What is the minimum speed at which the Antonov An-2 can maintain level flight?

Question

The An-2 famously has "no stall speed", as control can be maintained in descent at arbitrarily low airspeed. As wikipedia says:

The An-2 has no stall speed, a fact which is quoted in the operating handbook. A note from the pilot's handbook reads: "If the engine quits in instrument conditions or at night, the pilot should pull the control column full aft and keep the wings level. The leading-edge slats will snap out at about 64 km/h (40 mph) and when the airplane slows to a forward speed of about 40 km/h (25 mph), the airplane will sink at about a parachute descent rate until the aircraft hits the ground."[4] As such, pilots of the An-2 have stated that they are capable of flying the aircraft in full control at 48 km/h (30 mph) (as a contrast, a modern Cessna four-seater light aircraft has a stall speed of around 80 km/h (50 mph)). This slow stall speed makes it possible for the aircraft to fly backwards relative to the ground: if the aircraft is pointed into a headwind of roughly 56 km/h (35 mph), it will travel backwards at 8.0 km/h (5 mph) whilst under full control.

But there has to be some minimum speed at which it can generate just enough lift to counteract gravity, what is this speed (and does it have a general name)?

Answer 1

"No stall speed" just means no stall break in the traditional sense. The AN-2's slatted wing's maximum AOA is very high (typically about 10+ degrees higher than un-slatted, or mid-high 20s vs mid teens) and there isn't enough tail power to get the AOA high enough to get any kind of break.

Stall speed is normally published as the speed at which the wing is at maximum lift coefficient. A typical wing makes a Clmax of about 1.5, slats raise that to about 2.5, and a slotted flap raises that again to about 3.5-ish. The AN-2 has full span slats and flap-flaperons so you can assume that just about all of its 770 sqf of wing area is producing a Clmax of mid 3s with slats out and flaps down.

You can use the handy calculator on this page (click on the "Stall Speed Calculator" link) to work out what the speed is at which this is achieved. For the AN-2 you could assume with 770 sqf of wing area, with, for argument's sake, a Clmax of 3.5 for the entire wing, and operating at, say, a relatively light 9000lbs, you get a "stall" speed of 32.8 kts (37 mph), the speed that the wing is making maximum lift based on those assumptions and technically, this is the answer to your question.

With a slatted wing, the lift curve has a more rounded top; this is, lift declines fairly gently after the peak, so you can continue raising AOA and all that happens is sink rate goes up, until the tail runs out of downforce authority.

With power, thanks to the slats, you get both more tail downforce with the slipstream blowing on it, and because you can reach very high deck angles, you start to get a significant boost from the vertical component of engine thrust itself when the thrust line is canted up at, say 25 degrees. And on top of that you get added lift from the slipstream itself passing the wings..

If the engine is making, for argument's sake, 4000 lbs of thrust when at full power (you get roughly 4 lbs/hp) and the thrust line is canted up 25 degrees, there is a vertical thrust component of about 1700 lbs. This has the effect of reducing your weight by 1700 lbs, and plugging in a 1700 lb weight reduction into the calculator gets you down to about 29 kts (or 33 mph). Add in the additional lift from slipstream passing part of the wings dropping the minimum speed a few more mph, and you can see how you can get to the point of the plane being able to back up at 5 mph in a 35 mph headwind using power in the slow-flight regime, at a relatively light weight at least.

So, the AN-2, at a relatively light 9000 lbs, using the standard formula and using typical assumptions, should be able to fly at a minimum speed of 37 mph power off and about 30 mph or a little less power on without sinking, which agrees more or less with the article's statements.

Plus, there is enough tail power with power on to increase AOA a little more, getting speed down to 25 mph, but while it's under control, total lift will be declining and the airplane will be sinking while doing so.

None of this is particularly special. The AN-2 achieves its performance with lots of wing area and full span slats and flaperons. Other STOL aircraft with full span flaps and slats can do the same thing.

Answer 2

Generally speaking, the stall speed doesn't exist as the actual speed at which you might stall a wing depend on the loading of the wing. In a 60° level turn you'll experience a force of 2g's and the stall speed of any given aircraft will be increased by roughly 1.5. What is important is the stall angle of attack (AOA) which is defined by the profile of the wing. Keep in mind that lift doesn't vanish when you stall a wing but rather it's the drag vs lift coefficient that increase significantly.

I don't know much about the AN-2 but my explanation of what seems to be described in the Wikipedia quote would be a lack of elevator authority. This means that the elevator cannot pitch the nose up significantly to increase the AOA of the main wing beyond its stall limit. With the engine out, you can reach an equilibrium point where for a given speed (here 40km/h) your elevator generates just enough force to pitch the nose up to a given AOA. And let's say that at this AOA none of the surface are stalled. If your speed decreases the elevator will lose efficiency and the nose will pitch down, thus increasing your speed, giving you more elevator authority, pitching the nose up again, losing speed .... and so on. You'll never stall the aircraft because you can't pass beyond the critical AOA and thus you can keep aileron authority and "fly" the aircraft. But there are no way to ease your landing so this is pretty much the same situation as pulling the emergency chute of your Cirrus in case of the engine dies out in IMC conditions.

"Control can be maintained in descent at arbitrarily low airspeed." Following the above explanation I'm actually not sure you will be able to slow the aircraft below 40km/h so you don't have arbitrarily low airspeed.

For the second part of your question there are 4 forces interacting in flight. Thrust, gravity, lift and drag. To fly level, you need to balance out everything.

The lift equation can be written as $C_l*AOA*V^2$ where Cl is a constant with air density, surface area and lift coefficient of the wing. Depending on the AOA the speed required to have lift=gravity may vary. And you will still have to balance drag with thrust. And at high AOA, thrust will have a non-negligible vertical component that will be added to the lift to balance out gravity. Thus your minimal speed required to fly level will also depend on your engine power. If thrust to weight ratio is greater than 1, the speed required to fly level can be 0.