Jet force

Last updated

Jet force is the exhaust from some machine, especially aircraft, propelling the object itself in the opposite direction as per Newton's third law. An understanding of jet force is intrinsic to the launching of drones, satellites, rockets, airplanes and other airborne machines.

Contents

Jet force begins with some propulsion system; in the case of a rocket, this is usually some system that kicks out combustible gases from the bottom. This repulsion system pushes out these gas molecules in the direction opposite the intended motion so rapidly that the opposite force, acting 180° away from the direction the gas molecules are moving, (as such, in the intended direction of movement) pushes the rocket up. A common wrong assumption is that the rocket elevates by pushing off the ground. If this were the case, the rocket would be unable to continue moving upwards after the aircraft is no longer close to the ground. Rather, the opposite force by the expelled gases is the reason for movement.

Jet force in action, the force that propels this rocket into take off Soyuz TMA-5 launch.jpg
Jet force in action, the force that propels this rocket into take off

Thrust, lift, weight and drag

The jet force can be divided into components. The "forward" component of this force is generally referred to as thrust. [1] The upward component of jet force is referred to as lift. [2] There are also two other forces that impact motion of aircraft. Drag, which is also referred to as air resistance, is the force that opposes motion. As such, it acts against both components of the jet force (both the thrust and the lift). The fourth and final force is the weight itself, which acts directly downward.

Thrust

To analyze thrust, we take a mathematical perspective.

  1. First, an aircraft takes off at some angle with respect to the ground. For a rocket traveling straight "up", this angle would be 90°, or at least close to 90°. For airplanes and most other aircraft, this angle will be much less, generally ranging from 0° to 60°. We shall define this angle as θ.
  2. θ is constantly changing as the aircraft moves around. At any given moment, however, the cosine of this angle θ will give us the component of the force that is acting in the forward direction. Multiplying the total force by this cosine of θ would yield the thrust:

Because θ ranges from 0° to 90° and the cosine of any angle in this range is 0 ≤ cos θ≤ 1, the thrust will always be either less than or equal to the jet force- as expected, as the thrust is a component of the jet force.

Lift

Similar to our analysis of thrust, we begin with a mathematical look:

  1. We define angle θ the same way we did in step 1 for thrust. Again, this angle θ is different at any given time.
  2. For lift, however, we are looking for the vertical component, rather than the forward component. The sine of angle θ will give us the component of the force acting in vertical component. Multiplying the jet force by the sine of θ will yield the lift:

Similar to cosine, the sine of an angle ranging from 0° to 90° will always between at least zero and at most one. As such, the lift will also be less than the jet force. Of jet force, lift and thrust, we can find any one of these if the other two are given using the distance formula. In this case, that would be:

As such, jet force, thrust and lift are inherently linked.

Drag

Drag, or air resistance, is a force that opposes motion. Since the thrust is a force that provides "forward motion" and, lift one that produces "upward motion", the drag opposes both of these forces. Air resistance is friction between the air itself and the moving object (in this case the aircraft). The calculation of air resistance is far more complicated than that of thrust and lift- it has to do with the material of the aircraft, the speed of the aircraft and other variable factors. However, rockets and airplanes are built with materials and in shapes that minimize drag force, maximizing the force that moves the aircraft upward/forward. [3]

Weight

Weight is the downward force that the lift must overcome to produce upward movement. On earth, weight is fairly easy to calculate:

In this equation, m represents the mass of the object and g is the acceleration that is produced by gravity. On earth, this value is approximately 9.8 m/s squared. When the force for lift is greater than the force of weight, the aircraft accelerates upwards.

Analysis with momentum

To calculate the speed of the vessel due to the jet force itself, analysis of momentum is necessary. Conservation of momentum [4] states the following:

In this situation, m1 represents the mass of the gas in the propulsion system, v1 represents the initial speed of this gas, m2 represents the mass of the rocket and v2 represents the initial velocity of the rocket. On the other end of the equation, v1f represents the final velocity of the gas and v2f represents the final velocity of the rocket. Initially, both the gas in the propulsion system and the rocket are stationary, leading to v1 and v2 equaling 0. As such, the equation can be simplified to the following:

After some more simple algebra, we can calculate that v2 (the velocity of the rocket) is the following:

This gives us the velocity of the aircraft right after it takes off. Because we know all forces acting on it from this point on, we can calculate net acceleration using Newton's second law. [5] Given the velocity that the aircraft takes off with and the acceleration at any point, the velocity can also be calculated at any given point. [6]

Related Research Articles

<span class="mw-page-title-main">Rocket</span> Vehicle propelled by a reaction gas engine

A rocket is a vehicle that uses jet propulsion to accelerate without using the surrounding air. A rocket engine produces thrust by reaction to exhaust expelled at high speed. Rocket engines work entirely from propellant carried within the vehicle; therefore a rocket can fly in the vacuum of space. Rockets work more efficiently in a vacuum and incur a loss of thrust due to the opposing pressure of the atmosphere.

<span class="mw-page-title-main">Thrust</span> Reaction force

Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that system. The force applied on a surface in a direction perpendicular or normal to the surface is also called thrust. Force, and thus thrust, is measured using the International System of Units (SI) in newtons, and represents the amount needed to accelerate 1 kilogram of mass at the rate of 1 meter per second per second. In mechanical engineering, force orthogonal to the main load is referred to as static thrust.

Specific impulse is a measure of how efficiently a reaction mass engine, such as a rocket using propellant or a jet engine using fuel, generates thrust. For engines like cold gas thrusters whose reaction mass is only the fuel they carry, specific impulse is exactly proportional to the effective exhaust gas velocity.

<span class="mw-page-title-main">Projectile</span> Object propelled through the air

A projectile is an object that is propelled by the application of an external force and then moves freely under the influence of gravity and air resistance. Although any objects in motion through space are projectiles, they are commonly found in warfare and sports.

<span class="mw-page-title-main">Work (physics)</span> Process of energy transfer to an object via force application through displacement

In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force strength and the distance traveled. A force is said to do positive work if when applied it has a component in the direction of the displacement of the point of application. A force does negative work if it has a component opposite to the direction of the displacement at the point of application of the force.

<span class="mw-page-title-main">Flight</span> Process by which an object moves, through an atmosphere or beyond it

Flight or flying is the process by which an object moves through a space without contacting any planetary surface, either within an atmosphere or through the vacuum of outer space. This can be achieved by generating aerodynamic lift associated with gliding or propulsive thrust, aerostatically using buoyancy, or by ballistic movement.

<span class="mw-page-title-main">Recoil</span> Backward momentum of a gun when it is discharged

Recoil is the rearward thrust generated when a gun is being discharged. In technical terms, the recoil is a result of conservation of momentum, as according to Newton's third law the force required to accelerate something will evoke an equal but opposite reactional force, which means the forward momentum gained by the projectile and exhaust gases (ejectae) will be mathematically balanced out by an equal and opposite momentum exerted back upon the gun.

<span class="mw-page-title-main">Aircraft flight dynamics</span> Science of air vehicle orientation and control in three dimensions

Flight dynamics is the science of air vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of gravity (cg), known as pitch, roll and yaw. These are collectively known as aircraft attitude, often principally relative to the atmospheric frame in normal flight, but also relative to terrain during takeoff or landing, or when operating at low elevation. The concept of attitude is not specific to fixed-wing aircraft, but also extends to rotary aircraft such as helicopters, and dirigibles, where the flight dynamics involved in establishing and controlling attitude are entirely different.

<span class="mw-page-title-main">Wing loading</span> Total mass divided by area of wing

In aerodynamics, wing loading is the total mass of an aircraft or flying animal divided by the area of its wing. The stalling speed of an aircraft is partly determined by its wing loading.

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular arc. It can be uniform, with a constant rate of rotation and constant tangential speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves the circular motion of its parts. The equations of motion describe the movement of the center of mass of a body, which remains at a constant distance from the axis of rotation. In circular motion, the distance between the body and a fixed point on its surface remains the same, i.e., the body is assumed rigid.

Thrust-to-weight ratio is a dimensionless ratio of thrust to weight of a rocket, jet engine, propeller engine, or a vehicle propelled by such an engine that is an indicator of the performance of the engine or vehicle.

<span class="mw-page-title-main">Projectile motion</span> Motion of launched objects due to gravity

Projectile motion is a form of motion experienced by an object or particle that is projected in a gravitational field, such as from Earth's surface, and moves along a curved path under the action of gravity only. In the particular case of projectile motion on Earth, most calculations assume the effects of air resistance are passive and negligible. The curved path of objects in projectile motion was shown by Galileo to be a parabola, but may also be a straight line in the special case when it is thrown directly upward or downward. The study of such motions is called ballistics, and such a trajectory is a ballistic trajectory. The only force of mathematical significance that is actively exerted on the object is gravity, which acts downward, thus imparting to the object a downward acceleration towards the Earth’s center of mass. Because of the object's inertia, no external force is needed to maintain the horizontal velocity component of the object's motion. Taking other forces into account, such as aerodynamic drag or internal propulsion, requires additional analysis. A ballistic missile is a missile only guided during the relatively brief initial powered phase of flight, and whose remaining course is governed by the laws of classical mechanics.

<span class="mw-page-title-main">Spacecraft flight dynamics</span> Application of mechanical dynamics to model the flight of space vehicles

Spacecraft flight dynamics is the application of mechanical dynamics to model how the external forces acting on a space vehicle or spacecraft determine its flight path. These forces are primarily of three types: propulsive force provided by the vehicle's engines; gravitational force exerted by the Earth and other celestial bodies; and aerodynamic lift and drag.

<span class="mw-page-title-main">Rotation around a fixed axis</span> Type of motion

Rotation around a fixed axis or axial rotation is a special case of rotational motion around an axis of rotation fixed, stationary, or static in three-dimensional space. This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will result.

A banked turn is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a road or railroad this is usually due to the roadbed having a transverse down-slope towards the inside of the curve. The bank angle is the angle at which the vehicle is inclined about its longitudinal axis with respect to the horizontal.

<span class="mw-page-title-main">Rocket engine nozzle</span> Type of propelling nozzle

A rocket engine nozzle is a propelling nozzle used in a rocket engine to expand and accelerate combustion products to high supersonic velocities.

<span class="mw-page-title-main">Proper acceleration</span> Physical acceleration experienced by an object

In relativity theory, proper acceleration is the physical acceleration experienced by an object. It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured. Gravitation therefore does not cause proper acceleration, because the same gravity acts equally on the inertial observer. As a consequence, all inertial observers always have a proper acceleration of zero.

A reaction engine is an engine or motor that produces thrust by expelling reaction mass, in accordance with Newton's third law of motion. This law of motion is commonly paraphrased as: "For every action force there is an equal, but opposite, reaction force."

<span class="mw-page-title-main">Steady flight</span>

Steady flight, unaccelerated flight, or equilibrium flight is a special case in flight dynamics where the aircraft's linear and angular velocity are constant in a body-fixed reference frame. Basic aircraft maneuvers such as level flight, climbs and descents, and coordinated turns can be modeled as steady flight maneuvers. Typical aircraft flight consists of a series of steady flight maneuvers connected by brief, accelerated transitions. Because of this, primary applications of steady flight models include aircraft design, assessment of aircraft performance, flight planning, and using steady flight states as the equilibrium conditions around which flight dynamics equations are expanded.

This glossary of aerospace engineering terms pertains specifically to aerospace engineering, its sub-disciplines, and related fields including aviation and aeronautics. For a broad overview of engineering, see glossary of engineering.

References

  1. "What is Thrust?". Glenn Research Center, NASA. Retrieved 6 November 2016.
  2. "The Four Forces". How Things Fly. National Air and Space Museum. Retrieved 6 November 2016.
  3. "Aerodynamics". How Things Fly. National Air and Space Museum. Retrieved 6 November 2016.
  4. "Momentum Conservation Principle". The Physics Classroom. Retrieved 6 November 2016.
  5. Jim Lucas (27 September 2017). "Force, Mass & Acceleration: Newton's Second Law of Motion". Live Science. Retrieved 6 August 2023.
  6. "What are the kinematic formulas?". Khan Academy. Retrieved 6 November 2016.