Dont know if this is any help, i'm not sure of actual figures but I travel two ID's, one is 16.1 but the other is 17.0 and she seems to have plenty of headroom in our Ifor Williams HB510 trailer.
I drive a Renault Master 3.5 tonne with 7 foot headroom. When I first saw them I didn't think it would be tall enough for my mare who is 16.2 1/2hh, but she is fine and travels in it very happily
I did ask myself 'what if she threw her head up for any reason'? Then quickly realised that if she did that she would also hit a 7ft 3in or indeed a 7ft 6in and the extra inches would just allow her to put more power behind it.
Remember also that so much depends on their wither, length of neck etc. I'd say try your horse in the box and see what you think then.
Thats nice to know! Lorry I have just brought has 7ft headroom and was concerned cos think my horse is growing into a full up 16.2hh, but sounds like we will be fine for some time!
My friend just bought a IW505 for her 16.3hh and I thought OMG as my 16.1hh seemed too big especialy length ways but her horse is fine. I would go for a 7'3 min headroom, Bateson or HB510 though. Think it depends on head carriage and travel experience.
Thanks everyone.
Stella I do tend to agree, to get a lorry with enough headroom for my horse not to be able to hit his head, well he'd have to be tied down and the box would need to be about 9ft!! lol