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# Re: [Phys-l] Science Fair Project Question

Hi Mike

Try giving the authors of

http://onlinelibrary.wiley.com/doi/10.1017/S0952836904005813/abstract

an email.

Cheers Fletch

Quoting "M. Horton" <scitch@verizon.net>:

I'm trying to help a young student with the calculations for her science
fair project. She read that some of the lift generated by a hummingbird is
created by swirling votices coming off of the wings. She wants to know what
percentage of the lift comes from traditional downward acceleration of air
and what percentage comes from other effects during hovering. So, she got a
hummingbird to land on a hummingbird feeder that was on a digital scale and
got a reasonable mass (4.2 grams). She then used high speed video to
determine how long it takes for a wing to go back and forth and got a
reasonable answer (7/300 of a second). She then used a life-size photograph
to build a model of the wing beating and determined its volume to estimate
the volume of air moved by the wings. She then used the equation F=mv/t
(equation 1 on this site: http://jeb.biologists.org/content/207/8/1345.full)
from to calculate the force applied to the air. She used the middle of the
wing since it starts at 0 at the shoulder and a maximum at the tip. She
used the average velocity over the entire stroke. The answer came out about
an order of magnitude smaller than I expected. I expected for the upward
force to be at least as large, if not larger than the downward force due to
less than 100% efficiency.

Here are the calculations. Did we make a mistake?

Force down = weight of bird
W=mg = .0042 kg (9.8m/s^2) = 0.041 Newtons

Force up = force applied to air by the wings
volume of air moved = 37 mL in one back and forth stroke (measured by
building a model and using water displacement)
mass of air = (37 mL)(.0013 g/mL) = .0481 g or .0000481 kg
Distance traveled by the center of the wing (as measured on the model) is
9.6 cm or 0.096 m
One back and forth motion takes place in 7 frames of 1/300 second each on a
high speed camera or .023 seconds
So, the average velocity during the motion is .096/.023 or 4.2 m/s
So, the force generated is equal to (4.2m/s)(0.0000481 kg)/(0.023 seconds) =
.0088 Newtons

According to this calculation, only 21% of the bird's lift is provided by
forcing air down. This seems pretty small. Did we miss a decimal somewhere
or make an invalid assumption?

Mike

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