gps72 speedo

Better than 1kph in practical situations with commercial GPS's - much better in good conditions.

gpsinformation.net/main/gpsspeed.htm

Mike Harding

I'd say no. The GPS could have been in your mates car travelling the same route as you in a convoy etc while you were fanging it to try and catch up with him after getting stuck behind a slower vehicle.
Plus the cost of fighting a speed ticket is probably higher than just paying it, unless demerit points are a major factor.

Thought of that while ago too.
Have my GPS to always record a track, and I can look at the track on Oziexplorer.
Oziexplorer can give me a track profile using speed or height versus distance or time.
Have GPS set to record at 50 metre intervals.

But it is not accurate enough, if it misses a reading (does a reading every second) speed on the track jumps.
Have had the pajero track record showing 200km/hr, and I know I didn't do more than 130 (overtaking down a hill) on the whole trip.

Hi Shaker,

That's not actually correct. A GPS works out speed by determining the distance it has moved between fixes and dividing it by the delta of the time. With accurate fixes, an error in speed occurs when travelling around a curve because the GPS presumes that it has moved in a straight line. In fact you can travel as far as you like between fixes, but if you get back to where you started from the GPS thinks your speed is zero.

I know I'm being pedantic and in normal use the error is not significant, but the distance error is accumulative and I don't know of any GPS that tries to allow for the error.

At 100 km/h with a curve of radius 50 metres the distance the car travels in one second (time between GPS fixes) is 27.77, however the straight line distance between the two positions is 27.42 m. At 200 km/h the difference is 2.81 metres and at 320 km/h (the top speed of my motorcycle) the difference is 11.25 m.

If you want to work out the distances then you can do the following. The formulae are in MS Excel format.

1. Work out how far the car has travelled between the fixes by dividing the speed by the time between fixes and multiply it by 1000 to change to metres. [=speed/60/60*1000]

2. Work out the circumference of the circle the curve would form by doubling the assumed radius and multiplying by pi. [=2*PI()*radius]

3. Work out the rotational distance in degrees by multiplying 360 by the distance travelled and dividing it by the circumference.

4. Work out the straight distance between the two points. This is done by dividing the triangle formed inside the circle into two right angle triangles. For each triangle, the sine of the angle (the one in step 3 divided by 2) in the middle multiplied by the radius gives half of the distance between the points. Multiply it by 2 to get the distance the GPS thinks you have travelled.
[=2*SIN(RADIANS(angle/2))*radius]

The error in speed will be the proportional to the error in the distance. Although the speed error is insignificant, the accumulated error in distance does become significant if the trip follows many tight curves.

Cheers Frank.

Damn good point - and one I hadn't thought of.

Where do you get the update rate of one second for GPS' though? It sounds reasonable but the update rate would be a decision made at the early design stage of a model and, I imagine, based upon the processing power available in that particular model, indeed under poor conditions the update rate could be much slower.

I think the same issue occurs with vertical changes (hills) as well? So bendy hills would be a real bugger :)

Mike Harding

G'day Mike,
Yes, you're right. The update rate depends on the GPS and my choice was arbitrary. I have one that updates every 1 second and three others that update every 1.5 seconds. The shorter the update interval, the less the error, so I just chose 1 second because it least favours my argument and is one less thing I might be challenged on. Driving through trees the update rate can blow out considerably without being noticed.

Hills would cause the same error if the gradient is curved, though not if the incline is constant. A GPS calculates altitude so changes in position are three dimensional. The error is introduced if the path taken between the positions isn't straight. Cresting a hill could give an error, as could going through a dip.

I'm glad you get this, Mike. I mentioned it briefly some time back and everyone seemed to think I was an idiot. That's why this time I showed how to work it out.

Cheers Frank.

_Four_ GPS'!? You got a _thing_ for GPS or do you just get lost a lot? :)

The one second assumption is perfectly reasonable, there is no good reason a commercial GPS would want to update faster than that.

I appreciate they calculate altitude (although rather inaccurately I think?) but I doubt most GPS' would factor changes in altitude into the speed equations - but they might?

>I'm glad you get this, Mike. I mentioned it briefly some
>time back and everyone seemed to think I was an idiot.

Not at all. I had simply never thought of it before but as soon as you described the issue it became blindingly obvious. However, in reality – and as you mention, it generally won't have much impact upon speed readings (more on distance) but... it might... and should be understood by people using GPS for speed or distance calculations.

Well done for highlighting it.

Mike Harding

PS. Essentially, it’s a practical manifestation of Nyquist’s theorem.

Site Link

Actually I have 5, I missed one.... my original Magellan which I bought in 1989 for $7,500. It was worth every cent at the time.

I read your Nyquist’s theorem page and now I need a little lie down.

i use my garmin III on my microlight as well as in the gu, and i must admit i've never looked at the speed on the gps when i am in a steep dive or tight circle. i note the gps speed mainly to compare airspeed against 'over ground speed'.
most of the time i have my eyes closed, especially landing.
however, i will attempt to look through my fingers the next time i go flying and report back.

The Australian Design Rules for vehicles (commonly called the ADRs) prohibit the speedo _ever_ reading less than true speed. iirc it can read significantly faster than true but, generally, modern cars will be pretty accurate up to about 80kph then tend to gain a bit and be in the region of 8 or 10kph over at a true speed of 160kph. General figures, of course.

Mike Harding

(See Mark, another reference for you - that's two in one thread :)

Right Mike, hence my comment that it is much less common for the speedo to read slower than actual. Unless there is an underlying problem, this would normally only occur if bigger than standard tyres are fitted.

I was paranoid about this when I fitted larger tyres and had made up a conversion chart to put on the dash of the 4B, only to find that I had made the speedo more accurate with the bigger tyres.