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<\/a>Using a Turn-Twist strategy, once on the arc, the heading to fly is tangent to the arc. This makes the no-wind control law: Turn to heading = Radial plus 90 deg when CW or Radial minus 90 deg when CCW. Unfortunately, this control strategy contains inherent divergence; in other words, the aircraft always tracks outside the desired arc (Figure 2, left). With a Turn 10\/Twist 10 step, the cross track error is 1.5%. For example, a 20 nm arc with 10 degree radial steps, would give 0.3 nm error every step. <\/p>\n\n\n\n
Is there a correction to exactly remain on the arc given a Turn-Twist step?<\/em> Yes, and amazingly enough, the result is exact and a trigonometric identity. The right portion of Figure 2 derives a correction angle (gamma) such that the exact track is from point A to point B, both on the same arc. The result is that exactly half the Turn\/Twist angle is applied inside the normal +-90 heading. <\/p>\n\n\n\n For example, using a Turn 10\/Twist 10 in a counter clockwise direction at the R-040 would require the heading be 305 degrees; this heading will precisely keep you on the exact DME arc at the R-030 radial.<\/p>\n\n\n\n<\/a>