at around 0.16 – 0.086 kg⋅m/J

The Spirit of Butt’s Farm was a record setting model airplane that crossed the Atlantic on one gallon of fuel.^{1} Fully fueled it weighed 4.987 kg, dry it weighed 2.705 kg.^{2}

The record setting flight used 117.1 fluid ounces of fuel.^{3} The straight line distance of the flight was 3,028.1 km.^{4} It was powered by 88% Coleman lantern fuel, mixed with lubricant.^{5} Coleman fuel is based on naphtha ^{6}, so we can use the energy density of naphtha—31.4 MJ/L^{7}—as a rough guide to its energy content, though naphtha appears to vary in its content, and it is unclear whether Coleman fuel consists entirely of naphtha.

From all this, we have:

Distance per energy = 3,028.1 km / (117.1 fl oz * 0.88 * 31.4 MJ/L)

= 31.67 m/kJ

For weight times distance per energy we will calculate a best and a worst score. To calculate the best score we will use the fully fueled weight, and to calculate the worst score we will use the dry weight. All other values are the same in both calculations.

Best score:

Distance*mass/energy = 4.987 kg * 31.67 m/kJ

= 0.16 kg⋅m/J

(4.987 kg * 3,028.1km) / (117.1 US fluid ounces * 31.4MJ/litre) = 0.1389 kg*m/j

Worst score:

Distance*mass/energy = 2.705 kg * 31.67 m/kJ

= .086 kg⋅m/J

*Primary author: Ronny Fernandez*

Photo by Ronan Coyne, licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license, unaltered.

]]>The MacCready *Gossamer Albatross*:

- covered around 2.0—4.6 m/kJ
- and moved mass at around 0.1882 —0.4577 kg⋅m/J

The **MacCready Gossamer Albatross **was a human-powered flying machine that crossed the English Channel in 1979.

We do not know the pilot’s average power output, however:

- Wikipedia claims at least 300W was required to fly the craft
^{4} - Chung 2006, an engineering textbook, claims that the driver, a cyclist, could produce around 200W of power.
^{5} - Our impression is that 200W is a common power output over houres for amateur cycling. For instance, one of our researchers is able to achieve this for three hours.
^{6}

The best documented human cycling wattage that we could easily find is from professional rider Giulio Ciccone who won a stage of the Tour de France, then uploaded power data to the fitness tracking site Strava.^{7} His performance suggests around 318W is a reasonable upper bound, supposing that the pilot of the *Gossamer Albatross* would have had lower performance.^{8}

To find the energy used by the cyclist, we divided power output by typical efficiency for a human on a bicycle, which according to Wikipedia ranges from .18 to .26.^{9}

For distance per energy this gives us a highest measure of:

35.7 km / ((200W * (2 hours + 49 minutes))/0.26) = 4,577 m/MJ

And a lowest measure of:

35.7 km / ((318W * (2 hours + 49 minutes))/0.18) = 1,993 m/MJ

For weight times distance per energy this gives us a highest measure of:

(100kg * 35.7 km) / ((200W * (2 hours + 49 minutes))/0.26) = 0.4577 kg⋅m/j

And a lowest measure of:

(100kg * 35.7 km) / ((318W * (2 hours + 49 minutes))/0.17) = 0.1882 kg⋅m/j

*Primary author: Ronny Fernandez*

The Boeing 747-400:

- covers around 0.0021m/kJ.
- and moves mass at around 0.39 – 0.83 kg.m/J

The *Boeing 747-400 *is a 1987 passenger plane.^{1}

The plane uses 10.77 kg/km of fuel on a medium haul flight.^{2} We do not know what type of fuel it uses, but typical values for aviation fuel are around 44MJ/kg.^{3} Thus to fly a kilometer, the plane needs 10.77 kg of fuel, which is 10.77 x 44 MJ = 474 MJ of fuel. This gives us 0.0021m/kJ.

According to Wikipedia, the 747’s ‘operating empty weight’ is 183,523 kg and its ‘maximum take-off weight’ is 396,893 kg.^{4} We use the range 183,523 kg—396,893 kg since we do not know at what weight in that range the relevant speeds were measured.

We have:

- Distance per kilojoule: 0.0021m/kJ
- Mass: 183,523 kg—396,893 kg

This gives us a range of 0.39 – 0.83 kg.m/J

*Primary author: Ronny Fernandez*

The Airbus A320:

- covers around 0.0078 m/kJ
- and moves mass at around 0.33 – 0.61 kg.m/J

The *Airbus A320 *is a 1987 passenger plane.^{1}

The plane uses 2.91 kg of fuel per km on a medium haul flight.^{2} We do not know what type of fuel it uses, but typical values for aviation fuel are around 44MJ/kg.^{3} Thus to fly a kilometer, the plane needs 2.91kg of fuel, which is 2.91 x 44 MJ = 128MJ of fuel. This gives us 0.0078 m/kJ

According to modernairliners.com, the A320’s ‘operating empty weight’ is 42,600 kg and its ‘maximum take-off weight’ is 78,000 kg.^{4} We use the range 42,600—78,000 kg, since we do not know at what weight in that range the relevant speeds were measured.

We have:

- Distance per kilojoule: 0.0078 m/kJ
- Mass: 42,600—78,000 kg

This gives us a range of 0.33 – 0.61 kg.m/J

*Primary author: Ronny Fernandez*

The North American P-51 Mustang:

- flew around 0.073—0.092 m/kJ
- and moved mass at around 0.25 – 0.50 kg.m/J

The *North American P-51 Mustang *was a 1940 US WWII fighter and fighter-bomber.^{1}

According to Wikipedia^{2}:

**Empty weight:**7,635 lb (3,465 kg)**Gross weight:**9,200 lb (4,175 kg)**Max takeoff weight:**12,100 lb (5,488 kg)

We use the range 3,465—5,488 kg, since we do not know at what weight in that range the relevant speeds were measured.

Wikipedia tells us that cruising speed was 362 mph (162 m/s)^{3}

A table from *WWII Aircraft Performance* gives combinations of flight parameters apparently for a version of the P-51, however it has no title or description, so we cannot be confident. ^{4} We extracted some data from it here. This data suggests the best combination of parameters gives a fuel economy of 6.7 miles/gallon (10.8km)

We don’t know what fuel was used, but fuel energy density seems likely to be between 31—39 MJ/L = 117—148 MJ/gallon.^{5}

Thus the plane flew about 10.8km on 117—148 MJ of fuel, for 0.073—0.092 m/kJ

We have:

- Distance per kilojoule: 0.073—0.092 m/kJ
- Mass: 3,465—5,488 kg

This gives us a range of 0.25 – 0.50 kg.m/J

*Primary author: Ronny Fernandez*

The Vickers Vimy:

- flew around 0.025—0.050 m/kJ
- and moved mass at around 0.081 – 0.25 kg.m/J

The *Vickers Vimy *was a 1917 British WWI bomber.^{1} It was used in the first non-stop transatlantic flight.

According to Wikipedia^{2}:

**Empty weight:**7,104 lb (3,222 kg)**Max takeoff weight:**10,884 lb (4,937 kg)

We use the range 3,222—4,937 kg, since we do not know at what weight in that range the relevant speeds were measured.

We also have:

**Power:**360 horsepower = 270 kW^{3}**Efficiency of use of energy from fuel:**we did not find data on this, so use an estimate of 15%-30%, based on what we know about the energy efficiency of the Wright Flyer.

From these we can calculate:

Energy use per second

= power of engine x 1/efficiency in converting energy to engine power

= 270kJ/s / .15—270kJ/s / .30

= 900—1800 kJ/s

Wikipedia gives us:

100 mph (160 km/h, 87 kn)**Maximum speed:**^{4}

Note that the figures for power do not obviously correspond to the highest measured speed. This is a rough estimate.

We now have (from above):

- speed = 100 miles/h = 44.7m/s
- energy use = 900—1800 kJ/s

Thus, on average each second the plane flies 44.7 m and uses 900—1800 kJ, for 0.025—0.050 m/kJ.

We have:

- Distance per kilojoule: 0.025—0.050 m/kJ
- Mass: 3,222—4,937 kg

This gives us a range of 0.081 – 0.25 kg.m/J

*Primary author: Ronny Fernandez*