Hazardous Conditions you may encounter and how to avoid them
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Moving your quad in three dimensions is usually intuitive, simply requiring manipulation of the two control sticks to make it do what you want.
So to move the quad in a combination of horizontal and vertical flight, you are actually commanding the CPU to change the RPM of each rotor in a coordinated way to grow and tilt the Big Green Arrow to propel the quad around the sky.
There are limits to its speed though, both physically and legally. This chapter discusses some of these issues.
Whilst hovering is a key part of operating a quad, for example to obtain a stable camera platform, it would not be a lot of use if a quad could not move around.
Moving a quad follows the same concepts that we have already discussed in Rotor Dynamics. You should revise these concepts if it has been a while since you read that chapter.
Before we go too far, it is important to understand that from an aerodynamic point of view, there is no front, back or side to a quadcopter. Moving a quad forward, backwards or sideways is aerodynamically identical. It is only when a payload, such as a camera, is mounted that we need to know which end is the ‘front’.
So, whilst I will now discuss forward motion, all that follows also applies to rearwards and lateral movement.
Remember that the Aircraft Control chapter explained that the individual Rotor Thrust vectors are fixed in relation to the fuselage and we can combine these vectors as the Big Green Arrow to make the total force the rotors produce easier to visualise.
So, to get a quad moving forward without losing altitude, two things must happen.
The CPU must pitch the quad in the desired direction to tilt the Big Green Arrow and provide a horizontal component as Thrust, and
it must increase the magnitude of the Big Green Arrow so that the vertical component (Lift) still balances the Weight of the quad.
To do this, the CPU individually changes the RRPM, and therefore the Rotor Thrust, of each of the four rotors. Given that the Rotor axes, and the Rotor Thrust vectors, are fixed with relation to the quad’s fuselage, this tilts the entire fuselage in the direction we want the quad to move.
To move the quad forward the CPU must pitch the whole quad forward. To do that, it increases the Rotor Thrust on the two rear rotors by increasing their RRPM. Figure 8.1 shows the initial action the CPU has taken to initiate the pitch forward.
You can see that the RRPM of the two rear rotors has increased, giving a greater Rotor Thrust on those two rotors, but as yet, the quad has not pitched forward or commenced to move forward.
Some internal command changes are occurring within the CPU at this time too. It ceases to maintain its hover position with reference to the GPS and starts to pursue a forward Ground Speed as commanded by the magnitude of the control input we have put into the control stick in our hand.
The CPU also determines that a small amount of increased Rotor Thrust on all rotors are required to help increase the length of the Big Green Arrow as the quad pitches so that the Lift still equals the Weight.
Figure 8.2 shows the situation as the quad settles into a stable forward ground speed with all forces in balance.
Here we have all the same concepts that were introduced in the single disk discussion. If you look closely you can see that the horizontal (cyan) Thrust vector is equally opposed by the (red) Drag vector and the (yellow) Lift vector balances the (orange) Weight vector. The quad is said to be in level unaccelerated flight.
All rotors are spinning faster than they were in the hover to provide the power required to keep the quad at the same altitude and to overcome the drag produced during forward flight at the desired speed.
To increase speed, without losing altitude, once again the CPU must increase the length of the cyan Thrust vector. As before, it must tilt the Big Green Arrow further forward and increase its length. To do that, two things must be done:
all rotors must spin faster than before to increase the magnitude of the Big Green Arrow, and
the rear rotors must spin faster than the front ones to provide the pitch attitude required.
Figure 8.3 illustrates a quad in high-speed flight:
Once again, all the vectors are in balance. Depending on the type and role of the particular quadcopter, this may be close to the maximum speed the quad can go without losing altitude.
As mentioned at the head of this chapter, the design layout of the quadcopter means that, from an aerodynamic point of view, a quadcopter has no ‘front’ as is the case for an aircraft or another type of vehicle. So to move a quad laterally or backwards just means that the CPU commands different rotors to spin at difference speeds to achieve the inputs that the command sticks give it.
As an example, Figure 8.4 illustrates a quad in a 30° roll to the right, which would quickly lead to a rapid movement to the quad’s right.
Limits to Quadcopter Speed
The aerodynamic profile of the quadcopter’s fuselage, landing gear, camera, etc impacts on its maximum forward speed. It is hard to streamline something like this and the more protrusions the aircraft has, the greater the Drag. In the Figures above, this is represented by the red vector.
To accelerate the aircraft, the cyan Thrust vector must exceed the red vector and, as we have already seen, the cyan vector is produced by tilting and lengthening the Big Green Arrow. To increase this vector, we must increase the Rotor Thrust produced by each rotor.
To maintain the pitch attitude on the quad that is required to provide the necessary Thrust, by definition, the front rotors must be spinning at less than their full capacity. Additionally, the usual requirement to keep the quad at a reasonably level altitude (so it does not descend into the terrain) means that the Lift vector must always be approximately equal to Weight and so the pitch attitude has limits too.
So you can see that there are a number of imperatives for safe, high-speed flight and the CPU must command all four rotors to perform as it requires to control the quad. Everything is a compromise.
This means as soon as one rotor reaches its limit, or the CPU cannot maintain the desired control, there can be no further increases in aircraft performance.
There are aerodynamic limits to how fast rotors can spin but in the case of quadcopters, the limitation is usually simply the maximum speed of the motors. The quad’s firmware will have limits programmed into it and the CPU will prevent these limits being exceeded.
Another limit will simply be the amount of battery power available. Commanding a flight profile that requires all four rotors at their maximum speed (some sort of high-speed climb) is likely to exceed the power that the battery can provide. The CPU will limit performance in this case also.
The final limit may be a legal limit, set by the FAA or some other regulatory authority. This will be hard coded into the CPU and will be relative to the GPS speed of the aircraft. By definition, this will be a Ground speed limit not an Airspeed limit. We will discuss the significance of this difference soon.
Control in Flight
Climbing and Descending
Unsurprisingly, moving your quad in three dimensions at once is a combination of all the above. Within the limits I discussed above, the CPU can move the quad simultaneously vertically and horizontally, and in some cases can even conduct aerobatic manoeuvres.
Just keep in mind that it is all about changing the magnitude and direction of the Big Green Arrow and how it overcomes the negatives of Drag and Weight.
While climbing and descending in forward, rearward or sideways flight is fairly easy to understand as a combination of the above techniques, turning requires just a little more explanation.
When an aeroplane or helicopter turns, that is when it changes it’s heading, it normally banks in the direction it wants to turn. This means that the pilot rolls the aircraft to an angle of bank, say 30°, and uses the rudder or tail rotor pedals to ‘coordinate the turn’.
If done correctly, a coordinated turn means that while the aircraft turns, we the passengers only feel a downwards force – a slight increase in the force we normally feel due to gravity – and no sideways force.
This is different to driving a car. In a car, assuming we are driving on flat ground, the front wheels provide the turning force and the car’s occupants feel a sideways force which moves our bodies towards the outside of the turn. In aerodynamic terms, this is called ‘skidding’ and is undesirable. It would cause your breakfast to slide off your tray table!
Because quadcopters are less sophisticated than larger aircraft, and they don’t carry passengers, their designers have decided to use the skidding method to turn the quad. So when you want to change the heading of the quad, for example to bring it home, you use the yaw control stick and the CPU commands a yaw in the direction we asked for and the quad ’skids’ its way to the new heading.
By the way, ‘racing drones’ are far more sophisticated than what I describe here. They do have more advanced flight models incorporated in their firmware, which gives them substantially greater performance than commercial quads. This includes the ability to ‘bank’ when changing heading. A good example of the performance of this type of quad can be seen in this Youtube video of the World Drone Prix in 2016.
What all this means is that quads are ’steered’ in a similar way to cars and not the way aircraft are usually turned. If you have some flying experience you might find this a little weird at first. If you want to know a little more about the technicalities of airborne turning, Wikipedia has a good explanation.
Next, we are going to look at some of the less desirable aerodynamic issues that you may encounter while flying your quad. Ignorance of some of the ‘gotchas’ has caused many people to lose, or at least damage, their expensive assets.
Understanding the pitfalls should help you minimise the risk to your quad and enable many safe, fun hours of flying.
And by the way, as far as I’m aware, there are no aerodynamic aspects to the infamous ‘flyaway’. So I’m afraid the following chapter is unlikely to help you with that risk.
In a typical quadcopter, four rotors are mounted in the extremities of the fuselage to provide Lift and control. Hexacopters use 6 rotors to provide the same control, but are usually capable of carrying a greater payload/camera.
In the hover we can control the quadcopter in all three axes (pitch, roll and yaw) by adjusting the RRPM, and therefore the Rotor Thrust, of each Rotor. Controlling these three axes allows us to move the quad vertically and horizontally through the air.
What We Already Know
So far we have looked at how a moving Aerofoil, and a spinning Rotor Disk, produces a force by moving air downwards. For the rotor disk, we call this force Rotor Thrust. We have determined that for a quadcopter the only option we have to vary that thrust is to vary and control the angular velocity of the Rotor blades. The conventional way to measure this is called the Rotor RPM or RRPM.
We know that the faster the rotor spins, the more rotor thrust it produces. We also know that we can break the rotor thrust vector down into vertical (Lift) and horizontal (Thrust) components. In stable flight, these components balance and oppose the aircraft’s Weight and Drag vectors.
We will now look at how we can use a combination of rotor disks to fly and control a quadcopter.
The primary quadcopter configuration, and the one I will deal mainly with here, is an aircraft that has a central fuselage and four Rotors in each ‘corner’.
The fuselage normally houses the CPU and the battery. It also provides mounts for ancillaries, such as a camera or a hopper. The landing gear, fixed or retractable, is usually mounted below.
In Figure 7.0 you can see how I depict a quad in this document. It is shown as it would be sitting on the ground with its Rotors idling, producing minimal Lift.
Quadcopters may also be configured with two rotors fore and aft and two laterally. From an aerodynamic point of view, there is little difference with this config, as the ‘front’ of a quadcopter is often irrelevant to its operation.
Hexacopters have six rotors and often have retractable landing gear. They are usually designed to be larger, more stable and carry greater payloads. Aerodynamic considerations are broadly similar. I will deal with specific hex issues later on.
In all cases, the rotors are mounted rigidly, usually at the end of pylons or outriggers. The rotor is mounted horizontally with its Thrust axis vertically upwards. Each rotor is driven by a motor, also mounted on the pylon, which is powered electrically and controlled by the CPU.
The rigid mount means that the rotor can spin of course, but cannot move in the pitch or roll axes relative to the body (fuselage and outriggers) of the quadcopter.
Control in the Hover
As discussed in the previous chapter, the only ‘control’ we have over the rotors is increasing or decreasing their RRPM. If you have skipped that discussion, you should go back and review it now.
These changes in RRPM are controlled by the CPU, it would be far too hard to do this manually. In most modern quads, the CPU receives internal control inputs from the GPS receiver and external inputs from your controller. Higher performance quads can be controlled without a GPS, but for now, we will only consider the common basic concept where a GPS keeps the quad stable and, with our controller we can move it where we want it to go.
The GPS provides a position to the CPU in three dimensions. That is, laterally in the form of a latitude and longitude, and vertically, in the form of an altitude. This altitude position is actually relative to the centre of the earth, but the CPU is clever and takes the initial, start-up position and calls that zero and measures subsequent altitudes relative to that position.
The CPU is programmed to maintain the current GPS position unless it receives an external input from the controller in your hand. You control this external input by moving the two control sticks. These sticks can move the quad in the following ways:
Climb and descend
Fore and aft
Yaw, that is changing the heading of the quad around its vertical axis.
These changes can be made in isolation, that is one control stick is moved in one direction only, or both sticks can be moved in a coordinated way to make the quad move in three-dimensional space efficiently.
Let’s start by assuming that our quad is in a stable hover about 1 metre or 3 feet above the ground as shown in Figure 7.1.
You can see that each rotor is providing an equal amount of lift (the four green arrows are the same length). You can also see that adjacent rotors are turning in opposite directions. I have coloured the rear arrows red and the front ones white for orientation. The width of these arrows, as before, indicates the relative RRPM.
Because each rotor disk is providing an equal amount of lift everything is level and stable. The total of the four equal green vectors is exactly equal and opposite to the orange weight vector and so the quad doesn’t climb or descend. As it is a little hard to see the relative length of the various lift vectors it is better to combine these into a single Big Green Arrow as you can see in the following figure.
Climbing and Descending
With the lateral position being controlled by the CPU with reference to the GPS, climbing and descending the quad is straight forward. To make the quad go up, we manipulate the control stick to sign; to the CPU that we want the quad to climb. It commands the electric motors to increase the RRPM of all four rotors equally.
You will remember that the amount of lift produced by an aerofoil is proportional to the velocity of that aerofoil squared so, for example, the RRPM does not have to be doubled to provide double the lift. If you are a little hazy on this concept, the explanation is here.
So, when the CPU spins each rotor faster, each one produces more Lift. The total lift represented by the Big Green Arrow is now greater than the weight of the quad, represented by the orange Weight vector and the quad rises vertically.
Similarly, if you want the quad to descend, moving the relevant control stick commands the CPU to reduce the RRPM of all rotors so that less lift is produced and the lift vector has a lesser magnitude than the weight vector.
Before we move on to yawing a quadcopter, we need to learn a little more about Torque Reactions. You may have noticed that most helicopters have a tail rotor as well as a main rotor. Without getting too technical, the tail rotor is required to counter the torque reaction on the helicopter’s fuselage caused by the engine and transmission driving the main rotor. If you want to know more, you can read more about helicopter anti-torque design features here.
In the case of quadcopters, this torque reaction from the electric motors turning each rotor still exists. The designers counter it with an elegant concept that does away with the requirement, complexity and weight of an anti-torque system but still provides the lift and control required.
By changing the direction of rotation of two of the four rotors the torque reactions usually cancel out. That is why you will notice that adjacent rotors have their blades mounted so the angle of attack is opposite and those rotors rotate in opposite directions.
Yawing is what occurs when you change the heading of the quad in the hover. When it yaws, a quad rotates around the vertical or ‘Z’ axis.
The way the CPU yaws the quad is a little more complex than simple climbing and descending. It involves manipulating the torque reaction and how the rotors rotate with respect to each other. The torque reaction is caused by, as is proportional to, the motor’s effect on the fuselage as it spins the rotor. So, the higher the RRPM, the greater the Torque Reaction.
Let’s assume again that the quad is in a stable hover about one metre (3 feet) above the ground and heading North. Without moving fore/aft or laterally and without changing altitude, we want to change the quad’s heading left around to South, through West. To command this yaw we move the appropriate control stick to the left to tell the CPU our intentions. The CPU takes care of the difficult coordination of the quad’s Rotors to control the yaw.
Usually, with all rotors turning at the same RRPM, the sum of the individual torque reactions from each rotor cancel each other out. The CPU adjusts this situation to ‘unbalance’ the individual torque reactions so that there is a residual turning moment around the central Z axis of the quad. By changing the RRPM of each rotor, the CPU can control this residual moment and change the quad’s heading. Figure 7.5 shows a turn to the left in an oblique view.
Figure 7.6 shows the view from directly above.
You can see that the CPU has increased the RRPM of the left front and rear right rotors, and hence their Rotor Thrust (green vectors) and also their torque reaction (light blue arrows). The CPU has reduced the RRPM of the other two rotors and their rotor thrust and torque reaction (pink arrows) have reduced. The yaw that the quad undergoes is indicated by the larger blue arrow.
It is important to note that the sum of the four rotor thrusts, as represented by the Big Green Arrow, are still equal and opposite to the Weight vector and hence the quad does not climb or descend.
As the quad’s heading approaches South, we can take out the control stick input and command the CPU to stop the yaw. It controls the four rotors’ RRPM so that the rotor thrust and torque reactions equalise and the quad settles into a stable hover again.
Next, we will look at Forward Flight and how we can fly our quad and have some fun.
Spinning rotors (or propellers) act like a disk that produces Lift. For ease of interpretation, once the basics are understood, we can think of these disks in isolation or as a group to understand how quadcopters fly and are controlled.
The CPU of the quadcopter has sensors that know the aircraft’s position and attitude and receivers that know what you, as the operator, want it to do. The CPU then sends commands to the electric motor to increase or decrease its RPM to change the lift produced by the connected rotor. When multiple rotors on a quadcopter are commanded individually to vary their lift, this can be used to steer, climb and descend the quadcopter.
Forces on a Rotor Disk
Vectors in the Hover
As we have seen previously, with the theory of flight we prefer to break down the various forces that apply to lift producing aerofoils or rotors into four main vectors. For convenience and consistency, these same four vectors can be defined for a rotor disk.
Fundamentally, a spinning rotor disk provides Rotor Thrust perpendicular to the disk by forcing air through the blades and away from the disk. This is the principle of the cooling fan you may use in summer. Rotor thrust can be thought of as a vector that points in the opposite direction to the movement of air. In the case of a quadcopter in the hover, the rotor thrust vector points vertically upwards and the displaced air, called ‘downwash’, is accelerated downwards.
When hovering in still air, where the disk is moving neither vertically or horizontally, the rotor thrust counters the weight of the aircraft in a similar way to the aerofoil we have discussed previously. In a vector sense, the rotor thrust vector is vertically upwards and the Weight vector is vertically downwards as depicted in Figure 6.1:
Here you can see the green rotor thrust vector ‘equal and opposite’ to the weight vector. These vectors both represent forces, rotor thrust being the force applied to the rotor disk by the acceleration of the downwash; and weight being the mass of the system multiplied by the acceleration due to gravity.
Note also in Figure 6.1 the representation of the Rotor RPM by the crimson circular arrow. As we have discussed previously, in quadcopters the CPU controls the amount of rotor thrust produced by varying the RPM of the rotor or RRPM. In these graphics, the magnitude of that RRPM is represented by the thickness of the crimson arrow.
Tilting the Disk
Let’s have a look at what happens to the vectors if we now tilt our rotor disk. We will worry about how we do that a little later on.
Here is a depiction of our rotor disk tilted forward 10°:
The RRPM hasn’t changed and therefore the Rotor Thrust is the same as in Fig 6.1. But because the rotor thrust vector is now tilted 10° forward it no longer balances the Weight vector. Left unchanged, the disk will move forward and descend.
As our desire is to remain at a constant altitude, the CPU must counter this descent by increasing the RRPM and therefore the rotor thrust as seen in Fig 6.3:
The increase in the magnitude of the ‘big green arrow’ is a little hard to see, but it is there. An easier way to see this change, and subsequently imagine it in flight with your quad, is to break down the Rotor Thrust vector into vertical and horizontal components. Fig 6.4 does this:
So here you can see that the vertical component (yellow vector), or Lift, is now equal to, and opposes, the weight (orange vector). So the rotor disk remains at a constant altitude.
You will have noticed that most quadcopters don’t have propellers on the front of them or jet engines firing out the back, so in Figure 6.4 we can also begin to see how rotor disks, and therefore quadcopters, get to move around.
The small blue horizontal vector in 6.4 can be thought of as the Thrust vector. As it is currently unopposed, the rotor disk will accelerate from the hover to some forward speed, all the while remaining in level flight (that is, not climbing or descending).
Hopefully, you may by now be starting to see similarities with the discussion we had on Aerofoils, which you can review by opening in a new tab by clicking here.
Early on, when the Thrust vector is unopposed the disk will accelerate. But over time, the Drag or wind resistance of the disk, will reduce the acceleration and the disk will stabilise at a velocity, neither accelerating or decelerating. In this stable state, all forces on the disk will be balanced. The Lift (or vertical component of Rotor Thrust) will balance Weight and the Thrust (horizontal component) will be balanced by Drag.
To further increase speed, the disk may be tilted further forward to increase the magnitude of the Thrust vector. The disk would increase its velocity until once again Thrust and Drag were balanced and the disk would maintain this new, constant velocity.
Of course, if the Rotor Thrust wasn’t increased at the same time, the Lift would no longer equal the Weight and the disk would descend. To maintain a constant altitude, these two vectors must always remain balanced. To increase Rotor Thrust in a quadcopter, the RRPM must be increased.
Figure 6.5 illustrates the situation when a rotor disk is in stable, unaccelerated flight with a 20° ‘tilt’ or pitch attitude.
In theory, we could keep tilting the rotor disk forward and continue accelerating. But there are two practical reasons why this won’t work forever.
Firstly, the power available to the rotor disk, in the case of quadcopters from the battery, is limited and so the ability to spin the rotor and ‘grow’ the green Rotor Thrust vector, and hence the blue Thrust vector, is limited.
And second, the ‘trigonometry’ of the vectors means that the more we tilt the green vector, the exponentially longer it must be to allow the yellow Lift vector to continue to match the orange Weight vector.
Practically, about 40° is likely to be a limit as shown in Figure 6.6:
Here you can see high RRPM, indicated by the thick crimson circular arrow, producing maximum Rotor Thrust, with Weight and Lift balanced, and Thrust and Drag balanced.
(By the way, for those vector analysts out there, I’m aware that there are unaddressed turning moments in my diagrams and that the whole thing is a little more complex than I portray, but we are talking basics here.)
So, we have learned that if we change the RRPM of our Rotor, the Rotor Disk produces more Rotor Thrust. In these diagrams we portray this as the ‘big green arrow’. If we want to hover our rotor disk in nil wind, we hold the rotor disk horizontal, allow the big green arrow to remain vertical, and adjust the RRPM so that the Rotor Thrust is equal and opposite to the Weight of the disk. If we want the disk to climb, the RRPM is increased therefore increasing Rotor Thrust to be greater than the Weight and the disk will climb. Descending is the opposite, reducing RRPM will reduce Rotor Thrust.
When the disk is tilted, some of the Rotor Thrust acts in the horizontal plane. This causes the disk to move in the direction of the tilt. This movement can be sideways or backwards of course, which is how helicopters and quads move in directions that are not the way they are heading.
The downside of tilting the disk is that the vertical component of the Rotor Thrust or Lift is reduced and unless we increase RRPM, the disk will descend. This is especially the case if we tilt the disk excessively, expecting too much acceleration, and exceeding the maximum power or RPM of the motor.
So how do we tilt the rotor disk?
In a helicopter, it is done with a sophisticated series of mechanisms that can change the pitch (or Angle of Attack) of the rotor blades as they spin around. Words like ‘swashplate’, ‘pitch change links’, ‘cyclic’ and ‘collective’ are things you will see if you read about this.
Quadcopters don’t have or need such complexity. The rotor blades, and hence rotor disk, are fixed so that they always rotate in the same plane as the body of the quad. The necessary tilting of the Rotor Thrust vector is done by tilting the whole quad. How this is done is discussed in the next chapter.
Aerofoils are extended in three dimensions to become wings or rotors. The forces on these rotors are what provide the power to lift, control and fly a quadcopter.
Rotors are designed for specific purposes and applications. A key difference between quad rotor systems and others, for example on a helicopter, is that most lift variables are fixed and only the rotational speed, or angular velocity, is varied to change the lift of each individual rotor.
What We Already Know
In the previous chapter, we discussed aerofoil design and how we might employ it to provide Lift to oppose Weight. We saw how moving an aerofoil through air forces some of that air downwards and how the aerofoil gains lift as a result.
In the case of a fixed wing aircraft, this is achieved by moving its wings through the air. But with rotary wing aircraft, such as helicopters and quadcopters, the movement through the air can be gained by spinning suitably designed and constructed rotor blades. As we discussed, there are several variables that control the amount of lift produced by an aerofoil and therefore a rotor.
In this chapter, we will expand on these principles.
Forces on a Rotor Blade
Here is a refresher on the forces on an aerofoil as it moves through the air:
Lift – the vector that opposes gravity in normal circumstances, and
Drag – the vector that opposes the movement of the Aerofoil through the air.
To keep things in balance at this stage, two further ‘equal and opposite’ forces are needed to keep the aerofoil in equilibrium. They are:
Weight – the force applied to the aerofoil due to gravity, and
Thrust – the force required to oppose the Drag and keep the aerofoil moving at a constant velocity.
For the next little while, we can assume that the Weight is constant with the vector always pointing towards the centre of the earth. Thrust is provided by an engine normally, or in the case of our quadcopter, an electric motor powered by a battery. Apart from a reducing voltage, this Thrust is relatively constant too. We can disregard these two vectors for now.
You will remember that the force applied to the aerofoil is called the Total Reaction or TR. Lift and drag are the vector components of this TR. They change as the environment and the quad’s controls change to counter the outside environment and/or to move the quad around.
A rotor blade or wing is an aerofoil extended in 3D. When it moves through the air, lift is produced along the full span. We have seen previously that in the lift formula, one of the variables is the area of the wing, that is, the length of its chord multiplied by the length or ‘span’ of the wing. You can see that concept illustrated in Figure 5.1 below. Below that is the Lift Formula if you need a refresher.
Lift = CL ½ ρ v2 A
If the aerofoil cross section is the consistent across the wing, the lift produced is (theoretically) equal across it as it moves through the air. If the angle of attack remains constant, the only way that we can change the amount of lift produced is by increasing the velocity of the wing. The faster it goes, the more lift produced. This is why fixed wing aircraft need runways for take-off and landing. Their wings only produce enough lift to carry them airborne once they reach a certain Airspeed.
The whole point, of course, of helicopters and quads is to be able to hover, which means that the lift produced by the rotor must exceed the weight of the aircraft while it has zero airspeed. To achieve this, the rotors spin and the aerofoils can produce lift as they rotate.
Design of a Rotor Blade
So, let’s consider Figure 5.2
The Aerofoil from Fig 5.1 is now mounted on a hub and is spinning at a constant RRPM. Its Angle of Attack is fixed by the hub (at 10 degrees in this case), the aerofoil cross-section is constant and the rotor system itself is not moving through the air. As expected, the Rotor is producing some lift, as indicated by the green arrows, but their height, representing the force produced, is not constant across the Span of the rotor.
How is this so if everything is constant?
Of course, the Lift Formula provides the answer and points us to the fact that the velocity of the air over the span of the spinning rotor increases as we move from the hub to the tip. Wikipedia tells us that angular velocity is proportional to the radius and the RPM of a particle moving around an origin. So, in our case, the Airspeed of a section of the rotor as it rotates increases as we move towards the tip.
Because the Lift Formula tells us that the lift produced is proportional to the square of the velocity, the green arrows increase exponentially from the hub to the tip. Figure 5.3 shows this more clearly.
But while this increase in lift may seem desirable, it comes with one distinct disadvantage. Applying an increased force a relatively long way from the hub creates a significant bending moment on the rotor blade, forcing the blade itself to rise at the tip. This reduces the efficiency of the rotor but worse still, creates stresses and ultimately fatigue that may cause the blade to fail. To stiffen the blade to resist this force usually means weight or cost penalties. Helicopter and quad design engineers want to avoid both.
So a design method has been developed to reduce this spanwise increase in lift without requiring additional strengthening of the rotor and avoiding the weight penalty.
As the increase in span-wise RAF is unavoidable with rotor aerodynamics, other variables are adjusted to attempt to equalise the lift across the blade. The two that are usually chosen are the Angle of Attack and the length of the Chord Line.
Decreasing the AoA from the blade root to the tip is called Washout (or Twist) and allows for a decreased AoA to compensate for the relatively greater airspeed at the tip.
Decreasing the Chord Line dimension reduces the area of sections of the blade near the tip thus reducing the lift produced. This is called Taper.
Figure 5.4 illustrates the concept:
If you look carefully at your quad’s rotor blade, you should be able to see both its Washout and Taper. DJI Phantom blades display considerable taper while Yuneec blades are less noticeable. Usually, the washout is a little less pronounced than the illustration above with the AoA running from about 10° at the root to 2-3° at the tip.
So, looking back on our rotor system model, if we adapt the blade with both washout and taper we can see that the lift is now more evenly distributed across the span:
For any spinning object, dynamic balance is very important. Therefore, rotor assemblies are constructed such that the centre of gravity of the whole system is coincident with the centre of rotation. The easiest way to do this for our quadcopter is to attach another identical blade on the opposite side of the hub.
Now with an extra blade attached and the washout and taper built in, the only variable now required to control the lift equally across the rotating blades is the RRPM of the rotor. Speed up the rotation and the lift increases, slow it down and the lift reduces. It is convenient and far simpler to indicate this lift as a single arrow that grows and shrinks with changes to the RRPM is shown below in Figure 5.6.
We are going to call this the ‘Big Green Arrow’. It represents the Rotor Thrust of the spinning blade assembly or Rotor disk.
So now I am going to introduce some more representative graphics. I have modelled all of the coming graphics and illustrations on my Yuneec 4K. I have developed an OpenSCAD 1:1 scale model of it and will use it in future chapters as we go through the more advanced concepts. But first, let’s look at a standalone rotor assembly and disk. Figure 5.7 shows a rotor and motor assembly:
Here is the spinning rotor disk which I use in future chapters. You can see the Big Green Arrow and a circular arrow that indicates the direction and speed of rotation. The taller the Big Green Arrow, and the thicker the crimson arrow, the faster the rotor is spinning and the more Lift it is producing.
In the next chapter, we are going to look at the forces related to an individual rotor disk. We will build on this to see how all four rotors come together to control our quad through all of its flight regimes. As a primer, here is a graphic showing our quad, shutdown but ready to go:
During the development of these last couple of chapters, I did some reading about racing quads. This is not an area I am familiar with but it is worth a quick few paragraphs to link them to the discussion above.
Take a look at this page: 5 Fastest Racing Drones (I hope it hangs around for a while!) I want you to focus on the rotor blades that are fitted to these racing quads (I dislike the term ‘drone’).
Whilst I acknowledge that we haven’t gone into the details around the control of quads yet, we have covered the basics above and we can discuss how this type of quad is controlled.
Clearly, the main priorities for these types of quads are speed and manoeuvrability. To achieve this, they not only need lots of Rotor Thrust but they also need to be able to change this thrust (max to min and back again) quickly and responsively. To make this work what the rotor system doesn’t need is lots of angular momentum. If you get into that Wikipedia link there, you can see that angular momentum is a function of RPM and the mass of the spinning body.
A racing quad’s rotors need to spin up quickly but similarly need to slow down (and reduce the lift they are producing) quickly also.
The way to overcome excessive angular momentum, in this case, is to reduce the rotating mass. They do this by reducing the length (Span) of the rotor blades. Stubby rotors have less mass and it is distributed closer to the hub and hence the rotor can increase and decrease its RPM (and therefore, lift) rapidly.
But these quads still need lots of power to fly and accelerate, so their rotors must produce lots of Rotor Thrust. They do this several ways in comparison to ‘normal’ quads like a Yuneec or a Phantom. The motors are extra powerful and can spin the rotors at a greater RRPM. The rotors also have higher AoAs and lots more Washout or twist. They are also very Tapered, with the tips only roughly half the Chord at the widest part of the blade.
All these attributes make up for the lack of length of the rotor blades and lead to a very manoeuvrable and quick aircraft. The cost is higher powered motors and hence greater battery demands.
Aerofoils are specially designed and constructed to produce a force called Lift as they move through the air. Other forces, such as Drag, Thrust and Weight also act on the aerofoil as it moves.
The Lift an aerofoil produces depends on a number of factors, some of which are beyond our control as quadcopter operators. Others, such as the rotational speed of the Rotors and hence the velocity of the air passing the aerofoil, can be adjusted and this is how we control the quadcopter as we fly it.
In this chapter, I’m not going to attempt to establish how Aerofoils work and Lift is produced in any great detail. However, I will summarise the concepts and I suggest some links for you to visit if you are interested in finding out more. I encourage you to do this.
What is an Aerofoil
An Aerofoil (or ‘airfoil’ for North Americans) describes the cross section of a wing, rotor, rudder, propeller or other lifting surfaces. They come in many shapes and sizes and are usually designed for a specific purpose or application. For a broad description and more information go to the Airfoil page on Wikipedia.
If you take some time to read that Wikipedia page you will see that there are a few characteristics of aerofoils that help define it. While they may vary in size, two key qualities help define the type of aerofoil:
The Chord Line is defined as a straight line joining the leading edge with the trailing edge.
The Camber Line is defined as the line equidistant between the upper and lower surfaces.
On the diagram below you can see pictorial descriptions of the Chord and Camber lines. This aerofoil has an Angle of Attack of zero degrees, which is defined as the angle between the Relative Air Flow (RAF) and the Chord Line. This means it is streamlined to the direction of travel which usually implies it is producing the least Drag or wind resistance.
How Lift is Produced
As an Aerofoil moves forward through the air, it displaces some of that air. Unless the aerofoil is perfectly symmetrical and perfectly aligned with the direction of the RAF, some of the air is forced away from the aerofoil.
In this case, the force applied to move the air is opposed, in and equal and opposite sense, to the aerofoil. Those familiar with basic physics will have heard of Newton’s Third Law; this effect on the aerofoil is an example of that Law.
This force that moves the Aerofoil is called the ‘Total Reaction’ or the ‘Total Aerodynamic Force’. For convenience, aerodynamicists resolve this force into two vectors:
Lift – the vector that opposes gravity in normal circumstances, and
Drag – the vector that opposes the movement of the Aerofoil through the air.
To keep things in balance at this stage, two further ‘equal and opposite’ forces are needed to keep the aerofoil in equilibrium. They are:
Weight – the force applied to the aerofoil due to gravity, and
Thrust – the force required to oppose the Drag and keep the aerofoil moving at a constant velocity.
This diagram shows these four forces in equilibrium. In this case, the aerofoil has an Angle of Attack of 10 degrees. You can see that the Chord Line is at 10 degrees relative to the horizontal, which is the direction of the RAF.
What Affects the Lift
The Lift produced by an Aerofoil can vary due to a number of reasons. Some are within our control, either in the design and contraction phase or when operating the quadcopter. Others are due to environmental factors beyond our control.
There is a lot of physics and maths theory involved in understanding how lift is produced and controlled. The general concepts are covered well in the Lift Wikipedia page for those who want more info. I suggest you continue reading here then follow up there for any concepts that you need further explained.
For our purposes, the main design criterion an Aerofoil needs for its specific task is its profile or Camber. The actual cross-sectional shape of the aerofoil can be symmetrical, that is the Camber Line and the Chord Line are coincident, or asymmetric, where the Camber varies, sometimes significantly, from the Chord Line.
An aerofoil’s thickness, or more specifically its thickness to chord (or t/c) ratio, also affects its performance. A ‘fatter’ aerofoil has to force the air further away from its resting position as it passes. In principle, this means that a fatter aerofoil may produce more Lift, but there is also the penalty of the Drag or wind resistance, to consider and hence the thickness to chord ratio is often a compromise.
Most quadcopters have an aerofoil that is moderately cambered with a low t/c ratio, or ‘thin’ profile. This provides a compromise between Lift production at the relatively high speed of rotation of the blades and the Drag that is produced and hence the power of the motors required to spin them.
For those really keen to learn more, try the NACA Airfoil Wikipedia page.
Angle of Attack
As a fixed Aerofoil design moves through the air at a constant velocity it would be beneficial to be able to vary the Lift produced. This is done by changing the Angle of Attack (AoA) of the aerofoil to the Relative Air Flow (RAF) and thus changing the amount and direction that the aerofoil moves the air out of its path.
As we have discussed above, moving more air increases the ‘equal and opposite’ force on the aerofoil which we have described as the Total Reaction, and which we resolve as Lift and Drag vectors.
So, increasing the AoA, up to a specific angle, proportionally increases the amount of lift the aerofoil produces. In scientific terms, the AoA is often referred to as ‘alpha’ and its Greek letter ‘α’ is used to denote AoA in aerodynamic formulas. Therefore we can say that Lift is proportional to α.
So in this next figure, you can see that increasing the α to 22 degrees gives a corresponding increasing in Lift. Because to is actually the Total Reaction that is increased, we also get a corresponding increase in Drag. Thrust must be increased to counter the Drag if we want to maintain equilibrium. The increased Lift would normally cause the aerofoil (and the attached aircraft) to increase altitude or climb. In this illustration, the Weight has increased and so the aerofoil remains at equilibrium.
When a certain α (that is particular to the design of the aerofoil but usually between 20 and 25 degrees) is exceeded, the airflow over its surface breaks away and becomes turbulent. This means the aerofoil is unable to force the air downwards and hence Lift is dramatically reduced. In this case, the aerofoil is said to be ‘stalled’.
There are many Youtube videos available that show wind tunnel video of aerofoils in smoke streamlines that may help you visualise these concepts. Two good ones are here and here.
In a fixed wing aircraft, whilst the wings are set at a fixed angle to the aircraft fuselage, the Angle of Attack of its wings to the RAF can be varied by adjusting the tailplane and elevators. This ‘pitch attitude’ change adjusts the Angle of Attack and hence the Lift produced by the wings and determines whether the aircraft climbs or descends.
A helicopter works similarly with the pitch angle of the Rotor blades being able to be adjusted both collectively and cyclically by the pilot’s controls as the rotor spins.
In the case of our quadcopters, however, you will have noticed that the rotor (or propeller) blades are fixed to the hub and hence the Angle of Attack is fixed by the construction of the rotors. So how can we control the Lift?
As we have learned above, as an Aerofoil moves through the air it displaces some of the air away from itself. If you have read the Wikipedia articles on Lift you will know that in a normal aviation application aerofoils are mounted in a way to deflect this air downwards and hence provide an upwards force to counter gravity.
It follows that the quicker the aerofoil moves through the air, more air is displaced and hence more lift is created. As the lift force exceeds the Weight (which is also a force, described as the mass of the aircraft multiplied by the acceleration due to gravity) the aircraft climbs. This fact is the reason why planes must accelerate along a runway to takeoff.
It happens that Velocity is so important to the production of lift that its effect is proportional to its square (that is, velocity times velocity). To learn more, read about it on the NASA website.
With normal planes and helicopters, whilst velocity is important for lift production, their sophistication allows other design features, such as controls that change their aerofoils AoA, to help control their lift so they can climb and descend. For quadcopters, with fixed angles of attack on their rotors, the only available method of lift control is velocity. The various motors that drive the quad’s rotors are able to increase and decrease their speed as required by the quad’s CPU to control the quad as commander by you as you pilot the aircraft around. We will see how this is done in further chapters.
We have seen that an Aerofoil’s production of Lift, and by necessity Drag, is dependent on shifting a mass of air downwards (in the case of wings and rotors). The more air that is moved, the more lift is created. As we need this lift to exceed Weight (which, in the case of quadcopters, is a fixed amount), we need increasing amounts of lift to climb the quad and fly it around.
The density of air decreases as Pressure Altitude (that is, the height above sea level) increases. This is due to two main factors. Firstly, the closer the air molecules are to the centre of the earth, the greater the gravitational attraction, and secondly, the air near the surface of the earth has more molecules above it and the ‘weight’ of these molecules helps compress the air near the surface more. See this link for a greater explanation.
Air Density is also affected by the temperature (and to a lesser extent, the humidity) of the air. Simply put the hotter air molecules whizz around more and take up more volume than cooler ones. If the same number of molecules are in a larger space, the density is less. This principle explains how a hot air balloon works.
One of the main causes of an increase in air temperature is contact with the ground. It is no surprise that the air near a hot and high location, such as Denver in summer, is less dense than the air at 5,000 feet overhead San Francisco on the same day.
This relationship between the pressure, temperature and humidity of air is described as its Density Altitude. This concept gives us the best measure of the performance of an aerofoil as environmental factors change. It tells us that if we keep the Aerofoil, AoA and Velocity constant but increase the density altitude, the lift produced will be less. So, a quad that is able to hover at a lower altitude may not be able to hover at, say, 5,000 feet.
This concept of density altitude is why some manufacturers advise a maximum altitude for the operation of their quads. On a hot day, in a high place, the motors may not be able to spin the rotors fast enough to provide the lift to control the quad satisfactorily. We will explore this concept more in future chapters.
Up until now, we have concentrated on an Aerofoil which is essentially a two-dimensional shape. If we extend an aerofoil in 3D we get an increase in lift that is proportional to the area of the wing or rotor. This is due to the 3D aerofoil interacting with a greater number of air molecules along its length.
The absolute length and hence area is a compromise of course, with rotor designers having to contend with the strength and tensile requirements of a longer rotor with the management of the mass of the component and therefore its effect on the weight of the aircraft.
So we have seen that the Lift produced by an Aerofoil is dependent on a number of factors. They are:
Angle of attack
Rotor or wing area
For the mathematically inclined, aerodynamicists have developed a Lift Formula which looks like this:
Lift = CL ½ ρ v2 A
CL is the ‘Coefficient of Lift’ which combines all the fixed factors of a particular aerofoil, or rotor blade. These include:
The aerofoil design, including NACA profile, Chord, Camber, etc and
The aerofoil’s Angle of Attack
ρ (rho) is the symbol that represents Air Density
v is the velocity of the rotor through the air
A is the area of the rotor blade
The formula, therefore, advises us that the lift produced, and hence the performance of our quadcopter, is proportional to each of these factors. As we have seen, though, most of them are fixed, that is we cannot change them, for a particular day and place where we choose to operate.
Fortunately, we can control one key factor: the velocity of the blades as they travel through the air. How that works and how we can control our quad is what we will discuss in the next chapter.
The atmosphere is complex. You should know that many factors that you may not have thought about could affect the performance of your quad. Your Elevation above sea level is one, as is the effect of wind and turbulence.
Greater temperatures and/or height above sea level leads to reduced quad flying performance. Failing to be more cautious in windy or turbulent conditions may also be hazardous.
It is possible to lose control of your quad if you don’t consider these and other aerodynamic effects.
In this, and any other discussion, a term with a capital letter and in italics is defined on the Key Terms page.
There are many atmospheric properties that influence ’normal’ or commercial aviation, such as flight in cloud, icing, and transonic effects that are not relevant here. But there are three qualities of the atmosphere that do relate to flying quads at the altitudes that they are operated (Quadsphere?). Let’s discuss them.
Air density is affected by three main factors – altitude above sea level, temperature and humidity. The higher any or all of these are, the less dense, or thinner, the air.
For example, at Denver CO – roughly 5,500 feet above sea level, on a standard day the air is only 86% of the sea level density.
As you will see soon, Lift is produced as an aerofoil moves through the air. The Lift produced is proportional to a number of factors, with air density being the main one. So it follows that Lift (and therefore the Weight that an aircraft can carry) reduces as the Density Altitude increases.
Air density is usually represented by the greek letter ρ (rho) and Wikipedia has more info if you need it.
Wind is simply the movement of air relative to the ground. When a quad is airborne, its flying capability is unaffected by the wind (if we ignore turbulence for the moment). Its Airspeed, the speed with reference to the surrounding air, is what matters when considering the performance of its rotors and how fast or high it can go.
Normally, an aircraft’s Airspeed performance is only constrained by Air Density. The Thrust it’s engines produce and the Lift its wings or rotors can produce are both limited similarly.
However, with GPS-equipped quads, whose maximum speeds are usually limited by a GPS sensed Ground Speed, wind can become a factor at higher speeds, especially with high-performance quads.
The effect of the Wind is really only relevant as the quad approaches the ground. As we will see later, an understanding of the Wind and how it may impact on the desired flight profile is crucial to avoid some of the more dangerous conditions, such as Vortex Ring State.
Turbulence is created by changes in the wind vector, that is a change in its speed and/or direction. These changes may be small, and in our quad world, produced in very isolated areas for short periods of time. For example, if you are flying downwind of a single tree your quad may experience significant turbulence.
As we will find out later, the Lift any aerofoil produces is proportional to the speed it is moving through the air. If the wind vector changes, this changes the airflow over the aerofoil causing a change in the Lift produced.
The turbulence we feel in an aircraft is the effect of the rapidly changing Lift produced by the wings of that aircraft. It can be uncomfortable.
With a quad, turbulence is not about comfort but instead can cause control difficulties as the software struggles to sense the quad’s attitude and altitude changes and send the required control signals to the appropriate rotors. This can especially be a problem when the quad is near to the ground, landing or taking off. This is one of the reasons that your quad manufacturer may advise you not to fly it in high winds.
If you are interested to know a little more about the fundamentals relating to the atmosphere, here is some good background courtesy of Decoded Science.
Knowledge of these terms will help you understand the more in-depth concepts discussed here. I have endeavoured to keep them consistent with the equivalent terms in helicopter aerodynamics to avoid confusion. Terms that are not relevant to quadcopters will not be listed.
Absolute Altitude (above ground level – AGL) – This is the quad’s height (in feet or metres) above the ground. In most modern quads, the software/telemetry actually measures the height above the GPS elevation of the take off location.
Aerofoil – The cross section profile of the Rotor blade.
Air density – The local density of the air. This also takes account of the air temperature and humidity.
Airspeed – The quad’s velocity relative to the surrounding air. The aerodynamics of aircraft and rotors depend on Airspeed, not Ground Speed.
Angle of attack (AoA) – The angle between the Chord Line and the Relative Air Flow.
Camber – The ‘shape’ of an Aerofoil. The camber line is a line equidistant from the upper and lower surfaces of an Aerofoil.
Chord Line – A straight line connecting the leading edge and the trailing edge of an aerofoil.
Density Altitude (DA) – The Pressure Altitude when adjusted for temperature. For a given Pressure Altitude, the greater the temperature, the higher the Density Altitude. The aerodynamic performance of a Rotor system is proportional to the Density Altitude it is operating in.
Drag – The horizontal, rearwards force that is produced by moving a body (aircraft or Rotor) through the air. Sometimes called ‘wind resistance’.
Elevation – The height (in feet or metres) of the terrain above sea level. This is not the quad’s altitude.
Fuselage – The central body of an aircraft, in this case, a quad or hexacopter. This normally houses the CPU and the battery.
Ground speed – The velocity of the quad with reference to the ground, which is not necessarily the same as its airspeed. A GPS measures Ground Speed. Most modern quads have some reference to GPS for speed control.
Lift – The vertical force produced by the rotors of a quad to overcome the force of gravity. This is the vertical component of Rotor Thrust.
Pressure Altitude (above mean sea level – AMSL) – Pressure altitude is an aircraft’s altitude as determined by air pressure. It is referenced to sea level and hence has no reference to the surrounding terrain. Elevation plus Absolute Altitude approximately equals Pressure Altitude.
Relative Air Flow (RAF) – The flow of air relative to the Aerofoil as the rotor rotates and produces lift.
Rotor Revolutions per minute (RRPM) – The number of revolutions of the rotor in each minute.
Rotor – In this guide I use the term rotor rather than propeller. I know some people won’t agree but my reasons are (1) for commonality with helicopter principles and (2) because as a general concept in an airborne sense, rotors provide lift (ie oppose weight) whereas propellers provide Thrust (ie oppose Drag).
Rotor disk – An imaginary disk described by the spinning rotor.
Rotor thrust – The total force provided by the Rotor Disk when operating. Rotor Thrust changes roughly proportionally with changes in Rotor RPM
Span – The length of a single blade from root to tip.
Thrust – The horizontal propulsive force provided by the Rotor Thrust.
Torque Reaction – The reaction of the Fuselage in the opposite sense and proportional to the force required to turn the Rotor.
Total Reaction (TR) – The force applied to the Aerofoil as it moves through the air. This force is usually broken down into its component vectors Lift and Drag.
Velocity – The speed vector. Velocity has a magnitude (speed) and a direction (in our case, usually roughly horizontally into the RAF).
Washout – The change (usually a reduction) in the angle of the chord relative to the hub along the span of a rotor blade or wing.
Weight – The force (ie Mass times the acceleration due to gravity, written mathematically as W=mg) applied to the quad by the Earth. To hover the quad without climbing or descending, Lift must equal Weight.