Page 59 - Aeronautical Engineer Data Book

46 Aeronautical Engineer’s Data Book
The parametric form of the equation is x =
a sec , y = b tan where s the eccenteric
angle.

, y ) is
The equation of the tangent at (x 1 1
–
xx 1 yy 1
33 33 = 1.
a 2 b 2
Sine Wave (see Figure 2.13)
y = a sin(bx + c)
y = a cos(bx + c') = a sin(bx + c) (where c =
c'+π/2)
y = m sin bx + n cos bx = a sin(bx + c)
where a = � ��, c = tan (n/m).
2
2
–1
+
m
n
y axis
a
x axis
0
c/b

2π/b

Fig. 2.13 Sine wave

Helix (see Figure 2.14)
A helix is a curve generated by a point moving
on a cylinder with the distance it transverses
parallel to the axis of the cylinder being
proportional to the angle of rotation about
the axis:
x = a cos
y = a sin
z = k
where a = radius of cylinder, 2πk = pitch.