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Flight Safety: Low Altitude Turns and Margin-Over-Stall

By Jack Dueck

One early morning an experienced pilot is so thrilled by the smooth air, that on impulse he throws the aircraft into a tight 60-degree bank shortly after takeoff. The airspeed is registering a substantial margin-over-clean, wings-level stall, and he is totally surprised to hear the stall warning over cockpit noise and earphone attenuation.   Instinctively and through training, his immediate reaction was to push on the yoke while simultaneously leveling the wings.

Later, during debriefing, he remembers his instructors admonition; “Angle of attack is independent of aircraft attitude. An aeroplane can be maintaining a 12-degree angle of attack regardless of whether it is in level flight, a 20-degree climb, or a 20-degree descent, or for that matter in a tight turn!”

Why do we continue to have ‘stall-spin’ accidents when pilots have been performing turns starting with their very first flight lesson?
 
With an automobile, we control our travel in only one axis. However, we maneuver an aircraft in three axes, so we have six inputs into our flight envelope. And in almost all of these, several combined control inputs are used. So how do they impinge on our safe flight?

Consider This Example:
Let’s say our aircraft’s take-off weight is 1800 pounds. In straight and level flight, the lift produced by the wings is equal to the weight of our aircraft. If we then input a nose-up or climb input, we add an additional weight component to the flight envelope.  By allowing the angle of attack to increase, we add the increased weight or g factor. 

In the above description, our flight path is vertical, but if we bank the aircraft and then pull back on the stick, we have done the same in a horizontal flight path. Keeping the math simple, this factor is equal to the number (1) divided by the cosine of the bank angle. For example, with a bank angle of 40-degrees, its cosine (from tables or from your calculator) equals 0.766. Therefore, the g factor becomes 1/.766 = 1.305. This means that the aircraft now has an effective weight of 1800 x 1.305 = 2349 pounds.

What happens to our stall speed as our load factor increases? Let’s assume that our clean configuration stall speed for our example is 50 mph. Again, keeping the math simple, the new stall speed multiplier (due to the increased effective weight) can be shown to be equal to the square root of the quotient of the new weight divided by the original weight. To make the math really simple, the new speed multiplier is simply thesquare root of the g factor.

In the above example, dividing 2349 by 1800 gives us 1.305. Taking the square root of 1.305 gives us 1.142. We multiply our 50 mph stall speed by 1.142 and see that our stall speed has increased to 57.1 mph.
 
We fly with a sense of security that our airspeed in straight and level flight gives us a margin-over-stall. We have been trained to perform stalls by slowly raising the nose and holding a higher angle of attack, allowing the airspeed to bleed off until the aircraft stalls.  What is not as readily understood is that we can just as easily stall the aircraft by performing maneuvers while maintaining the same airspeed; since it reduces the margin of safety over stall by allowing the stall speed to increase until the aircraft stalls at what we normally feel is a safe airspeed.

Consider the following scenario: Our pilot flies the aircraft in the landing pattern at 65 mph indicated. This gives a margin of 15 mph over the clean configuration stall speed of 50 mph (1.3Vs). Then during the turn onto final, the aircraft is slowed to 60 mph. As the final leg is approached, a strong crosswind blows the aircraft across the final approach path. The pilot realizes this and immediately increases his or her bank to return to the desired path. Since the return to the glide path is not achieved quickly, the pilot increases the bank to beyond 40-degrees, but is too involved with maneuvering the aircraft and doesn’t realize that the reduced ‘margin-over-stall’ is dissipating.

The aircraft reacts to the reduced airspeed and approaching stall by following its inherent design safety factor; by lowering the nose to avoid the stall. The pilot, however, reacts with survivor instinct and pulls back on the stick. This continued process deepens the stall and the aircraft falls out of the sky. The margin-over-stall has dissipated even though the airspeed is still higher than the magic 50 mph stall speed. 

The following table shows the effect of g or load factor on stall speed.

Bank Angle

Speed

 

 

 

Stall Speed

 

 

 

(degrees)

Multiplier

35

40

45

50

55

60

65

  

 

 

 

 

 

 

 

 

0

1

35

40

45

50

55

60

65

10

1.008

36

41

46

51

56

61

66

20

1.031

37

42

47

52

57

62

68

30

1.074

38

43

49

54

59

64

70

40

1.143

40

46

52

58

63

69

75

50

1.247

44

50

57

63

69

75

82

60

1.414

50

57

64

71

78

85

92

70

1.71

60

69

77

86

95

103

112

Reviewing
The pilot in our example has a stall speed of 50 mph in mind as a reference ‘minimum’ safe flight speed. But as he or she enters a 40-degree correcting bank, the stall speed has increased to 58 mph. As the pilot allows the aircraft to slow further by pulling back on the stick, the speed drops below the 58 mph and the aircraft stalls. Hopefully, there is enough altitude and time for reaction and stall recovery. Too many times both reaction time coupled with approach altitudes work against the pilot.

We would do well to discard the concept of a magic safe stall speed, and rather bend our minds around the concept of ‘margin-over-stall’.

 
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