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All birds, independent of their size, must maintain a power output of \(10-25\) watts per kilogram of body mass in order to fly by flapping their wings. (a) The Andean giant hummingbird (Patagona gigas) has mass 70 \(\mathrm{g}\) and flaps its wings 10 times per second while hovering. Estimate the amount of work done by such a hummingbird in each wingbeat. (b) A \(70-\mathrm{kg}\) athlete can maintain a power output of 1.4 \(\mathrm{kW}\) for no more than a few seconds; the steady power output of a typical athlete is only 500 \(\mathrm{W}\) or so. Is it possible for a human-powered aircraft to fly for extended periods by flapping its wings? Explain.

Short Answer

Expert verified
(a) The work done per wingbeat is approximately 0.123 joules. (b) Humans cannot sustain the required power to fly by flapping wings.

Step by step solution

01

Convert Hummingbird Mass to Kilograms

The mass of the Andean giant hummingbird is given as 70 grams. First, convert this mass into kilograms by dividing by 1000. The mass in kilograms is \( 0.07 \) kg.
02

Determine Power Output Range

Birds need to maintain a power output between 10 to 25 watts per kilogram to fly. Therefore, for the hummingbird with a mass of 0.07 kg, the power output range is \( 0.07 \times 10 = 0.7 \) watts to \( 0.07 \times 25 = 1.75 \) watts.
03

Calculate Work Per Wingbeat

Given that the hummingbird flaps its wings 10 times per second, calculate the work done per wingbeat. Power is work done per time unit (work/time), so the work per wingbeat (W) is \( \frac{\text{Power}}{\text{wingbeats per second}} \). Take the average power \( 1.23 \) watts (halfway between 0.7 and 1.75 watts). Then, \( W = \frac{1.23}{10} = 0.123 \) joules per wingbeat.
04

Compare Human Power Output

A person with mass 70 kg flying would need the same power range of 10 to 25 watts per kilogram, equaling 700 to 1750 watts. Given that a typical athlete's steady power output is 500 watts, which is less than the lower required power of 700 watts, humans can't fly like birds by flapping wings for extended periods.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Work done per wingbeat
To understand the concept of work done per wingbeat by a bird, let's take a closer look at the Andean giant hummingbird. This bird performs the remarkable feat of hovering mid-air by flapping its wings quickly. Flapping wings involve doing a certain amount of work continuously.
Firstly, we need to understand that power is defined as the work done per unit of time. Therefore, the work done per wingbeat can be calculated using the equation:\[ W = \frac{P}{n} \]where:
  • \( W \) is the work done per wingbeat,
  • \( P \) is the power output required, and
  • \( n \) is the number of wingbeats per second.
For the hummingbird, with a power range of about 10-25 watts per kilogram, and with the bird weighing 0.07 kg, its average power output is found to be approximately 1.23 watts. Since it flaps its wings at 10 times per second, the work done in one wingbeat is about 0.123 joules. This work is the energy expended in each wingbeat in order to maintain flight.
Understanding this helps elucidate how birds manage energy distribution and highlights the efficiency with which they sustain flight. Each wingbeat represents a careful balance of energy that keeps the bird aloft.
Wing flapping frequency
The frequency of wing flapping, or how fast a bird flaps its wings, is another vital aspect of avian flight. For many birds, the ability to hover or maneuver swiftly in the air depends significantly on their wingbeat frequency. For example, the Andean giant hummingbird flaps its wings at an impressive rate of 10 times per second.
Frequency can be directly linked to the power output and energy efficiency of birds. Higher frequencies often correlate with higher energy needs, but they also provide greater control and stability in the air.
Pinpointing the wing flapping frequency not only offers insights into the bird’s energy expenditure but also clues about its evolutionary adaptations. Smaller birds like hummingbirds require rapid wingbeats to maintain their hover and agile flight, allowing them to feed on nectar without losing balance or altitude.
Thus, wing flapping frequency is a fascinating and essential element in understanding the biomechanics of bird flight. It showcases how different species adapt their flight patterns to navigate their environments efficiently.
Human-powered flight feasibility
Exploring human-powered flight unveils a formidable challenge. Unlike birds, humans are not naturally equipped for flight and hence depend on machines to soar through the skies. Human-powered flight, particularly by flapping wings, demands a significant power output, which poses a major hurdle.
A bird like the hummingbird requires about 10-25 watts per kilogram to maintain flight. If we apply this to a human with a mass of 70 kg, the required power output climbs to a staggering 700 to 1750 watts. However, even a well-trained athlete can only sustain a power output of about 500 watts for a prolonged period.
Given this discrepancy, human-powered flight using solely flapping is impractical for extended durations. Current human engineering attempts aim to mimic the motion of birds, but the sheer power requirement makes it daunting.
While innovations and technology might bridge this gap, human-powered flight remains predominantly experimental and limited to short durations. This explodes the ingenuity behind natural flyers and underscores the energy efficiency present in nature's designs.

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