Base-to-Final Overshoot at a High-Density-Altitude Field With an Aft CG
You are flying a 2,550-lb four-seat single into a 6,200-ft-MSL airport on a 28 degree C afternoon with an altimeter setting of 29.92. Two passengers and bags put the computed CG at 45.8 in; the aft limit at that weight is 47.3 in. Clean stall speed is 48 KIAS and the airplane is loaded to maximum gross. Traffic pattern altitude is 7,400 ft MSL. On base to final you overshoot the centerline, so you steepen the bank to about 45 degrees and add inside rudder to tighten the turn. At 500 ft AGL the stall warning horn sounds at 60 KIAS and you feel a buffet.
1. Compute the density altitude and explain how it changes what you see out the window versus what the airspeed indicator shows.
Read the worked answer
DA = 6,200 + 120 x (28 - (15 - 2 x 6.2)) = 6,200 + 120 x (28 - 2.6) = 6,200 + 3,048 = about 9,250 ft.
At 9,250 ft, true airspeed is roughly 2 percent per 1,000 ft above indicated: 60 KIAS is about 71 kt TAS. The airspeed indicator, the stall warning, and the buffet are all telling the truth about the wing - the wing only cares about indicated speed. What changes is the geometry:
- Ground speed in the pattern is about 18 percent higher, so the downwind leg takes less time and the runway appears to arrive faster.
- For a given bank angle, the radius of turn over the ground is about 18 percent larger. The same bank angle that works at sea level does not close the overshoot at 9,250 ft DA - and the sight picture makes it feel as though it should.
- Rate of climb is dramatically reduced, so any go-around must be flown promptly and at the correct speed; the airplane will not bail you out of a low, slow, banked situation the way it does at sea level.
That mismatch - visual ground speed and turn radius out of phase with indicated airspeed - is exactly what drives pilots into steep, skidding, low-altitude turns at mountain airports.
2. Using the load factor at 45 degrees of bank, explain whether the stall warning at 60 KIAS is a false alarm - and what the added rudder does.
Read the worked answer
Load factor at 45 degrees of bank = 1 / cos(45) = 1.41 g. Stall speed rises with the square root of load factor: sqrt(1.41) = 1.19. So the accelerated stall speed is about 48 x 1.19 = 57 KIAS in a coordinated 45-degree turn.
Now add inside rudder to tighten the turn. The airplane is cross-controlled: the nose yaws toward the inside of the turn while the bank tends to shallow, producing a skid. The relative wind now arrives from the side, the fuselage and the raised wing are exposed, and - critically - the aft CG at 45.8 in reduces the pitch authority available and makes the wing more reluctant to un-stall once it does.
So the stall warning at 60 KIAS is not a false alarm; it is a margin of about 3 kt over the coordinated accelerated stall speed, and the skid eats that margin. The correct response is: release the rudder, reduce bank, lower the nose, and take the overshoot. A go-around from 500 ft AGL with full power and a wings-level pitch attitude is a non-event; an un commanded stall at 45 degrees of bank 500 ft above the ground, with the CG near the aft limit, produces a very high sink rate and a spin entry that many pilots do not survive. The overshoot costs you a traffic pattern; the alternative costs the airplane.
3. If the airplane does stall in this configuration, how does the near-aft CG change the recovery, and what should you brief before the next approach?
Read the worked answer
A near-aft CG moves the center of gravity toward the wing's center of pressure (and, depending on the airfoil and thrust, toward or beyond the neutral point). The practical consequences in a stall:
- Weaker nose-down pitching moment at the break, so the airplane may hold the stalled angle of attack without the natural pitch-down that normally unloads the wing.
- Reduced elevator authority on the recovery, so the usual burst of forward pressure produces less pitch rate than expected.
- Higher probability of a spin and of a flat, oscillatory spin that is difficult to break, with higher rotation rates and slower recovery.
- Higher stall speed already, since an aft CG reduces the tail download that the wing must otherwise carry.
Brief before the next approach: approach speed additive for the conditions, a stabilized final by 500 ft AGL, no bank beyond 30 degrees below pattern altitude, no inside rudder to fix a bad turn, and a stated go-around trigger - for example, not on centerline and on speed by 400 ft AGL. At 9,250 ft DA the go-around must be briefed as the primary option, not the fallback.