Wednesday, November 8, 2017

Characteristics of Orbits

The science behind the legion of satellites and spacecraft which humanity launches and uses right now is at the same time both complicated and simple, and is surprisingly also very old, much older than spacecrafts and indeed, flight itself. 

An orbit is the path a body takes around another. There are several shapes of orbits, from elliptical to circular to hyperbolic. Orbits have many properties, but only 6 of them are required to completely describe them mathematically. They are the semi-major axis, the eccentricity, the inclination, the argument of periapsis, the time of periapsis passage and the longitude of the ascending node.

Semi-major axis: The semi-major axis of an orbit is the average distance of an orbiting body from the body it is orbiting (its primary). For elliptical orbits, the semi-major axis is half the length of the ellipse's major axis, which is the longest line that can be drawn inside an ellipse which goes through a focus. For a circular orbit, the semi-major axis is the radius of the circle.

Eccentricity: The eccentricity of an orbit is a measure of how elliptical it is. It is defined as the ratio of the distanced between the two foci of an orbit to its semi-major axis. For circles, this number if zero; for ellipses, between zero and one; for parabolas, one; and for hyperbolic orbits, greater than one. 

Inclination: The inclination of an orbit is the angle between the orbit and the equatorial plane of its primary. An inclination of 0 degrees indicates and equatorial orbit in the direction of the primary's rotation, while an inclination of 180 degrees indicates an equatorial orbit in the opposite direction to the primary's rotation.

Time of periapsis passage: The time for periapsis passage is the amount of time an orbiting body takes to pass through its periapsis, which is defined as the point on the orbit closest to the primary.

Argument of the periapsis: The argument of the periapsis is the angular distance from the ascending node of the orbit to the periapsis of the orbit. The ascending node of an orbit is the place where the orbit crosses the equatorial plane of the primary.

Longitude of ascending node: The longitude of the ascending node of an orbit is the celestial longitude of the ascending node as measured in the celestial positioning system.

With these 6 parameters, one can calculate almost all of the other parameters of that orbit, of which there are many.

(Below): The picture below shows the parameters described above graphically.

Thursday, September 14, 2017

Aeronautical Terms: Drag

Drag is one of the four fundamental forces affecting aircraft in flight, with the other being lift, thrust and weight. It is the force that opposes the movement of a body through a fluid.

Drag is a force that has to be considered in all objects, flying or not. Even in sports, drag is an important consideration. However, this post will be focusing only on drag as experienced by aircraft.

Types of Drag

There are many types of drag that affect aircraft. They include:
  1. Parasitic drag, which consists of form drag, skin friction and interference drag.
  2. Lift-induced drag
  3. Wave drag
Out of these, wave drag is only experienced by aircraft that are flying at transonic or supersonic speeds.

Parasitic Drag
Parasitic drag is the drag a body feels as a result of moving through some fluid. This drag is caused by the force of fluid particles impacting the surface of a body. It thus increases with increases in speed. Parasitic drag consists of three parts: form drag, skin friction drag and interference drag.

Form drag is the drag a body experiences because of its shape. Shapes with a large cross-section in the way of the flow will experience a higher drag. One can get a feel for this form of drag intuitively. A more streamlined body will pass through a fluid with less drag than a blocky, heavy one. This is why, to minimize form drag, bodies are shaped in streamlined ways.

Skin friction drag is the drag that arises from the friction of fluid particles against the surface of an object. It depends on the surface area of the object in question. As a body moves through the air, it causes a thin film of air to stick to it, much like how water sticks to your body after a shower. This layer of stuck air causes the layer above it to stick as well, and so on, until the body is dragging a layer of air around with it. The force required to overcome this is known as the skin friction drag. One way to reduce skin drag is to make the body longer and thinner. The length of an aircraft divided by its width is known as the fineness ratio, and increasing this decreases skin drag. For subsonic aircraft, it is usually around 6:1.

Image result for wing body fairing
Interference drag is the drag that is caused when two or more streams of air interfere with each other. It is caused when airflow from different parts of an airplane interact with each other. When two streams interact, there is an increase in turbulence and thus drag. For example, air that is going around the wing may interfere with air that is going around the fuselage, increasing drag. Interference drag is detrimental to all aircraft, and designers keep this in mind when building them. For example, one way to combat this form of drag is to introduce a wing-body fairing, which smooths the point of contact of the streams of air from the wing and fuselage. (Above right): The wing-body fairing of an airplane.

Lift Induced Drag
The process by which wings generate lift also generates drag. This drag is known as the lift-induced drag of a wing.

Lift is accompanied by different air pressure on the top and bottom of a wing. This difference is pressure allows air at the bottom of the wing near the tips to flow to the top of the wing. This happens on both wings of an aircraft, and creates two counter-rotating vortices on either wing-tip, which create eddies of air behind the wing itself. These vortices can sometimes be seen if there is a lot of water in the air; a thin stream of water will appear to be coming out from the wing tip. (Above right): The direction of the wing-tip vortices are indicated by the two grey arrows at the ends of the wings.

These vortices reduce the amount of lift which can be generated by the wing at that angle of attack. They also introduce a force in the downstream direction which is known as the induced drag.

Induced drag would not be produced by a wing of infinite length as there would be no wing tip for air to flow around. However, as wings cannot be infinitely long in real life, lift-induced drag exists and must be dealt with. It is added to parasitic drag as another form of drag on an airplane. 

(Left): Water which has condensed due to the low pressure-low temperature vortices created by air moving from under the wing to over the wing.

Wave Drag
Image result for sound barrier
Wave drag is drag that is experienced by aircraft that are moving at transonic and supersonic speeds. It is most commonly seen as a sudden increase in drag as an aircraft approaches the sound barrier. It is caused by shock waves that form around a body that approached supersonic speeds. The increase in drag experienced by aircraft attempting to break the sound barrier are so dramatic that, before the advent of supersonic flight, many believed that it would be impossible to even fly faster than the speed of sound. However, in modern times, many methods have been developed to negate wave drag as much as possible, although they will not be discussed here. (Above right): An incredible picture of an aircraft breaking the sound barrier.

The Power Curve

In aerodynamics, the power curve is a plot that shows the total parasitic drag and lift-induced drag vs. the airspeed. (Left): The power curve for an airplane.

As you can see from the graph, there is a particular velocity at which the drag is the least. This speed for powered aircraft is the speed at which the plane will achieve the greatest range, and is also the speed where it is flying at optimal efficiency. 

This particular curve does not include wave drag as it refers to a plane which flies only at subsonic speeds.

One point to take away form this curve is that, until the optimal velocity, it actually takes more thrust to maintain a lower speed, and it is not until you pass the optimal speed that you actually need more thrust to go faster.

Tuesday, September 5, 2017

Aeronautical Terms: Lift

Lift, along with thrust, weight and drag, is one of the main forces which come into play on an aircraft in flight. Any fluid which flows around the surface of a body exerts a force on it. The component of this force that is perpendicular to the direction of the flow is lift, while the component which is parallel to the direction of flow is the drag. Lift is not a force only associated with flying; it is a force caused by all fluids, and is experienced by marine vehicles as well.

The term lift is most commonly associated with aircraft, which is why most think that it always opposes gravity. However, this is not always the case. If an aircraft is flying straight and level, then true, most of the generated lift opposes gravity. In the case of race cars however, their spoilers generate a lift force which points downward! This force is responsible for keeping the car firmly on the ground. In sailboats, the lift produced by the movement of air around the sail points sideways. So as seen, lift does not always have to point upwards.

In this post, I will be focusing on lift as generated by aerofoils. This lift, which is generated by the movement of air around an object, is known as aerodynamic lift.

A Simple Explanation of Lift

There are many ways to explain lift: one can use Newton's Laws of motion directly, or one can use Bernoulli's principle.

Newton's Law of Motion state, among other things, that every action has an equal and opposite reaction. An aerofoil deflects the air the flows around it downwards, in the process exerting a downward force on the air. This, courtesy of Newton's Third Law, causes the air to push the wing upward. (Right): A wing being pushed up as it pushed the air around it down.

Bernoulli's Principle (discussed here) states that the faster a fluid flow, the less pressure it exerts around it. Air over an aerofoil speeds up and exerts less pressure, causing the slower air under it to produce a net upward force-hence, lift. However, this explanation is not entirely satisfactory. For one, the explanation does not describe why the air flows down over the wing. For conventional cambered wings, one can say that the curved shape of the wing causes parallel moving air to hit it, slowing it down; however, even flat wings, sails and upside-down wings generate lift. These are not explained by this theory.

Image result for bernoullis principle liftA common explanation for lift is that, as air splits over and under a wing, the air on top has to cover a longer distance, and thus travels faster. Then, through Bernoulli's Principle, it has lower pressure than the slower air under it, thus generating lift. However, there is no reason why air particles which were in the same line before hitting the wing should be in the same line after doing so, and this is confirmed by real world tests. This is a often given as the reason for lift, but it is not correct. (Right): The explanation provided on the right is not correct.

A More Complicated Explanation

Now, while the other two elucidations do give correct answers as to why lift is generated, they do have holes in them, as stated above. A more complete explanation for the production of lift requires a deeper understanding of the way fluids flow in fields.

First, consider the situation where a paper is hanging vertically. Blow air down one side of the paper, and hypothesize about its movement. You will think that, since there is clearly a difference in the velocity of the air between the side you blow next to versus the other side, the paper will move towards the side you blew next to, courtesy of Bernoulli's principle. However, you will observe that the paper does not move. This is because Bernoulli's Principle does not describe the relationship between two streams of air separated by an object, as in the case of the paper, or a wing.

To better explain lift, we have to consider some other situations. Consider first a particle of fluid i.e. a small quantity of air moving in a straight line. If pressure increases behind the particle, it will be pushed forward, and will accelerate. Conversely, if the pressure behind it decreases, then it will decelerate. This is proven by Newton's Second Law.

Next, consider a particle travelling in a curve. Because it is constantly changing direction, it will be subject to centripetal force, which must be caused by something else, i.e. another force. This force has to be a pressure (all other forces not counted). Thus, across a curve, the pressure is higher on the outside than the inside.

It is by the exploitation of this phenomenon that wings generate lift. A curved wing moving through the air will cause the air it hits to split and curve around it. The curved stream of air that flows above the wing will induce an area of low pressure under it (and between the top of the wing) while the stream that flows below the wing will induce an area of high pressure above it (and below the top of the wing). This creates a zone one high pressure just under the wing and an area of low pressure just above the wing surface, causing lift.

Image result for angle of attack wind tunnelIt is also for this same reason that increasing angle of attack increases lift up to a point. As angle of attack increases, the curvature of the airflow above the wing also increases, which leads to a lower and lower pressure between the bottom of the airflow and the top of the wing. This causes a higher net lift from the high pressure zone below the wing. (Right): You can clearly see the increased curvature of the air at the leading edge at this high angle of attack.

Thus, this offers a much more complete explanation for the cause of lift. The other two are not wrong, but nor are they completely right, and I prefer a proper, long explanation to an incomplete, short one.

Please read this article here for more information.

Saturday, September 2, 2017

Bernoulli's Principle

Published by Daniel Bernoulli in 1738, Bernoulli's Principle is an important principle in fluid mechanics, and has many applications in the real world, including generating lift for aerofoils.

Bernoulli's Principle states that the faster a fluid moves, the less pressure or potential energy the fluid has. This principle is based on the conservation of energy: at all times, the energy in a system has to remain constant. Thus, if a fluid starts to move faster, it will gain kinetic energy and dynamic pressure (the pressure exerted by a moving object) and lose potential energy and static pressure (the pressure exerted by a static object). This ensures that the amount of energy in the fluid remains constant.

Bernoulli's Equation

Bernoulli's Principle is a principle that is obtained from Bernoulli's equation. This equation relates the pressure, speed and height of a liquid at two different points in a steady flow. The equation is as follows:
Here, all the values marked with 1 apply to the first point in the flow, while those marked with 2 indicate the second point in the flow. P refers to the pressure, V to the velocity, g to gravitational acceleration and h to the height. The rho symbol refers to the density of the liquid.

This equation states that the sum of the pressure, kinetic energy density and potential energy density of a liquid at any two points in a laminar flow are equal, which is basically the conservation of energy for liquids. Bear in mind that this equation assumes a great many things, such as smooth flow, an in-compressible liquid, lack of any outside outside forces, among others. However, it works.

Bernoulli's equation relates the energies of a liquid flowing from one height to another. Bernoulli's principle is a simplification of this. It relates the pressure and speed of a liquid at two different points in a horizontal line.

Please do bear in mind that this equation is valid only for in-compressible fluids flowing at low speeds. There are more advanced equations for compressible fluids flowing at high speeds.

(Above): Bernoulli's equation.

Bernoulli's Principle

As mentioned earlier, Bernoulli's principle relates the pressure and speed of a liquid at two different points in a horizontal line. This means that, from the above equation, there will be no difference in potential energy density, as there is not difference in height. So those two terms cancel each other out.

Now we can say that the sum of the pressure and kinetic energy density of the fluid at point 1 is equal to the sum of the same at point 2. Thus, for constant pressure and kinetic energy density at point 1, if there is an increase in the speed of the liquid at point 2, it must be accompanied by a drop in the pressure at point 2. This point is elaborated on below.

In a system like the one pictured above, water is flowing from the wide side to the narrow side. For the liquid to flow at the same rate, it must speed up at the narrow section. But if speed increases, so does kinetic energy, and this energy has to come from somewhere. Since the water is flowing toward the right, it can only be assumed that it is being pushed along by the slower water to the left, indicating that the pressure at point 1, in the slower bit of water, is more than that at point 2, in the faster stream. And this is the essence of the principle: the faster a liquid goes, the less pressure it exerts.

(Above): Water flowing from a wide area to a narrow area of a pipe.


There are several applications of Bernoulli's Principle in real life, but I will focus on the aeronautical one here.

An aerofoil shape moving through a fluid causes the fluid underneath it to flow slower than the fluid on top. From the principle, we know that the faster a fluid moves, the lesser the pressure it exerts. Thus, the fluid on top exerts less pressure than the fluid at the bottom. This causes the underlying fluid to exert pressure on the underside of the wing, lifting it up. This force which it exerts is known as lift.

Thus, if we know the speeds of the fluids on top and bottom, we can calculate the force of lift quite accurately using Bernoulli's equations. The equations, however, do not explain why the fluids flow faster over the top than the bottom.

Friday, September 1, 2017

Aeronautical Terms: Angle of Attack

The angle of attack of an aircraft is the angle between the air coming at it from the front and a certain reference line along the plane (usually the chord line). It can simply be described as the angle between where the wing is going and where the wing is pointing.

Image result for angle of attackThe angle of attack of an aircraft or wing determines how much lift it produces. In general, the higher the angle of attack, the more lift is generated, up to a point. After that point, the lift generates starts dropping dramatically. this point is known as the critical angle of attack of an aircraft. (Right): A diagram describing angle of attack.

Critical Angle of Attack

The critical angle of attack of an aircraft is the angle of attack at which is produces the maximum lift. This angle is sometimes also known as the stall angle of attack. 

Image result for angle of attackAt angles below the critical angle, life increases with increase in angle. Above it, lift decreases with increase in angle. Maximum lift is generate close to the critical angle. As the angle of a wing increases, air flowing over the top of the wing starts separating (i.e. not flowing smoothly over the top) from of the wing. At angles above the critical angle, this airflow separates completely, leading to drops in lift generation and stall, a condition where an aircraft cannot generate enough lift to keep itself in the air. (Above right): A diagram showing detached airflow at an angle above the critical angle of the wing.

Different planes have different critical angles. Most typical aerofoils stall at angles above 15-20 degrees. Commercial aircraft have built in software which prevents them from flying above their critical angle regardless of pilot input.

Image result for high angle of attackFighter aircraft, on the other hand, can fly at much greater angles of attack before stalling. Modifications to the wings and fuselage can allow such planes to fly at angles of attack as high as 45 degrees stably. Such high angles can be useful at high altitudes for maneuvers in thin air, but they cause a massive loss in speed and also place significant stress on the plane itself. Thus, most fighter aircraft limit the angles of attack they can achieve to well below what they could. (Left): A F-35 flying at a high angle of attack.

Extreme angles of attack

FA18 LEX.jpgThere have been experiments into achieving stable flight at extremely high angles of attack. One such experiment was the High Alpha (angle of attack) Research Vehicle (HARV), a modified F-18 Hornet developed by NASA. This plane used modified lifting bodies and thrust vectoring, among other techniques, to achieve stable flight at a massive 70 degrees of angle of attack. The program started in 1987 and was terminated in 1996, and provided significant information on stable flight at high angles of attack. (Above right): The F-18 HARV performing a high angle of attack maneuver.

Thursday, August 31, 2017

Methods of Propulsion: Afterburners

Afterburners are one of the most iconic feature of modern fighter aircraft. Who doesn't love the twin spikes of flame the burst out from the engines of a fighter? Afterburners are the machines that are responsible for this incredible sight.

Afterburners are a method of increasing thrust massively for a short amount of time. They are used almost only on military combat aircraft to augment the thrust output of fighter aircraft jet engines. They are used to achieve short bursts of very high velocities for use in certain situations.

Afterburners may look cool when switched on, but they consume fuel voraciously. They are thus used only when really needed.


Image result for afterburnerThe thrust produced by a jet engine depends on both the engine exhaust's mass and its velocity. Thus, an increase in thrust can be achieved by increasing either of the two values. The turbofan engines used on commercial airliners expel large masses of exhaust at low velocities, which allow them to remain fuel-efficient and quiet at the cost of being large and bulky. (Right): A aircraft taking off on full afterburners.

Image result for variable geometry nozzleMilitary engines, on the other hand, cannot afford to be bulky. Thus, to generate more power, they need to increase the velocity of the exhaust gases, which is exactly what an afterburner does. 

An afterburner is located right behind the turbines of an engine. Due to thermal limitations of turbine blades in an engine, all the oxygen that enters the engine cannot be burnt (as this would lead to overheating of the turbine). Thus, excess oxygen is present in the exhaust gases. The afterburner injects fuel into this excess oxygen and burns it, increasing the temperature of the exhaust greatly. This causes a increase in pressure, which leads to much higher exit velocities.

The extra pressure and velocity requires a wider nozzle than usual. For this reason, when the afterburners are switched on on a fighter plane, the variable geometry exhaust nozzles are widened. (Above left): The variable geometry nozzles of a fighter airplane.


The main use of afterburners is to assist takeoff on short runways or aircraft carrier runways. Other uses include gaining extra speed to punch past the sound barrier and also for evading enemy attacks.

Image result for sr 71 afterburner

(Above): A SR-71 Blackbird in flight with afterburners on.

Wednesday, August 30, 2017

Methods of Propulsion: Turbofan Engines

The turbofan jet engine is one of the most common type of propulsion used in aircraft. They are used in planes both commercial and military, big and small. They are also one of the most recognizable means of propulsion, found in airports around the world.


A turbofan engine consists of five main parts: the fan, the compressor, the combustor, the turbine, and the exhaust nozzle.

The Fan
Image result for turbofan fanThe fan is one of the most iconic features of modern commercial airplanes. It is the large, bladed structure that is present at the front of the engine, and which can be seen from the front of the engine. The fan is usually made out of titanium.

The main job of the fan is to suck in huge quantities of air into the engine proper. In all turbofans, the air splits into two parts: one stream goes into the engine itself, while the second stream goes around the engine. This is known as the bypass airflow. (Above): The main fan of a turbofan engine.

Image result for turbofan cutawayThe Compressor
The compressor consists of a series of blades and aerofoils. It's main job is to compress the air, as the name suggests. The compressor's longer name is the axial flow compressor, a name it has received because it compresses air that flows parallel to the axle of the blades.

Inside the compressor, the air moves through sets of spinning blades which add energy to the air. In between each set of blades are static structures of fins known as stators or vanes. These stop the rotating air from spinning and transform their rotational energy into pressure before sending them on to the next set of blades. 

Several such series of blades and vanes may exist, and they compress the air to a great degree before passing it on to the next part in line. (Above left): In the picture above, the compressor is the series of small blades present behind the main fan.

The Combustor
The combustor is the region of the engine where the fuel is actually burned. It consists of many parts, all of which serve to maintain a steady rate of combustion in the face of high-speed airflows.

Once air has passed through the compressor, it is pushed into the diffuser, a structure which slows down the speeding air to make it easier to ignite. Further on, domes and swirlers add turbulence to the air, making it easier to mix fuel with. The air is then allowed into the combustion zone through liners, which are basically the perforated walls of the combustion zone. Finally, the fuel is injected into the sowed-down, turbulent air and then ignited with an igniter, which is quite similar to a spark plug.

Once the fire has started, the igniter is switched off. The flame is self sustaining, and keeps going for as long as there is fuel or until the pilot switches it off.

(Above left): In the picture in the Compressor section, the combustor can be seen right behind the compressor, in the middle of the picture.

The Turbine
Image result for turbofan turbineThe turbine is a set of fans present at the rear end of the combustion chamber. it is connected to the same axle that the main fan at the front and the compressor blades spin on. Hot exhaust from the combustion of fuel inside the combustion chamber spins the turbine and by proxy the main fan and compressor. The main fan and compressor blades are thus turned by the turbine, which is turned by the hot exhaust gases of the engine itself.

(Above left): In the picture in the Compressor section, the turbine can be seen near the very end of the engine.
(Above right): The turbines of this engine can be seen clearly.

The Nozzle
The nozzle is the final part of the engine. Through it, hot exhaust gases produced by the engine shoot out, pushing the engine forward, curtsy of the Third Law of Motion.

Some nozzles include a mixer, which mixes the bypass-air with the exhaust gases. This serves to make the engine quieter, which is a boon for commercial planes. Nozzles may also include chevrons, which are saw-tooth patterns found on the end of the nozzle. These serve to reduce engine noise by allowing a smooth mixing of hot and cold air. (Right): Chevrons on an engine.


There are two main types of turbofan engines: high-bypass and low-bypass.
  1. A high-bypass engine sends more air around the engine than though the engine itself. This serves to make the engine quieter and more fuel efficient. These kind of engines are used mainly on commercial aircraft.
  2. A high-bypass engine sends more air into the engine than around it. These kind of engines are used mainly on military aircraft. In military aircraft, many times, an afterburner is attached to the end of the engine.

(Above): A high-bypass engine awaiting installation. Note how the main fan is much wider than the actual engine.

(Above): A Pratt and Whitney afterburning turbofan undergoing testing. Note here how the main intake is not much bigger than the engine itself.