Kinetic Hiker Backpack becomes Solenoid Piston array

[quantumtangles]

By way of thought experiment, I considered whether it might be possible to make a kinetic harness for hikers or walkers. If so, could cylindrical solenoids (conventional ferrous cylinders with copper wire windings and mobile neodymium magnets inside) be used to generate electricity, and in that event, how much electricity would such a device be capable of generating.

Having begun with the idea of a backpack generator, I soon turned my mind to a larger array, having in mind the idea of considering the maximum amount of electricity a human being can generate using muscle power alone.

This soon descended into consideration of an enormous machine. A wheel, with ten large (10m) piston-like solenoids arranged around its circumference. Inside each piston or solenoid, a neodymium magnet would move up and down. Could an electric motor power such a wheel so as to provide more output than input?

A backpack could probably only contain a single 0.25m solenoid (due to the weight of the system) and it would be quite inefficient as only a fraction of the backpack 'movements' would be in the desired 'up and down' direction. Output of more than 100 watts would be an achievement, and even then, it would require fairly vigorous movement, so the backpack idea soon seemed uninteresting.

There follow preliminary mathematical thoughts about a more ambitious wheel arrangement. Solenoids arranged around the circumference of a large wheel, with magnets whizzing up and down inside them as the wheel rotated.

The magnetic flux density B induced by a solenoid of length L with a current I through N loops is given by a well established equation which need not be repeated here.

The mystery value is usually current. We would need to insert calculated or reasonable values for B, N and L.

B = 1.3 Teslas (The Tesla value depends in large part on distance from the magnet. Very high Tesla values are always available with neodymium magnets, but the tricky part is getting the moving magnet to pass within fractions of a millimetre of the copper windings. Greater distance between magnet and interface reduces the Tesla value almost exponentially, so this is an engineering issue rather than an immediate problem for electrical engineering theorists).

Assume for the moment N = 300000 helical loops of copper over 10 meters of solenoid length.

In that event:

B = Remanent flux density = 1.3 Teslas
Uo = Magnetic constant = µ0 = 4π×10âˆ'7 V·s/(A·m)
Ur = 30000 (permeability of magnetic field in Neodymium magnetic material relative to a vacuum)
I = current = unknown (Amps)
N = 300000
L = Solenoid Length = 10 meters

1.3 = 4π×10âˆ'7 x 30000 x I x 300000 / 10
1.3 =  1130.973355 I
I = 1130.973355 / 1.3
= 870 amps

A very high amperage value (indicating the result may be unreasonable).

To calculate the number of copper wire turns/windings on the solenoid we can use another well established equation.

For a solenoid of given length (m) in which we require a specific uniform magnetic field (T), the optimal number of windings maybe calculated (if we know the current) as follows:   

N = L.B / 4π×10âˆ'7 V·s/(A·m).I

N = number of turns of copper = mystery value
L = length of Solenoid (m) = 10m
B = Remanent flux density (T) = 1.3 Teslas
Upsilon Zero = 4π×10âˆ'7 V·s/(A·m)
I = current (A) = 870 A

N = 10 x 1.3 / 4π×10âˆ'7 V·s/(A·m) x 870

= 11890 turns of wire on the solenoid would be optimal.

This should really have been my starting point..the number of windings, so it was very much a chicken and egg situation.

What would be the strength of the uniform magnetic field inside the solenoid were a current of 870 amps to be passed through 11890 windings?

The equation for calculating the strength of a magnetic field is:

Bsolenoid = 4π×10âˆ'7 V·s/(A·m).N.I / L = 4π×10âˆ'7 V·s/(A·m).N.I

= (4π×10âˆ'7 V·s/(A·m) x 10-7 Tm/A) (11890) x 870) / 10M

= 1.29990375 Teslas

But we need to revisit the first equation and insert N = 11890 to project electrical output power.

B = Remanent flux density = 1.3 Teslas
Uo = Magnetic constant = µ0 = 4π×10âˆ'7 V·s/(A·m)
Ur = 30000 (permeability of magnetic field in Neodymium magnetic material relative to a vacuum)
I = current = unknown (Amps)
N = 11890
L = Solenoid Length = 10 meters

1.3 = 4π×10âˆ'7 x 30000 x I x 11890 / 10
1.3 =  44.82424398 I

I = 44.82424398 / 1.3
I = 34.48 amps

34.48 amps is still very high, but relatively speaking it is a more reasonable result than the earlier 870 amps.

Equation for calculating voltage

Where N is the number of turns of wire and ΦB is the magnetic flux in webers through a single loop, a flux density of one Wb/m2 (one weber per square meter) is one tesla. The tesla (symbol T) is the SI derived unit of magnetic field B (also known as "magnetic flux density" and "magnetic induction").

Therefore if our magnetic flux is 1.3T, it is precisely equivalent to 1.3 webers/m2

E = 11890 x 1.3 /1s
E = 15457 volts

Again this may be unreasonably high voltage.

Total electrical output in watts

Power (watts) = 34.48 (amps) x 15457 (volts)
= 532.957 kW

Alarm bells always ring when results like this appear. It just seems far too high an output. Then again, it is a 10m solenoid and it is much too entertaining to stop now).

Remember that this is the output of one 10m solenoid. But what if we arranged ten such solenoids around the circumference of a large rotating wheel, each one containing its own magnet and in which each magnet travelled along the entire length of their solenoids in one full rotation of the wheel?

In that event, total electrical output = 532.957 x 10

= 5.32956 mW

Only fictional superheroes could generate the required torque (N.m) to rotate such a device. My best guess is required torque would exceed 10000 N.m. A human being could probably generate 100 N.m with a bike wheel arrangement, maybe twice that for a few seconds. However, an electrical motor would be able to rotate the wheel. Therefore we need to look at output versus input.

Note that the acceleration of the magnets as they move through the coils has not yet been taken into account. A critical consideration.

Acceleration (rate of change of velocity and therefore the rate of change in the Magnetic field leading to induced EMF) is a key factor determining EMF and therefore in determining electrical output. If you move a magnet slowly through a solenoid, very little current is induced. Move the same magnet rapidly through the same solenoid, and much greater current is induced.

Acceleration will be that due to gravity acting over 10m (the length of the solenoid).

En passant, this raises the question 'what does the output figure actually mean when acceleration has not been taken into account?'

Moving on to my favourite question. How much electrical power would an electric motor capable of rotating the array at optimal rpm require?

If this wheel rotates too quickly, the magnets inside the solenoids will get pinned to the upper ends of their solenoids by centripetal force.

However, the force of gravity (9.81m/s) would not be exceeded if a 25m wheel were to rotate at 7-8 rpm. This would be critical in preventing centrifugal forces (more accurately centripetal forces) pinning the magnets to the outer ends of the solenoids and preventing movement.

Lets check this. (Note that the machine keeps getting bigger even though we are still using 10m solenoids)

Wheel specifications (required to mount 10m solenoids around the circumference):

Diameter = 25m
Radius = 12.5m 
Circumference = 2.pi.r
= 78.53981634m

= 78.53981634 meters per full rotation
= 549.7787144 meters in 7 rotations
= 549.7787144  meters in one minute at 7 rpm
= 549.7787144  meters in 60 seconds
= 9.162978573 m/s

Cross checking the velocity calculation:

7rpm = 9.162978573  / 0.116628766 revolutions per second
= 0.116628766 revolutions per second x 2.pi
= 0.7330 radians per second.

Angular velocity = 0.7330 radians per second.

0.7330  = 12.5 x v / (12.5 x 12.5)
0.7330  = 0.08 v
v = 0.7330  / 0.08
Velocity of perimeter of wheel @ 7 rpm = 9.1625 m/s

This is less than the force exerted by gravity. Accordingly we can safely assume the magnets will be able to move up and down.

Required rotational speed of wheel = 7 rpm = 9.1625 m/s

Weight of assembled wheel

Each magnet = 7453.3kg
x 10 magnets = 74,533kg

Wheel and solenoids x 10 = approximately 5500kg

Total weight = 80,000kg

Force required to rotate system at 7 rpm

Force = mass x acceleration
But for rotating systems:
Frot = m.v2/r
Frot = 80000 kg  x (9.1625 m/s x 9.1625 m/s) / 12.5m
= 537289 Newtons

Monster force. No human being is ever going to able to power this thing. But it is of interest in terms of whether an electric motor can power a wheel with a solenoid array on its circumference so as to provide more output than input.


Double checking figures:
Frot = 80000 kg x 12.5 x (0.7330 x 0.7330)
= 537289 Newtons

Total force in Newtons to rotate wheel array @ 7 rpm = 537289 N

Power consumption of an electric motor capable of producing the rpm and torque (N) to rotate a wheel weighing 80000kg at 7rpm

where
ω is the angular speed in radians per second = 0.7330 rad/s
the moment of inertia kg/m2 (which takes the role of mass) 
the kinetic energy in joules

Calculating the moment of inertia requires the formula:

I = moment of inertia (Kg/m2) which substitutes for linear mass
M = mass Kg = 80000 kg
R = radius (meters) = 12.5m

Therefore:

I = 80000. 12.5 x 12.5 / 2
I = 6,250,000 kg/m2

Krot = 6,250,000 x (0.7330 rad/s x 0.7330 rad/s ) / 2
= 1679 kjoules

1 joule per second = 1 watt
1679000 joules per second = 1679kW
The electric motor consumes 1679kW

However the system appears at least on paper to generate over 5000kW.

The ideas in this abstract are open source. They are not capable of being copyrighted or patented by companies or individuals.

We are working together in the open source community to help protect the poor and vulnerable from rising energy prices.

[quantumtangles]

A scaled down version of the rotating solenoid array can be tested experimentally. I am aiming for a system than can be powered by a commonly available 1.5kW motor, so we can check the power output of the array when powered by such a motor. I am also aiming for a wheel of diameter 1m (slightly larger than a 0.7m diameter bike wheel for easy testing).

Each solenoid contains its own internal cylindrical neodymium magnet of height 10cm and diameter 5cm.

The density of Neodymium is approximately 7g/cm3. Some Neodymium magnets may have a density of 7.3 to 7.5 g/cm3.

Magnet specifications:

H = 10cm

R = 2.5cm

D = 7g/cm3 (density)

Weight = Volume x Density

Volume = p r2 H

= 196.34954 cm3

= 0.00019634954 m3

Weight = 196.34954 x 7

= 1374.44678 g

= 1.372 kg

10 magnets = 1.372 kg x 10 = 13.72kg

Estimated weight of solenoids x 10

+ central wheel of diameter 1 meter = approximately 7kg

Total estimated weight of rotary magnet solenoid array and central wheel = 20.72kg

Let us say the total weight of the entire apparatus that has to be moved by the electric motor is 21 kg.

Wheel specifications:

The wheel is 1 meter in diameter. We want to calculate the mechanical or electrical power in watts (for which we will need to calculate the required force in Newtons) required to rotate such a wheel at 200 rpm.

Very high RPM would result in centrifugal force causing the magnets to adhere to the outer/upper ends of the solenoid cylinders, preventing upwards and downward movement and resulting in no changes in the magnetic fields and no induced EMF.

Hence the low figure of 200 rpm is a reasonable initial suggestion, but we can fine tune this mathematically.

So, to rotate a 21kg apparatus of radius 0.5m at 200 rpm, how much power will we need?

Force = mass x acceleration

We know the approximate mass of the apparatus is 21kg.

We have to calculate the distance the outer circumference of the wheel has to travel for it to move at 200rpm.

Radius = 0.5m

Circumference = 2.pi.r

= 3.141592654 meters per full rotation x 200 rpm

= 628.3185308 meters in one minute at 200 rpm

= 10.47 m/s


Cross checking the velocity calculation:

200 rpm = 3.333333 revolutions per second x 2pi

= 20.943951 radians per second.

w (angular velocity) = 20.943951 radians per second.

20.943951 = 0.5 x v / (0.5 x 0.5)

2v = 20.943951

v = 10.471975 m/s
The same result using a different method of calculation is always good

So, Force = mass x acceleration

Force in Newtons = 21kg x 10.471975 m/s2

= 219.911475 Newtons

This is the force required to rotate the wheel at the required RPM

Summary:

Wheel radius = 0.5m

Wheel weight = 21kg

Wheel velocity at 200rpm = 10.47 m/s

Force required to rotate wheel at 200 rpm = 220N

Electrical Power consumption of Motor

What sort of mechanical/electrical power in watts will be consumed by an electric motor capable of providing 220N of force to the wheel?

Using Jazz maths:

Pmech (watts) = 220N x pi  x 0.5m x 200rpm / 60

= 1,151.9 watts

Accordingly a 1.5 kW electric motor should generate sufficient torque to rotate a 21kg wheel with radius 0.5m at 200 rpm.

Electrical Output

How much electrical energy will the solenoid array generate?

Based on the reasonable assumption that 200rpm will not result in centrifugal forces preventing the neodymium magnets moving freely up and down inside the solenoids (and assuming the system does not act in totem as a magnetic brake) the central question is how much electrical energy the solenoid array will generate.


The magnetic flux density B induced by a solenoid of length L with a current I through N loops can be calculated.


We know from Faradays law of induction that the EMF generated is proportional to the rate of change of the magnetic flux. But what is the magnetic flux generated by each magnet?

Assuming:
L = 0.5m
N = 3000 copper windings
I = current
Ur = 1 (assuming here a vacuum value for the relative permeability or ratio of induction B in a material subject to a field H)
Uo = magnetic constant = 4Ï€ ×10âˆ'7 V·s/(A·m)
B = 4π×10âˆ'7 x I x 30000 / 0.5
B = 7.539822369 x 10-2 x I
= 0.075398223 I

But we still need to calculate B.
B = magnetic field in Teslas

Neodymium magnets have a remanence of approximately 1.3 Teslas.
B = 1.3 Tesla
1.3 = 7.539822369 x 10-2 x I
I = 7.539822369 x 10-2 / 1.3
I = 5.799863361 x 10-2 amps
= 0.058 amps

N is the number of turns of wire and ΦB is the magnetic flux in webers through a single loop.

A flux density of one Wb/m2 (one weber per square meter) is one tesla. The tesla is the SI derived unitof magnetic field B (also known as "magnetic flux density" and "magnetic induction").

Therefore
E = 3000 x 1.3 /1s
E = 3900 volts

Watts = volts x amps
= 3900 x 0.058
= 226.2 watts per cylinder x 10
= 2262 watts
= 2.262 kW

Note that a greater number of windings would increase power output.

Projected power in watts required to turn the solenoid apparatus = 1,151.9 watts

Projected output = 2,262 watts

Net output = 1110.1 watts

I should be most grateful for mathematical responses in SI units.

For example, it may well be that losses due to friction account for the apparent anomaly.

A unit-less efficiency coefficient of 0.85 would probably account for friction and heat losses, indicating an energy profit of 943.585 watts.

[SkyWatcher123]

Hi folks, Hi quantumtangle, i like that idea, closest thing i know of is the perkins type generator that johnny cool pants showed, it used tubes with magnets sliding through and coils wrapped on outside.
How about continuous long magnet/coil tubes like 2 foot long and one could have 12 or more on shaft and have them next to each other staggered so as to minimize shaft power needed to rotate. This way with tubes the full length of the diameter of the rotor wheel, the free fall would be long and gain much speed for coil generation.
I posted an idea at EF, which is basically wind generators mounted at the periphery of a wheel or in this case computer fans for cheap testing.
Though they don't have symmetrical blades, it should give an idea if the energy needed to rotate might be less than energy output from the fans.
Could you or anyone give your thoughts on this idea. here is a pic and a pic of quantums generator idea reposted here.


peace love light
tyson