Page 288 - Introduction to Naval Architecture

MANOEUVRING 273

9
The equations can be manipulated to derive a number of interesting
relationships:
(1) The steady path in the vertical plane cannot be a circle unless BG
is zero.
(2) The rate of change of depth is zero if

(3) The pitch angle is zero if M$ H/Z$ H ~ M^/Z^ but the depth rate is
not zero but given by <5 HZ3 H/^v
(4) The ratio M W/Z W defines the distance forward of G of a point
known as the neutral point. A vertical force applied at this point
causes a depth change but no change in pitch angle.
(5) A second point, known as the critical point, is distant mgBG/VZ^
aft of the neutral point. A vertical force applied at the critical
point will cause no change of depth but will change the pitch
angle. A downward force forward of the critical point will
increase depth, a downward force aft of the critical point will
reduce depth. Thus at this point there is a reversal of the
expected result of applying a vertical force.
(6) As speed drops the critical point moves aft. At some speed,
perhaps two or three knots, the critical point will fall on the after
hydroplane position. The speed at which this happens is termed
the critical speed.

Figim 10.12 Neutral and critical points