Shady,
As Biffo has already stated direct routings are offered when they can be, and at weekends and from late evening to early morning whe our military cousins are flying less and danger areas are cold we will offer routings as a matter of course.
The main problem with a direct route is that they can involve a fair amount of coordination, especially if the sectors involved are not expecting and have no details on you. It makes conflict detection a bit more difficult which is why sometimes you will be told that a direct route is not available only to be offered the route later on. this is because you can now point out the aircraft involved on the radar and can mentally judge you against his/her traffic and agree or not as the case may be.
If a routing involves just me and one other agency (ie maas, or ekch for example) then i know i am more likely to ask the next centre if a direct is available. the exceptions to that are routings into londons airspace where, in my experience directs can be a bit limited until the mil give off route approval at which point LACC are very accomodating. They have the same problems as us and no doubt others with regard to the complexity of the airspace and the placement of the many danger areas throughtout the uk which restict the use of directs.
If a routing involves more than one agency then the coordination required gets to a point where it becomes too involved to be worthwhile. not exactly the news you want to hear as a user of the system i know, but we have to draw the line somewhere
For instance in scottish airspace we get requests for direct DIK from luxembourg arrivals coming down the north sea via TOPPA. No. 1 problem is that if the danger areas are active then you haven't a hope in hell. that corner of airspace is too small to shoot you through on a direct track between them. if they are not active and we send you too early(obviously dependent on which direction you're coming) you cut across the bottom right hand corner of londons airspace at lamso which can be very busy late into the evening with east and west bound traffic and they will have no details of you at all so coordinating would be a nightmare. Better to wait until the LACC person can see you and then ask (provided i dont get side tracked and forget that you asked for direct in the first place
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Hope this helps you understand a little as to why you get turned down and that we will give you direct when we can. That said, like biffo i dont mind you asking. if you dont ask you dont get!
