Slow-flyers


Propeller measures

This document explains how we measured several propellers and provides several hints on how to adapt the shape of a propeller to a given motor-gearbox. See our selection guide to optimize the gearbox in order to select a motor and a gearbox for a given propeller .

Experimental set-up

The setup consists of a balance and a simple lever that transmits the thrust force of the propeller. A frequency-meter determines the rotation speed. It is important to measure the voltave on the motor directly; the voltage drop in the Ameter and the wires may be important. Power source may be a variable number of battery cells; dur to the linarity of curves on the log plots, rather few measures are required.

Propeller tests

Propellers are tested with a good motor of known characteristics. We use a
Maxon A-Max 22mm R=1.71 Ohm, k=5.9 mNm/A , 6V nominal, encoder 16 slots/turn.
Our frequency meter is designed for 60 slots/turn, hence the 60/16 correction to get turns/s.

For a propeller of diameter D ([m], we measure U[volts], I [A], F frequency-meter value,T [g] propeller thrust on balance (further correction due to lever length), and apply the formulas:
Electrical power [mW]          Pel = U* I
Mechanical power [mW]      Pmec = U * I - R * I * I
Torque [mNm]                     M = k * I
Angular speed [rad/s]           w = F*(60/16)*(2*PI/60)
Propeller power [mW]         Phel = M* w

The thrust is theoretically proportional to the square of the rotation speed, and the power proportional to the cube of the rotation speed. Since we are interested to the maximum thrust for a given power, we define a Quality factor Qp as 1000 times the thrust [g] divided by the power [mW] exponent 2/3. Qpm is this factor divide by the propeller mass.

We plan to do a set of measures in a wind tunnel. Preliminary tests have shown that for the speed we are concerned for very slow flyers, the change is less than 10% at 1.6 m/s.

Propeller plots

The important parameters are the trust and the power. We need also the torque and the rotation speed (RPM) in order to understand the matching of the propeller and the motor. E.g, for propeller #5 (Wes Technik 16/12, 160mm, 1.35g), our measure gives three interesting plots.

The thrust vs RPM is in theory a straight line (on the log plot) of slope 2/1 (two decades vertically, one decade horizontally) since the thrust is proportional to the square of the rotation speed. At low speed, the curve must be below the theoretical line, due to lower Reynolds number. At high speed, deformation of the blades due to a lack of mechanical strength degrades also frequently the curve.
The power vs RPM is in theory a line of slope 3:1
The torque vs RPM is in theory a line of slope 2:1.
Our selection guide explains how to exploit these curves.

Propeller's measures (selection 090804)

#
Make/material
Diameter
[mm]
Pitch
[mm]
Mass
[g]
Thrust range
Qp
Qpm
1
150
220
0.94
5-10
220
240
3
185
150
0.48
2-15
240
510
4
200
125
2.96
10-50
260
88
5
160
120
1.35
10-50
250
180
7
155
120
3.5
10-50
190
55
10
200
 
4.14
10-50
280
68
11
230
 
5.17
20-100
300
58


Other propeller tests

In order to analyze the influence of shape, we built several balsa propellers, curved on a 100 mm tube, with a 15 degrees inclination. More carefull construction would be required to get better performance, but the objective was to compare the effect of shape and pitch. More measures would be required to give some design rules, and we beleive now that cutting the propeller shape in a formed carbon foil must bring better results. Our propeller connectors are quite convenient for preparing the blades and adjusting the pitch.

#
Make/material
Diameter
[mm]
Pitch
[mm]
Mass
[g]
Thrust range
Qp
Qpm
17
260
180
1.32
5-10
240
180
18
230
150
0.48
5-25
220
240
19
200
125
0.55
5-25
210
230
20
122
100?
0.59
2-12
120
210
21
167
140
0.5
5-15
140
280
22
160
140
0.52
5-15
175
330
23
160
140
0.44
5-15
145
330
24
160
140
0.58
2-12
115
200

It is difficult to conclude. The long rod seems to be good for the aerodynamics (19 better than 21-24), but it is a catastrophy for the rigidity, that is the ability to absorb higher torques. A wide area next to the shaft does not seem to be good (22 better than 23and 24), except for rigidity.

Propeller size

Changing the size of a propeller influence its parameters. In theory, if L is the diameter, and for a constant thrust
Rotation speed is proportional to 1/L^2
Torque is proportional to L
Power is proportional to 1/L
Reynold number is the same (no aerodynamic changes)

There is hence a theoretical advantage to increase the size of the propeller, at the expense of a larger gear train and an increased propeller fragility and rigidity, plus a look incompatible with scale models.

Good luck for doing your own experiments with propellers.


CH-1092 Belmont/Lausanne Switzerland
Tel +41 21 728-6156 Fax -6157
info@didel.com www.didel.com
Last update: 09.05.02/jcz