Crucial Concepts

Outline

Welcome to the 'Crucial Concepts' section. Like the alliteration? This section is the precursor to 'The Mechanics of Flight', and 'Development of Flight' sections (a work in progress…). It will take you over the fundamental physics knowledge required to successfully understand their content - don't worry, this section is designed to be easy to understand even if new to Physics, and no advanced Maths is required either. Without further ado, let's dive right in.

Basic Mechanics

Tip:

It is very important to be aware that in Physics, one word only has one defenition, and it is not necessarily the same as it is in English; e.g. massive ≠ huge, speed ≠ velocity, etc.

Quantities

In Physics there are two types of quantities. Vectors, and scalars. Vectors have a magnitude (size), and direction, while scalars only have a magnitude. I.e. vectors tell you how much and in what direction, while scalars only tell you how much. For example, speed (30kmh^-1) is scalar, while velocity (30kmh^-1 northwards) is a vector. Distance is the total distance you've covered (scalar), while displacement is the distance from your start point to your end point (vector), i.e. your net distance. Because of their properties, vectors are often represented as arrows, as they have both size and direction. When adding vectors, you can put said arrows end to end, and join the first and final points to form what is known as a resultant vector. As such, each vector can be split into components, of other, smaller vectors. In 2d, they can be split into an x component and a y component. Reducing them into the same components allows us to compare and work with vectors. Now that we have established these distinctions, let's move on to discussing actual quantities.

All right, everybody has heard of energy, forces, pressure and maybe even momentum, but what actually are they? Lets start from the bottom up. Consider an object of mass m, moving at velocity v. The velocity is a measure of the change in displacement over time. Defining mass is a little more complicated, so for now, consider it as a measure of the 'stuff' inside something. Now, this object is in motion. The 'quantity' of motion, is known as momentum, m*v (kgms^-1). For an intuitive way to grasp this, consider a bowling ball moving at the same speed as a football. The bowling ball will have more momentum, because more mass is moving at the same speed, hence more motion, making it harder to stop.

Newton's Laws and Energy

Ok, so this object has mv momentum. If we don't do anything to it, it will continue to have mv momentum, and so will continue moving in the same speed and direction (remember, v is a vector). I.e. If you do nothing, nothing will happen. Genius right? Well this is the essence of Newton's first law. An object will remain in constant (or 0) motion, unless acted upon by an external resultant force. Right, so then, if we want to change our momentum, we need to exert a force on our object. Then for now, we can define a force as something that causes a change in momentum over time, that is: F = (mv)/t. Should the mass of our object remain constant, then this means F = m * v/t. And what is the change of velocity over time? Acceleration. This means that for a constant mass, a force will cause an acceleration, F = ma. That's Newton's second law in a nutshell.

All right, so, for a constant mass, a force causes an acceleration, which causes a change in velocity, and thus momentum. But how is a force exerted? Where does it come from? For this, we need to discuss energy. Energy is a fundamental property of matter, like mass, that we can define, as the capacity to do work. What is work? The transfer of energy, from one store, to another. Consider throwing a ball upwards. It starts off with a lot of velocity upwards, and so, with a lot of kinetic energy (E = 1/2 * mv²), and little gravitational potential energy (E = mgh). As it rises up, it gains gravitational potential energy (GPE), and loses kinetic energy, i.e. energy is transferred from the kinetic energy store to the GPE store. But why is it losing kinetic energy? It is slowing down. Why is it slowing down? It is experiencing an acceleration downward. What does this mean? It is experiencing a force. (we won't consider gravity with general relativity here). Right, so this means that the transfer of energy, occurs via a force. In other words, doing work, causes a force to act over a displacement. (W = Fs).

Okay, so energy, is the capacity to do work, where work is done by a force acting over a distance, with said force causing a change in momentum, and thus, for a constant mass, an acceleration. But no, this energy bit is not Newton’s third law. Newton’s third law, is slightly different.

Newton’s third law states that when two objects interact, they exert equal and opposite forces onto each other. Let’s break this down, understand it, and then address common misconceptions.

One can think about Newton’s third law with regards to energy. A force manifests itself as a transfer/change of energy. Now, one object experiences a gain in energy, and thus must be experiencing a force, while the other experiences a reduction/negative gain in energy of the same magnitude. Thus there must be two equal forces, acting in opposite directions, one on each object. The fact they act on different objects is very important. A common source of confusion with Newton’s third law, is that, if every interaction has equal and opposite forces, how can there ever be a resultant force? It is the fact that the forces are not acting on the same object, hence each respective object still can experience a resultant force. To visualise this, consider an example: a punching bag. When you punch a punching bag, your fist slows down to a stop (thus experiencing acceleration towards you), while the bag in turn accelerates away from you. Equal forces, opposite directions, different objects. If this weren’t true, energy and momentum wouldn’t be conserved.

You can see this everywhere: when you walk, your foot pushes backward on the ground, and the ground pushes you forward with equal force. The same principle will soon explain how wings push air down — and the air pushes the aircraft up.

Pressure

Before we look at flight though, we need to understand several more concepts. Initially we mentioned pressure, but never discussed it. Pressure is defined as force per unit area, P = F/A. The same force, over a larger area results in less pressure. This why a sharp nail will go further into a wall than a blunt one. Pressure is more complicated when discussing gases, and you can consider it to do with the concentration of gas particles inside a given area. Note that gases exert pressure when the air particles flying around hit the walls of their container e.g. a balloon. More gas in a given volume, or the same gas in a smaller volume will result in more pressure, as those collisions will happen more, and so more force be exerted on the container walls.

Conservation of Momentum

Apart from pressure, earlier we hint at the concept of momentum conservation. In order to understand it, we must consider systems. Consider systems to be per say, a collection of objects you are looking at – they could be anything - be it air particles, two masses etc. Note that a system does not have to stay together. E.g. Imagine two cars. Your system can consist of those two cars, as long as you are only considering those two cars, it doesn’t matter how far away they are from each other. What are we getting at here? If you don’t do anything to the objects in that system, some net fundamental properties are not going to change. That means net mass, net energy, and as mentioned before, motion, i.e. momentum. This kind of system, we call a closed system: a system in which no external forces act on it, and no external input of energy is received. It doesn’t mean that energy stores within the system can’t interact, e.g. two cars can collide, a tennis ball can go up and then down (interchanging kinetic energy with gravitational potential energy), it just means the net sum of the quantities doesn’t change.

Common Forces

So, momentum is conserved. Now that we understand that, lets discuss some common forces. First off, we have weight. Inside a gravitational field, every object experiences an acceleration towards the centre of mass. By F=ma, a force must be acting on it, and this force we call weight. On Earth, we typically take this to be W=mg, mass times gravitational acceleration. The greater the mass, the greater the weight — though it’s worth remembering that mass and weight aren’t the same thing. Mass is a measure of how much “stuff” is in something, while weight is the gravitational pull on that stuff.

Next, we have the normal reaction force. This is the supporting force a surface exerts to stop an object from moving through it. It always acts perpendicular (normal) to the surface. The source of it is a bit more complex to understand, and it is due to the electrostatic forces between molecules. If it wasn’t for this, your hand would just pass straight through a wall when you leant on it. Instead, because of this force, you experience an equal and opposite Normal force. Another example is when you stand on the ground and gravity pulls you down, but the floor pushes you up with an equal and opposite reaction force — thanks again to Newton’s third law.

Then there’s friction — the force that resists motion between surfaces in contact. If you think about it, surfaces are practically never smooth, and when they interact, those little nooks and crannies get ‘stuck’ on each other, and require work to be done to overcome that. This work is done by Friction. It is given by F = N*μ, where N is the normal force, and μ the coefficient of friction – a measure of how ‘frictiony’ a surface is. If you think about it intuitively, the Normal force reflects how strongly an object is pushing down on a surface, so it makes sense that Friction is proportional to it. Friction itself, acts parallel to the surface and opposite to the direction of motion (or potential motion). It’s what stops you slipping when you walk, and what lets a car’s tyres grip the road. Friction dissipates energy, usually into heat, which is why things can get warm when rubbed together. There are two main types:

• Static friction, which prevents movement from starting.
• Kinetic (or dynamic) friction, which resists movement once it has begun.

Next up, we have tension, the pulling force transmitted along a rope, cable, or string when it’s stretched, again, due to the forces between molecules. If you pull on one end, the rope transmits that force to the other end. I.e. the tension is the same on both sides. It’s a simple but very important example of how forces can be transferred through materials.

Another special kind of contact force is air resistance, or drag. This acts when an object moves through a fluid, like air or water. Drag always acts opposite to the direction of motion, slowing the object down. However, while in part, it is due to the friction from air particles colliding with the object, drag is much more complex than simple friction — it depends on the shape of the object, its speed, and fluid flow. Because of this complexity, we’ll revisit drag in depth later, when we explore how it affects aircraft performance and the generation of lift.

In most real-world situations, several of these forces act at once. When they balance, the object remains in equilibrium — either stationary or moving at constant velocity. But when they don’t, the resultant force causes acceleration in the direction of the unbalanced force.

This interplay between forces — balance versus imbalance — is what determines how things move. And in the case of aircraft, that dance between lift and weight, thrust (which causes acceleration forward) and drag, is what keeps them aloft. If lift equals weight and thrust equals drag, the aircraft will fly at a constant altitude and speed. If lift exceeds weight, it climbs; if thrust exceeds drag, it accelerates. And if lift is too small or drag too great, well… Of these four forces, the one that allows flight to actually happen is lift.

Mechanics of Flight

Lift

All right then. Lift. The magic that makes planes fly. How do we do it? What is it? How is it generated? Where does it come from? Let’s answer these fundamental questions.

Lift at its core, is a reaction force, that is caused by the bending of air around a wing. As a wing moves through the air, as seen in the figure, it results in a downward diversion of it, called downwash. As a result, the air is experiencing a change in momentum, and must be experiencing a force from the wing. Thus, by Newton’s Third Law, the air must be pulling back on the wing with an equal and opposite force upwards. This upward reaction is what we call lift.

If this vertical displacement of air seems abstract, consider a rocket engine, which is more intuitive to grasp. In a rocket engine, you are causing a displacement of air, opposite to the direction in which you want to go. It’s the same idea.

One common misconception is to imagine air “smacking” into the bottom of the wing and being deflected down, creating lift. In fact, this is what even Newton himself thought of birds centuries ago. However, while some lift does come from air interacting with the underside, most of it comes from the airflow over the top of the wing being displaced downwards.

Wings and Fluid Flow

But hold on a minute. What causes downwash? Why does air actually bend around a wing in the first place?

For an intuitive explanation, consider what happens when you place your finger under a running tap. As soon as your finger touches the flow, the water bends towards it. By Newton’s first law, the water must then be experiencing a force from your finger. By Newton’s third law, this means that the water must in turn, be exerting a force on your finger – this is the slight pull you feel as the water clings to it.

The same phenomenon applies for air flowing around a wing. As seen in the figures, the wing exerts a force on the air, altering its direction (and thus momentum). The air reacts, pulling the wing up and producing lift. But where does this force making the air follow the curvature of the wing come from? Why doesn’t it just shoot straight past?

At subsonic speeds (below the speed of sound), air can be approximated to behave like an incompressible fluid – meaning the volume of a given mass of air remains constant. In other words, the air can’t simply just leave gaps or voids as it flows. This means adjacent streams must stick together, and as a result, fill in around the wing’s shape. This principle is called flow continuity.

To explore it, let’s consider streamlines – which represent the paths of individual air particles. Their behaviour and interactions are caused by two key factors: pressure and viscosity.

• Pressure – differences in pressure between adjacent streamlines. This is what prevents voids and gaps from forming, as we’ll explore below.
• Viscosity – essentially friction between layers of air. This friction allows momentum to be transferred between neighbouring streamlines. E.g. imagine two adjacent streamlines moving at different speeds. The friction will try to speed up the slower one, and speed up the faster one.

Now let’s apply this to a wing. At the wing surface, if you think about it, the velocity of the airflow is 0 relative to the wing, because the air particles, due to friction, are moving with the wing itself. This principle is known as the no-slip condition, and is central to any kind of viscous flow. Consequently, there must be a region around the wing, where the airspeed transitions from 0 to the freestream velocity – enabled by viscosity increasing the velocity of each adjacent streamline away from the wing. This region, is known as the boundary layer, and it is fundamental to aerodynamics, as you will see.

Now we can consider how pressure impacts the flow of air around a wing. Consider the streamline closest to the wing, i.e. the first with non-zero velocity. If it tried to travel in a straight line instead of following the contour, it would leave behind a void of stagnant air between itself and the wing. The pressure in that region would drop sharply, and the pressure differential formed between it and the streamline, would result in a force that would bend the streamline back towards the wing. By the same process, the next streamline above would be bent to follow the first, and so on. This chain effect causes the entire airflow to bend around the wing’s shape, accelerating over the top and creating a region of lower pressure above the wing.

This pressure difference isn’t confined to the immediate surface. It propagates outward at the speed of sound, influencing air well beyond the wing’s physical outline. This is why the air’s downward deflection — and therefore lift — does not just happen at the wing, but in the wider region surrounding it.

With this fundamental grasp of lift, we have ventured into the topic of fluid flow. Once we explore it in a bit more depth, we can then move on to explore drag – the force designers have been contending with since the beginning of aviation.