Vx, Vy, and EFATO
A recent thread discusses yet another very sad loss of life following an [presumed] engine failure after takeoff. It would also be presumed that the pilot attempted a turn during the glide. The "impossible turn" has certainly been the subject of a lot of discussion, as we would all agree that at some altitude, and airspeed combination, it does become possible. But more basically, has the pilot set themself up for a difficult time of it with a steep climbout?
Modern airplanes will have a published Vy (best rate of climb) and Vx (best angle of climb). They will also have a published "best glide" speed, though best for exactly which maneuver is not always entirely clear. As the best glide speed is usually associated with the data on how far you can expect to glide from a given altitude, we'll presume its the best "range" glide speed. Experience on type may show that the best speed for a power off flare and landing could be a little faster (it won't be slower) than the published best glide speed. So many flight manuals also include a desired speed after liftoff, if there is no obstacle to clear, which we expect will be close to Vy.
So you've lifted off, and are climbing away, with no obstacle to clear, and for reasons of your choosing, you're climbing at a speed slower than Vy. You suffer a power loss, and promptly lower the nose to enter a glide. We're going to presume that you don't have time for a cause check, and wisely are planning to land ahead. You're at 200 feet, slower than Vy, and now descending power off. At this very moment, you're suddenly thinking that being at at least best glide speed would be a good thing. So, you lower the nose to accelerate to that airspeed. But you have a windshield full of ground in front of you, so you raise the nose to establish a reasonable glide attitude, but now, you're slowing down again. When you raise the nose further to begin your flare, you immediately hear a stall warning horn, and there's nothing left to trade to arrest your descent. It's not going to be the good power off forced landing you've practiced before from altitude.
I've done the certification testing on this a number of times - it's scary near a runway! Fortunately, as it was flight testing, I could go back to using power to arrest the rate of descent. It fails the test objective, but saves the plane! In a Cessna Grand Caravan carrying a very draggy external load, I was required to demonstrate a power off landback at 80 knots, rather than the 87 knots which Cessna states is your no obstacle after liftoff aim speed. It was messy. I didn't slam the plane on, only 'cause I burst in a sudden bunch of power as I flared. So I learned, with no obstacle to clear, Vy+. If it's a "STOL" takeoff, okay; "Short Take Off" - get the plane off the surface, level, accelerate as you can, then climb to clear the obstacle. Hopefully, you can accelerate from Vr to Vy, or at least better than Vx, anything more than Vx will reduce the risk you are in.
All helicopter flight manuals are required to publish a "height velocity avoid curve". This is a pictorial of airspeed plotted against altitude, with a hatchered portion to avoid being in needlessly. It is understood that if you're flying in that area, and you suffer a power loss, a successful autorotative landing is not certain. The same theory applies to airplanes, but for some silly reason, there is no certification requirement to present the "avoid" data to the pilot! I've done the testing! I have the data! But, there's no requirement to publish! So, you can read the flight manual, and still be unaware of the risk.
When I type train pilots, I demonstrate this at altitude - it's an easy demonstration: Establish a "hard deck" several thousand feet up in the training area - a hard deck altitude you'd be comfortable doing stalls from. Slow into slow flight, slower than Vy for the type at the hard deck altitude you chose. Increase to takeoff power, and climb at Vx. Climb 200 feet on the altimeter, and close the throttle. Lower the nose, and establish a glide. Flare the airplane power off, so as to pause the altimeter at your hard deck altitude. Did you hear a premature stall warning? (The plane was still going down with the stall warning sounding). Could you pause the descent long enough to see the altimeter needle pause at your hard deck altitude? It is a certainty that power off, you're going to bust that altitude, but the exercise is just to momentarily arrest your descent at that altitude as if you had flared to land. If you cannot, flaring for a safe power off landing would be difficult!
When I type train a pilot in a amphibious floatplane (generally Cessna 180/182/185/206) this is a dramatic demonstration, as those planes are heavy and draggy. They slow down very quickly, and you have to get the nose way down in the glide to increase your speed. That type has a large "avoid" curve. Sure a sleek type like a DA-40 probably does quite well in the demonstration, but still has a very small "avoid" curve. I demonstrated it while checking out a new owner in his Decathlon, and the airplane did quite well - and, he got the point too!
When I have received training in helicopters, this is always a discussion point. I have found it could be one of two different discussions: One MD500 I have had occasion to fly is a privately owned recreational machine - no risky flying. My mentor pilot is unforgiving in wanting a departure profile which keeps the helicopter out the avoid curve the whole time (which is possible). When I was "mountain" trained (including longline training) in a different "work" MD500, it was very different. I longline trained for a straight 45 minutes once, in the "avoid" curve the entire time, it's just an accepted risk for a work machine. Similarly "towering" departures, where you climb vertically 100 feet out of a hole in the trees, then accelerate forward from the tree tops. Again, in the avoid curve the whole way up, and for a portion accelerating off the treetops. Again, accepted risk, it's the work you're there to do - but very risky if the engine quits!
So, sure, there are some true "STOL" operations. They are typically military, or specialized commercial operations. Are they recreational or civil airshow/competition operations? Not really. If you need to climb away at slower than Vy, that's something you should be doing with a very heightened awareness of risk. Hopefully, you have practiced as described above as to how much altitude you'll loose trying to accelerate in the glide to get to best glide speed. And have practiced a full landing from a power off approach at that best glide speed. It can be done, but there's less room to find the ideal flare. And the other thing, the attitude the airplane is in at a Vx climb, is less good for fuel flow an low fuel quantities - I friend of mine found this at the cost of a Cessna 185 amphib, and months of recovery for both of them - and they were surrounded by ideal power off landing area, including another runway just ahead.
When I teach power off landings in the amphibians, I suggest pick a more close site, and make a good approach, rather than somewhere further, and find too late that you've been overly optimistic. I would rather have to sideslip at the last bit to force the plane in sooner, and go off the end of my selected spot not completely stopped yet, than undershoot, or actually stall, and maybe drop a wing.
We're all trained for this, but do we continue to practice? Accidents from time to time remind me that some pilots may have been optimistic as to the capabilities of their airplane power off.