"Assume the Earth is a perfect sphere, and its circumference is 25,000 miles. You have a 25,000 mile long rope looped all the way around the Equator, so it is tight against the surface. Now you want to raise the rope one foot in the air, all the way around. How much more rope do you need?"

I thought about this and said, "You need a lot more rope! I don't know how much, but it will be a lot. It has to reach all the way around the Earth, only higher!"

Of course the real answer is "You only need about three more feet. To be specific, you need another 3.14159... feet."

That's all you need to raise a rope a foot in the air, all the way around the Earth.

https://en.wikipedia.org/wiki/Spherical_cow

I'd better buy an extra 3-4 feet of rope before I try this experiment.

For someone who doesn’t know, or hasn’t calculated/thought about it that is pretty astounding.

ground speed is the speed of the plane, relative to an observer on the ground, air speed is how fast the people on the plane are going relative to themselves.

Airspeed = Ground Speed - Wind Speed (wind blowing towards front of plan is positive, tailwind is negative)

That makes no sense. How can people be moving relative to themselves?

If tail wind (moving with the plane) were negative, then air speed would exceed ground speed. Intuitively, that doesn’t make sense. Air speed can only exceed ground speed if the wind is blowing in an opposing direction, i.e., the plane must travel faster against the wind to achieve the same speed relative to a ground observer.

Then, ground speed = air speed - wind speed.

Thus, GP seems to have either the sign wrong, or ground and air speed mixed up (but not both :-)

This is absolutely true, but has always infuriated me because it seems needlessly contrary as compared to the way we speak about anything else travelling in a direction as read from a compass. Does anybody know why it's the case?

I can understand that it might be just an ancient tradition originating from a particular part of the world, that we've turned into a convention, but it loses meaning when you go elsewhere.

If you go to Cape Town, a "north wind" presumably doesn't mean cold, because the area north of the city isn't colder than the city itself. This didn't matter to the people who first said "north wind" and I don't think it means much nowadays either. Just another little thing to watch out for in intercultural communication.

KIAS: Knots Indicated Airspeed (i.e. the speed at which air is hitting the pitot tube) WS: Wind speed

To calculate ground speed (as required for navigation and fuel planning) you need true airspeed (not indicated) as well as wind direction and speed.

See some discussion here: https://www.quora.com/In-aviation-what-is-the-difference-bet...

IAS is what the pilots care about while flying because it’s what matters for aerodynamics (ie stall speed)

You mean relative to the air outside the window. Relative your yourself you're always standing still.

I'll show myself out.

Ground speed = true airspeed + wind component (where you're computing a vector based on wind direction to determine what amount of it is either tail wind (+) or headwind (-).

If acceleration is zero.

(Internet, therefore pedantry).

Then came DME, distance measuring equipment. I don't know if DME ever took altitude into account or if the error resulting from altitude was just ignored, but analog DME radios would just tell distance at first and then digital versions had a groundspeed feature. At least instrument rated pilots were aware of the increasing error the closer to the NAVAID.

At some point in the ATC radar system, a controller's screen could show groundspeed. Pilots can ask ARTCC what ground speed is, although I would never ask approach or departure control such a question. This would have the same error as DME.

Today it's a value reported by GPS. I don't know if this is based on the plane's movement, or its shadow, or if there's a regulation that dictates it for aviation certified GPS. From a pilot perspective we don't distinguish between kinds of ground speed, whereas we do distinguish between kinds of airspeed: indicated, calibrated, and true. Mainly groundspeed is important navigationally to know if there's an unexpected headwind that'll lengthen enroute time and thus impact fuel management. And while there can be big enough error between estimated winds aloft and actual that this computation will affect enroute planning, I tend to only care about tens of minutes or hours, not seconds.

It's colloquially called "slant range" for this reason, and if you care about actual ground distance you have to use trigonometry.

EDIT: assuming a constant altitude flight

If you fly from point A to point B in one hour at 10,000 feet, and then fly from point A to point B in one hour at 30,000 feet, GPS will report the same speed for both flights. It does not bother to correct for the slightly longer path at 30,000 feet because that level of precision is simply not needed for commercial aviation.

GPS is inherently 3 dimensional.

The solution is a datum, a model of the Earth's surface that is used for the conversion. WGS84 is the datum used by GPS, and approximates the Earth as a specified ellipsoid. However, maps can use use different datums (data?), so there can be a discrepancy of many meters between what GPS says the location is, and what the map says the location is, and they can both be right relative to their datum.

GPS allows you to directly measure displacement of any 2 points in 3 dimensions.

You're speaking of the altitude + lat/lon instead, which is in polar coordinates.

Airspeed takes into account how fast you are going you are going AS WELL as how fast and in what direction the air around you is going.

Another example would be a person walking on a motorized walkway (like at an airport.) Person A is going WITH the direction of the walkway like someone normally would. Person B is going AGAINST the direction of the walkway but still making progress forward. How fast the person is going when observed from off the walkway is ground speed. To maintain the same ground speed, Person A needs to only walk slowly (less effort/lower airspeed) while Person B needs to be sprinting all out (more effort/high airspeed.)

* Here is an interactive example from NASA: https://www.grc.nasa.gov/www/k-12/airplane/Animation/airrel/...

You are explaining the difference between airspeed and ground speed, which can be much more substantial (e.g., ~10%, or ~%100 in extraordinary situations).