# Why is there a difference between GPS Speed and Indicator speed?

I just played with flight simulator and noticed that the GPS shows different speed from the speed indicator in the cockpit. Also, GPS speed is higher than the Indicator. Any Idea why?

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tail or headwind? –  ratchet freak May 28 at 8:36
Acctually, I'm not sure –  Super Hornet May 28 at 8:39

The speed indicator in the cockpit shows indicated airspeed. Indicated airspeed is usually different than GPS speed, due to wind and aerodynamic effects.

GPS speed is your speed with respect to the ground. If you are standing on terra firma it reads 0. If it reads 100 knots you will be 100NM away from where you are now if you maintain that speed and track angle.

Airspeed is a bit different. It is not your speed with respect to the ground, but with respect to the surrounding air. So if you are standing on terra firma with 20 knots wind blowing in your face, your airspeed will be 20 knots. If you would do 100 knots airspeed against a 20 knots wind, your ground speed is 80 knots. If you do 100 knots airspeed with 20 knots tailwind, your GPS speed reads 120 knots.

But even in calm wind conditions you'll notice that the airspeed indicator will read lower than the GPS speed. This has to do with the way airspeed is measured.

Airspeed is measured with a pitot tube. A pitot tube has two pressure measurement ports. One that measures the total pressure $P_t$. This port is facing the incoming airflow. The other measures the static pressure $P$ and is placed perpendicular to the airflow. The difference between the two pressures is called impact pressure (pressure rise do to the airflow impacting the pitot tube) and is denoted $q_c$.

The impact pressure is related to the speed of the airflow the pitot tube is exposed to. If the flow is considered incompressible (which is an acceptable approximation for speeds up to 200 knots) the impact pressure can be derived from Bernouilli's equation.

$q_c = \frac{1}{2}\rho V^2$

• $q_c$ is the impact pressure in Pa
• $\rho$ is the density in kg/m3
• $V$ is the true airspeed in m/s

The airspeed indicator is calibrated for standard sea level conditions, where $\rho$ is 1.225 kg/m3. In reality the aircraft will fly at altitude and therefor the actual density of the air is lower. Therefor the indicated airspeed will be lower as well. For example if an aircraft flies 75 m/s (about 146 knots) at 6000 ft the density will be 1.02393 kg/m3.

$q_c = \frac{1}{2} 1.02393 \cdot 75 ^2 = 2879.8 \textrm{ Pa}$

The equivalent airspeed at sea level for the same $q_c$ is:

$V_{EAS} = \sqrt{\frac{2 q_c}{\rho_0}} = \sqrt{\frac{2 \cdot 2879.8}{1.225}} = 68.6 \textrm{ m/s}$

Your airspeed indicator will read only 68.6 m/s (133 knots) despite the fact that you are moving with 75 m/s (146 knots) with respect to the air.

Conversion of true airspeed to the equivalent airspeed can be done directly by:

$V_{EAS} =V\cdot \sqrt{\frac{\rho}{\rho_0}}$

• $V_{EAS}$ equivalent airspeed (m/s)
• $V$ true airspeed (m/s)
• $\rho$ actual air density (kg/m3).
• $\rho_0$ density at standard sea level conditions (1.225 kg/m3)

The effects of the lower density on your aispeed indicator become more pronounced the higher you go. Once you go faster than about 100 m/s true airspeed the effects of compressibility can no longer be ignored and the above no longer applies. Airspeed indicators are corrected for effects of compressibility and therefore don't use the equivalent airspeed but instead use calibrated airspeed for calibration.

$V_{CAS}=a_{0}\sqrt{5\left[\left(\frac{q_c}{P_{0}}+1\right)^\frac{2}{7}-1\right]}$

• $V_{CAS}$ is calibrated airspeed
• $a_{0}$ is the speed of sound under standard sea level conditions (340.3 m/s)
• $P_0$ is the static air pressure under standard sea level conditions (101325 Pa)
• ${q_c}$ is the impact pressure

The impact pressure is also a bit more complex for compressible flow:

$\;q_c = P\left[\left(1+0.2 M^2 \right)^\tfrac{7}{2}-1\right]$

• $P$ the static pressure
• $M$ the Mach number

Effectively, the higher and faster you get, the greater the difference between the indicated airspeed and the true airspeed. For example, Mach 0.8 at 40000 ft in no wind will result in a GPS speed of 489 knots, but a calibrated airspeed of only 242 knots, which is less than half.

Therefore at high altitudes and speeds, the indicated airspeed will be lower than the ground speed / GPS speed, unless you have extreme headwind.

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Very thorough answer, but I feel it's too advanced and math-heavy, unnecessary for a casual enthusiast (or even for a professional pilot). It reads more like an aerodynamics textbook than a conceptual overview. –  dvnrrs May 28 at 14:02
@dvnrrs I tried to write it in such way that when you skip over the formulas the basic concept still comes across. I included numerical values to illustrate the effects described in the formulas and included text blocks that explain what is happening. –  DeltaLima May 28 at 14:12
You definitely put a lot of effort into it, and it's great information for someone who is interested in that level of detail. For the context of this question though, I think the math should be skipped entirely, and the answer presented instead from a standpoint of what a typical pilot would know or need to know. Links to the more advanced stuff can always be provided for interested readers. Just my thoughts! –  dvnrrs May 28 at 14:17
@dvnrrs No! Please do not skip the math and explanation. Even though it's more than what was asked for it's relevant, useful, and fascinating, and (as usual on aviation.sx) I learned an answer to a question I didn't even know I had. Definitely filing this one away for reference. –  Jason C May 28 at 15:26
@dvnrrs It may be nice to break the answer into two parts. One for more casual users and one for more technical users/people who want to keep reading. That being said, I don't think that this is too bad as it is. –  Lnafziger May 28 at 16:20

Here's a very simple graphic of what you could be seeing:

And this is why we land into a headwind rather than the tailwind, since otherwise we would land at a faster speed and require more runway to stop.

GPS measures ground speed, or absolute speed. The pitot tube on the aircraft will measure the speed relative to the airflow around the aircraft.

Here's som helpful graphic from NASA on relative velocity:

Footnote: As Ratchet Freak demonstrates in his equation, you have to of course remember that this is simplifying it as flying straight into the wind and not taking account of the wind direction.

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That graphic makes my head hurt, but I cant stop staring at it –  David Grinberg May 28 at 15:31
Indicated "airspeed" is not a speed. At all. –  Jan Hudec May 28 at 17:56
@JanHudec for the non-pilots or aerospace engineers, care to explain? –  Nick T May 29 at 4:21
@NickT: It is a dynamic pressure, expressed as speed at which that pressure would occur at sea level at standard conditions. There are already two answers that explain it, so I don't have to. –  Jan Hudec May 29 at 4:38
Anyway, by missing the distinction between true and indicated airspeed this question is misleading. Despite the nice graphics. –  Jan Hudec May 29 at 4:42

The other answers about wind are true, but this isn't what you're seeing in your simulation. What you're actually seeing is the difference between true airspeed and indicated airspeed.

True airspeed is the plane's actual speed through the air. With no wind, this is the same as the plane's speed across the ground. This is what your GPS displays.

The airspeed indicator, on the other hand, is really just a "dynamic pressure" sensor. It works by measuring the pressure of the ram airflow. But as we know, as you climb up into the atmosphere, the air gets thinner - less dense, and lower pressure. This makes the airspeer indicator read lower than true airspeed.

The reason it's done this way is because all of the important aerodynamic stuff that can happen to a plane (like stalling) really is tied to dynamic pressure rather than true airspeed.

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How do you know the difference in the simulation isn't due to groundspeed vs. airspeed? –  user2168 May 29 at 4:14
@Articuno Because sims usually have wind off by default (for ease of flight); the question didn't mention wind; and because the question's wording suggested a non-expert who wouldn't know about IAS. –  dvnrrs May 29 at 12:15
@Articuno (Also I write software for professional flight simulators and am very used to fielding questions about sim behavior from people of all types. Call it professional intuition.) –  dvnrrs May 29 at 12:19
Then, i would add those caveats into the answer. People other than this specific asker will be coming to this question. Future questions will be marked as duplicates based on this question. I'd say something like "This isn't necessarily what you're seeing in your simulation." Because it's totally possible the other answers are correct. –  user2168 May 29 at 15:01

Indicated airspeed is an approximation of the plane's speed in the air. Wind can cause the true airspeed to differ from ground speed (what the GPS shows).

To convert it to ground speed you need to know the wind speed and add them.

$$\vec v_{air}+\vec v_{wind}=\vec v_{ground}$$

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Indicated "airspeed" is not a speed. At all. –  Jan Hudec May 28 at 17:56
@JanHudec Agreed, and it is even less accurate to say it's a "speed in the air." This answer seems misleading as currently worded. –  dvnrrs May 29 at 1:17