I'm currently working on an aircraft design project for a regional turboprop. I wanted to know if there are any regional TP's with leading-edge devices. It seems that a lot of them have deicing boots on the leading edge that make high lift devices difficult to install. Also maybe TPs just don't need the additional lift.
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Neither the Dash 8 nor ATR families (which cover the bulk of regional TP market) do.
Your last two sentence pretty much summarizes it. Some of the additional lift potential of a slatted wing is from the camber increase when the slat is extended, but most is from the ability of the wing to operate well beyond the normal stalling AOA of around 15-16 degrees, into the low-mid 20s. You have to design your airframe to operate at very high pitch angles to exploit this. I'm not sure that boots are a factor because there isn't really anything stopping a designer from installing boots on a slat (it's effectively a rubber air mattress glued on the LE with contact cement).
Jets use slats to improve safety margins at reference (approach) speeds (also lowering the reference speeds somewhat) with their more highly loaded, high speed wings (over 100 lbs/sqf, with supercritical airfoils that have poor stall characteristics - the 737 is in the 140 lb/sqf range). Turboprops operate with somewhat lower wing loadings (under 100 lbs/sqf - the Q400 is about 97 lb/sqf) and more gentle-stalling airfoils, and don't really need slats to achieve the mission objectives cost effectively.
None of the DeHavilland Canada products, even those designed for extreme STOL like the Caribou/Buffalo or Dash 7, have used slat systems. It was preferred to use fixed leading edge cuffs (drooping LEs) and elaborate double slotted flaps (full span in some cases) to get the desired lift coefficients at "normal" approach deck angles.
The regional airliners like the Dash 8 are not designed for STOL operation in the first place (the Dash 8 is a redo of the STOL Dash 7, which was a marketing mistake, developed around a "stub runway" concept based on MLS that never materialized), so there even less of a need for them.
