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Energy from Gravity

Obtaining energy from gravity.

I am not talking about the change between potential and kinetic energy like in a damn but getting energy at the same level or height.

Who has not enjoy the wind just in front of a beach watching seagulls doing their apparently effortless fly. It seems like magic the way they hang up there in the air.  Even more magic seems (at least to me) a 747 flying at low-speed just about to land. How this monster can hang up there? Even though I understand the principles of aerodynamics that explain it, I keep thinking that is almost poetry.

This poetry only works on Earth. In outer space, wings work only on movies. The wind energy that comes from the circular move of a wind turbine is in part due to gravity action over the air passing the turbine (see formula). Wind is a consequence of temperature differences in different points on Earth (also caused by rotation of Earth itself) but gravity is essential.

Wind Energy

The Maximum Theoretical Power (MTP) Output of a turbine is represented in the formula:

MTP = 1/2 * Air density * Turbine Swept Area * (Wind Speed) ^ 3

Air density depends on gravity. Air is thinner at 6000 meters than at 0 meters. The weight of all air above us increase the air pressure and also the density at sea level.

But the most important factor in the above formula is the wind speed.

If energy output depends on relative air speed; could we get energy from a vehicle due to its own speed, from the relative air speed created?

Is there any vehicle that gets energy from this relative air speed created?

The Greenbird is a clear example: http://en.wikipedia.org/wiki/Greenbird

Greenbird land yacht

The Greenbird has been capable of run at 126.1 mph with constant wind speed of 30 mph.

All energy has come from the wind especially from rest. But the gained speed also produced “apparent wind” (The wind that blows against you as a result of your passage through still air is known as the apparent wind. Read more: http://www.answers.com/topic/apparent-wind#ixzz21TXJ4jBi)

Resuming; the Greenbird has been capable of using its own speed in order to generate more energy and as a consequence more speed in a virtuous circle up to a 126 mph!

But why not getting up to let’s say 300 mph! This web page (http://www.answers.com/topic/apparent-wind ) explain it:

Implications on sailing speeds

In sailboat racing, and especially in speed sailing, apparent wind is a vital factor, when determining the points of sail a sail-boat can effectively travel in. A vessel traveling at increasing speed relative to the prevailing wind will encounter the wind driving the sail at a decreasing angle and increasing velocity. Eventually, the increased drag and diminished degree of efficiency of a sail at extremely low angleswill cause a loss of accelerating force. This constitutes the main limitation to the speed of wind-driven vessels and vehicles.

Force vectors on vessel

http://www.rationalskepticism.org/general-science/one-man-s-quest-to-outrace-wind-t20155.html

This image makes a good visual representation of forces on the vessel. The forward force will be reduced to zero if sail gets parallel to vessel direction of movement. Note that the sail force is still considerable at zero angle (while speed is still high) but in this vessel is not useful.

Once you know why Greenbird can’t go faster than 126 mph, the remarkable thing is that this vehicle is generating more energy from its own speed.

This is very Counterintuitive for any person that has taken a basic physics course. One of the first things that one learn in such a course is about drag.

It is a very well-known fact that a car needs more power from the engine as it increase the speed due to drag. As a matter of fact, drag gets incremented by the square of speed. So where comes the energy for the Greenbird to accelerate up to 126 mph?

All that energy comes from the Greenbird sail (or wing)!

Some background information

A bird or a plane wing gets lift from the air that pass thru it.

An airfoil is the shape of a wing or blade (of a propeller, rotor or turbine) or sail as seen in cross-section. (from Wikipedia: http://en.wikipedia.org/wiki/Airfoil)

Depending on form and other variables, there are very advance airfoil capable of having 100 times more lift than the drag they produce. A typical Cessna airplane can have 7 times more lift than drag. A Boeing 747, 17 times.

To measure lift and drag in airfoil, coefficients are used (Lift and Drag Coefficients). Lift to Drag ratio (L/D) is also a coefficient. The most advanced airplanes like the Virgin Atlantic GlobalFlyer can have a L/D coefficient of 37!

Virgin Atlantic GlobalFlyer

Virgin Atlantic GlobalFlyer

(http://en.wikipedia.org/wiki/Virgin_Atlantic_GlobalFlyer )

In modern sailplanes, L/D numbers higher than 40 are normal. (http://en.wikipedia.org/wiki/Lift-to-drag_ratio).

Another important factor is the “Aspect Ratio” or how long is the wing in proportion to the width. The longer the wing is, the better. The wings of the Virgin Atlantic GlobalFlyer have big “Aspect Ratios”.

So a wing with a good “Aspect Ratio” an a big L/D number can be considered an efficient wing. Creates big amount of lift with very low drag.

That is the secret of Greenbird incredible speed; a very efficient wing.

Greenbird is designed to use wind. It will not work even though we impulse it somehow in absence of wind.

A good question

Can we make a vehicle that can use relative wind speed in absence of wind?

The first thing I thought answering this question was: Why not install a wind turbine to a vehicle that use the electric energy to drive the wheels and start a virtuous cycle?

There are a lot of patents about this same idea. Much of those patents don’t take the “Thrust Force” that a typical wind turbine makes when they turn. “Thrust Force” is a force that pulls in the wind direction (then will be braking the forward movement of any vessel).

Big wind turbines design take this force into consideration to build the tower. Too much thrust and the tower can collapse.

In an airplane propeller the force that impulse the airplane is called thrust, as you can see in this diagram.

Thrust propeller

Thrust in an airplane propeller

Thrust is the force that impulse propeller planes

In a wind turbine is just the other way around as you can see in the following diagram.

Thrust force for a wind generator

Thrust in a wind turbine goes in the wind direction

This force would oppose the advance of our vehicle. So as we get speed, the turbine would oppose further with more force. The end result is a failed design.

A solution

It is clear that the Greenbird wing (or sail) produce enough force to reach 126 mph. At this speed almost all force is perpendicular (this is key) to the vehicle direction, or said it other way, it is wasting almost all wing energy produced. And still can go up to 126 mph! Just imagine the speed that could reach if it could use all the wing potential!

What if we connect several advance wings (like the ones in the Greenbird) around a single axle and connected to an electric generator? Remember all that wasted energy? Here we can use it to produce torque (remember that perpendicular force!) and then electricity.

You could think that this is very similar to a wind turbine but the main difference is the wing elements themselves and the “angle of attack” of the wings. Wings need to be long enough to produce torque in significant quantities and very low drag (angle of attack around 4 degrees) to get easy acceleration.

This proposed design turns very low if we compare it with a traditional wind turbine (and produce less energy) but drag is reduced even more.

The net result is a design that can be used in a vehicle impulsed by the generated energy.

Imagine a train with two generators attached:

Train front view

Proposed train with two generators attached

This train obviously needs to be very well link to its track to withstand lateral wind.

Generators could be design to start at low speeds but then wings should be big enough (remember that wing lift is proportional to the square of speed). At the end is a compromise between diameter of generators and starting speed (speed that kick-start generators).

This train needs to be supplied with the energy to reach that speed (from batteries or from the track). After that, generators will produce the necessary energy to go on.

Resuming.

What is the relation between the Greenbird, the proposed train and gravity?

To begin with, atmosphere existence is due to gravity (as so many other things). Without air our generator will not work (nor any wind turbine). In outer space, acceleration is very easy to get due to lack of drag, but a wind turbine will not work out there.

Also you could ask: where comes the energy to accelerate Greenbird?

The first of Newton’s laws of motion (http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion) says: “Every object continues in its state of rest, or of uniform motion in a straight line, unless compelled to change that state by external forces acted upon it.”

Greenbird are exposed to drag forces from air and soil but also accelerates due to lifting forces on the wing.

Gravity on Earth creates drag forces on the wing but also creates (the right conditions to produce) the lifting force.

From the right use of the lifting force of a very efficient wing with very low drag, our proposed generator and vehicle will get gravitation energy to move itself.

So we need to address this tech limitation (an a mental one) to have a vehicle moved by gravity energy.

This proposal hopes to change the state of things.

This really is a gravity engine.

Calculations explained!

The laws that govern our generator are based on lift and drag forces:

Lift = ½ * air density * (wind speed)^2 * wing area * lift coefficient

Drag = ½ * air density * (wind speed)^2 * wing area * drag coefficient

Another important coefficient is L/D coefficient:

L/D Coefficient = lift coefficient / drag coefficient

In this chart it can be seen the relation between both coefficients and the angle of attack.

Curves Graph

Lift and Drag coefficients for an airfoil.

Let’s take an angle of 4 degrees:

drag coefficient = 0,03

lift coefficient = 0,70

Then L/D = 23,33

This means that lift force is 23 times grater than drag force. This is what makes birds fly and also airplanes.

We are going to make a series of assumptions:

  1. Central hub of generator does not have friction.
  2. For torque calculation, all lift from wing will be at the geometric center (half of length).
  3. Angular speed it’s based on angle of attack and wing width as if it was going thru jelly.
  4. Wind speed is the same all along the wings (angular speed is low)
  5. Wings flexes along all its length to minimize the frontal wing resistance

These are the formulas:

Lift force (F):

F = ½ Dens * Area * Wind Speed ^ 2 * LiftCoeff.

Dens: Density in kg/m3.

Area: Total area of generator.

Wind Speed: real speed from air relative to generator.

LiftCoeff: Lift Coefficient

Torque on generator axle (T).

T = F * distance from axle.

F: Lift force

distance from axle: Wing length divided by 2

Power (P):

P = T*2*Pi*n * wings on axle

T: Torque on generator axle

n: Revs per second.

wings on axle: number of wings on generator

Drag Force (Fd):

Fd = ½ Dens * Area * Wind Speed ^ 2 * DragCoeff.

Dens: Density in kg/m3.

Area: Total area of generator.

Wind Speed: real speed from air relative to generator.

DragCoeff: DragCoefficient

Power necessary to overcome drag force (Pd):

Pd = Fd * Wind Speed * wings on axle

Fd: Power necessary to overcome drag force

Wind Speed: real speed from air relative to generator.

wings on axle: number of wings on generator

Some calculations examples: