the airspeed velocity of an unladen swallow

[Chromana]

I found this on facebook. Any idea if it is true and what the variables might be? LOL I like the power of 2/7.

Oh, and on aeroplanes when they show on the TVs the stats like temperature and ETA why does it give the speed as "ground speed" rather than just speed?

[JayDee]

That formula I haven't seen, but I liked the calculation's on this site.

[Sir_Elderberry]

Oh, and on aeroplanes when they show on the TVs the stats like temperature and ETA why does it give the speed as "ground speed" rather than just speed?

Imagine swimming in a fast-moving river, swimming straight across. You might say your velocity is directly across. But someone from the shore would say that your velocity is diagonal, because from an external frame, they can take into account the water's movement.

In other words, the plane is moving at a certain speed, that's it's airspeed, but because the air is moving, it's moving differently relative to the ground. That's its ground speed.

[niteice]

My physics teacher is an avid birdwatcher.

We asked him if he knew the airspeed velocity of an unladen swallow.

He had no idea what we were talking about.

[Hawknc]

Dimensional analysis doesn't work out (and I mean REALLY doesn't work out), so I'm going to say that equation isn't right. Assuming Q is flow rate and P is pressure, there would at the very least need to be some sort of density term in there.

As for the first question, "ground speed" is the speed of the aircraft relative to the ground. They add ground to the front to differentiate it from airspeed, which is the velocity of the aircraft relative to the air.

Edit: okay, now that I'm awake, having Q_c as flow rate doesn't even make any damn sense. Maybe it's pressure, which still wouldn't work. Got a source for this so we can investigate it further?

[Interactive Civilian]

That formula I haven't seen, but I liked the calculation's on this site.

That was just about the most wonderful thing I've seen this week. Thanks for that.

It's a shame there isn't more data on the African swallows, so that one could completely answer the question.

[Steve]

A_o = speed of sound
Q = dynamic pressure (.5*rho*v²)
P = Static pressure

The formula looks very familiar, I want to say it has to do with compressible flow at subsonic levels, however I feel like there really needs to be a gamma in there somewhere, and there are too many +/- 1's

edit: the 2/7 comes from (gamma-1)/(gamma) where gamma is assumed to be 1.4 (an approximation for lower atmosphere). This is most certainly a formula relating to compressible subsonic flow.

[Steve]

This has been a splinter in my mind, as I couldn't place the formula for the life of me, so finally I looked it up, and the closest relation I could find was to that of velocity measurement through a pitot tube in compressable subsonic flow.

V=a*sqrt[5*(p_o/p₁)^{(gamma-1)/gamma}-1]

which means that (p_o/p₁) must equal (Q_c/P₀)+1

Without doing a full derivation (or really knowing for sure what the measurements in are), I justify this by saying that P₀ must be the total pressure (dynamic + static), with Q_c being the dynamic pressure.

This implies that p_o/p₁ can be translated into (q_o+p_o,s)/(q₁+p_1,s)
where q_n is dynamic and p_x,s is static pressure.

Therefore the bottom half of the equation can be summarized as P (total pressure) and the fraction split into Q and 1, as the dynamic pressure is zero due to the properties of a pitot tube.

[lindenosk]

Just thought i'd suggest another reson why airoplanes give you ground speed rather than actual speed. The earth is curved, so if you are traveling at a constand distance from the earth's surface you will be going faster than the point on the ground directly below you (just like the way the person on the outside lane in a track race has to run faster than someone on the inside lane to keep up). The reason they would show the passengers the groundspeed would be because it would be more useful for working out how long it would take until you reached your destination. I haven't done the maths, so I'm not sure if it is a relevently large difference in speed. I might be wrong, but at least i tried.

[Kabann]

Airspeed is, basically, an object's (flying contraption's) velocity relative to the air. Ground speed is its velocity relative to the ground. When there's no wind, the two are the same. When a plane is flying into a headwind, the airspeed is equal to the ground speed + the wind velocity. Since wind velocities are not exactly constant in direction or magnitude, ground speed is the best variable to use for an ETA. Or something like that.

Nasa's got a decent page giving the lowdown. http://www.grc.nasa.gov/WWW/K-12/airplane/move.html

Damn, I gots nothin' to say bout the swallows.

Edit: Doubledamn, Hawknc said something about this way up there, I should really read more carefully.

[ThinkerEmeritus]

Just thought i'd suggest another reson why airoplanes give you ground speed rather than actual speed. The earth is curved, so if you are traveling at a constand distance from the earth's surface you will be going faster than the point on the ground directly below you (just like the way the person on the outside lane in a track race has to run faster than someone on the inside lane to keep up). The reason they would show the passengers the groundspeed would be because it would be more useful for working out how long it would take until you reached your destination. I haven't done the maths, so I'm not sure if it is a relevently large difference in speed. I might be wrong, but at least i tried.

The fractional difference between air speed and ground speed due to the curvature of the earth is the height of the airplane above the ground divided by the radius of the earth. I think I would stick with the explanation using the velocity of the wind the plane is flying through.

[Steve]

Just thought i'd suggest another reson why airoplanes give you ground speed rather than actual speed. The earth is curved, so if you are traveling at a constand distance from the earth's surface you will be going faster than the point on the ground directly below you (just like the way the person on the outside lane in a track race has to run faster than someone on the inside lane to keep up). The reason they would show the passengers the groundspeed would be because it would be more useful for working out how long it would take until you reached your destination. I haven't done the maths, so I'm not sure if it is a relevently large difference in speed. I might be wrong, but at least i tried.

The fractional difference between air speed and ground speed due to the curvature of the earth is the height of the airplane above the ground divided by the radius of the earth. I think I would stick with the explanation using the velocity of the wind the plane is flying through.

This. The Earth's radius is ~6300km. The altitude a standard jet flies at is ~6-9km. Dividing one into the other yields a very very low percentage, while a head or tailwind due to the jetstream can be fairly notable. Another interesting tidbit is that due to the change in density between sealevel and altitude, it is entirely possible to be subsonic at velocities that would normally be > M1 on the ground.

[slig]

hang on, is that an african, or a european swallow?

[Dobblesworth]

hang on, is that an african, or a european swallow?

That all depends on whether our specific swallow is migratory or not.

[Steve]

hang on, is that an african, or a european swallow?

That all depends on whether our specific swallow is migratory or not.

Actually it is irrelevant, as its a general equation, you can use it to calculate either!

[Kabann]

More relevant would be is the swallow in a hurry or not?