All birds, independent of their size, must maintain a power...

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 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-kg athlete can maintain a power output of 1.4 kW for no more than a few seconds; the $steady$ power output of a typical athlete is only 500 W or so. Is it possible for a human-powered aircraft to fly for extended periods by flapping its wings? Explain.

Key Concepts

Wingbeat Frequency

Wingbeat frequency is the number of times an organism flaps its wings per second during flight. It directly influences calculations of work per wingbeat, because each wingbeat represents a discrete event where mechanical energy is generated. Understanding this frequency helps in deriving the amount of work done in each cycle, thereby linking the overall power output with the mechanical work performed.

Physiological Constraints

Biological systems have inherent limits regarding the power they can generate and sustain, dictated by muscle efficiency, energy metabolism, and overall body mass. This concept is crucial when comparing different species, as it explains why birds, with their high muscle efficiency and low mass, can sustain high power outputs for flight, while humans, with lower relative power outputs and heavier mass, face significant challenges in generating enough sustained power for flight using flapping mechanisms.

Work-Energy Principle

This concept refers to the physical relationship where work is defined as the energy transferred when a force is applied over a distance. In the context of flight, it is used to determine how much energy is expended during each wingbeat by relating the power output of an organism to the work done over the duration of one wingbeat.

Power

Power is the rate at which work is done or energy is expended over time. It provides a measure of how much energy is delivered per unit time and is critical for assessing whether a biological system can sustain the energy demands required for activities such as flying. In both birds and human-powered mechanisms, comparing power capabilities to the energy needed is essential for understanding flight feasibility.

Transcript

00:02 Welcome once again to a new problem.

00:05 This time we have a power output.

00:10 So we have a power output of our 10 to 25 watts and this is connected to the power of the wings of, you know, of birds that are flying.

00:27 So this is a bird.

00:29 This is a bird flying.

00:32 And so what they're saying is that on average the power output for the wings, for all birds, for all birds, happens to be 10 to 25 watts per kilogram.

00:49 You know, that's the power output.

00:51 And it's independent of the size.

00:53 There's a specific type of bird called indian giant hummingbird.

01:05 It's a hummingbird and has a scientific name.

01:09 I think it's called patagona giga.

01:16 That's just the scientific name of the bird.

01:19 It happens to have a mass of 70 grams.

01:26 Easily you can transform that to kilograms.

01:29 So one kilogram is a thousand grams.

01:32 If you multiply that, you get these two zeros cancel out.

01:36 So you have 0 .07 kilograms.

01:39 That's the mass of the of the bird.

01:42 The other piece of information that we're given is that it flaps its wings 10 times per second.

01:55 So it flaps its wings 10 times per second and and that allows it to you know to go up to fly up, you know goes up by flapping its wings 10 times times per second so the question is how much work is done each time it flaps its wing which we call the wing bit okay that's the wing bit so the 10 to 25 watts that's the range for all the birds but then if the bird weighs 0 .07 kilograms we can say that its range is going to be 10 to be 10 to joules or rather its range is going to be i need to simplify that its range is going to be 10 watts so it's going to be 10 watts times 0 .07 so that's a fraction based on the weight 225 watts times 0 .07 so what's happening here is remember we we have a an indian giant hummingbird and a typical bird any kind of bird has wing power of 10 to 25 watts so if you bring in the weight we can get the fraction of the power based on the size of the bird changing we can change this to this becomes 0 .7 watts all the way up until 1 .75 watts...

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