Collimated Mirror Design Calculations

[Jack Sprat]

Hi to all the dedicated knowledgeable enthusiasts on this great site. I need your help!

I am a newbie to the world of sim design, but it is a field that fascinates me.

I am trying to get my head around the subject of collimated display design; this site has really opened my eyes and helped enormously.

Having gleaned the basic principles from this site, i.e. to start at the view point and send a beam of parallel light rays to the spherical mirror and find where the ‘reflected’ rays then converge to identify the screen surface location, I have constructed a basic spreadsheet that does this and draws the results.

I chose some rough parameters, e.g. for how far the crew sits apart, mirror radius, etc. I positioned the mirror-viewpoint first in the vertical plane, to give me a screen solution for the required vertical field of view.

In the horizontal plane I used two viewpoints, one for the pilot and one for the co-pilot.

For each viewpoint I identified the corresponding screen surface location. I also did this for a central viewpoint located in between the pilot and co-pilot.

The results are shown in the pictures attached. Also drawn is the focus position of the mirror.

The results in the horizontal plane show that for each viewpoint the screen surface is located in a different position. As real simulators work fine with one screen only, there is a difference between my calculated solution for screen position (two screen locations) and the real solution (single screen location).

I want to understand why this is the case. Are my calculations wrong or should I use a single viewpoint to design the mirror?

If my calculations are right then it implies that in the real simulator the single screen is in fact a compromise position to accommodate both viewpoints of the pilot/co-pilot. This would mean that there is a tolerance associated with the screen location i.e. there is a zone around the viewpoint of the ideal position in which the display still functions properly. I would like to be able to calculate this zone.

Can anyone tell me if these assumptions are correct? Also how can the zone in which the mirror display can be properly viewed, be calculated? I would hate to build a cockpit and find that the display does not work for the positions of pilot/co-pilot.

I would appreciate any feedback anyone can give on this.

[Jack Sprat]

My original has hit a glitch that has now deleted the post from viewing, during an attempt by me to edit it and include pictures. I have repeated my post below.

I am a complete new guy to the sim world and I would like to understand the principles of a collimated display. From reading other posts I have learned the basics of start at the viewpoint and send parallel rays from there to the mirror and then determine where the reflected rays meet and that point represents the location of the screen surface.

I made a spreadsheet to calculate these points and draw the results of viewpoints, mirror and screen surface, in the vertical and horizontal planes. I did this for each viewpoint of the pilot and the co-pilot separately; I also included the results for a viewpoint located midway between the pilot and co-pilot.

The results from this are shown in the diagrams below; it shows that a different screen surface is optimum for each viewpoint of pilot and co-pilot. As real simulators only have one screen I wondered if there is an error in how I have calculated the screen surface points.

From documents in another thread I now suspect that my mistake was treating each viewpoint separately, when i should have used a single light ray from each viewpoint to determine the screen surface. I will do this and see how the results change.

My original question was how to calculate the locations of viewpoints from which a given setup of mirror-screen works properly. If anyone can give any feedback on how to do this I would really appreciate it.
JS