Definition of ground speed

[ATCast]

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.

[bumpyflight]

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

[Pugilistic Animus]

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

an E6B flight computer is often used to calculate groundspeed

the wind side:E

what if you have a pencil failure?:}

[John Farley]

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

[Genghis the Engineer]

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

[Pugilistic Animus]

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

[Wizofoz]

(b) the horizontal component of the absolute speed

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.

[Pugilistic Animus]

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:

[ATCast]

Wizofoz:
You cannot express speed without specifying speed
relative to what.

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


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).

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.

[PBL]

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

[Tmbstory]

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

[Pugilistic Animus]

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

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



:suspect:

[Pugilistic Animus]

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

[Pugilistic Animus]

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

[selfin]

PA,

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.

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 (http://naca.central.cranfield.ac.uk/report.php?NID=2451) (Aiken, W. 1946. Langley.)

[Pugilistic Animus]

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:)

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. 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

[Checkboard]

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?

[BOAC]

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.':)

[Pugilistic Animus]

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:}

:\

[clunckdriver]

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

[FE Hoppy]

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?

[LH2]

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.

[LeadSled]

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!!

[hawk37]

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?

[clunckdriver]

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

[PBL]

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

[Tim Zukas]

"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?

[clunckdriver]

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!

[bumpyflight]

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

[LH2]

Ground speed is the horizontal (i.e. tangential to the reference ellipsoid) component

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?

[clunckdriver]

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!

[bumpyflight]

I fly a dash 8

[mcgoo]

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

[bumpyflight]

tranfered mcgoo

[bumpyflight]

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

[Right Way Up]

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

Intriguing!! :rolleyes:

[PBL]

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?

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

[bumpyflight]

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

[PBL]

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

[bumpyflight]

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

[ATCast]

PBL, many thanks for that summary of this thread, captures the discussion very effectively. I wish more people provided such overviews, especially on those 20+ pages rumour threads.

But I am even more grateful for the reference you provided. :ok:
It's a big help. And it's the definition that works best for most applications I think. (The context that provoked this question is the GPS reported velocity accuracy.)

Genghis, BOAC, Wizofoz, Pugilistic Animus and others with thoughtful contributions to this thread, thank you as well.

ATCast

[ATCast]

Originally Posted by PBL
Quote:
Originally Posted by LH2
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?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.) Full points again for PBL!

[Genghis the Engineer]

Somebody's attempt to regularise the whole thing, with maths. (http://bura.brunel.ac.uk/bitstream/2438/937/1/Gratton%20GPS%20AeroJ%20V2%20Feb%202007%20A%20FINAL.pdf)

(Aeronautical Journal. 111 (1120) 381-388, June 2007).

G

[Checkboard]

It's a big help. And it's the definition that works best for most applications I think.

Might just point out, it isn't a "reference definition", but an interpretation of a diagram by an anonymous poster. :hmm:

I don't think it even goes towards answering the question.

[Pugilistic Animus]

PBL could you post your reference?...

No I don't design IRS/INS/GPS systems,...but I think that it is the position solution that gets "jiggy wit it":)

Ghenghis that article was for calibration. techniques..interesting though


at the exact same GS two crafts one above the other should be over the same point at all times assuming constant Vw and TAS

and if one look at the definition for TAS I think the answer is apparent

but,
I'm like quintuple confused now :\

[PBL]

ATCast, I'm glad it helped answer your question!

PA, if you are asking me to scan the Figure in, I would rather suggest looking at the entire Sections 2.2-2.4, pp 23-32, because they also include the equations of motion associated with the quantities in the diagram.

amazon.com (the US branch; local country branches of amazon might be different) has scanned the book, and if you have an account with them, you can search it. The relevant sections in Chapter 2, The Navigation Equations, are 2.2 Geometry of the Earth; 2.3 Coordinate Frames; 2.4 Dead-Reckoning Computations.

Concerning Gratton's paper; yes, it is not nav, but he calculates true airspeed using vector triangles in a way that is only correct if ground velocity is taken to be the the horizontal component of the resultant of the air velocity vector with the wind vector (where by "horizontal" I mean in a plane parallel to the tangential plane of the reference ellipsoid). So that is indirect confirmation, even though not explicit definition.

Checkboard, Kayton and Fried is a canonical reference; I am not really anonymous; and I suggest you may rely on my interpretation.

PBL

[pattern_is_full]

Ground Speed can only be measured relative to - and at - the ground. The surface. Terra Firma.

If it takes 5 hours to fly from directly above point A on the ground to directly above point B on the ground, and A-B is 1000 nm, then the ground speed was 200 kts. Period. It does not matter whether the trip was made at ground level or FL320 or in a low earth orbit of 320 nm.

One's actual speed through the Universe or through the "ether" may have to be higher at FL320 or 320 nm than at the ground, due to flying an arc following the curvature of the Earth at a wider radius (or fighting heavier headwinds, or no significant atmosphere at all) - but actual speed is not Ground Speed.

It is possible an E6-B or GPS or other calculator does not take into account that wider radius (and thus longer distance at altitude) so it may not tell you the correct IAS or CAS to fly to achieve a given ground speed, or it may display an inaccurate calculated (as opposed to actual) Ground Speed. But that is an error in the calculation algorithm - not a "higher" or "lower" ground speed itself needed to cover a given ground track in a given time.

[Pugilistic Animus]

Relative Velocity - Ground Reference (http://wright.nasa.gov/airplane/move.html)

I went to these muppets for the definitive answer:E

:}

[LH2]

Nope, perpendicular to the geodetic latitude

Indeed it is according to your reference, which I've now looked up. But my question arises from the fact that, in a gyrocompassing Inertial Navigation System, the "down" channel is aligned with the local vertical[1], and the corresponding velocity equations provide a "basic description of the Earth relative velocity evolution in a local level navigation frame"[2] (my emphasis).

A GNSS-derived velocity, on the other hand, will be expressed directly in an Earth-centered Earth-fixed (ECEF) reference frame[3], as long as the standard broadcast or precise ephemerides are used[4] (admittedly I've never heard of an application where a non-standard ephemeris was being used, perhaps referenced to a different system or using non-Keplerian elements, although in theory that would be entirely possible).

Note however, that as long as navigation is taking place in a different reference frame (typically ECEF, for any long range terrestrial navigation) then presumably every relevant output will be transformed to the target system. This, I assume, will be the case in a modern craft with INS-derived velocities before they are presented to the user, which would validate Kayton's definition.

Now, the difference in geoid-referenced to ellipsoid-referenced groundspeed is negligible for all but the most demanding applications. To put this in perspective with a practical example, consider that an aircraft travelling at 400kt G/S will cover 2000nm in 5 hours. Let's assume that said ground speed was referenced to the "wrong" vertical and that the vehicle travelled over relatively rugged terrain resulting in an average vertical deflection in the direction of travel of 20 arc-seconds over the entire distance covered. The corrected groundspeed in this case would be 400*sin(20"), giving an ETA difference in our example of 2000/400 - 2000/[400*sin(20")] = 5*10^-4, or about 1.8 seconds, which is likely well below the measurement precision of most systems.

An interesting discussion, nevertheless.


[1] M. Grewal et al. "Global Positioning Systems, Inertial Navigation, and Integration", 2nd ed., Wiley Interscience, New Jersey, 2007, p31.

[2] R. Rogers, "Applied Mathematics in Integrated Navigation Systems", 3rd ed., AIAA, Blacksburg VA, 2007, p105.

[3] Grewal, p92-93

[4] A. Leick, "GPS Satellite Surveying", 2nd ed., Wiley Interscience, 1995, p487.

[p51guy]

An example of " in reference to what" are the geosynchronous orbits of our Directv satellites that have a ground speed of zero but are moving over 20,000 mph through space.

[italia458]

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.

Yes speed is relative to a point. For this, let's say speed is relative to a point on the surface of the earth. Makes things easy.

Now about the definition of groundspeed. It's just that!... the speed over the ground (surface of the earth). This is going to be true for navigation at any altitude.

Now looking at different altitudes, an aircraft traveling around the earth at 35,000' AGL will travel a further distance relative to the "same" point on the earth as an aircraft flying at 1000' AGL. Therefore, to travel over the surface of the earth at the same speed, the 35000' aircraft will have to travel faster! It will have a faster TAS. The TAS is how fast the aircraft is traveling through the air. Now to understand this concept we should state that we are disregarding density of the air, like TAS does.

In this little diagram I whipped up, the "groundspeed" is the same, but the TAS is not! The TAS would be the definition (2) that the OP wrote. The 1.0 and 1.42 are just rough estimates and nothing here was calculated, it was just made to clearly illustrate a point.

http://lh3.ggpht.com/_R8Od6auTHiw/TCZxeC5MOvI/AAAAAAAABGs/_YOhcUuql4A/11.png

[PBL]

[PBL:
perpendicular to the geodetic latitude]
Indeed it is according to your reference, which I've now looked up.

Just to clarify in case of misunderstanding: my answer addressed the question what is perpendicular to the reference ellipsoid, and I think the answer is standard, isn't it?

You point out that the accuracy of inertial navigation is dependent amongst other things upon the integrated effects of local gravity over the route of flight, not over some purely mathematical (engineering) construct such as the geodetic latitude. Indeed so, but I haven't worked in navigational avionics so have no idea of the magnitude of the difference between construct and reality, so in particular I can't comment on your numerical example.

Thanks for the references!

PBL

[PBL]

Well, italia458, it's nice to have your opinion on what "groundspeed" means, but unfortunately it's wrong! You might like to look up some of the references which have been cited here.

PBL

[xuejiesandi]

Yerrraaa Eishhhh!! :eek:
All this time I thought Ground Speed is the Speed indicated by GPS :}

[BOAC]

Whatever 'high-fallutin' references you come up with, GROUND speed is ALWAYS speed relative to the ground. Nothing else, pure and simple. The OP sought a way of correcting for the circumference of an ellipsoid shell, which is relevant when dealing with travel around an object rather than travel along an object, and the cause of many conundrums and fixes in science and aviation, including such concepts as 'profile rate' which needs to be applied to an inertial attitude reference platform when moving around a body.

To derive either circumferential distance/speed travelled around the shell or convert that to distance relative to the surface of the shell is indeed a problem for the OP (and will also depend on whether the GPS has an altitude function and on which datum that is based), but what he/she refers to is not necessarily GROUNDspeed but some other speed - hence the confusion. As I said earlier, what is sought is to derive 'groundspeed' from 'Tangspeed' or some derivative of Orbital Velocity. (Never did get those postcards....). That can easily be derived by schoolboy mathematics. The moment you begin to 'orbit' just 1mm from the surface of a body the 'speed' link with that surface is broken.

We should think ourselves indeed lucky that our earth is not cuboid - then we'd have some fun..

[Genghis the Engineer]

We should think ourselves indeed lucky that our earth is not cuboid - then we'd have some fun..

As opposed to the current situation of it being sat on the back of a giant turtle held up by four elephants?

G

[PBL]

Whatever 'high-fallutin' references you come up with, GROUND speed is ALWAYS speed relative to the ground.

Yes, well, whatever that means precisely.

If high-falutin' is too rarified, let's take the low-falutin' route.

Consider. The earth is a perfect sphere, with circumference about 21,600nm (if we take a nm to be a second of arc, which is what it was supposed to be). You fly at your preferred altitude of FL370, let's say in a standard atmosphere. I fly at 1,000 ft because I like to bird-watch. Both of us without wind (we should be so lucky!). We are both pretty fast - say we go around the earth in a day. Just under 1,000 kts per (let's not worry about the logistics of refuelling, or about the number of windows shattered in my wake).

But you are about 6 nm higher than I (1 nm is about 6,000 ft) so you actually travel 21,637.7 nm, whereas I travel 21,601 nm. You do nearly 37 more air miles than I! So your TAS is about 1.5 kts faster than mine.

Those NASA "muppets" (as PA dubbed them) says your ground speed is 1.5 kts faster than mine. Myron Kayton says that also. What do you say?

PBL

[BOAC]

Well, THAT is easy, requiring a simple application of the Loxodontal Tranformation.

[italia458]

PBL you're really confused about this! No, I'm not wrong about ground speed is.

In your little example you just explained to me what True AIRspeed is! NOT, what ground speed is.

[LH2]

Just to clarify in case of misunderstanding: my answer addressed the question what is perpendicular to the reference ellipsoid

Ok, I think I might have misunderstood it to mean that the definition of ground speed as given by Kayton was relative to the ellipsoid (which is also correct, even if that's not what you wished to emphasise!).

You point out that the accuracy of inertial navigation is dependent amongst other things upon the integrated effects of local gravity over the route of flight, not over some purely mathematical (engineering) construct such as the geodetic latitude. Indeed so,

That's correct. Inertial navigation systems incorporate a gravity model in order to account for the differences in the mass distribution of the Earth (as well as centrifugal acceleration due to rotation), and barometric (or GNSS) height aiding to control vertical channel instability. And I have the feeling you already know this perfectly well :)

Note that the "integrated effects of local gravity" are modelled to within the precision of the provided gravity model, and unmodelled residual errors are accounted for and controlled during Kalman filtering. So, as you say, the source of residual errors is neither purely mechanical nor mathematical, but a combination of the design limitations in both.

BOAC,
GROUND speed is ALWAYS speed relative to the ground. Nothing else, pure and simple.

Not so "pure and simple" I'm afraid. You will find that what we call ground speed is in effect the first integral of acceleration in a given reference frame which may or may not be physically referenced . What I think you might be thinking of would be the first derivative of change of position over time, which could be a perfectly valid definition (not without its own set of complications, mind you) but unfortunately is not what is used.


Consider the following practical example: If you were measuring the ground speed of the Eiffel tower you will find that your answer will be either about zero, or ~3cm/yr, depending on whether you were using the ETRS89 or ITRF2008 reference systems (due to different velocity fields). In other words, even defining what "the ground" is presents a major problem, past a certain threshold of accuracy.

[BOAC]

PBL - I say you were right about 'muppets'. Anyone got a link to the NASA muppet forum?

LH2 - Let me know when the tower is forecast to fall in to the Seine on your reference systems - then I'll take notice, I promise. Until then....................dear oh dear!

On the other hand, the fact that I didn't need to step out of the way of the leg of the tower as it rushed past MIGHT have simply meant I am in the same reference system. I had not thought of that. Tisk tisk.

[italia458]

Not so "pure and simple" I'm afraid. You will find that what we call ground speed is in effect the first integral of acceleration in a given reference frame which may or may not be physically referenced . What I think you might be thinking of would be the first derivative of change of position over time, which could be a perfectly valid definition (not without its own set of complications, mind you) but unfortunately is not what is used.
Consider the following practical example: If you were measuring the ground speed of the Eiffel tower you will find that your answer will be either about zero, or ~3cm/yr, depending on whether you were using the ETRS89 or ITRF2008 reference systems (due to different velocity fields). In other words, even defining what "the ground" is presents a major problem, past a certain threshold of accuracy.

That is ridiculous. The OP was asking groundspeed regarding aircraft in flight. Ground speed is speed traveled over the surface of the earth, at sea level. Please refer to my diagram I drew in a previous post. It is quite simple in this case and there is no need to over complicate it.

[Pugilistic Animus]

no such animal as a 'first integral'...double, triple etc integrals are for each axis with the other mutual axes held constant....but I know what you meant:)

it all depends on local wind velocity and the displacement between nav fixes

I was only jokingly referring to those folks as muppets:\


this has got to be one of the most complicated discussions I've seen, but really for no reason :confused:

:eek:









Edit: Nature laughs at mathematical complexity

[Loose rivets]

And just when you thought you were flying level.



BBC News - Goce satellite views Earth's gravity in high definition (http://news.bbc.co.uk/1/hi/sci/tech/8767763.stm)

[Pugilistic Animus]

http://www.pprune.org/jet-blast/416513-last-beginning-understand-women-2.html#post5727910


the ground speed equation was already done on JB
:}

[ft]

I'd say that ground speed should be defined as the speed of the aircraft over level ground, as defined by the rate of change of the position of the aircraft as projected vertically onto the same level ground.

Then again, "vertically" is not constant and usually not "directly towards the center of the earth", nor is "level" usually "perpendicular to a vector through the center of the earth". The geoid is rather uneven, meaning the speed of movement of the vertical projection on the surface is not simply a function of the radii of the geoid surface, the radii of the path of the aircraft and velocity. Constant velocity, constant radii of travel => varying ground speed, as defined in the first paragraph.

I thought I'd throw that in, as the discussion so far was oversimplifying the subject somewhat. :E

(Edit: Darn. Loose Rivets beat me to it!)

[Pugilistic Animus]

Don't worry lots of folks don't understand the wind:E

[italia458]

I'd say that ground speed should be defined as the speed of the aircraft over level ground, as defined by the rate of change of the position of the aircraft as projected vertically onto the same level ground.

Then again, "vertically" is not constant and usually not "directly towards the center of the earth", nor is "level" usually "perpendicular to a vector through the center of the earth". The geoid is rather uneven, meaning the speed of movement of the vertical projection on the surface is not simply a function of the radii of the geoid surface, the radii of the path of the aircraft and velocity. Constant velocity, constant radii of travel => varying ground speed, as defined in the first paragraph.

I thought I'd throw that in, as the discussion so far was oversimplifying the subject somewhat.

Please stop complicating probably one of the most simplistic definitions in the aviation world!!

[PBL]

ft,

I pondered weighing in again on this, since there appears to be a certain amount of noise on the channel which I don't wish to amplify. Your proposal raises a question.

I'd say that ground speed should be defined as the speed of the aircraft over level ground, as defined by the rate of change of the position of the aircraft as projected vertically onto the same level ground.


Yes, but it isn't so defined by the nav community, as we have seen. They take the angular velocity as definitive and multiply by the radius of the flight above the nominal centre of the earth (radius of earth + altitude).

Definitions are usually given for a purpose. If you say the definition "should" be as you say, what is the purpose you have in mind?

Then again, "vertically" is not constant and usually not "directly towards the center of the earth", nor is "level" usually "perpendicular to a vector through the center of the earth".


Indeed so. But these difficulties apply to all reasonable attempts to define it.

PBL

[ft]

italia,
if you try to make definitions simplistic, you are often in for it. Definitions are, by definition (:E), to be exact rather than simple. As has been made clearly apparent, there's a lot of room for different interpretations as to what ground speed is.

PBL,
looking at Kayton and Fried, I see an figure from an avionics text book (which I am grateful for the reference to!), illustrating varius concepts and terms used, rather than a strict definition. In other words, I'd say they made a for most purposes perfectly reasonable simplification, but a definition it is not.

Going for definitions, The United States Air Force Dictionary (Heflin) defines ground speed as:

"The speed of an aircraft, esp. an airborne aircraft, measured by the distance it travels over the ground either by reference to check points on the ground, or by taking wind velocity into account."

The U.S. Navy Hydrographic Office (1955) define ground speed as:

"the rate of motion of the aircraft relative to the earth's surface. It is the speed of the aircraft over the ground; hence the name."

Clearly these definitions do not agree with Kayton and Fried (with the possible exception, and slight ambiguity, introduced after the last comma by Heflin), as can be illustrated by taking it to the extreme of very high altitude flight. If we look at the primary purpose of ground speed, namely navigation, the definitions presented here remain useful while errors would creep into the navigation solution using the IMO simplified explanation in the figure in Kayton and Fried - which is intended for a different audience than navigators.

The definitions listed above still leave it up to the reader to decide what being above a place on the surface of the earth actually means, but it is to the bet of my knowledge widely accepted in geodesy that being above something is referenced to the geoid and not the ellipsoid. In other words, you are above a place on the surface of the earth when a dropped penny will hit that place. Using the ellipsoid as the level gives interesting effects such as streams flowing uphill in places, so it is best avoided.

I think the hobgoblin of this discussion is that for all normal practical purposes, a simplified definition by far exceeds the required precision and hence, many more or less authorative publications will go with the simplification - without explicitly stating so.

References

Heflin, W. A. (Ed.). Publication year unknown, but probably 1950s or 1960s. The United States Air Force Dictionary. D. Van Nostrand Company, Inc., Princeton, NJ, U.S.A.

The U.S. Navy Hydrographic Office, H.O. Pub. No. 216. (1955). Air Navigation. U.S. Navy Hydrographic Office, United States Government Printing Office, Washington, U.S.A.

[PBL]

looking at Kayton and Fried, I see an figure from an avionics text book.... illustrating varius concepts and terms used, rather than a strict definition.

The strict definition, I think, follows from Kayton's definitions of Vnorth and Veast along with equations (2.5) (and reference 2.10 for confirmation of this interpretation.

I am generally wary of quoting definitions from engineering sources and taking them as "definitive", for in my experience many engineering definitions are messy and ultimately inappropriate.

See, for one of the most fundamental examples in safety-critical systems engineering, Problems Calculating Risk via Hazard (http://www.rvs.uni-bielefeld.de/publications/books/ComputerSafetyBook/Chapter_5_Problems_calculating_risk_via_hazard.pdf). See this essay on the International Functional Safety Standard IEC 61508 (http://www.causalis.com/IEC61508FunctionalSafety.pdf) for some (notorious) problems with the definitions there, and Definitions For Safety Engineering (http://www.causalis.com/DefinitionsForSafetyEngineering.pdf) for my suggestion of how to do it right. (Full disclosure: I wrote all of these.)

I read Heflin as wisely leaving it open which definition to use. For many purposes, they will agree, especially when the margins of error due to non-uniformities of the geoid are taken into account.

You make the point that in geodesy, one references to what Kayton calles the "astronomic latitude", the direction of apparent gravity (where the force vector points where you are). That may be (I wouldn't know). But the WGS84 system is referenced to an ellipsoid. Kayton says that national ellipsoids may differ, and there are conversion tables. The differences may amount to hundreds of feet. He also points out (p23) that any ellipsoid is appropriate for "the navigator" as long as there is a one-to-one mapping between its surface and the earth's surface (also p23).

I think you are right about the hobgoblin!

PBL

[ft]

PBL,
yes, and they do indeed go on using a ground speed as given by a doppler radar to derive Vnorth and Veast. Ground speed given by a doppler radar would in fact (more or less... subject to inherent errors and inaccuracies in the system) be the rate of change of position of the aircraft as projected orthogonally onto the geoid, as per my preferred definition above.

This also agrees with the initial use of ground speed for a ground-bound vehicle.

For all flights which are not very local in nature, I suspect that we can happily ignore the geoid vs. ellipsoid debacle as the errors introduced on the momentary ground speed will even out.

Interesting, this! :ok:

[clunckdriver]

Here it is right from our local Garmin rep. "Ground speed is what you see in the bottom right corner of your 530". Garmin cant be wrong!

[xuejiesandi]

:D:D:D:D:D

That's what I've been trying to explain to everyone..

[italia458]

Definitions are, by definition (), to be exact rather than simple.

I'd totally disagree... in a way! Take "attractiveness" in humans for example. It's very wide in range and in no way, specific! Some ppl would find one girl/guy attractive while the others don't. The definition is very specific in the case that it accurately shows that attractiveness is NOT exacting in nature.

So yes definitions are exact, but can represent something that is not exact at all!

The reason I'm saying not to overcomplicate it is because if you're talking about groundspeed of an aircraft, it's that damn simple! It's kind of stupid to bring it up on a forum like this because all the little nerdy/geniuses of this board LOVE to pick apart the simplest definition and make it the most complicated, and then in the end they find they've gotten nowhere! Believe me I like picking apart stuff too (partly the reason I joined), but I think groundspeed should be left alone!

[Pugilistic Animus]

The NASA "Muppets" use the simple definition....Of course I'm in awe of all the complicated equations:rolleyes:

GS is a function of TAS, Wind vector, and nav fix displacement...easy...that's why we can't stop the leak
So much crap:ugh:


did you know that dG = [dU+pdV+VdP] - [SdT+TdS]

it's true; but as written it's a little pedantic, as I have included all possible contributions:8..of course it can be expanded a little too:}:}:}

Lester:E

[PBL]

Folks, please excuse this slight digression.

The reason I'm saying not to overcomplicate it is because if you're talking about groundspeed of an aircraft, it's that damn simple!

italia, I for one have registered many times that you prefer one definition of ground speed. I don't know what it contributes to a discussion to have it repeated many times. What would contribute, to my mind, would be to have new, good, reasons for preferring it over another.

It's kind of stupid to bring it up on a forum like this because all the little nerdy/geniuses of this board LOVE to pick apart the simplest definition and make it the most complicated, and then in the end they find they've gotten nowhere!

I don't think it is at all stupid. Indeed, I enjoy it! Being one of the "little nerdy/geniuses... [who] LOVE to pick apart the simplest[-seeming] definition", indeed having made much of a career doing that, I don't see anything wrong with it. Especially since I have seen the effects of what I do improve safety for some and derive appropriate compensation for not-so-lucky others.

Consider, the people whose views on "ground speed" we are discussing actually built the equipment you use on a daily basis in your flying. Some people think flying isn't half as much fun and full of expertise as it used to be, but the statistics say that it's noticeably safer!

PBL

[italia458]

I don't think it is at all stupid. Indeed, I enjoy it! Being one of the "little nerdy/geniuses... [who] LOVE to pick apart the simplest[-seeming] definition", indeed having made much of a career doing that, I don't see anything wrong with it. Especially since I have seen the effects of what I do improve safety for some and derive appropriate compensation for not-so-lucky others.

Consider, the people whose views on "ground speed" we are discussing actually built the equipment you use on a daily basis in your flying. Some people think flying isn't half as much fun and full of expertise as it used to be, but the statistics say that it's noticeably safer!

What is your career/job?

Oh yes I'm very sure these random ppl on here built my Garmin GPS and avionics suite from Rockwell Collins.... :ugh:

EDIT: Like I said before, I'm one of those nerdy/geniuses too and I enjoy topics that provoke thought, however, I still do retain a sense of reality and the relationship of concepts. Some of the greatest minds in the world have said the simplest things and those quotes are used all the time because of the truth they contain! Not everything has to be complicated PBL!

[Pugilistic Animus]

the thermodynamic sound velocity 'c' or 'a' is the slope of the isoentrope passing through -rho^2*c^2 and that is equivalent to [dp/dv]s

so c =[1/rho^2* [dp/dv]s}^1/2:8

but for flight this is more useful

http://www.faa.gov/library/manuals/aviation/pilot_handbook/media/PHAK%20-%20Chapter%2015.pdf

:zzz::suspect:

[PBL]

What is your career/job?


You could check my profile.


Oh yes I'm very sure these random ppl on here built my Garmin GPS and avionics suite from Rockwell Collins....

My colleagues apparently built your kit. Not that they turned the screws personally, of course.

I think there is somewhat of a disconnect here. There are people on PPRuNe who know as much about or more about what they write than any others in the world. A wise PPRuNe participant learns to distinguish such people from those who sit at home and participate in so-called flight-simulation games and pretend they are pilots. We have all types here. My tip is to try to distinguish who is who and not be rude to the wrong people :)

PBL

[Pugilistic Animus]

Speed Over Ground (SOG)
The actual speed the GPS unit is moving over the ground. This may differ from airspeed or nautical speed due to such things as head winds or sea conditions. For example, a plane that is going 120 knots into a 10-knot head wind will have a SOG of 110 knots.

source Garmin

[italia458]

Like I said in the other thread, PBL you never answer questions! I didn't ask if I could look at your profile.

My colleagues apparently built your kit. Not that they turned the screws personally, of course.

Haha ya right! That's the biggest lie ever. First of all, if they're your colleagues I'm pretty sure you would know if they did or not, "apparently" wouldn't be used in that case. Second, the second sentence is perfect lawyer speak for making sure you can squirm your way out with an excuse. If they didn't "turn the screws personally" then what the heck does building it have to do with?! Also, if they did actually have a part in it then saying something like they developed the software, or they did the testing for it would help make things add up, especially since they were your "colleagues" and you couldn't say what they did. And last point, garmin and RC are two different companies, with two different products stated in my case. Again, if you were telling the truth, something a little more specific would help! Ya I got a bit of psychology and investigative background and you, PBL, are the equivalent to an imposter!

Regarding your last paragraph, are you seriously threatening me?!... A completely anonymous person on the Internet?! I thought that kind of ignorance only happened on YouTube.

[Pugilistic Animus]

Italia458--I agree most of these computations and definitions are from the ground and are therefore useless to aviation:}

[ft]

Some people realise the importance of proper definitions, and how to make them. These people should include all scientists and engineers, or there'd be trouble.

Other people do not understand how important it is to know exactly what you are talking about. These may be fine using the equipment designed by the engineers based on the knowledge from the scientists, but they should be kept well away from science and engineering or there will be trouble.

And italia, noone is threatening you. You got a very friendly bit of equally sound advice, that's all. Take it to heart.

Yawn. Now let us get back to the topic at hand. No more troll feeding in this zoo until Tuesday next week, sorry if you missed it! :p

[Pugilistic Animus]

Some people realize the importance of proper definitions, and how to make them. These people should include all scientists and engineers, or there'd be trouble.
Exactly, that's why I use the definition used in aviation by EVERYONE

These may be fine using the equipment designed by the engineers based on the knowledge from the scientists, but they should be kept well away from science and engineering or there will be trouble.
Yes, so except for about three people here on this thread, who are engineers and one who is also a scientist...the should stop pretending they are because they are NOT!!!..


no more here:* 83 posts of ridiculous and wrong conventions and 'definitions' through serious misinterpretation of technical works:yuk:

the fake 'mensa club' is ground based...go stop that oil gusher:rolleyes:

...all the self proclaimed geniuses...you don't need to hand wave your genius if you are a genius it is recognized subtly by all.... and not forced down people's throats

:=


the work done here is given by the following equation:

work = ∫axdx between the bounds{s,0}:E

[Pugilistic Animus]

just in case there's interest, as I don't like muddling in obscurity

here's the solution:as I have given in JB:}

in order 'integrate' a function of the form [ax^n] one applies the following formula:

∫ax^n dx =ax^n+1/(n+1) so ∫ax dx = ax^2/2 and ∫ax^5 dx = ax^6/6 ...and so on....

for a definite integral between two bounds for example between 2 and 0 and where 2 = b and 0 =a you have to replace those X's with the numbers always subtracting the [b-a]

so for this integral equation ∫axdx =AS^2/2 - [A0^2/2=0]

and since S^2 =S*S we can say that ∫axdx between the bounds{s,0}

= 1/2 ASS http://images.ibsrv.net/ibsrv/res/src:www.pprune.org/get/images/smilies/badteeth.gif

[PPRuNe Pop]

And its STILL the speed of the aircraft relative to the ground!! It is not necessary to add anything more than plus or minus wind speed. Simples.

[Pugilistic Animus]

Finally Reason!!!:ok:

just to add nav fix displacement is important only in the planning stage the mileage is given on the charts, or using a plotter so that fuel can be determined...local winds vary anyway so the planning device flight computer, dispatch,..and so on is always trumped by actual conditions...i.e what the GPS or your clock and eyes, if done by DR, tells you, it is as referenced from over the ground...so you don't run out of fuel and crash....I just wanted that part clear.... as looking at this thread I now see that such a statement is open to serious interpretation:rolleyes:...Elmer Sperry must by gyrating:eek:

[Pontius's Copilot]

Rate of change of position!

[SLFguy]

Methinks Italia will eventually get around to reading some of PBL's other contributions to discussions on this site and begin to feel just a little embarrassed..

[italia458]

Me thinks not so!

We have had private messages discussing this and I believe our quibble should be resolved now.

[Mr Optimistic]

Two observers on the ground (ie dirt, either geoid, ellipsoid or prolate spheroid), measured distance apart. Aircraft flies directly over the two of them. From observer zenith (straight-up) to observer zenith measure the time taken. A bit of arithmetic and hey presto ground speed ! If aviation has managed to come up with an alternative definition I'll be unsuitably impressed (ps for PA this is the non-relativistic version).

[john_tullamarine]

How did this thread get to 5 pages

.. the joys of PPRuNe .. often the journey is more interesting than the destination.

[PBL]

Mr Optimistic asks:
How did this thread get to 5 pages

Because there are at least two coherent possible definitions out there, and people are voting one by one for their favorite. Mostly without giving coherent reasons for so doing, unfortunately.

its STILL the speed of the aircraft relative to the ground!!


Lots of people have said this. One must ask "what do you mean by that?", because there are at least two coherent interpretations, as we have seen.


It is not necessary to add anything more than plus or minus wind speed.

Looks like he votes for Kayton.

Then there is
Rate of change of position!

Rate of change of position with respect to what? With respect to the fixed stars?

Best to illustrate with the questioner hisself:
Two observers on the ground (ie dirt, either geoid, ellipsoid or prolate spheroid), measured distance apart. Aircraft flies directly over the two of them. From observer zenith (straight-up) to observer zenith measure the time taken. A bit of arithmetic and hey presto ground speed !


So he votes against Kayton.

If aviation has managed to come up with an alternative definition I'll be unsuitably impressed.

I guess he has not yet checked for himself.

And so it goes on!

PBL

[Mr Optimistic]

I've seen one coherent definition (in which ground speed = ground speed), and something else which is hard to describe. Some even believe that it is necessary to hold the nose up a bit to get the necessary lift for level flight. Given that the earth is not flat, it is clearly necessary in fact to maintain a continuous descent to maintain a constant height above ground, with a bit of a bank to the left to counter coriolis when flying north in the northern hemisphere. That's why INS systems are so expensive as they take this drudgery away.

[ft]

it is clearly necessary in fact to maintain a continuous descent to maintain a constant height above ground

Oh, terrific! Now we can get cracking on defining a descent, as there will clearly be some differing opinions on that one. :D

As for ground speed, define zenith as "above as defined by a plumb line" and I'll drink to the ground speed being the distance covered between being in zenith above point A and being in zenith above point B divided by the time taken to cover the same ground. Now, the question is... what distance?

(Above paragraph edited to avoid GS always being unity due to a brain fart in the denominator)

If you define instantaneous ground speed in the only sensible way, i e as the ground speed acquired when the distance between A and B approaches zero, we end up with it having to be the distance along the geoid. Otherwise, you'd end up with a difference between the distance A to B and the distance acquired when integrating the instantaneous ground speed over time.

And for those still suggesting that this complicating things unnecessarily, I suggest looking at the original post stating that this is for flight test purposes. What's good enough for plodding along from airfield to airfield is frequently no longer good enough in that scenario. Methinks this thread would have unfolded rather differently in the flight testing forum, without a lot of the "why on earth bother" posts.

[BOAC]

Mr O raises some interesting points which go a long way to explaining why IRS systems need Profile Rate and Schuler Loops, and the Coriolis effect is actually covered (in 737s) by the built-in 'crab' you can see when they taxy, which derives from an offset vertical stabiliser setting.

The 'constant descent' requirement has, of course, become much easier to achieve with the growing use of GPS with altitude determination.

[Pugilistic Animus]

what about WGS84..aren't GPS waypoints all referenced to a standard datum?

and I guess we can just ignore the wind as it does not seem important for GS determination

I think that the position solution is the difficulty with modern navigation..No?

[ft]

PA,
the GPS waypoints are in reference to the WGS84 ellipsoid, which is a gross simplification of the shape of the earth. For most practical purposes, you need to use the geoid which defines MSL. The geoid is a lot bumpier.

In practise, this means many things (as we have seen). One of them is that the distance between 45N 37E and 45N 38E, as travelled at sea level, may not be the same as the distance between 45N 40E and 45N 41E.

There are many difficulties with modern navigation, and I'd say sevaral are more intricate than the position solution. Position accuracy and positioning availability would be two tricky ones off the top of my head in the modern day of GNSS.

[Pugilistic Animus]

Everything in engineering is an inexact solution...everything!
the position solution is probably given an error analysis algorithm

WIND;)

PS the calibration for the ASI i.e flight testing methods were detailed in the report provided by Genghis:hmm:

:sad:

[SomeGuyOnTheDeck]

Why should you need to define ground speed in an aircraft anyway? You should be moving through the air (if you aren't, you've got bigger problems than this), and the air tends to move relative to the ground. You can calculate an approximate 'ground speed' using normal navigation techniques, and figure out if you will probably arrive at where you are trying to get to before you run out of fuel, the bar closes, or whatever priority you choose to set. Since you never really know exactly what the air is going to do relative to the ground (butterflies in Amazon rainforests, amongst other things, stop you knowing for sure), you can only ever rely on approximations. This doesn't prevent aircraft from being useful - in fact, I'm not sure having an exact definition of what 'ground speed' consists of is of any significance at all as far as getting from one point on the ground to another without colliding with somewhere in between is concerned...

[PBL]

Everything in engineering is an inexact solution...everything!

Hard to let this one go by without comment.

The question as to whether a computer algorithm implemented in code fulfills its specification under the given environmental constraints has two answers: Yes, or no.

It is not at all inexact. This engineering task is an increasingly important part of the world of airplanes nowadays, as it is in other safety-critical domains, so I would have expected people familiar with airplanes to know of it.

PBL

[PETTIFOGGER]

Isn’t this just a trick question? Groundspeed is simply distance/time at that level when other speed influencing factors are accounted for, one of those being the slight increase in distance travelled at altitude.

[Pugilistic Animus]

no,...perfect 'accuracy' is impossible,.. and not necessary,...as I said nature laughs at complex math...


altitude is irrelevant to an airplane because it is only interested in the wind speed direction:ugh:





6 The wind goeth toward the south, and turneth about unto the north; it whirleth about continually, and the wind returneth again according to his circuits.
7 All the rivers run into the sea; yet the sea is not full: unto the place from whence the rivers come, thither they return again.
8 All things are full of labor; man cannot utter it: the eye is not satisfied with seeing, nor the ear filled with hearing.
9 The thing that hath been, it is that which shall be; and that which is done is that which shall be done: and there is no new thing under the sun.
10 Is there any thing whereof it may be said, See, this is new? it hath been already of old time, which was before us.
11 There is no remembrance of former things; neither shall there be any remembrance of that shall come after.
:}:}:}

[Mr Optimistic]

....because when a concept is good enough we stop looking and accept it. When better precision comes around we have to challenge the accepted models (eg GPS and location on the ground and the representation of this on a map projection). When the basics of physics trip up, we just invent a new concept and if it works accept it into the family (eg em waves having momentum and all those new quantum numbers they keep inventing). Science presents a model of the world, not the world itself. Engineering takes one more step back.

[Rushed Approach]

Surely what most pilots mean by "groundspeed" is the distance over the ground (i.e. the Earth's surface) covered in unit time. Therefore, the fact that you may be at altitude and cover a longer distance by virtue of your distance from the centre of the Earth is irrelevant. Otherwise your groundspeed becomes a function of altitude.

If you want to be pedantic with the physics, nobody seems to have mentioned Einstein's relativistic effects of both General and Special Relativity.

The general relativistic effect will mean that because gravity is slightly less up there the aircraft clock will run faster than it would do on the ground, and this is countered by the special relativistic effect of high speed motion which means that the faster you go, the more time slows down.

It is quite possible with modern atomic clocks to demonstrate these effects in aircraft.

So every time you go flying, so long as you don't fly too fast, you are actually aging slower than you would do on the ground.:D

[italia458]

Surely what most pilots mean by "groundspeed" is the distance over the ground (i.e. the Earth's surface) covered in unit time. Therefore, the fact that you may be at altitude and cover a longer distance by virtue of your distance from the centre of the Earth is irrelevant. Otherwise your groundspeed becomes a function of altitude.

If you want to be pedantic with the physics, nobody seems to have mentioned Einstein's relativistic effects of both General and Special Relativity.

The general relativistic effect will mean that because gravity is slightly less up there the aircraft clock will run faster than it would do on the ground, and this is countered by the special relativistic effect of high speed motion which means that the faster you go, the more time slows down.

It is quite possible with modern atomic clocks to demonstrate these effects in aircraft.

So every time you go flying, so long as you don't fly too fast, you are actually aging slower than you would do on the ground.

Yes, the clock will run faster but at an altitude of ONLY 30,000 ft the effect would be so minute that only an atomic clock would be able to recognize it... a very accurate atomic clock at that!

Altitude plays a big role and I'd say the biggest in factors with regard to groundspeed. If you're on the earth and are travelling at 100mph, your groundspeed is 100mph. Simple as that! If you're travelling at a higher altitude, since the earth is round, as you travel you will cover less distance over the ground than you will in your flight path through the air. Then you could go into how the earth is actually slightly stretched at the equator because of it's spin and all that ridiculous stuff. Seeing the earth from space or the moon confirms that the earth is a pretty damn good sphere and the stretching effect is soo minute! Taking anything more into account than the altitude of the aircraft for groundspeed is just a waste of time and is not really relavant. I drew a little diagram posted earlier in this thread illustrating the effect of altitude.

[Rushed Approach]

My post was somewhat tongue in cheek, and I agree the relativistic effects are negligible at normal aircraft altitudes and speeds, which is an accurate decription of the physics knowledge of most of the posters on this thread.

Since we are clearly talking about the Earth as a fixed frame of reference, its spin is irrelevant. If you are going down that road what about the fact that the Earth is moving at 18.5 miles a second around the Sun in its inertial frame, the Sun is moving in the Milky Way's inertial frame, etc, etc, etc! Take your pick - your aircraft can be doing any speed you like if you pick the right reference frame.

Speed only has meaning when it is related to a reference frame, which in this case is that of the Earth's surface. My understanding of aircraft "groundspeed" is the component of tangential speed at right angles to a radius drawn from the centre of the Earth, averaged over the distance of the route. Yes the start and finish points may have different elevations in terms of distance to the centre of the Earth, but nevertheless that is what groundspeed to a pilot is. Nothing more and nothing less.

[italia458]

yup I totally agree about the reference frame. I think some people are taking the reference frame issue just a teenie bit further than it should be! haha groundspeed is reference to the "ground"... fancy that!

I complete agree with your definition of groundspeed in the last paragraph! Elevation shouldn't have any effect on groundspeed. If you fly over a mountain range, your groundspeed doesn't change at all.

It's simple and directly to the point and that's the way it should be. :ok:

EDIT: 6 pages to come to this conclusion?! and they say "together everyone achieves more".... lol :hmm:

[PBL]

My understanding of aircraft "groundspeed" is the component of tangential speed at right angles to a radius drawn from the centre of the Earth, averaged over the distance of the route.

That's the Kayton definition.

I complete agree with your definition of groundspeed in the last paragraph!

Good, because in this post from the 26th June (http://www.pprune.org/tech-log/418855-definition-ground-speed-3.html#post5776113) you chose the other interpretation.

Yes, 6 pp. For those not here at the beginning, it ran as follows. ATCast pointed out there were two non-equivalent definitions of groundspeed and asked for clarification. I found out that navionics engineers use the "tangential speed" definition (aka TAS corrected for wind speed) by looking it up in Kayton and Fried, Avionics Navigation Systems, 2nd edition, Wiley-Interscience 1997 where it may be found in Sectiona 2.2 to 2,4, in particular Figure 2.4; Genghis pointed to a paper by Guy Gratton (http://bura.brunel.ac.uk/bitstream/2438/937/1/Gratton%20GPS%20AeroJ%20V2%20Feb%202007%20A%20FINAL.pdf) on calibration which used a similar definition. LH2 supplied the further references
[1] M. Grewal et al. "Global Positioning Systems, Inertial Navigation, and Integration", 2nd ed., Wiley Interscience, New Jersey, 2007, p31.

[2] R. Rogers, "Applied Mathematics in Integrated Navigation Systems", 3rd ed., AIAA, Blacksburg VA, 2007, p105.

[3] Grewal, p92-93

[4] A. Leick, "GPS Satellite Surveying", 2nd ed., Wiley Interscience, 1995, p487.
in this interesting post (http://www.pprune.org/tech-log/418855-definition-ground-speed-3.html#post5775583)

Newcomers might want to take a look at these references.

People weighed in with their "favorite" definition (one of the two), or for an ambiguous statement.

I had some interesting discussion with LH2 and ft about technical subtleties, inter alia to do with how one determines which way is "down" (there are at least three non-equivalent definitions). Others have their own ideas about what constitutes "interesting", not necessarily similar.

Is there anything else to say?

PBL

[Wizofoz]

Rather than "Favourite" how about trying to determine "Most Useful".

If ATC want to know when you be over point B while you over at point A, the means of determination will be the rate of change of your position over the surface. As you say, PBL, this will be slightly different from your rate of change of position REFERENCE the surface, but I can't really think of a useful application of that speed.

I suspect GPSes show the "Tangential" speed as that is the easiest one to determine, and the difference is, after all, pretty notional.

[PBL]

Wizofoz,

"useful" is in the eye of the beholder, as well as in the task of the moment, and the state of the art.

PBL

[Mr Optimistic]

A bit ironic that in a discussion about 'ground speed', a clock and ruler job, a heroic attempt to introduce relativity (another clock and ruler job but with a shed load of maths) is attempted ! Perhaps need to pass 'Spherical Earth 101' first ?

[italia458]

Good, because in this post from the 26th June you chose the other interpretation.

PBL... If i'm not mistaken, that post on the 26th June is virtually the same as what was being said by Rushed Approach. How does my June post differ from what I just said?

[ft]

There seems to be a misunderstanding among some participants in this thread that geoid undulation has to do with the elevation of the surface of the earth.

It doesn't.

[PBL]

italia, I think by now it's for you to figure out.

ft,

There seems to be a misunderstanding ..... that geoid undulation has to do with the elevation of the surface of the earth. ...It doesn't.

Guilty as indirectly charged of oversimplifying. Your contributions suggest there are at least three definitions, with two of them being TAS in the "tangential", corrected for ("tangential") wind. "Tangential" is orthogonal to "vertical", and the vertical can either be defined as (a) normal to the surface of the model (the "reference ellipsoid", WGS84, or national ellipsoid, or some other mathematical model) or as (b) "true" vertical (the direction in which the gravity vector actually points).

As to the difference between (a) and (b), I am (passively) informed that The angle between the gravity vector and the normal to the ellipsoid, the deflection of the vertical, is commonly less than 10 seconds of arc and is rarely greater than 30 seconds of arcreferencing a U.S. Defence Mapping Agency report from 1959. You said in this post (http://www.pprune.org/tech-log/418855-definition-ground-speed-5.html#post5795891) that this makes a practical difference. Can you maybe give an example that illustrates this well?

PBL

[italia458]

italia, I think by now it's for you to figure out.

PBL... that's classic. I can't say I expected anything more. Can we stop the false accusations then, please? All these posts are public for everyone to see, so no use in using those antics.

[PBL]

So, to partially answer my question to ft, and to answer my question Is there anything else to say? affirmatively,

Let me consider the earth to be a sphere with circumference 21,600 nm (i.e., 1nm = 1 minute of arc), giving a radius of 3437.75 nm. Flying level at 1,000 ft (about 1/6 nm) in a great circle, you are flying a circle radius 3437.916 nm. So your TAS is a factor of 0.00004829, that is, 0.004829%, higher than the speed of a vehicle on the ground vertically underneath (i.e. on the same radius to the center as) you. Generally, for every 1,000 ft higher you fly, your GS (Kayton defn) will increase by this factor.

Kayton suggests that the deflection of the vertical is "commonly less than 10 seconds of arc and rarely greater than 30 seconds of arc", as I quoted. Taking his 30 sec figure, that would yield a correction cos(30 sec) to TAS, therefore to GS. The correction factor is (1 - cos(30 sec)) = (1 - cos(0.0001454 rad)) = 1.057 x 10^(-8), which is about 1/4000th of the 1,000-ft-altitude factor. The correction factor for 10 sec of arc, (1 - cos(10 sec)), which is what Kayton suggests "commonly" is the case, is 1.1752 x 10^(-9), about 1/40,000th of the 1,000-ft-altitude difference.

That suggests that the difference in GS (Kayton defn) due to geoid undulations is negligible compared with a difference in GS (Kayton defn) due to an altitude difference of about 1,000 ft.

PBL

[ATCast]

Kayton suggests that the deflection of the vertical is "commonly less than 10 seconds of arc and rarely greater than 30 seconds of arc", as I quoted. Taking his 30 sec figure, that would yield a correction of cos(30 sec) to TAS, therefore to GS. Cos(30 sec) = cos(0.0001454 rad) = 0.0001454, which is about 1/6 of 0.000873. Cos(10 sec), which is what Kayton suggests "commonly" is the case, is 0.00004848, about 1/18 of 0.000873.Wow, you've lost me now. Last time I checked, the cosine of a very small angle was almost 1, but they might have changed that in the mean time :E.

The fractions of 1/6 and 1/18 do work out though, but I have no idea how you come up with 0.000873 :confused:.

Maybe you need to finish your morning coffee before posting...

Assuming the figures of 30 arcsec and 10 arcsec are right, the ratio of the speeds in the two different reference frames (vertical orthogonal to ellipsoid & vertical = aligned with gravity) is then 1/cos(30 arcsec) =1.000000011

That difference is really too small for me to worry about.

ATCast

[PBL]

Wow, you've lost me now. Last time I checked, the cosine of a very small angle was almost 1, but they might have changed that in the mean time

It was changed very briefly between 0700 and 0800 UTC this morning, but it is now changed back, so I corrected my note to reflect that :O

....I have no idea how you come up with 0.000873
That is the factor for 6,000 ft = 1 nm of altitude, since I was expressing radius in nm. I forgot to edit it out.

Maybe you need to finish your morning coffee before posting...

Yes, well, that is an astonishingly accurate statement (I didn't know we had a hidden webcam in the house). I will certainly keep it very much in mind for the future.

That difference is really too small for me to worry about.

Use is in the eye of the beholder, in this case ft. I wonder what he has in mind?

PBL

[Pugilistic Animus]

Just let'em talk:}












they're crazy