Ta Fred.
To put things in a slightly simpler note;
The makers of the HSI have designed the instrument in such a way that the arrow is pointed in the direction that one wishes to travel in. Consequently, the information displayed is only representative of the true horizontal situation when the arrow is set to the desired track.
However, the statement of "The arrow has no function when working with a VOR, the Beam Bar will always show the correct "picture". But it is vital to set the inbound track (QDM) on the arrow when using the HSI for an ILS, or you will get reversed demands - and quickly become confused!" is incorrect because if one fails to set the required track to or from the VOR, one will never establish on the correct radial.
Example.....ILS 28 has only one course.....280deg. Regardless of the direction the arrow is pointing, working on the basis that the arrow "points at the runway", the aircraft at the centre of the instrument will be displayed in the correct position relative to the beam bar. Thus if the aircraft is right of centerline, this will be displayed as such regardless of the position of the arrow provided that one remembers that the arrow points at the runway. In order to make that idea easier to understand, one must ignore the compass card...otherwise one gets confused.
Note we are talking about the aircraft position. Not the direction in which it is pointing.
Now if one wants to establish inbound to a VOR on a course of 280deg, unless the arrow is pointed to 280, the indicator will never directly tell where the required track is relative to the aircraft. Example......if the aircraft is SSE of the VOR and say the arrow just happens to point to 300, the beam bar will be out to the right and the flag will show TO. When the aircraft crosses the 310 inbound track, the beam bar will start to move towards the centre, reaching the centre as the aircraft crosses the 300deg inbound track and then move out to the left reaching full left deflection as the aircraft crosses the 290 inbound track. From that point on, no further information is provided and at no time has any information been provided relevant to the 280deg inbound track. That is why it is essential to set the required track when using the HSI to track a VOR.
To try the above, fail the slaved compas system i.e. the compass card driver and use the magnetic compass to find direction. Having done that, place the arrow straight up regardless of direction and track a few localisers.....the info provided will always be correct regardless of what number is behind the arrow on the compass card.
Now try tracking arround a VOR and one will find that in this case, the aircraft will only ever establish on the track indicated on the compass card.
Hope that is a better explanation!!!
Regards,
DFC