Moving boats

[omar]

There is an interesting forum thread at
http://www.virtualregatta.com/forums/viewtopic.php?f=35&t=11678
The guy studied how VR algorithm moves boats in regattas.

(zedstar http://www.virtualregatta.com/forums/memberlist.php?mode=viewprofile&u=1560205)

To me there are 3 possibilities:
1- Move boats using flat trigonometry.
2- Move boats using spherical trigonometry (Great Circle formulas).
3- Move boats using an ellipsoid model (such as WGS84).

Number 3 probably gives the results closest to the real thing
(since gps devices give wgs84 coords)
This calculation can be done using Vincenty formulas. Check this site:
http://www.movable-type.co.uk/scripts/latlong-vincenty-direct.html
Needless to say, the formula is big and slow to calculate.

I tried to check the differences between the results of the 3.
Let's say our boat is sailing at 20 knts. In 10 minutes it sails a distance=6.17 km.

for lat1=0, lon1=0
Course=0 --> GC= 0°03.33'N / 0°-0.00'W | flat= 0°03.33'N / 0°-0.00'W | vincenty dest= 0°03.35'N / 0°00.00'W - flat-vinc=34.63 m | flat-sphe=0.002 m
Course=45 --> GC= 0°02.35'N / 0°02.35'E | flat= 0°02.35'N / 0°02.35'E | vincenty dest= 0°02.37'N / 0°02.35'E - flat-vinc=24.96 m | flat-sphe=0 m
Course=90 --> GC= 0°00.00'N / 0°03.33'E | flat= 0°00.00'N / 0°03.33'E | vincenty dest= 0°00.00'N / 0°03.33'E - flat-vinc=6.90 m | flat-sphe=0 m

for lat1=45N, lon1=0
Course=0 --> GC=45°03.33'N / 0°-0.00'W | flat=45°03.33'N / 0°-0.00'W | vincenty dest=45°03.33'N / 0°00.00'W - flat-vinc=3.47 m | flat-sphe=0.002 m
Course=45 --> GC=45°02.35'N / 0°03.33'E | flat=45°02.35'N / 0°03.33'E | vincenty dest=45°02.35'N / 0°03.32'E - flat-vinc=9.25 m | flat-sphe=3.34 m
Course=90 --> GC=44°60.00'N / 0°04.71'E | flat=45°00.00'N / 0°04.71'E | vincenty dest=44°60.00'N / 0°04.70'E - flat-vinc=17.48 m | flat-sphe=2.98 m

for lat1=80N , lon1=0
Course=0 --> GC=80°03.33'N / 0°-0.00'W | flat=80°03.33'N / 0°-0.00'W | vincenty dest=80°03.32'N / 0°00.00'W - flat-vinc=25.70 m | flat-sphe=0 m
Course=45 --> GC=80°02.35'N / 0°13.61'E | flat=80°02.35'N / 0°13.56'E | vincenty dest=80°02.34'N / 0°13.55'E - flat-vinc=26.69 m | flat-sphe=18.93 m
Course=90 --> GC=79°59.99'N / 0°19.17'E | flat=80°00.00'N / 0°19.17'E | vincenty dest=79°59.99'N / 0°19.09'E - flat-vinc=31.80 m | flat-sphe=16.94 m

The larger difference between the 3 formulas seems to be around 34 m (0.55% in 6.17 km)
Pretty small. Note that flat to spherical differences are even smaller.
So it doesn't make much difference which formulas you use..

[Ricoo]

Thanks Omar, for having made this study and publishing your result.
If you allow me, I'd contest a little your conclusion.
According to me, 0.55% in 10 minutes is a tremendous shifting.
What would it make after 5 hours, which is not that much ?
About 1 km ?

[omar]

Ops.. removed code for correction... be back soon..

After 5 hours it could be 100 seconds. This may be large when
comparing boat times (=competition).
But if every one is subject to the same formula,
its really not much.. In geological time

[Photophore]

Thanks Omar, for having made this study and publishing your result.
If you allow me, I'd contest a little your conclusion.
According to me, 0.55% in 10 minutes is a tremendous shifting.
What would it make after 5 hours, which is not that much ?
About 1 km ?

It may even been more than that, considering that a little shift in lat or lon involves sometimes a change of wind square.

Note: with VR, the travel of the boat does not follow a great circle course but small 10-minutes-long great circle segments.
Each of these segments start the same bearing (boat bearing).

[omar]

I run an experiment with 3 boats, starting from the
same point ( 36S 56W near Punta) and time.
Velux boat, nice 20 knts SW wind.

Each boat used a different model (formula) for movements.
- Spherical formula - boat passoca (blue)
- Flat Mercator Trigonometry - boat pangrilo (orange)
- Vincenty WGS84 - boat jacare (green)

In the figure below we see the result.

After 7 hours (122.1 NM) the difference between
green and orange is about 0.25 NM.
Flat and spherical are pretty close.
WGS84 (green) is a little out.
Maybe this is because this is geodetic coordinates ?

You say for this to be right, one should integrate a rhumb line?





http://en.wikipedia.org/wiki/Geodetic_system

[Photophore]

I run an experiment with 3 boats, starting from the
same point ( 36S 56W near Punta) and time.
Velux boat, nice 20 knts SW wind.

Each boat used a different model (formula) for movements.
- Spherical formula - boat passoca (blue)
- Flat Mercator Trigonometry - boat pangrilo (orange)
- Vincenty WGS84 - boat jacare (green)

In the figure below we see the result.

After 7 hours (122.1 NM) the difference between
green and orange is about 0.25 NM.

Nice test.
Have you used the same value as Zedstar for the Earth radius in the great-circle computation?

One note about the 0.25 nm: at most 1" (angle) = 60 nm/3600 = 0.017 nm
=> Estimation for 0.25nm : about 15"

[omar]

The Radius of the earth was assumed to be 6371 km
for spherical and flat formulas.
Used the formulas from the excellent website:
http://www.movable-type.co.uk/scripts/latlong.html

For WGS84 ellipsoid it goes:
a = 6378137 m //a & b semi-axis
b = 6356752.3142 m
f = 1/298.257223563

To be really realistic, one should
use a rhumb line ( a segment sailed with fixed course ),
integrated over the 10 min period, using WGS84 ellipsoid.
This is what a real sailor would read in the GPS device.

That would be some formula...

[reves de gosse]

Thanks for your study, Omar.
Practicaly, the roads are so close that it's almost invisible.
Except in one case : if you are very close to the wind limit, and with a 90° bearing, you can pass the limit unwilingly. And the result can be quite bad (I know it by experience ).
Hervé