# Where does the difference between calculated and actual groundspeed come from?

I'm a paragliding pilot. At school we learn that the trim speed of a paraglider is about 38km/h airspeed, the accelerated airspeed is about 45km/h and the minimum airspeed is 22km/h - being inside the weight range of the wing.

If I fly with a headwind of 25km/h, my groundspeed should be: 38-25=13km/h.

Well, from my flying experience (1200 flights in total) with that kind of headwind I never went forward +13km/h groundspeed but much less, near the minimum relative speed (22km/h).

Why there's a difference between the calculated groundspeed 13km/h and the actual groundspeed?

• I second @ymb1's question; I don't see how you could know what your actual headwind component was at any given location without having at least an airspeed indicator which allowed you to compare computed true airspeed to GPS groundspeed. When I have flown with a strong headwind resulting in near zero groundspeed, I have always found that the headwind approximated my true airspeed.
– J W
Commented Mar 11, 2017 at 16:31
• @ymb1: At the landing area (beach) the Vw was about 20km/h calculated with a weather station. Commented Mar 11, 2017 at 16:50
• @Paragliding: The wind is generally stronger at altitude than at ground level. Commented Mar 11, 2017 at 18:46

I have a little paragliding experience. While only a tiny fraction of yours, I think I can answer your question, which boils down to: data accuracy.

The trim speed of a fixed-wing aircraft would depend on its weight. Without accurately measuring the pilot's weight (FYI the measurement in small aircrafts is precise to pounds / kilograms) and plotting that against a chart, the speed you were told in school is only an approximation.

I (like others in the comments also) question the accuracy of your speed data.

• To accurately measure forward airspeed, you'd need a pitot tube pointing in the right direction.
• Or you can use a wind measuring device which measures speed and direction
• To measure your ground speed accurately you'd need a GPS.
• To combine the two (wind speed + ground speed), you'd need some sort of computer to do the computation, either in real time or with recorded data.
• The ground station only measure wind speed at ground level. When you're up in the air (albeit relatively low compared to aircraft), the wind can be different.
• For sure data accuracy is one of the problems and the speed component at ground level. But in my experience, flying forward with 25km/h or more into the wind, makes it really harder to have some Vg. Thus, or the paragliding data from the manufacturers are not real or the formula Vg=Va-Vw has some limitations due to many other components. Amon others, again in school they teach that 25km/h headwind is the limit for us to fly forward. Commented Mar 11, 2017 at 17:15
• @Paragliding the only situation when the formula is wrong is when the speed concerned are comparable to the speed of light. Aircraft manufacturers use detailed lab tests (or computer simulations nowadays) to come up with a detailed chart where you can just plug in the weight on one axis and you'll get the exact speed on the other. Therefore the data you're getting is inaccurate is the most likely explanation. Commented Mar 11, 2017 at 17:19
• It's inaccurate because wind measured at ground level is usually much different as you get away from the surface. Commented Mar 11, 2017 at 17:21

It depends on the difference between the predicted wind speed for the winds aloft vs what was actually up at that altitude at a given time.

It also depends on doing your winds aloft calculations correctly and accounting for both the wind speed AND angle relative to the direction of flight. Take the winds at a 60° angle, our headwind component is only going to be half the total wind speed, etc.

Then there are installation and calibration errors. I don't know what a paraglider has on it in order to sense airspeed but a primitive pitot static system of some sort would be a reasonable guess. I don't know what kind of error may be associated with that as well.

• I know the value of my trim speed from the paraglider manufacture 37-39km/h. Then I fly into the wind, no brakes applied, no position change, 50m above the landing area in which the Vw is 18-20km/h. Then somebody down calculates my shadow path from point A to point B, 100m straight line. Based on theory, I should have a Vg of 38-20=18km/h. Based on what we measured I had a Vg of 8-10km/h. The difference is quite important for a paraglider. We did some other tests in windy conditions and the result is that the Vg is less then Vg=Va-Vw. Even in calm conditions the Vg is never equal to Va. Commented Mar 11, 2017 at 17:08
• The wind speed, and direction, can be significantly different on the ground versus 50 meters in the air. When the air is close to the ground it is subject to ground friction. Wind is usually stronger as you go higher which would correlate with your measurements. Commented Mar 11, 2017 at 17:13
• You are right but even flying in nil wind very early in the morning the Vg is not equal to Va calculated with the same method. I believe that one of the reasons has to be found on the fact that we do not have an engine to adjust thrust (just our body) and in real life the wind force/typology is never ideal, laminar and uniform. Commented Mar 11, 2017 at 17:21
• No wind on the ground doesn't mean none at altitude. I remember talking off on a calm day and when I transitioned to slow flight at 2000', I was actually flying backwards relative to the ground, which meant I had a 45kt headwind. Commented Mar 11, 2017 at 17:28

Actual groundspeed is not in itself a useful (or deterministic) number while flying. It's useful as a concept.

You get your measured ground speed from your instruments / sensors. They'll give you a reading that's as accurate as you can get. This isn't enough for most flights however. Even in 2017, our data is still faulty.

In engineering, the difference between actual and measured anything is called the error. In this case, groundspeed has an error while using instruments. Errors usually come in ranges. For example, in paragliding, you may see a measured groundspeed of 12mph, with an error of +/-1, meaning that the actual ground speed can be between 11 and 13 mph. Error can also have two parameters as it's range. For example, you may be going along at 12 mph, and have an error of +2/-0, meaning that actual speed is between 12 and 14 mph. usually one of the parameters in a two-parameter error will be zero. If they're both non-zero, non-equal values, you're going into probability distributions, and other mathematics of the sort.