Assuming a bar or cylindrical magnet with a length L
N
S
L
Attraction:
N
S
N
S
N
S
F
Repulsion:
S
N
F
F
d
Force F is proportional to
[1/d2+(1/(d+2L)2 -2/(d+L)2]
(d>=L)
http://en.wikipedia.org/wiki/Force_between_magnets
(In the simulation we will set L=dmin where dmin is the shortest distance between the magnets)
Let’s consider a wheel with 4 magnets:
S
N
N
S
Let’s approach a magnet:
N
S
N
N
S
1
The wheel will be subject to attraction and repulsion forces:
N
S
N
N
S
Those forces will generate a torque on the wheel and it will turn. Torque can be either positive or negative
which means that the wheel can turn clockwise or counter clockwise.
N
Until a new equilibrium point is reached where torque=0
2
Now let’s imagine 2 wheels connected with a belt:
In the example below there is balance and torque=0 on both wheels
S
N
N
S
S
N
N
S
Now let’s see what happens if the wheels are in such a position:
3
The 2 wheels will be subject to various forces:
A torque will be generated, the wheels will turn until a new equilibrium point is reached where torque on both
wheels=0. A torque measures the propensity of a given force to cause the object upon which it acts to twist
around a certain axis; A torque can be positive or negative depending on the direction of rotation
Wheel 1
Wheel 2
4
An IT program could evaluate the forces generated by one magnet from wheel 1 on each magnets of wheel
2. The program will repeat that process for each magnet on wheel 1.
For each force, the tangential component needs to be calculated and multiplied by the radius of the
corresponding wheel to estimate the torque.
The final torque on wheel 2 is
Final torque on wheel 2= (Speed ratio wheel 2/wheel 1)*(torque on wheel1) + (torque on wheel2)
Where
Speed ratio depends on the belt connection (i.e. 5 means that when wheel 2 turns 1° , wheel 1 would turn 5°
torque on wheel1 and 2 are torque generated by the magnets on the wheels
At the end of the video I will provide a link where the program that I wrote can be downloaded. It’s written in
excel and uses VBA macros. Very easy to use.
5
6
Examples
Range of angles simulated
number of series (levels) simulated
360
1
SERIES
1
ROTATING WHEEL NR 1
Radius 1
Number of magnets
Shift angle of magnets
6
4
0
Distance between the two wheel centers
(should be greater than radius 1 + radius 2)
17
permanent magnets arranged in alternating
polarity? (YES or NO)
ROTATING WHEEL NR 2
Radius 2
Number of magnets
Shift angle of magnets
Polarity (1= same as wheel nr 1, -1 opposite)
permanent magnets arranged in alternating
polarity? (YES or NO)
speed ratio (i.e. 5 means that there is a belt or
gear connnection between wheel 1 and 2 such
that when wheel 2 turns 1° , wheel 1 would
turn 5°. This ratio has an impact on the final
torque on wheel 2)
YES
10
4
0
1
YES
1
7
Range of angles simulated
number of series (levels) simulated
360
1
SERIES
1
ROTATING WHEEL NR 1
Radius 1
Number of magnets
Shift angle of magnets
6
7
0
Distance between the two wheel centers
(should be greater than radius 1 + radius 2)
17
permanent magnets arranged in alternating
polarity? (YES or NO)
ROTATING WHEEL NR 2
Radius 2
Number of magnets
Shift angle of magnets
Polarity (1= same as wheel nr 1, -1 opposite)
permanent magnets arranged in alternating
polarity? (YES or NO)
speed ratio (i.e. 5 means that there is a belt or
gear connnection between wheel 1 and 2 such
that when wheel 2 turns 1° , wheel 1 would
turn 5°. This ratio has an impact on the final
torque on wheel 2)
YES
10
9
0
1
YES
1
8
Range of angles simulated
number of series (levels) simulated
180
3
SERIES
1
2
3
ROTATING WHEEL NR 1
Radius 1
Number of magnets
Shift angle of magnets
6
7
0
6
9
0
6
11
0
Distance between the two wheel centers
(should be greater than radius 1 + radius 2)
17
17
17
YES
NO
YES
10
9
0
1
10
5
10
1
10
7
20
-1
YES
NO
YES
permanent magnets arranged in alternating
polarity? (YES or NO)
ROTATING WHEEL NR 2
Radius 2
Number of magnets
Shift angle of magnets
Polarity (1= same as wheel nr 1, -1 opposite)
permanent magnets arranged in alternating
polarity? (YES or NO)
speed ratio (i.e. 5 means that there is a belt or
gear connnection between wheel 1 and 2 such
that when wheel 2 turns 1° , wheel 1 would
turn 5°. This ratio has an impact on the final
torque on wheel 2)
1
9
CONCLUSION 1
The torque frequently moves from positive to negative
value. It means that there are plenty of equilibrium points.
The wheels will oscillate (turn slightly clockwise than counter
clockwise and so forth around one equilibrium point). If
someone spins the wheels, it will slow down and stop at one
of those equilibrium points.
To turn constantly, the torque should be either positive or
negative on a very wide range of angles. It should not
oscillate.
10
Let’s see the case of concentric wheels:
Stator (fixed)
S
Rotor (rotating)
S
N
N
N
N
S
S
11
We can even simulate 2 fixed wheels (cylinders) and one rotor:
Stator (fixed)
S
Rotor (rotating)
S
S
N
N
N
N
N
N
S
S
Fixed cylinder
S
12
Range of angles simulated
number of series (levels) simulated
180
1
SERIES
1
EXTERNAL FIXED RING
Radius of the external fixed ring
6
Number of magnets on the external ring
(if set at zero there is no external fixed
ring)
Shift angle of magnets
Polarity (1= same as rotating, -1 opposite)
4
0
1
permanent magnets arranged in
alternating polarity? (YES or NO)
ROTATING RING
Radius of the rotating ring
Number of magnets on the rotating ring
permanent magnets arranged in
alternating polarity? (YES or NO)
INTERNAL FIXED RING
Radius of the internal fixed ring
Number of magnets on the internal ring (if
set at zero there is no internal fixed ring)
Shift angle of magnets
Polarity (1= same as rotating, -1 opposite)
permanent magnets arranged in
alternating polarity? (YES or NO)
YES
5.5
4
YES
4
0
0
1
YES
13
Range of angles simulated
number of series (levels) simulated
180
1
SERIES
1
EXTERNAL FIXED RING
Radius of the external fixed ring
6
Number of magnets on the external ring
(if set at zero there is no external fixed
ring)
Shift angle of magnets
Polarity (1= same as rotating, -1 opposite)
13
0
1
permanent magnets arranged in
alternating polarity? (YES or NO)
ROTATING RING
Radius of the rotating ring
Number of magnets on the rotating ring
permanent magnets arranged in
alternating polarity? (YES or NO)
INTERNAL FIXED RING
Radius of the internal fixed ring
Number of magnets on the internal ring (if
set at zero there is no internal fixed ring)
Shift angle of magnets
Polarity (1= same as rotating, -1 opposite)
permanent magnets arranged in
alternating polarity? (YES or NO)
YES
5.5
9
YES
4
0
0
1
YES
14
Range of angles simulated
number of series (levels) simulated
180
1
SERIES
1
EXTERNAL FIXED RING
Radius of the external fixed ring
6
Number of magnets on the external ring
(if set at zero there is no external fixed
ring)
Shift angle of magnets
Polarity (1= same as rotating, -1 opposite)
13
0
1
permanent magnets arranged in
alternating polarity? (YES or NO)
ROTATING RING
Radius of the rotating ring
Number of magnets on the rotating ring
permanent magnets arranged in
alternating polarity? (YES or NO)
INTERNAL FIXED RING
Radius of the internal fixed ring
Number of magnets on the internal ring (if
set at zero there is no internal fixed ring)
Shift angle of magnets
Polarity (1= same as rotating, -1 opposite)
permanent magnets arranged in
alternating polarity? (YES or NO)
YES
5.5
9
YES
5
7
0
1
YES
15
Range of angles simulated
number of series (levels) simulated
180
3
SERIES
1
2
3
EXTERNAL FIXED RING
Radius of the external fixed ring
6
6
6
Number of magnets on the external ring
(if set at zero there is no external fixed
ring)
Shift angle of magnets
Polarity (1= same as rotating, -1 opposite)
13
0
1
11
0
1
9
0
1
YES
NO
YES
5.5
9
5.5
7
5.5
5
YES
NO
YES
5
5
5
7
0
1
5
0
-1
9
0
1
YES
YES
NO
permanent magnets arranged in
alternating polarity? (YES or NO)
ROTATING RING
Radius of the rotating ring
Number of magnets on the rotating ring
permanent magnets arranged in
alternating polarity? (YES or NO)
INTERNAL FIXED RING
Radius of the internal fixed ring
Number of magnets on the internal ring (if
set at zero there is no internal fixed ring)
Shift angle of magnets
Polarity (1= same as rotating, -1 opposite)
permanent magnets arranged in
alternating polarity? (YES or NO)
16
SAME CONCLUSION 1
The torque frequently moves from positive to negative
value. It means that there are plenty of equilibrium points.
The wheels will oscillate (turn slightly clockwise than counter
clockwise and so forth around one equilibrium point). If
someone spins the wheels, it will slow down and stop at one
of those equilibrium points.
So this 2 kind of supposedly Perpetual Magnet Motors,
seen in many videos are FAKE !
17
The Excel file is available at http://www.pascalroussel.net/?p=1619
It contains 7 sheets:





3 of them are working sheets which should not be deleted.
1 sheet is used to display the wheels,
1 sheet is used to simulate 2 external wheels,
1 sheet is used to simulate concentric rings,
and the last one contains some explanations.
Sometimes when you open the file a yellow bar will appear on the
top requesting you to confirm the usage of macros.
Let’s see how to use the first sheet which simulates 2 external
wheels linked together.
18
19
20
21