G, 2G is the published limit for a number of aircraft with flaps down. Those aircraft have the normal G limit of 3.8 when the flaps are up of course. I guess it's got to do with the load distribution across the wing.
It's to do with the structural limits on the flaps and their supporting structure.
I can re-work this later for a 2g flapped case, but here's a graph I just knocked up. Sorry about the lack of axes, but I plotted it for a PA28-161 at MTOW, flaps up, at 5000ft. The vertical axis is metres turn radius, the horizontal axis is IAS in knots. Where the lines stop on the left it's the stall, and on the right it's Vne.
The conclusions to my mind are a bit different to what I thought earlier but not much - best bank angle you can achieve, with as little speed as will sustain that.
G
N.B. Anybody know why this isn't showing as an image? [fixed - use the Image button and paste the URL in there]
I have taught a mountain flying course for many years and I have over 1500 hrs flying VFR in the Canadian Coast and Rocky mountains. I discuss but no longer actively teach, the "canyon turn" when we get to the in the air portion of the course. A review of mountain accidents show that if you are actually in a position where you only have room for a minimum radius turn you are allready so deep in the Shyte you are probably doomed. This because you are also almost certainly also dealing with subsiding air and/or imminent IMC conditions.
The absolute rule in safe mountain flying is to never get into the position where you have to do a min radius turn. Central to this is to practice a normal 30 deg banked turn at cruise speed so that you have a very good idea how much room you need, then never get into a position where you don't always have that much room to turn.
Mountain flying "technique" is almost all about pilot decision making, not hero piloting moves. However if the students makes a series of bad decisions that results in eliminating all his options and he is in a do or die situation then I tell them, for your average fixed gear light GA aircraft, to go to idle power, apply full flap regardless of the speed and then at around 90 kts go back to full power and roll to 45 degrees of bank in a level turn. If they survive land at the nearest airport and have the aircraft inspected for damage.
Here we go, I re-ran it - same aeroplane, full flaps.
It does indicate that putting full flap on and powering it around at 60 degrees of bank is the way ahead.
From a pure flying perspective this seems pretty close to BPF's advice, although I've no doubt that his airmanship advice should take precedence!
G
Genghis, I think Peter's point was a little different.
You used tan(bank) in your formula because (roughly, if I have it right), sin(bank) is directed towards centripetal acceleration (aka matching centrifugal force), and cos(bank) is directed at matching weight. This is the normal case where airspeed and rate of descent remain constant.
But I believe Peter was exploring the possibility of not matching weight, i.e. accepting a downward acceleration for a (short!) time.
Then cos(bank) is directed at matching say only 90% of weight, so the bank angle can be bigger, so then sin(bank) will be bigger, so we get a tighter turn, everything else being equal (until the wings come off or the remaining height proves inadequate).
Normal caveats. I know just enough about mountain flying to know I should not be teaching it any time soon!
I've never had to turn due to unintentionally entering a dead end, but have had to do so to avoid poor viz. I often do the manoeuver to set up to look at things. I don't follow the chandelle idea, if you mean a symetrical manoeuver. Canyons and glacial valleys have side canyons/valleys. However small they are - take advantage of one to get more space. Climb, losing speed, then bank, allowing the nose to drop and throttling back. Power on as required on pulling out of the steep descending turn.
G, what technique got you the lowest radius in your calculations? The graphs are not entirely conclusive whether that's the one with full flaps, 60 degree AoB, 2G and 63-ish knots (the red line in the second graph) or the one with zero flaps, 75 degree AoB, 4G and 100-ish knots (the black line in the first graph). They both seem to indicate around 100m radius, and that's broadly consistent with what I remember from my calculations.
There is another issue however, that would make the turn at Va my favourite technique. What speed are you flying when you notice the need for a canyon turn? Most likely this is a typical cruise speed, about 100 knots in the PA28-161. If you first need to slow down the aircraft to anything close to Vfe, or even the 50 to 60-ish knots that you need to get the smallest radius at 45 degrees AoB, you are wasting valuable seconds flying into that wretched canyon. Whereas your cruise speed is already close to Va, so no reconfiguration or slowing down is required. Just bank to about 75 degrees immediately (60 degrees is also OK - the turn radius won't change much from 60 to 75 degrees), apply full power and pull to the buffet.
On the other hand I agree with BPF that airmanship and pilot ability play a large role in this kind of flying too. I'm happy to do 75-degree AoB, 4G steep turns even in relatively limited visibility (no clear horizon) but that's because of aerobatics experience. In mountainous terrain, close to IMC and no aerobatics experience it is probably prudent to limit yourself to 45 degrees and fly a speed to match.
In any case it's good to see that your data supports my claim: Better have a higher speed so you can bank aggressively and pull it around the sky quickly, than flying a very careful, shallow banked turn at very low speed.
David - I used bank angle as a convenient shorthand rather than g, which isn't instrumented in most light aeroplanes. So, if you take 75 degrees as 3.8g and 60 degrees as 2g, you can use the same graph.
In reality few aeroplanes can pull to their g limits and maintain level flight without using potential energy to bolster the available thrust. So, descending will prevent speed bleeding off but for all reasonable purposes you'll still get the same turn radius.
(In WW2 clever people on both sides used to predict these things for the fighters on each side and so, for example, a Spitfire pilot would be advised what height / speed combination would give him a turning advantage over an opposing FW190 or bf109 - whilst I'm quite sure that the German pilots were given similar data about what altitude/speed combination gave them the best chance of out-turning a Spitfire or Hurricane.)
Backpacker - that seems pretty clear. Max roll rate to 60 degrees of bank, pull to get 2g, as soon as you're in the white arc dump full flap, keep pulling whilst letting the airspeed bleed until you're in the buffet and/or stall warner, then keep pulling to JUST stay on the edge of the buffet.
The numbers give a best result of 135m at 3.8g / clean, and 108m at 2g / full flap. (Plus I think most people are more likely to fly 2g well than 3.8g - particularly given the lack of g meter in most such aeroplanes, and that if you overstress the flaps by exceeding 2g or Vfe the airframe damage should be mostly limited to the flap structure and so less immediately life threatening than a damaged mainspar.
(A bit of an extrapolation of the graph, but a fairly safe one in my opinion).
G
Excellent reading! Early on, there was mention of level flight turn, or a chandelle. I would always vote for the level turn, if it's a quasi emergency. Chandelles are lots of fun, but are also a maneuver in which to some degree you will have to surrender some certainty of control and situational awareness. If things are getting bad, you want all of your control and situational awareness the whole way through. Save the chandelles for the open spaces, and your crop dusting!
Oh, and chandelles in a 182RG!!! 'Been there, done that, should not have... It flies them beautifully, but it sure speeds up fast coming out the other side. In a slick airplane, chandelles require a lot of practice and precision to be safe.
Seeing this unexpectedly is not good!
I just did the math for an aerobatic aeroplane, to see what happens if the g envelope is pushed. As GtE suggests, it does not help much to increase bank beyond an already steep bank. Even approaching 90 degrees bank, assuming that the aeroplane can handle the g, and just maintaining a given margin above stall speed, there is clearly a limit to how little turning radius is attainable, and it is only few percent smaller than at 75 degrees bank.
Someone with better math skills than mine could probably derive a formula for the theoretical minimum turning radius. I just ran the numbers for different bank angles and realized the radius goes asymptotic as the bank approaches 90 degrees.
