Definition of ground speed
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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...
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Originally Posted by Pugilistic Animus
Everything in engineering is an inexact solution...everything!
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
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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.
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
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.
altitude is irrelevant to an airplane because it is only interested in the wind speed direction
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.
well nearly everything in engineering is an inexact solution
....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.
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Relativity
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.
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.
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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.
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.
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.
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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.
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.
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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.
EDIT: 6 pages to come to this conclusion?! and they say "together everyone achieves more".... lol
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.
EDIT: 6 pages to come to this conclusion?! and they say "together everyone achieves more".... lol
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Originally Posted by Rushed Approach
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.
Originally Posted by italia458
I complete agree with your definition of groundspeed in the last paragraph!
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 on calibration which used a similar definition. LH2 supplied the further references
Originally Posted by LH2
[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.
[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.
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
Last edited by PBL; 13th Jul 2010 at 07:31. Reason: put in all the refs to have them in one place
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.
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.
Overreach
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 ?
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Good, because in this post from the 26th June you chose the other interpretation.
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italia, I think by now it's for you to figure out.
ft,
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
referencing a U.S. Defence Mapping Agency report from 1959. You said in this post that this makes a practical difference. Can you maybe give an example that illustrates this well?
PBL
ft,
Originally Posted by 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.
As to the difference between (a) and (b), I am (passively) informed that
Originally Posted by Kayton, p25
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 arc
PBL
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italia, I think by now it's for you to figure out.
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So, to partially answer my question to ft, and to answer my question
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
Originally Posted by PBL
Is there anything else to say?
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
Last edited by PBL; 14th Jul 2010 at 11:44. Reason: lack of coffee, brain damage, just seeing if anyone was reading, take your pick
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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.
.The fractions of 1/6 and 1/18 do work out though, but I have no idea how you come up with 0.000873
.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
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Originally Posted by ATCast
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
Originally Posted by ATCast
....I have no idea how you come up with 0.000873
Originally Posted by ATCast
Maybe you need to finish your morning coffee before posting...
Originally Posted by ATCast
That difference is really too small for me to worry about.
PBL