## Why buoyancy is important in Blue Energy research

Part of Blue Energy research is to design flying crafts that can overcome issues in aviation and space exploration. We want to find a technology that is an integral solution for anything relates to "fly", "float" and "speed" inside atmosphere and within a vacuum of space. This is a huge challenge because fundamentally it is not just issue of energy efficiency, it is also an issue of working medium efficiency. In aviation and space launch and travel, you will have different term to describe "working medium". Otherwise known as propellant that creates thrust. We know that aircraft belong to atmosphere region while spaceships belong to space. Aircraft can fly, which includes changing the course of fly path and speed. This requires consumption of energy, i.e., energy from fuel it carries. On the other hand, spacecraft doesn't have great mobility like aircraft, and neither has to consume a lot of energy once within an orbital travel path. One thing in common, both applications are within gravity field of some kind. Flying within atmosphere or outside is uniquely due to anti-gravity force. Aircraft depends on aerodynamic lift to offset gravity drag while spacecraft depends on orbital speed to offset gravity free fall momentum.

We will have a simple analysis on energy efficiency to use engine, energy and working medium to create "anti-gravity". The finding is quite contrary to what the public believes. In order to counter gravity drag on Earth, the energy consumption rate is relatively small. So small that it proves current technologies in aviation and space launch are completely inadequate.

How small is the energy consumption rate in order to achieve "anti-gravity". In our view, everything falls towards gravity field center until a buoyancy force offset gravity force, of which we refer as gravity and anti-gravity equilibrium. Commonly seen lighter than air balloons, ship floating on water and aircraft flying in sky are all due to such balance. In lighter than air case, the energy required for a balloon not to fall to the ground is ZERO. Neither a ship needs any energy to stay above the water. For aircraft, energy is required. In this scenario, engine and energy play the important role to create force that counter gravity drag.

Are there other solution to make engine and energy working together to achieve "anti-gravity" effect at the minimum energy consumption? We would like to leave the discussion to the book section. What we can say is that fixed wing aircraft, helicopter are anti-gravity technologies. They are not very energy efficient. The main reason is the engines onboard are poorly designed. Even if you have a highly efficient engine used in aircraft, it is still not good enough. We can't make aircraft leaving the atmosphere and becomes spaceship. In order to make something not confined by such condition, we must also consider propellant efficient. Because in space, there is NOTHING in there. We must have propulsion system that is truly propellant efficient. Energy is everywhere. Energy must reply on mass to do work. Propellant for a plane or spacecraft is like working medium. Here is another way to explain what is working medium efficient. If you ride a horse, you can not let the horse run away while you are not riding on it. You will not be able to walk in the air while suspended by a cable. These is well defined physics laws. So the future spacecraft must carry the propellant onboard ALL THE TIME. Some people called this type of propulsion system reactionless engine. Warp drive is an even better description. Reactionless propulsion isn't fit well into classic physics laws. So we need to do a little bit of alternative way to explain how a reactionless propulsion system works. It will eject very small amount of mass from a relatively larger mass, which will subject to reactionless force similar far more stronger than gravitational force. The ejected matter is so small, even all the fuel energy is exhausted, there will be plenty propellant left. This type of reactionless propulsion system we here refer as buoyancy engine.

Following the discovery, we believe we can use the principle of buoyancy theory to explain many branches of known study in aviation and space exploration. To use this principle, we hope to design an engine that is useful in all applications that require "float", "fly" and "speed". Especially the "speed" we aim for is well beyond the fastest recorded human technologies have managed to achieve. Moreover, we want to develop a "break" technology enable "speeding" vehicle slows down quickly in space as well as in midair. The break force is also due to this engine innovation. What does it mean when a speeding supersonic, hyper sonic aircraft or an orbiting spacecraft can stop quickly without falling towards a gravity center? That can change the many things we consider common senses.

Here we give you a few topics that you might have known which is possible or "impossible".

- VTOL, the type of aircraft that can take off and land without runway. So far only small numbers of products, such as Harrier Jump Jet. Otherwise, SpaceX's Grasshopper did make some success VTOL attempt. But these examples are not fuel efficient. Can you build a VTOL with payload of 1000 tons or more?
- Low cost launch vehicles using low g force to gain speed from subsonic to supersonic, hypersonic and then entering LEO. Vehicle entry/return is without heat shield technology.
- High speed space travel (1000km/s) with long specific impulse of one g acceleration and deceleration. (24×3600×10 = 864000 meter/second)
- Silent propulsion similar to what you can only see in Si-fi movies like Star Trek, Star Wars, etc.

Above mentioned challenges present the need to completely rewrite "textbook" in aviation and space launch. Blue Energy is trying to create this technology. We design BETE as the engine to handle thermal heat energy. As we know, fuel energy can only be released by combustion in the form of high temperature. We believe there is major problem in engine design to handle heat energy. Blue Energy Buoyancy Engine, also referred as BEBE, is a type of action/reaction engine for the purpose of imitating the effect of buoyancy. The main objective of BEBE is to solve the issue of propellant efficiency. Within our solar system, energy is not an issue. The Sun radiate plenty energy for a spacecraft to absorb. But the empty space is the issue. How to create massive momentum force for a spacecraft in a vacuum without running out of propellant very quickly is the key to open the doorway of future humanity one day.

Our civilization advances according to how we can intelligently utilize energy. We design engines for the purpose of particular applications. For example, vehicles can help us travel fast. So we design and build road, bridges, tunnels and railway to facilitate the technology. With population growth, these 2 dimensional main stream transport solutions are inefficient. We are wasting more and more time on road congestion than ever before and it is getting worse. Investment on road and bridge has huge cost. Likewise, the maintenance isn't cheap. People live where the jobs are. Most likely the jobs opportunities concentrate on where the infrastructure is better built. It is time to have flying cars. How do we have a flying car technology that is safe, efficiency and mainstream? The solutions will tilt the balance of living standard/cost and social equality in between urban and rural. In fact, we think, not only we can save money on ever expensive transport cost, we can save our travel time and live in a better quality of lives. Flying cars will be the catalyst to slow the asset price rise, mainly in housing affordability.

If we build colonies on Mars in the future, there will be no roads, bridges, railways, airports etc. Everything we will have on the red planet is flying, including a whole town of colony. This is my prediction: most of Martian infrastructure, food supply, equipment etc., will be build here on Earth. They will be "shipped" to Mars in days. All the colonies on Mars will be VTOL ready.

# Momentum Study

In order to explain the theory of buoyancy engine, many topics relate to physics have to be discussed. The simplest study is how two identical perfect ball behave when they have elastic collision.

Two objects of identical mass, preferably pure spherical, are resting on flat plane, with a wall C standing, until ball A can experience a constant force F, which points from ball A center to ball B center, and perpendicularly onto wall C. Assuming ball A acceleration is continuously, which results in first impact against ball B at the point of its standing. Then the collisions keep on happening in different distance from this initial impact point to wall C. If all collisions are perfectly elastic, can you use force F, and mass m to find out the final point L where collision will always happen in the distance from wall C? What is the frequency of collisions?

For simplicity, let us consider two balls of unit mass m=1 and zero radius. Also there is no wall C here. Wall C will be used when we consider reflection from it.

### Scenario 1:

Consider to balls A and B at position x and y. The center of mass is given by:

The balls A and B collide on position y. By using energy conservation theorem, the velocity of the ball A can be calculated by:

By the property of elastic collision for equal masses, the kinetic energy is exchanged between ball B and ball B i.e. the ball B gains this velocity. and the ball A comes at rest.

### Scenario 2:

Consider at any given time, the balls A and B collide and the velocity of ball A is u more than that of ball B. After collision, ball B gains more u velocity than ball A. Let the velocity of the ball A be v-u and that of ball B be v and let them collide again at d=p-q distance later.

If both ball B and ball A travels distance d in time T, then average velocity of ball A must be equal to the velocity of ball B. i.e.

For ball A, to change the velocity by v+u from v-u under the acceleration a, the can be calculated using the equation:

After the collision, the velocity of the ball B is v+u and that of ball A is v. The difference in velocity after collision is constant.

This is the time required for the collision of the two particles which is independent of their velocities, but rather depends on the difference in initial velocities. In first case, the initial velocity has been calculated as u=√(2a(x-y) ). Using this, we get

This is the time interval required for the two objects to collide.

### Scenario 3:

Consider at any given time the two balls collided and the velocity of the ball B is v and that of ball A is v-u.As time increases, the velocity of the ball B remains constant while velocity of ball A increases as:

The velocity of the center of mass is:

After collision, the velocity are interchanged, i.e. ball B velocity is v+u and ball A velocity is v and the time elapsed is T elapsed. The velocity of center of mass is given by:

If object starts from velocity zero on acceleration a for time T, the change in velocity is:

Therefore, the velocity of center of mass does not change on collision.

Using the time as t=T/2,3T/2,7T/2,... we can find the distance of collision right before the reflection. The factor T/2 accounts for the fact that the velocity of ball A increased only by u initially when first collision took place.

Integrating, we get (We are assuming that the center of mass is at (x+y)/2 and position decreases.

Here, z_{n} gives the position of center of mass at time (n+1/2)T, which is exactly the time where two objects collide. To check the consistency of the given equation, we simply put n=0,1,2,.. and verify it. For case n=0.

The first collision occurs at distance y. For n=1,

If there 5y−4x=0 -> 5y=4x, the collision occurs at wall C and at point y periodically. In this case, there are no other points where collision occurs. If 4x > 5y, the ball only collides once at point y.

Similarly we can calculate the distance at which they collide.

### Scenario 4:

Consider the ball A and ball B collide at point p such that the next collision can takes place only when ball B gets reflected. Out first strategy is to find the required criteria for such collision to happen.

To find the value of the position p, it must fulfill the criteria that ball B and ball A do not collide when they are travelling in same direction so p=zn where zn<y<z(n+1). in special case when zn=y for particular value of n then the collisions occur on same positions amount time. event will happen backwards. now let us not consider that situation. Ball B travels distance p+q while with velocity v and the ball A travels distance p-q so they collide at point q.

p+q=vt

p-q=(v-u)t+at^{2}

Solving these system of equations (By Mathematica), we get

We have the criteria that 0<q<p and 0<t<T, which gives us:

On, this time, velocity of ball A has changed to:

ball B gains this velocity and ball A has the velocity of the ball B i.e. v.

The time required by ball B to reach the wall C is:

In this time, the ball A reaches the velocity:

And distance traveled by ball A is:

Upon simplifying, we get:

Then we have the difference in velocity of the ball A and ball B as:

### Scenario 5:

Consider the ball B and A, with the velocity difference e of u over the distance d. If they meet approximately at distance D, then the set of equation governing their motion are:

solving this, we get:

The velocity of the ball A can be calculated as:

The velocities are flipped, i.e. ball A gains velocity v and the ball B gains the velocity v-(2ad+u^2 )^^{0.5}. The difference in velocities is u'=(2ad+u^^{2} )^^{0.5} using the same set of equations, we get:

This process will repeat over and over again as the time period for collision is independent of distance, we again consider the same approach to calculate the distance at which the collision occurs.