Oooohhh Genghis - you've hit sweet spot of mine. Unfortunately not shared by CAA or some worthy aeronauts of my acquaintance.
The short answer is no - haven't found anything in the literature. I've had honours student projects on the topic for the last 3 years and we've scoured the literature. We've also measured take-off performance (run and distance) using a hand held GPS (that's a story in its own right) for a range of aircraft
- Grob Tutor (thanks to the local UAS)
- Bulldog
- PA38
- Beagle Pup 1
- Bolkow 208c
We used 10 take-offs in each case, to get a reasonable stab at calculating 95% probability/confidence bounds on the results. With nil wind all aeroplanes meet the relevant FM/POH figures. In a x-wind (15 kts) , the 208 requires a factor of 1.2 to be applied to get the book figure. The others haven't been tested in a decent x-wind so the results there are inconclusive.
One might think that x-wind is an issue - after all the aeroplane is sideslipping during the take-off run so one might expect the drag to be higher. With this in mind an aircraft like the 208 might be amongst the worst, being boxy and slab-sided, whereas the Tutor might be the best with its slender tailboom.
I'm in the process of putting together a paper for the Aeronautical Journal on the subject, but it'll be a while yet - I need to get max x-wind days - believe it or not, quite difficult to get up here!
If anyone has any reference material on the subject, I'd be most keen to see it. BTW CAA view seemed to be that x-wind didn't need its own factor - that's what the 'recommended' PT 1.3 factor was there for.
Sorry for ramble....