Definition of ground speed
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Definition of ground speed
Here's a question I never thought I would ever ask:
Can anyone point me to the definition of ground speed?
You probably won't believe it (I still don't do), but I just discussed two different definitions of ground speed.
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
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.
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.
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
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.
Last edited by ATCast; 21st Jun 2010 at 17:52. Reason: changed "speed" to "velocity" in (b). Thnx Wizofoz
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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
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
G
I would think that they are equivalent, as the velocity parallelogram gives that vector compnent naturally and it is likewise useful for flight planning 
(b) the horizontal component of the absolute speed
People will try and say "Relative to a fixed point in space"- this ALSO does not exist.
perhaps they mean the absolute value of displacement/time forexample you can run round a circle the equivalent of five miles in 1 hour or a straight line in the first case the velocity vector changes continously in the second case it will the vector and scalar values would be equivalent...but the absolute value of diplacement/time would still be 5 mph...although funny enough the FARs have no definition for GS 
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Wizofoz:
Absolutely right Wizofoz. I was trying to avoid being too technical. Now I was too fuzzy I guess.
The reference frame I meant is Earth Centered Earth Fixed, so speed relative to the (non rotating) earth.
Rephrased:
Groundspeed is the absolute value of
(a) the horizontal part of the ECEF velocity
(b) of the differential of the aircraft's position projected on the earth's surface (modeled by the WGS84 ellipsoid)
Feel free to shoot holes in the new definitions.
Or see it like this:
Assume the earth is a perfect sphere with a circumference of 40.000 km. When flying halfway around this earth at 10 km high you travel 20.000+PI*10 = 20031.415... km through the air, or 20.000 km measured on the surface. If you manage to do this in 20 hours, what is the average ground speed?
Definition (a): 20.031 /20 = 1001.57 km/h
Definition (b): 20.000 /20 = 1000 km/h
Genghis, I use that same approach in my aircraft performance related simulations. In the context of pitot-static corrections it perfectly makes sense to use velocity, since that is what drives the physics of the system.
In addition to that, the accuracy of the pitot-static system is such that the 0.16% difference between the two definitions (at 10km height) is probably within the measurement noise / tolerance, so it does not really matter how you define the ground speed in such a case.
For assessing the accuracy of GPS reported ground speed, the definition suddenly is important. Not in practical terms, because I am sure few people will care about the 0.16% difference, but for standardization/ certification ambiguity is a big thing.
Thanks for the feedback so far.
You cannot express speed without specifying speed
relative to what.
relative to what.
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).
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.
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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
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
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
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
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
PA,
Emphasis added.
Do you mean uncorrected? The calibration law for CAS does take account of compressibility. EAS doesn't - it has nothing to do with compressibility. The Bernoulli equation for dynamic pressure, q = ½ ρ V², is an incompressible solution to Euler's equation. This is still true even if ρ V² is swapped for γ p M².
Calibration law is in NACA Report 837 (Aiken, W. 1946. Langley.)
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.
Do you mean uncorrected? The calibration law for CAS does take account of compressibility. EAS doesn't - it has nothing to do with compressibility. The Bernoulli equation for dynamic pressure, q = ½ ρ V², is an incompressible solution to Euler's equation. This is still true even if ρ V² is swapped for γ p M².
Calibration law is in NACA Report 837 (Aiken, W. 1946. Langley.)
Selfin, those are the FAA definitions based on such items as the NACA reports they are most certainly correct
FAR part 1 is defining EAS as CAS after having been corrected for adiabatic compressibility
I know what you're talking about...true! but I'm not getting into Fluid Mechanics, continuity and such right now...not enough sleep... and no patience for copying and pasting integrals
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.
Last edited by Pugilistic Animus; 22nd Jun 2010 at 09:42. Reason: adiabatic
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?
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?
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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.'
As to how you can consider any form of PEC calibration using 'groundspeed' when you have no idea of the motion of the containing airmass.............................. .you'll need to explain.
PBL's elegant maths conclusively prove that the 'angle' subtended by the horizon has nothing to do with Tangspeed.'
Normal vectors cancel
you are not subtending an arc about a fixed point
one aircraft would simply have to begin his descent earlier/ or much much steeper, to reach the same place
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