AE1110x - W09_1b - Equations of Motion

Summary

This video delves into Newton's laws of motion and their application to aircraft performance. It explains the concept of inertial and non-inertial frames of reference, particularly in relation to Earth's rotation and the motion of aircraft. The video covers the forces acting on an aircraft—gravitational, aerodynamic, and thrust—and how these forces relate to the aircraft's acceleration. By deriving the equations of motion, the script lays the groundwork for understanding aircraft performance calculations, making complex physics concepts accessible for students and enthusiasts alike.

Takeaways

• 😀 Newton's First Law states that a body at rest remains at rest and a body in motion continues at constant velocity unless acted upon by an external force.
• 😀 Inertial frames of reference are not accelerating, meaning the frame remains unaffected by external forces, like when a ball moves forward in a train during braking.
• 😀 Earth's surface does not provide an inertial reference frame because of its rotation and curvature, leading to small but notable accelerations in different directions.
• 😀 The centrifugal force, experienced due to the Earth's curvature and rotation, is an apparent force, similar to the ball in the train example.
• 😀 The acceleration due to Earth's curvature at typical cruise altitudes (10 km) is very small and often negligible in aircraft performance calculations.
• 😀 The flat Earth assumption is used to simplify calculations, treating the Earth as non-rotating and neglecting small rotational accelerations.
• 😀 The Earth's reference frame, despite its small accelerations, is commonly treated as inertial for aircraft performance calculations.
• 😀 Three main reference frames are defined: the Earth-fixed frame, the moving Earth axis system attached to the aircraft, and the body axis system attached to the aircraft itself.
• 😀 The airspeed vector often forms an angle with the aircraft's nose, with the flight path angle describing the direction of the airspeed relative to the horizon.
• 😀 The forces acting on an aircraft, including gravitational force, aerodynamic lift and drag, and thrust, must be considered to define its motion and acceleration.
• 😀 Newton's second law for aircraft motion involves breaking forces and accelerations into components parallel and perpendicular to the airspeed vector, forming the basis for performance calculations.

Q & A

What is Newton's First Law of Motion?

Newton's First Law states that a body at rest will remain at rest, and a body in motion will continue moving at a constant velocity in a straight line unless acted upon by an external force.

What is the condition for Newton's First Law to apply?

Newton's First Law applies only in an inertial frame of reference, which is a frame that is not accelerating.

Why doesn't Newton's First Law apply inside a moving train?

In a moving train, the train is a non-inertial frame of reference because it accelerates. As a result, objects inside, like a ball, will move forward or sideways without an external force when the train brakes or turns.

Is the Earth's surface an inertial frame of reference for aircraft?

No, the Earth's surface is not an inertial frame of reference for aircraft because the Earth is curved, and aircraft are moving in circular motion at constant altitude, which requires centripetal acceleration.

What is the centrifugal force, and how does it relate to Earth's rotation?

The centrifugal force is an apparent force that seems to push objects outward when they are in a rotating reference frame, such as an aircraft flying at altitude. It is not a real force but is due to the non-inertial nature of the rotating Earth frame.

How can the Earth's rotation affect high-altitude vehicles?

The effects of Earth's rotation, such as the variation in velocity depending on latitude, are small and negligible for most aircraft. However, they become significant for high-altitude, high-speed vehicles.

What are the different reference frames used in aircraft motion analysis?

The different reference frames used in aircraft motion analysis include the Earth-fixed reference frame, the moving Earth axis system attached to the aircraft, the body axis system fixed to the aircraft, and the air-path-axes system related to the direction of the airspeed vector.

How does the flight path angle relate to an aircraft’s motion?

The flight path angle is the angle between the aircraft's nose (or its airspeed vector) and the horizon. It plays a key role in defining the aircraft's trajectory and the required aerodynamic forces.

What forces act on an aircraft in flight?

The primary forces acting on an aircraft in flight are gravitational force (weight), lift (perpendicular to the airspeed vector), drag (parallel to the airspeed vector and opposing motion), and thrust (from the propulsion system).

How are the equations of motion for an aircraft derived?

The equations of motion for an aircraft are derived by applying Newton's second law (F = ma), where the forces are summed in both the parallel and perpendicular directions relative to the airspeed vector. The resulting equations describe the aircraft's acceleration and motion.