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Motor
/ Propeller
Characterization
24 Feb 06
Lab
3
Lecture
Notes
Nomenclature
r
radial coordinate
R
prop tip radius
V
ﬂight velocity
Ω
motor and propeller rotation rate
v
motor terminal voltage
i
motor current
η
overall propulsive eﬃciency
P
P
B
number of blades
D
prop diameter (
≡
2
R
)
P
prop pitch
T
prop thrust
Q
prop torque
thrust
thrust power (
≡
TV
)
elec
electrical power (
≡
iv
)
Motor/Propeller Characterization
The combination of a propeller and an electric motor, shown in Figure 1, can be viewed as
a propulsion unit whose thrust
T
(
V,v
) and current
i
(
V,v
) both depend on the air velocity
V
into the propeller, and the voltage
v
applied to the motor terminals.
We can then de±ne
the thrust power
P
thrust
, the electrical power
P
elec
, and the overall propulsive eﬃciency.
P
thrust
TV
P
η
(
V,v
)
=
=
(1)
elec
i v
+
−
υ
V
υ
υ
T (V,
)
i (V,
)
Figure 1: Propulsion unit consisting of a propeller driven by an electric motor. For any given
propeller and motor, the thrust
T
and current
i
depend only the oncoming air velocity
V
and applied voltage
v
.
Calculation of the
T
(
V,v
) and
i
(
V,v
) functions for any given propeller and motor combination
is rather complicated, and is beyond scope here.
However, these can be readily measured in
a motor/prop test stand in a wind tunnel.
Typical behavior of these functions is shown in
Figure 2. The rotation speed Ω(
V,v
) is also shown for interest.
Each thrust curve in Figure 2 is seen to drop to zero at a particular
aerodynamic pitch speed
V
o
(
v
), which is roughly proportional to the applied voltage
v
.
The reason for this drop to
zero is primarily due to the aerodynamic characteristics of the propeller, although the motor
characteristics also come into play to a smaller extent.
An electric aircraft in level ﬂight requires
T >
0, and hence its maximum levelﬂight speed
clearly
cannot
exceed
the
pitch
speed.
Hence,
to
increase
the
aircraft’s maximum
speed,
it is necessary to examine what features of the propeller and motor combination might be
changed to increase
V
o
(in addition to the obvious solution of increasing the voltage
v
).
1
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 Fall '05
 MarkDrela

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