Definition of ground speed
 

Here's a question I never thought I would ever ask:
Can anyone point me to the definition of ground speed?

You probably won't believe it (I still don't do), but I just discussed two different definitions of ground speed. :ugh::{

Here they are:
Ground speed is:
(a) the speed over ground
(b) the horizontal component of the absolute velocity.

The difference is that at altitude, (a) will be smaller than (b) .

Suppose you fly at FL320 (~10 km) at a horizontal speed of 700 Kts (def (b)).
If the local radius of the earth is 6371 km, you fly a curve at 6381 km from the earth's center. The speed over ground in that case is 700 * 6371/6381 = 698.9 Kts (def. (a)). A whopping difference of 1.1 Kts :8

So why bother? Well, for standardization / certification this very theoretical difference matters. If you need to validate a ground speed accuracy in the order of 3 m/s you can't afford to loose too much of it in the definition.

Any pointers to an official definition are greatly appreciated.

Ground speed is the speed of an aircraft relative to the ground. It is the sum of the aircraft's true airspeed and the current wind and weather conditions; a headwind subtracts from the ground speed, while a tailwind adds to it. Winds at other angles to the heading will have components of either headwind or tailwind as well as a crosswind component.An airspeed indicator can only indicate the aircraft's movement within an air mass. The air mass as a whole may be moving over the ground due to wind, and therefore some additional means to provide position over the ground is required. This might be through navigation using landmarks, radio aided position location, inertial navigation system, or GPS. When more advanced technology is unavailable, an E6B flight computer is often used to calculate groundspeed

I must say you are an interesting fella:confused::bored:

the wind side:E

what if you have a pencil failure?:}

Bumpy

I suspect ATC is well aware of now to work out his (a)

Do you have an answer to his question though?

I don't.

JF

Whenever I've used or calculated ground speed in issues related to aircraft performance or particularly calibration of pitot-static system pressure error corrections, the definition used has always been horizontal component of absolute speed (although I don't recall any document where that is explicitly stated).

G

I would think that they are equivalent, as the velocity parallelogram gives that vector compnent naturally and it is likewise useful for flight planning :)
:O

Well, it's not this one, as absolute speed does not exist. Speed is the scalar part of velocity which is a relative value. You cannot express speed without specifying speed relative to what.

People will try and say "Relative to a fixed point in space"- this ALSO does not exist.

perhaps they mean the absolute value of displacement/time forexample you can run round a circle the equivalent of five miles in 1 hour or a straight line in the first case the velocity vector changes continously in the second case it will the vector and scalar values would be equivalent...but the absolute value of diplacement/time would still be 5 mph...although funny enough the FARs have no definition for GS :confused::confused::confused:

Wizofoz:
Absolutely right Wizofoz. I was trying to avoid being too technical. Now I was too fuzzy I guess.
The reference frame I meant is Earth Centered Earth Fixed, so speed relative to the (non rotating) earth.

Rephrased:
Groundspeed is the absolute value of
(a) the horizontal part of the ECEF velocity
(b) of the differential of the aircraft's position projected on the earth's surface (modeled by the WGS84 ellipsoid)

Feel free to shoot holes in the new definitions.

Or see it like this:
Assume the earth is a perfect sphere with a circumference of 40.000 km. When flying halfway around this earth at 10 km high you travel 20.000+PI*10 = 20031.415... km through the air, or 20.000 km measured on the surface. If you manage to do this in 20 hours, what is the average ground speed?
Definition (a): 20.031 /20 = 1001.57 km/h
Definition (b): 20.000 /20 = 1000 km/h

Genghis, I use that same approach in my aircraft performance related simulations. In the context of pitot-static corrections it perfectly makes sense to use velocity, since that is what drives the physics of the system.
In addition to that, the accuracy of the pitot-static system is such that the 0.16% difference between the two definitions (at 10km height) is probably within the measurement noise / tolerance, so it does not really matter how you define the ground speed in such a case.

For assessing the accuracy of GPS reported ground speed, the definition suddenly is important. Not in practical terms, because I am sure few people will care about the 0.16% difference, but for standardization/ certification ambiguity is a big thing.

Thanks for the feedback so far.

ATCast,

what a brilliant conundrum!

Let me restate it in geometric terms.

Suppose the earth is a sphere, radius X. Suppose the aircraft is flying at constant altitude Y (in the same units). Then the aircraft trajectory is describing a circle of radius (X+Y). Let us suppose the aircraft is flying unaccelerated in Earth-fixed coordinates (1g force in the z-direction, no force in x or y, no rotational component in any axis). We may measure its progress by the constant angular velocity A of the CofG relative to the center of the earth (compatible units).

If the ground speed is the speed of the aircraft's projection on the ground, in Earth-axis coordinates, then the ground speed is (A x X). If it is the absolute speed, then it is (A x (X+Y)).

If it is the "horizontal projection of absolute speed", then we need to take into account the projection of the horizon on the aircraft's trajectory. The horizon is below the aircraft's trajectory by an angle Alpha, so the component of the aircraft's absolute velocity (in Earth-axis coordinates) on this would be (A x (X+Y)) x cosine(Alpha). Cosine(Alpha) appears from simple geometry to be X /(X+Y), so this yields (A x X) as ground speed.

This seems to me to be counterintuitive. I would prefer to take ground speed as the rate of change of the distance travelled by the aircraft in Earth-axis coordinates, which is (A x (X+Y)). This is also the "true airspeed corrected for wind" which is mentioned by some commentators.

I have a query out to see what reasons there might be for choosing the one over the other.

PBL

Ground speed
 

As a pilot, for all the years of my career, I thought it was my speed over the ground to assist in the navigation of the aircraft.

Tmb

What are these equation you guys are using...reference to what?...the ground???:confused:

gravity is not, an issue ....:confused::confused::confused:



:suspect:

Calibrated airspeed means the indicated airspeed of an aircraft, corrected for position and instrument error. Calibrated airspeed is equal to true airspeed in standard atmosphere at sea level.

Equivalent airspeed means the calibrated airspeed of an aircraft corrected for adiabatic compressible flow for the particular altitude. Equivalent airspeed is equal to calibrated airspeed in standard atmosphere at sea level.

Mach number means the ratio of true airspeed to the speed of sound.

Person means an individual, firm, partnership, corporation, company, association, joint-stock association, or governmental entity. It includes a trustee, receiver, assignee, or similar representative of any of them.:}


True airspeed means the airspeed of an aircraft relative to undisturbed air. True airspeed is equal to equivalent airspeed multiplied by (p0/p)1/2


Lester:E

Lastly, I should remind some that kinematics is the study of the the motions of a body irrespective of applied forces and applies to displacement, velocity and acceleration...in a linear and angular sense:8

PA,

Emphasis added.

Do you mean uncorrected? The calibration law for CAS does take account of compressibility. EAS doesn't - it has nothing to do with compressibility. The Bernoulli equation for dynamic pressure, q = ½ ρ V², is an incompressible solution to Euler's equation. This is still true even if ρ V² is swapped for γ p M².

Calibration law is in NACA Report 837 (Aiken, W. 1946. Langley.)

Selfin, those are the FAA definitions based on such items as the NACA reports they are most certainly correct:}

FAR part 1 is defining EAS as CAS after having been corrected for adiabatic compressibility:)

I know what you're talking about...true! but I'm not getting into Fluid Mechanics, continuity and such right now...not enough sleep... and no patience for copying and pasting integrals:8

As the only purpose for ground speed is for navigation in relation to the Earth's surface, ground speed must surely by speed over that surface. If the extra "circumferal" distance you are flying is significant enough to reduce that speed, then that correction must also be taken into account when navigating.

Lets say you are "flying" in a space shuttle at an altitude of 320 km - you work out the horizontal component of your velocity (in relation to the Earth's centre) as a groundspeed and then plot that distance over an hour across a surface map. Will you be anywhere near over the position you have plotted? Then it's not groundspeed, is it?

What a lot of twaddle! Checkboard (and, believe it or not, 'bumpyflight's' first sentence) are absolutely correct. IF you use the term 'ground speed' it is speed relative to the ground, and nothing else, and unless you have a plateau up at 'X+Y' altitude, that will do. If you wish to relate to the velocity along a tangent to the earth at any particular radius you'll need another word! How about we invent one if you have to? 'Tangspeed'? Orbital velocity? Answers on a postcard (positioned in an earth frame continuum) of course. Not forgetting the stamp to be positioned relative to the postcard frame.

As to how you can consider any form of PEC calibration using 'groundspeed' when you have no idea of the motion of the containing airmass.............................. .you'll need to explain.

PBL's elegant maths conclusively prove that the 'angle' subtended by the horizon has nothing to do with Tangspeed.':)

Normal vectors cancel:)

you are not subtending an arc about a fixed point

one aircraft would simply have to begin his descent earlier/ or much much steeper, to reach the same place:}

:\

Reading this stuff gives me a headache! You guys have WAY too much spare time!

Ground speed. The speed of an aircraft relative to the surface of the earth.

This is from ICAO doc 9426 AIR TRAFFIC SERVICES PLANNING MANUAL PART V TERMS AND REFERENCES.

I think it's pretty clear isn't it?

Unfortunately no, it isn't. If you look at the way what we call SOG is calculated (and some details have been posted above) you will realise that strictly it is not what the ICAO document describes, however, the difference is irrelevant for air traffic services (the document's subject matter).

Kudos to the OP for posting what must be the most interesting question I've read here so far this year. Although aware of it, I'd never consciously thought about it.

Folks,
What we have here is a clash of "Airplane Navigation of Dummies" and something a bit nearer to an engineering solution.

For the average pilot, the simplest definition is all that is required, a bit like the simplistic diagrams we use to illustrate the "forces" acting on an aircraft in cruise, climb and descent ( thrust, drag, lift and the CAA) --- but for an engineer it is not "that simple".

Try arguing with an engineer for an airframe or (particularly) an engine manufacturer about in-flight performance analysis versus contract guarantees --- right down to latitude and Coriolis effect --- that's really getting into the fine print.

Tootle pip!!

Another general situation that may affect the answer is whether the "distance" an aircraft travels **according to its flight plan** is dependent on the altitude of the aircraft. Consider 2 aircraft on long range great circle tracks, zero wind, one at 3000 feet and one at FL450, both to the same destination. Will the flight plan distances be different?

Lead Sled, the forces are in fact, MONEY, lift drag and thrust, the first one being the most critical!

ATCast asked for an official definition of groundspeed. Genghis the Engineer thought it is horizontal component of absolute velocity but could not pin a reference.

Pugilistic Animus thinks the two definitions are equivalent. Wizofoz thinks it is not the "horizontal component of absolute velocity" because "absolute velocity" is not defined, although I understood perfectly well what ATCast was asking, as did Genghis.

Tmbstory thinks it is "speed over the ground", and Checkboard "speed over that surface", so FEHoppy "speed relative to the surface of the earth". None of these contributors seem to have picked up that their "definitions" are ambiguous in just the way ATCast explained.

BOAC sees the difference, I think, but considers the discussion "twaddle".

I did what ATCast wanted. I looked it up in Kayton and Fried, Avionics Navigation Systems, 2nd edition, Wiley-Interscience 1997, otherwise known as The Book, when I had the chance.

Ground speed is the horizontal (i.e. tangential to the reference ellipsoid) component of the resultant vector of the air-velocity vector with the wind velocity vector (Figure 2.4, p30, notation Vg). Genghis is right.

As for PA, we may take it he doesn't build inertial nav instruments for a living. Serious nav takes altitude into account, for reasons which I hope I indicated in my earlier post.

PBL

"Ground speed. The speed of an aircraft relative to the surface of the earth."

An aircraft that's diving vertically at 500 knots clearly has a speed of 500 knots "relative to the surface of the earth". Is its ground speed 500 knots?

Tim, his ground speed will be about zero, {just watch your GPS next time you are doing aeros} I said about zero so as to avoid those who will find that it wont be quite zero due to many obscure factors, none of which amount to a hill of beans, however if he doesnt pull out it will indeed be zero!

I dont agree clunckdriver, the ground speed would be about 3 regardless of other factors

Wouldn't that be "perpendicular to the local vertical" or equivalently, "perpendicular to the local gradient of the gravity field"? Is the parenthesised phrase part of the quote from the book, or is that yours?

Bumpy Flight, I dont know what you fly, but in my world three knots is just about zero,{and about 100kts under my stall speed} even our Jet Ranger ASI aint too precise under five knots!

I fly a dash 8

Really, it was an A321 the other day! :ugh:

tranfered mcgoo

I fly the dash 8 for private hire and the A321 for thomson

What all two of them whilst you don't fly any of their 5 A320s?

Intriguing!! :rolleyes:

Nope, perpendicular to the geodetic latitude. The "local gravity field" is known as the astronomic latitude, apparently, and it is not necessarily the same. Indeed, it is explicitly distinguished in Figure 2.2 of the reference I gave. (The third possibility is "perpendicular to the geocentric latitude", referenced to the "center of the ellipsoid and mass center of Earth", which is different again.)

No, it's not a quote from the book, it is my words saying what Figure 2.4 shows as a vector diagram (triangle with arrows and labels).

PBL

Look, I fly as a private pilot for a buisness I wish not to state the name of and I fly for thomson

Folks,

is it too much to ask that we try to have a half-way serious conversation about ground speed - and only that - on this thread, and discuss other stuff elsewhere?

PBL

PBL, I agreeI would like to take this chance to say I am not a troll, I do not intend to cause trouble and everybody has pounced on me since I posted my first message, I am a freal pilot and I would like to enjoy my time on here without some of you getting at me