# Finding glider reachable area / catchment area with custom slope?

I'd like to produce maps for gliders in mountains.

I'm looking to display the reachable area by a glider taking off from a given point (obviously with the corresponding DEM).

For a first approach I'll suppose that we are in static air, no thermal ascent, no wind.

So like water gliders only go down.

Gliders have a specific slope (the glide ratio).

I started thinking that my problem is similar to a flood inundation analysis. But I cannot find how to input a specific slope in any of the hydrology modules I explored.

@Spacedman propose a first approach by creating a raster representing a shallow cone centered on the take off point and having the glide ratio as slope. It is a good approach without any obstacles.
Imagine you have an obstacle on the straight line for example there is a cylinder.
The area behind this cylinder may appear as "reachable" but the distance behind the cylinder from the take off point is (straight D)+𝚷(cylinder_radius). So obviously there is 𝚷(cylinder_radius)/glide_ratio difference in height.

Is there another approach that I could use?

Implementation of approach without any obstacles:
G is glide ratio (ie: ∆D/∆z)
(x₀,y₀,z₀) is taking off point
(x,y,z) are coordinates of a point on the glider reachable area
(x,y,zₑ) are coordinates of the projected point on the earth DEM
Hₑ is height over the ground

$z=z_{0}-\frac{\sqrt{(x-x{_{0}})^{2}+(y-y{_{0}})^{2}}}{G}$

$H_{e}=z-z_{e}$

$H_{e}=z_{0}-\frac{\sqrt{(x-x{_{0}})^{2}+(y-y{_{0}})^{2}}}{G}-z_{e}$

Obviously if Hₑ≥0 it is reachable otherwise not.

• Create a raster that is basically a shallow cone centred at the glider with the glide ratio slope. If that cone is greater than the DEM then its in range, otherwise it isn't. That gives you an upper limit that doesn't include obstacles... Apr 22 '19 at 8:31
• @Spacedman I've re-opened this to enable you to write your comment as an answer.
– PolyGeo
Apr 22 '19 at 12:52
• I'm going to have to implement this in R or QGIS now though! :) Apr 22 '19 at 14:24
• @Spacedman this is a good idea! It is working perfectly without obstacle. The main problem is if an obstacle is on the straight line for example a cylinder. The area behind this obstacle may appear as "reachable" but the distance behind the cylinder from the take off point is (straight D)+𝚷(cylinder_radius). So obviously there is 𝚷(cylinder_radius)/glide_ratio difference in height. Apr 22 '19 at 14:34
• Do you need to constrain it so there is line-of-sight from the starting point and the landing area? If not, will you still show hard-to-get-to potential landing areas, e.g. one that would require a sudden tight turn shortly after take off? May 1 '19 at 21:53

The only solution I found is to generate a geotiff/tfw world file with Matlab/Octave. This is my sample code for a glider with ratio 7 taking off from the "Aiguille du midi" near Chamonix Coordinates are in official french RGF93 (EPSG:2154)

``````%G is glider ratio (7)
%x0,y0,z0 is the take off point (Aiguille du Midi / Chamonix / France / EPSG:2154)
%r is the x resolution in meters (30m like SRTM)

G=7;
x0=1002092;
y0=6538705;
z0=3604;
r=30;
x=x0-(z0*G):r:x0+(z0*G);
y=y0-(z0*G):r:y0+(z0*G);
Xmin=x(1);
Ymax=y(end);
[X,Y]=meshgrid(x,y);
z=z0-sqrt((X-x0).^2+(Y-y0).^2)/G;
Z=uint16(z);
imwrite(Z,'cone.tif');
fid = fopen('cone.tfw','w');
fprintf(fid,"%f\n%f\n%f\n%f\n%f\n%f\n",r,0,0,r*(-1),Xmin,Ymax);
fclose(fid);
%For viewing the mesh uncomment next line
%mesh(x,y,z);
``````

This is tested with Matlab R2018b and GNU Octave 5.1.0, the generated cone.tif works in QGis 3.6.2

I'd like to find a more automatic solution. Hope someone can help.