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Comment by kgermino | Hacker News Reader

This is probably a stupid question, but how is "ground speed" measured?

Is it how quickly the airplane moves past a fixed point at it's altitude, or along the earth's surface? I.e. the plane is effectively moving along the surface of a sphere, but if the plane is 30,000 ft up, then the radius of the plane's sphere is 30,000 ft greater than the radius of the "ground" so traveling at the same angular velocity will require a higher speed the higher you go.

If I'm thinking about this right, across their respective "planes," the airplane will be moving faster than it's shadow. So maybe a better way to ask this is: is ground speed the speed of the plane, or the speed of its shadow?

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The Earth has almost a 4000 mile radius; 30,000 feet is less than 6 miles. The difference between movement over ground and movement with respect to the top of a 30,000 foot pole stuck in the ground is pretty negligible.

Private pilot here. As others have pointed out, the difference is mostly negligible, but ground speed is the speed of the vertical projection of the aircraft's location on the earth's surface.

So essentially the speed at which the plane's shadow on earth travels while projecting on level ground.

Mh no, the shadow's position depends not just on the planes movement, but also on earth's rotation and trajectory.

Is that not also true of the plane's projection onto the Earth's surface?

I think "trajectory" refers to the position of earth relative to sun, which affects the shadow but of course has no effect on the projection.

I don't think so, since projection would be like taking the line between the center of the earth and the plane and finding where that intersects the surface of the earth. That doesn't depend on the trajectory of the earth through space.

Whoops, I totally ignored the trajectory aspect and was just thinking both would be affected by the rate of rotation of the earth

No. If the sun were always directly overhead this would be correct, but it isn't, so it isn't. The difference depends on the angle of the sun. In the middle of the day it's negligible, but at sunset and sunrise it becomes very large.

The radius of the earth + 30,000 ft is about 0.14% more than just the radius of the earth. Basically ignore it, unless you are programming guidance control systems.

0.14% is enough to throw the number off by 1mph so it isn’t irrelevant.

lol, ok. Make that 800 MPH then.

It’s likely less than the reading error in most speedometers including those which are used for autonomous vehicles unless you are writing a guidance system for bombs or attempting to land on another planet that’s pretty negligible.

Given that the ground speed was likely drawn from gps data, which should have velocity readings more accurate than 1mph (particularly for an airborne gps unit), the choice of calculation method for ground speed does make a difference.

That's less error than slopes and oblateness introduce, so I think it is acceptable.

That is also an interesting question. If they’re measuring speed as if the airplane were at the surface rather than at 30,000 feet, is it speed along the WSG84 earth model?

This reminds me of a math puzzle I read many years ago. It went something like this:

"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.

circumference = 2 pi r, so increasing the radius by 1 foot will increase the circumference by 2 pi feet, not pi feet.

Thank you! I had a feeling something must be off in my 50-year-old memory of this puzzle.

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

I had a science test in high school with a question that involved something to do with calculating the air pressure inside an airplane at some high altitude. I went up to to the teacher and said "is this a trick question? Airplanes are pressurized at that altitude" He looked around the room nervously and then told me to assume the airplane wasn't pressurized.

Ah yes, the notorious spherical cow!

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

A related one is to add a second section to the question asking how much extra rope would be needed to go round a tennis ball the same 1ft further out from the ball.

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

https://www.grc.nasa.gov/www/k-12/airplane/move.html

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)

I’m a bit under the weather, so my comprehension may be lacking, but I think you’ve got your signs reversed (or your head/tail terminology flipped).

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.

Wind is "named" after where it comes from. If you fly north, and the wind is a north wind, you fly slower. (This terminology is in line with what GP said.)

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 :-)

> Wind is "named" after where it comes from.

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?

Probably because it matters where the air was before. Stuff like: north wind is could, south wind is warm, west wind is humid, etc

Doesn't that very much depend on where you are though? E.g., with respect to the equator, major bodies of water and landmasses, mountain ranges, prevailing weather conditions. Also perhaps on seasons.

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.

It rather depends on where you are, but so does language. The words we use were cast locally. If you speak English some words were cast in the Ukraine, some in Germany, some in Rome, some in France, some in Britain, but the people living in those places weren't obliged to make the words globally meaningful.

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.

Can you name anything else named after where it's going, not where it comes from? I can't think of anything named like that, but I guess there must be some.

Within a marine context, current is typically given as direction to while wind and waves are direction from.

Or when you're out walking you might say that you're "heading north". Granted if you wanted to report your rough position relative to someone else you might say something like, "I'm 500m north of you."

No you are right. In case of tailwind, it is KIAS + WS whereas headwind is KIAS - WS

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

Slight, but important (if you don't want to run out of fuel) nit, indicated airspeed (KIAS) is not the same as true airspeed (KTAS).

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...

Not so slight. At airliner altitudes they can differ by 50% or so.

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

> are going relative to themselves.

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

Most people on the plane were probably sitting still.

I'll show myself out.

For a given altitude, trim, and power, the airspeed is always the same no matter the wind. Wind only affects groundspeed.

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 (-).

> For a given altitude, trim, and power, the airspeed is always the same no matter the wind.

If acceleration is zero.

(Internet, therefore pedantry).

> air speed is how fast the people on the plane are going relative to themselves

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

relative to their own location Δt ago?

Location with respect to what?

Themselves meaning the ground observer as that was the point of view GP was speaking about.

In the old days, you'd take the time between two "fixes". A fix could be a visual reference, or a NAVAID. That'd result in your shadow's speed.

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.

DME equipment explicitly does not take altitude into account.

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

The difference is about 1.1 mph (edit: out of 800 mph) at 30,000 ft compared to ground, so I don't think it matters too much.

30k ft is nothing compared to the radius of the Earth which is 21M ft. The measurement instrument has larger error sources, so the answer is it doesn't actually matter.

Hm, I think the difference is marginal because of the large radius of the Earth, at least for planes.

Ground speed is measured by GPS on modern aircraft.

Which is probably measured in it's trajectory and then recalculated as ground speed, which is sea level? Wonder if it accounts for sea levers being higher at certain parts of planet?

It's measured by repeatedly taking GPS coordinates divided by time.

GPS measurements are comprised of a 2D surface coordinate system (e.g. lat/long) and an altitude above mean sea level. So, "speed" as measured by GPS is speed along the Earth's surface.

EDIT: assuming a constant altitude flight

>> GPS measurements are comprised of a 2D surface coordinate system

GPS is inherently 3 dimensional.

> and an altitude above mean sea level

Nah, you're clearly misunderstanding how GPS works.

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.

There's some interesting stuff going on behind the scenes. GPS inherently gives you a 3-dimensional coordinate, which is useless for most applications. So the coordinate gets converted to a 2D surface coordinate (latitude/longitude) plus an altitude, which is what you generally want. However, since the Earth isn't a perfect sphere, this conversion is not well-defined.

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.

No, GPS measurements are taken as receiver distance from orbiting satellites whose orbits are calculated in a 3-D+t inertial reference frame (ECI), which is then converted to an earth-centered-earth-fixed (ECEF) coordinate. From there an end user devices can transform to desired Datum reference (a model of the Earth's surface) depending on the application. Everything about GPS is inherently 3D+t.

Guys I am talking about how commercial aircraft GPS reports speed. I understand how it gets its fix from satellites; what it reports to the human is speed along the reference horizontal datum AKA "the ground."

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.

Ground speed is what most people would think of when they think of a speed. How fast is it moving from Point A to Point B.

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/...

kgermino is asking about the difference between (1) the actual speed (relative to the Earth) at the altitude where the plane is flying and (2) the speed of the path of the airplane when it is projected onto the ground. These are extremely close but not the same (~0.15%) because the Earth is a sphere and the airplane is at a slight further distance from the center of that sphere than it's projected point on the ground.
You are explaining the difference between airspeed and ground speed, which can be much more substantial (e.g., ~10%, or ~%100 in extraordinary situations).

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