center of gravity

 

Concept of the center of gravity 

The concept of the center of gravity has a rich history, rooted in the study of mechanics and the movement of bodies.

Here's a chronological overview:

Ancient Greece

Aristotle (384-322 BCE): The philosopher and scientist discussed the balance of bodies and the idea of a center, though not precisely defining the center of gravity.

Archimedes (287-212 BCE): A mathematician and physicist, Archimedes made significant contributions to understanding the center of gravity.

He worked on the equilibrium of planes and discovered the principle of the lever, which relates to the center of gravity.

Medieval Period

Islamic Golden Age (8th-14th centuries): Scholars like Alhazen (Ibn al-Haytham) and Al-Biruni worked on theories of balance and centers of mass in the context of astronomy and physics.

Renaissance and Early Modern Period

Leonardo da Vinci (1452-1519): Da Vinci studied the balance and motion of bodies, contributing sketches and ideas related to the center of gravity.

Galileo Galilei (1564-1642): Galileo’s studies on motion and mechanics laid the groundwork for classical mechanics, including concepts related to the center of gravity.

17th and 18th Centuries

Isaac Newton (1642-1727): Newton’s laws of motion and universal gravitation provided a deeper understanding of gravitational forces and the concept of the center of mass, which is closely related to the center of gravity.

Leonhard Euler (1707-1783): Euler made advancements in rigid body dynamics, further developing the mathematical description of the center of gravity.

19th Century

Carl Friedrich Gauss (1777-1855): Gauss contributed to the study of gravitational fields and potential theory, which has implications for understanding centers of gravity.

Louis Poinsot (1777-1859): Poinsot’s work on rotational dynamics and moments of inertia deepened the understanding of the center of gravity in moving bodies.

20th Century and Beyond

Modern Physics and Engineering: The concept of the center of gravity continues to be crucial in various fields, including aerospace engineering, robotics, and biomechanics.

Advancements in computational methods have allowed for precise calculations and simulations involving centers of gravity in complex systems.

Throughout history, the center of gravity has evolved from a philosophical idea to a precise scientific concept essential in many fields of study.

Center of gravity in Airplane 

Center of gravity: is the point  through which the total weight of the body will act 

pitch,roll,yaw,(all three axes ) act through the center of gravity (CG)

Key Concepts:

Uniform Objects: For symmetrical, uniform objects, the center of gravity is at the geometric center. For example, the center of gravity of a uniform sphere is at its center.

Irregular Objects: For irregularly shaped objects or those with non-uniform density, the center of gravity is found through calculations or physical methods like balancing or suspension.

Methods of determination

 

1- by caculation method 

2- Physical Methods: The center of gravity can also be determined through practical methods:

Balancing: Place the object on a narrow support and move the support until the object balances.

Plumb Line: Suspend the object from different points and use a plumb line to mark the vertical line from each suspension point. The intersection of these lines is the CG.

Applications:

Engineering and Design: Ensuring stability of structures, vehicles, and equipment.

Aerospace: Balancing aircraft for proper flight dynamics.

Position's of the center of gravity

1- Rearward: if the the CG is at or near the most Rearward limit the distance between the CG and rudder is reduced which reduces the amount of yawning leverage  the redder can exert .

The center of gravity range relates to the furthest forward and aft center of gravity positions along the aircrafts longitudinal axis inside which the aircraft is permitted to fly this is so because the horizontal tail plane can generate a sufficient lift force to balance the aircrafts lift weight moment couple so that it remains longitudinal stable and retains manageable pitch control (pitching moment balanced by horizontal tail plane)

2 - Forward : ability to control the airplane in an emergency is improved as the center of gravity is moved forward but to obtain maximum range   an aft center gravity position with nose up enroute attitude will allow it to achieve the maximum possible range an aft center gravity position normally is accomplished by using the aft cargo hold

While  forward center of gravity is accomplished by using the forward cargo hold

Forward center of gravity increase the stall speed while aft center of gravity reduce the stall speed

Jet aircraft needs a large center of gravity range because its center of gravity position can change dramatically with a large change in its weight during a flight .

Therefore to accommodate a large center of gravity movement the aircraft has to have a powerful horizontal tail plane to balance longitudinally  stable and retains its pitch controllability 

Center of gravity movement causes

1- fuel burn

2- passenger movement

3- High speed:lead to nose down profile.

Lateral center of gravity 

Lateral movement of the center of gravity (due to fuel imbalance between both wing tanks)

Understanding the center of gravity is crucial for analyzing and predicting the behavior of objects under various conditions, ensuring stability, and optimizing design and functionality in various fields.