Timid turns

As he did so, I didn’t realize until our shoulders bumped that I had been subconsciously leaning to the left as if I could somehow make the turn happen more quickly. I immediately sat up straight and hoped that he had been too busy to notice. Steve followed that with a lazy turn onto final and our shoulders bumped again. I cringed when he rolled the wings level and, just as I had suspected, discovered the runway way off to the left in the windscreen.

By overshooting final by so much, Steve now faced the decision to either make a herculean effort to intercept the extended runway centerline or to admit defeat and commence a go-around. Steve chose to save the approach by applying a small amount of left aileron, at first complemented by rudder in the same direction. Struggling to get back onto the extended centerline, he kept the bank angle small, but his over-enthusiastic left foot made the inclinometer brick swing to the outside of a turn. The once coordinated turn had evolved into a skid, a condition that is never appropriate and downright dangerous in the pattern.

In the debrief after landing, I asked him about overshooting the runway centerline while turning final and he confessed that it happens to him often. When I suggested that using a lower approach speed and a more aggressive bank angle could help, Steve explained that his instructor’s advice, “Never bank more than 20 degrees and keep your speed up,” is always on his mind. Instructors offer such advice in the interest of safety but, without more guidance, it may set the stage for the very accident it attempts to prevent—a stall/spin scenario at low altitude. To see why, let’s discuss the anatomy of a turn.

Suppose that an aircraft is in a level turn with bank angle B. The lift vector tilts away from vertical so the pilot must increase its magnitude by a combination of raising the angle of attack (by pulling back on the yoke) and applying more power to increase the speed. The vertical component of lift will compensate for the aircraft weight and the unbalanced horizontal component of lift will make the aircraft turn. The ratio of lift to weight is load factor that makes the pilots and passengers feel a greater acceleration than in normal flight. For example, in a 60-degree banked level turn, the aircraft must produce twice the lift it does during cruise flight so the load factor is 2.

Stall speed increases as the square root of load factor. In that 60-degree turn, then, the stall speed is 41 percent higher than in normal flight because the square root of two is about 1.41. Demonstrating this phenomenon—an accelerated stall—is required of all commercial pilot applicants. And it’s the reason that flight instructors warn their students to keep their speed up and bank angles to a minimum while operating in the pattern.

But such advice should be used with care because of the relationship among airspeed, bank angle, and turn radius. Turn radius in a no-wind scenario is given by V²/(g tan(B)) where V is the airspeed (in feet per second) and g is the acceleration due to gravity (about 32.2 feet per second squared). While this looks intimidating, it’s worth the effort to unpack. That velocity is squared means that it has a profound effect on turn radius. Double the velocity and the turn radius quadruples or cut it in half and the turn radius goes down by a factor of four.

For the kind of bank angles typically used in normal flight, the bank angle B (in radians) and its tangent are essentially the same. So, the fact that the bank angle appears in the denominator tells us that doubling the bank angle will cut the turn radius in half.

Steve’s downwind leg was half a nautical mile or about 3,000 feet offset from the runway. He used 90 knots on downwind and slowed to 80 knots on base and used 20- and 15-degree turns onto base and final. Using the formula above and adding the radii of his two turns together yielded over 4,000 feet and overshooting centerline was guaranteed to happen.

I then showed Steve that using 30- and 20-degree turns onto base and final respectively would prevent an overshoot. But the straight base segment would be only 200 feet long and allow him just 1.5 seconds to check for traffic on final and check his position with the runway to plan his second turn. This segment of the pattern is one of the most important since, during a turn, one of these will be impossible to see with the wing in the way.

We then saw that scaling back the airspeed during the first turn to 80 knots and the second to 70 would provide a straight base segment of more than 800 feet and 7 seconds. And these airspeeds continue to offer a healthy margin over stall in his Cessna 172. After all, the stall speed in a 30-degree level turn is only 7.5 percent higher than an unaccelerated stall. (Because this is a descending turn, the increase in stall speed is at most 7.5 percent and may even be lower.)

Designated examiners are not allowed to teach during a practical exam, so my favorite part is the debrief that follows when instruction is encouraged. Both Steve and his instructor left that day understanding that being too conservative with bank angles and airspeeds in the pattern can have the opposite effect and even reduce safety margins. With just a little math, they found a sweet spot in the middle and a lesson they won’t forget.