Speed Increase calculation for air over a wing.

[Angelus214]

Hi All,
This isn't really a physics course related question or anything (i barely passed secondary school science). But this seems like a place I might be able to find my answer. I'm trying to find the calculation to work out what the increase in speed is of air flowing over a planes wing but in lamens terms.

Also how the viscosity of water affects this for like hydroplanning and the such.

Thanks

 

[LURCH]

I suppose the simplest way would be to measure the difference in distances traveled. If you know the width of the wing (from the leading edge to the trailing edge), and the amount of curvature on the top of the wing, you can tell how far each air particle must travel to get from the leading edge to the trailing edge.

Now, these numbers are simplified for, well, simplicity. But, suppose the wing is 3 ft. wide. Air traveling across the bottom of the wing is going in a straight line, so it travels 3 ft. in (let's say) a 10th of a second. Because of curvature in the top of the wing, air going around the curve must travel 4 ft. in the same 10th of the second. So, if the two air masses are to travel from the leading edge of the wing to the trailing edge in the same period of time, then the air traveling over the top of the wing must travel 1 ft. farther per 10th of a second; or ten ft. per second faster.

 

[rcgldr]

I suppose the simplest way would be to measure the difference in distances traveled.

Except that the speeds vary with time as a wing passes through a volume of air, and you'd need the equivalent of a complicated airfoil program or actual measurement to determine the speeds.

There is no simple answer. Pressure and speed vary depending on where the pressure and speed are sampled relative to the aircraft. The air as high as 1/2 a wingspan above and a bit forwards of the center of an air craft is affected by a wing. The air below and behind a wing is also affected. (Note that the downforce applied by a wing onto the air eventually becomes downforce applied by the air to the Earth's surface). The range of the affect decreases as you approach the wing tips. Note that the speed of the air also involves vortices at the wing tips and near the wing surfaces.

If what you're looking for is how the air is affected by a wing, the work done would be equal to the integral sum of all the tiny masses of affected air times 1/2 their speeds^2 at the points when their pressures transition from non-ambient back to ambient. This eliminates the intermediate states where pressures are not ambient, but it's still complicated.

A propeller, which isn't as efficient as a wing, and peforms significant work on the air might be an easier case to study. A pair of links to related articles:

http://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html

http://www.grc.nasa.gov/WWW/K-12/airplane/propth.html