I originally asked the question:
If there is sufficient landing space, would it be possible in some
cases to replace the helicopter with a small fixed wing aircraft with
low stalling speed?
Looks like DARPA beat me to it:
https://news.usni.org/2014/03/19/darpa-awards-contracts-search-460-mph-helicopter
Many great answers here: I can summarize the solutions available as follows:
Add high lift devices to a 200 knot light aircraft, such as leading edge slats, double slotted Fowler flaps, blown flaps, canards and flaps such as the Robertson conversions, in-wing powered rotors or auto-rotating gyrocopter type rotors. (The last one is an idea I have not seen anywhere in print)
VTOL type aircraft such as the Canadair CL-84 fits the bill very well: 15 passengers and 200 knots or more. A smaller aircraft with less power would work, perhaps with modern electronic autostabilization.
Aircraft with low wing loading or variable incidence delta wings or low aspect ration wings such as the Flapjack. Variable incidence will solve visibility problems.
One option not mentioned are lighter than air hybrids, but I will not go into that right now.
Aircraft can match the high descent rates required for obstacle clearance (500 ft obstacle at 4000 ft from landing area), but land with too high a forward speed to stop within the helipad. It all depends then on the combination of how slow you can land the plane, and the landing roll required.
Taking off in a short space will require high power as well as a low take off speed, but low take off speed does not seem so critical.
The VTOL concept has been proven to be able to meet the requirements. It would be very interesting to see a mini V-22 or CL-87 and some of the newer electric VTOL proposals I think have this.
Without the 20 knot landing speed, the goal of landing in small spaces in an aircraft has been nicely demonstrated by this video I came across recently. Really amazing:
The 20 knot landing speed appears not be necessary, if the aircraft can land and stop within a short distance: this short distance is a variable and I would attempt several combinations of landing distances that will be useful for the aircraft operator. Basically I am looking for instances where the helicopter can be replaced by a STOL airplane. A piston single with high lift devices and a lot of power would be suitable with antilock brakes or reverse thrust.
Using a flight simulator has been useful for this purpose so far: I hope to do some testing and report. Here is one such trial:
Edit:
There are two ways to approach this: take the fastest two seat kit plans and add flaps and retractable slats, increase wing area or reduce fuel, or make the plane larger.
The Helio Courier is being developed as a turbine powered version: A re- arrangements of parts to make a sleeker aircraft will more or less result in what I am looking for:
http://www.helioaircraft.com/ourplanes_stallion.htm
The Stallion features a 750 shaft horsepower Pratt & Whitney PT6A
turbo-prop engine. The plane is designed to be fully maneuverable and
controllable at 37 knots and has a cruise speed of 175 knots.
Edit: It occurred to me that Light Sport Aircraft, with their stall speed limited to 35 knots, might fit the bill if they are fast:
This one with a further STOL kit would do nicely:
Stall Speed with Flaps 53 km/h / 29 kt
Max Cruise Speed 305 km/h TAS / 165 kt
Landing Groundroll and Takeoff Roll 150 m / 490 ft
https://www.jmbaircraft.com/aircraft