[R-sig-Geo] gdistance: working with vector speed data in two direction

[tf at devmag.net]

Dear Jacob,


thank you for your prompt response. I am not sure whether I really  
understand the material in the link. This is alll considering the case  
when one is aboard a ship and measures an apparent wind direction and  
a given speed of the boat.

Essentially, what I have is the direction and strength of the wind and  
I want to transform this into a speed of a boat going in a certain  
direction.

The example I was thinking about was something very simplistic:

Think of the boat being in the center of a 9x9 grid and hence  
technically it may be able to move into all 8 cells.  So lets just  
assume that the course the ship can take are courses -180 -135 -90 -45  
0  45  90  135 180  degrees (by assumption), where a course 0 degrees  
means going to the center row rightmost cell.

Next I assume that the ship "does not accumulate speed", going from  
cell to cell - think of this representing the water friction.

Also for simplicity I assume that the ship can sail at most at 90  
degree angles to the wind (in either direction), so for wind coming at  
angle alpha, the ships courses can range from alpha-90 to alpha+90.

I am really not sure how realistic this is, I guess it corresponds to  
the ship having a drag and a lift sail, see

http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/


I think these two features make the transition function less  
straightforward. I just computed a simple example.

Suppose the wind blows at 75 degree angle with speed 10 m/s.

Now the ship wants to move into a 45 degree course to reach the upper  
right cell. What is its speed?

The angle between wind and ship course is 75 - 45 = 30 degree. Of the  
10 m/s wind going in direction 75 degree, only a portion is used on  
the 45 degree course. This portion is:

v = cos(30)*10 m/s

For top center cell (90 degrees course)
v = cos(90-75) * 10
Top left cell: (135 degrees course)
v = cos(135-75)*10

The right center row cell (0 degree course)
v = cos(75-0)) * 10

The bottom row right cell as well as all other cells  can not be  
reached, as the course angle abs(course - 75) > 90 degrees.

So I need to assign these transitions speed 0.


This is not what I had originally in mind, as its a crude  
simplification but maybe its one on which I can iterate.


The key question is now, how do I implement this? I dont quite  
understand how I can define the transition function to use these  
different course angles for the 8 adjacent cells - essentially, it is  
a "different function" for each of the 8 adjacent cells.


I hope this is a bit more clear, thank you very much for your help,

best Thiemo


Zitat von Jacob van Etten <jacobvanetten at yahoo.com>:

> Dear Thiemo,
>
> Nice question.
>
>
> The wind direction/speed would need to be converted into a cost or  
> speed variable. This website explains how:
>
> http://sites.google.com/site/yoavraz2/sailingboatspeedvs.windspeed
>
> Best,
>
> Jacob.
>
>
>
> ________________________________
>  From: "tf at devmag.net" <tf at devmag.net>
> To: r-sig-geo at r-project.org
> Sent: Thursday, 8 December 2011, 11:11
> Subject: [R-sig-Geo] gdistance: working with vector speed data in  
> two direction
>
> Dear all,
>
> I have the following problem.
>
> I managed to use the gdistance package to give me computations for  
> shortest distances between two ocean points. I am working on a  
> simple 1 degree grid for that and it works fine.
>
> However, now I want to incorporate something slightly more advanced.  
> For each cell of the grid I have a wind vector with its horizontal  
> and its vertical wind component; the units are speeds in meters per  
> second, which can be positive / negative indicating the direction  
> north/ south, east and west.
>
> I have both of them as a raster object.
>
> Similar to the vignette hiking example, I want to compute the  
> fastest way to get from A to B. Imagine that the object that moves  
> from A to B is a sailing boat that wants to exploit the best  
> possible combiantion of winds along all possible paths from A to B.
>
> The data structure for now is as follows:
>
> vertical <- raster(nrows=10, ncols=10)
> vertical <- setValues(vertical, runif(10*10, min=-1, max=1) )
> horizontal <- raster(nrows=10, ncols=10)
> horizontal <- setValues(horizontal, runif(10*10, min=-1, max=1) )
>
> In the hiking example, the direction was either going up or going  
> down which was captured by the sign of the height difference (i.e.  
> the slope).
>
> They key difference here is, that I essentially have "two signs" for  
> both speed direction components.
>
>
> I am not sure whether this is possible using the gdistance package;  
> I would be happy to hear your thoughts and comments.
>
> Best,
> Thiemo
>
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