Problem 90 - College Physics

Question

\(\bullet\) \(\bullet\) 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) \(\mathrm{A} 70\) -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.

Step-by-Step Solution

Answer

a) 0.07-0.175 J per wingbeat; b) Human-powered flight is not feasible for extended periods due to power limitations.

Step 1: Determine Power Output

Given that the power output for the Andean giant hummingbird is between 10 to 25 watts per kilogram, convert this range to the gram scale. Since 1 kg = 1000 g, the power output per gram is 0.01 to 0.025 watts/gram.

Step 2: Calculate Bird's Total Power Output

The Andean giant hummingbird has a mass of 70 g. Therefore, the total power output is between 70 g * 0.01 W/g = 0.7 W and 70 g * 0.025 W/g = 1.75 W.

Step 3: Estimate Work Per Wingbeat

Since power is the rate at which work is done, and the hummingbird flaps its wings 10 times per second while hovering, we can calculate the work done per wingbeat as follows: Work per wingbeat = Total Power Output / Flaps per second. For the lower estimate: Work = 0.7 W / 10 flaps/s = 0.07 J. For the upper estimate: Work = 1.75 W / 10 flaps/s = 0.175 J.

Step 4: Evaluate Human Power Output for Flight

For a 70-kg athlete, the maximum power output is 1.4 kW, which equals 1400 W, but it can only be sustained for a few seconds. The steady power output is 500 W, which is significantly lower than the burst output, and even lower compared to the power per kilogram required for hummingbirds. Human-powered flight utilizing flapping wings is not feasible for extended periods due to the inability to sustain necessary power output akin to birds.

Key Concepts

Power Output

Power output measures how much energy is used over time to perform work, like maintaining flight for birds. In the Andean giant hummingbird, this converts to about 10-25 watts per kilogram of body mass. This small bird's mass is 70 grams, making its power output range 0.7 to 1.75 watts. When a bird flaps its wings, it uses this power to lift its body. Power output is crucial to keep them airborne and affects how much work they do per wingbeat.
Understanding power output helps us comprehend the energy required for various activities, and applies not only to animals but every mechanical system. It's a key concept in physics, linking energy, work, and efficiency together.

Hummingbird Flight

Hummingbirds are fascinating creatures that excel in energy efficiency and power output. Their rapid wing flapping—about 10 times per second—enables them to hover, which requires precision in using energy. The work done per wingbeat needs to correspond to the total power output.
The hummingbird's lightweight design and efficient power usage enable this impressive movement. It's a testament to evolutionary adaptations, where every flap must support the bird's body weight. Understanding hummingbird flight showcases biology's efficiency and offers insights into energy management in small, fast-moving systems.

Human-Powered Aircraft

Human-powered aircraft represent an intriguing challenge in applying human strength to mimic bird flight. While a 70-kg athlete can momentarily output 1.4 kW, sustainable power drops to 500 W. Birds like hummingbirds have specific power outputs per body mass that humans cannot replicate at length due to biological limits.
This fact limits the feasibility of human-powered flight merely by flapping wings, as maintaining necessary energy over time surpasses human capability. However, efficient design in aircrafts—drawing from principles seen in engineering and avian flight—could yield different possibilities.

Energy Conversion

Energy conversion is transforming stored energy into usable power, such as the chemical energy in muscles turning into mechanical energy for wing flapping. For hummingbirds, energy from food is used for their flights, highlighting a natural energy conversion process.
In machines and human-powered systems, similar conversions are crucial. Energy must transition effectively without excessive losses, improving performance and functionality. Mastering energy conversion can lead to more efficient technology and understanding how biological systems optimize this can inspire innovation.

Sustainable Flight

Sustainable flight emphasizes energy efficiency and minimizing long-term impacts using renewable resources or efficient energy use. Birds, like hummingbirds, naturally achieve this through efficient power and minimal waste. They are perfect models of sustainability in flight tasking. In human-engineered systems, achieving sustainable flight means leveraging new technologies and smart design to reduce energy consumption or utilize renewable energy, such as solar power. Advancements in this area lead to reduced carbon footprints and more eco-friendly transportation solutions.