AerE442
Homework #2
Fall 2002
1. Show that for a rotor producing constant thrust in non-axial translation moving at a speed of V0 and,
at an angle α, the induced velocity vi and the ideal power Pi are given by the following equations.
4
3 2 2
vi
V0
vi
V0
vi
+2
sin α +
−1=0
vh
vh
vh
vh
vh
Pi
V0
vi
=
sin α +
Pi,h
vh
vh
2. Show that for a rotor supplied with a constant power in non-axial translation moving at a speed of
V0 and at an angle α, the induced velocity vi and the thrust produced T are given by the following
equations.
" 3
2 2 # 2
4
V0
vi
V0
vi
V0 sin α + vi
vi
+2
sin α +
−1=0
vh
vh
vh
vh
vh
vh
−1
T
V0 sin α + vi
=
Th
vh
3. Write a computer program and generate graphs with vVh0 and α as the parameters. Vary α and vVh0 from
0 to 90 degrees in step of 10 degrees. Keep α as the running parameter on the curves and vVh0 as the
x-axis. Plot
vi
V0
vs.
for constant thrust
vh
vh
Pi
V0
(b)
vs.
for constant thrust
Pi,h
vh
V0
vi
vs.
for constant power
(c)
vh
vh
V0
T
vs.
for constant power
(d)
Th
vh
(a)
1