Principles & why

S-turns build on the rectangular course (B) by replacing four discrete bank changes with continuous bank modulation through each semicircle. The bank-with-groundspeed principle is identical; the difference is the rate of change. S-turns also introduce a new constraint — symmetry of the two semicircles across the reference line — which is what makes the maneuver harder than the rectangular course.

Continuous bank modulation

In a rectangular course, you set four bank values, one per corner. In an s-turn, the bank changes smoothly and continuously through each 180° semicircle.

Recall the principle from B: a turn at constant bank produces a circle of fixed radius through the air mass, which the wind drifts into an oval over the ground. To get a circle (or semicircle) of fixed radius over the ground in wind, the bank must vary with groundspeed:

• Steeper when groundspeed is high (tailwind portion of the semicircle).
• Shallower when groundspeed is low (headwind portion).

Inside a single semicircle, your heading rotates 180°. As the heading rotates, the wind transitions from tailwind to headwind (or vice versa), and groundspeed transitions correspondingly. The bank must transition with it.

With wind, holding constant bank produces unequal semicircles — one bulges past the road, one cuts inside. The intended figure-eight requires the bank-vs-heading modulation shown below the track.

The symmetry constraint

V.C.S2 requires the two semicircles to have equal radii. This means each pass across the road must hit the ground track at the same offset distance from where the previous one started.

The implication: the time-averaged bank on the downwind semicircle (high groundspeed → steeper) must produce the same ground radius as the time-averaged bank on the upwind semicircle (low groundspeed → shallower). This is the practical proof that the bank-with-groundspeed pedagogy isn't theoretical — if your modulation is wrong, the asymmetric semicircles tell on you.

Worked example: 15-kt wind, road perpendicular to wind

You're flying 90 KIAS true. Wind is 15 kt from the north. The road runs east–west; you enter heading north (downwind) over the road.

• Entry crossing: wings level, heading 360°, groundspeed = 90 + 15 = 105 kt. Steepest bank required at roll-in.
• Mid-first-semicircle (heading 090°, east): groundspeed = 90 kt. Medium bank.
• Heading 180° approaching road from north: groundspeed = 90 − 15 = 75 kt. Shallowest bank — almost wings-level if you've modulated right.
• Second crossing: wings level, heading 180°.
• Mid-second-semicircle (heading 270°): groundspeed = 90 kt. Medium bank.
• Heading 360° approaching road from south: groundspeed = 105 kt. Steeper bank again.

The bank traces a sine-wave-like profile: maximum at the tailwind point of each semicircle, minimum at the headwind point.

Why we fly it as Private Pilot

S-turns are the bridge between the discrete bank changes of the rectangular course (B) and the fully continuous modulation of turns around a point (D). Each maneuver in the sequence adds one degree of difficulty:

• B (Rectangular Course): 4 discrete bank changes at corners
• C (S-Turns): continuous bank modulation through each 180° semicircle + symmetry constraint
• D (Turns Around a Point): continuous bank modulation through a full 360° with the radius held against a fixed point

Master B first, then C, then D — they're meant to be flown in that order.