You have 17 cm (53-38) to play around the gap with the track and air corn lah.
You need to those the aircorn folk who install the pipi where and how high your track be, they will know how to arrange it.
How my aircorn folk measure is start from the "bottom of the aircorn water pipe" till 15 inch, those will belong to aircorn.
I have done by aircorn piping around April, where the aircorn folk have done a good measurement which allocated 22 inch from pipe to the root, included 7 incn after plaster ceiling. But end up it need to drill again, as the plaster ceiling folk make it 9 inch, which cause the pipe and plastec ceiling on leave 13 inch. With this 2 inch I have to pay extra to drill again as I didn't want to open a Box at the plaster ceiling.
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This is another area which short of almost 4 inch after plaster ceiling in place

, and you could see how the whole measure should be, and ease you to understand
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Thank you, I'm clearer now.. But really.. installing air con seemed like a nightmare to coordinate between these folks.