A helicopter earns its lift the hard way, with one large rotor and a tail rotor whose only job is to stop the body spinning. A quadcopter reaches the same place with four small fixed propellers and no moving control surfaces at all, which is why it can be built on a bench from parts that cost less than a phone. Everything the machine does, from holding still in the air to flipping over and catching itself, comes from varying the speed of those four propellers, so the first thing to understand is what a spinning propeller actually gives you.
A propeller is a fan that pushes air. By Newton's third law, throwing a stream of air downward pushes the propeller, and the aircraft bolted to it, upward. The upward push is the thrust , and it is a force, measured in newtons. To hover, the four propellers together must produce a thrust equal to the weight of the machine, and no more:
where is the mass in kilograms and m s⁻². A 500 g quadcopter weighs N, so each of its four propellers has to make about 1.23 N of thrust just to hold the craft motionless. Thrust in this hobby is almost always quoted in grams, meaning grams-force, the weight of that many grams: 1.23 N is 125 gf. It is a sloppy unit but a convenient one, because a component's specification and a kitchen scale speak it directly.
Thrust to weight, and why hover is not the target
A craft whose motors can each make exactly the hover thrust and not a gram more can hover and do nothing else. The moment it needs to climb, or to tilt and correct a gust, it has to push harder than its own weight somewhere, and it has nothing left. The number that matters is therefore not the thrust but the thrust to weight ratio, the total thrust available at full throttle divided by the weight:
At a ratio of 1 the craft can just hover. At 2 it hovers at roughly half throttle, which leaves half in reserve for climbing and correcting, and this is about the minimum for a machine that is pleasant and safe to fly. A racing quadcopter is built for a ratio of 8 or more, so that it spends most of its life near idle and has violent acceleration on tap. The ratio, not the raw thrust, is what decides whether a design flies well, and it is why a heavier battery is not a free upgrade: it adds thrust demand as fast as the larger motor it justifies adds thrust supply.
Example. A quadcopter has a mass of 650 g and four motor and propeller combinations that each produce 620 gf at full throttle. What is its thrust to weight ratio, and roughly what throttle does it hover at?
The total thrust is gf. The weight is 650 gf. The ratio is . Thrust rises steeply with throttle, closer to the square of it than to a straight line, so a ratio near 4 puts the hover point at roughly half throttle. The craft has plenty in hand.
Now you. A 1.1 kg camera drone uses four motors rated at 900 gf each. What is its thrust to weight ratio?
Answer
Total thrust is gf and weight is 1100 gf, so the ratio is . Comfortable for a stable camera platform, well below a racer.
Where the thrust comes from
A propeller's static thrust, meaning the thrust it makes while the craft is not moving through the air, depends on how fast it spins and how big it is. A useful scaling, derived properly in the momentum theory lesson, is
where is the density of air, is the rotation rate and is the propeller diameter. Two features of that expression run the whole design. Thrust grows with the square of the speed, so doubling the rate quadruples the thrust, which is why control is fast and why a motor near hover has so much authority left. And thrust grows with the fourth power of the diameter, so a slightly larger propeller is enormously more effective than a faster small one: a 5 inch propeller turned into a 6 inch one, other things equal, makes roughly times the thrust at the same speed. Big slow propellers are efficient and big slow propellers are what a long flight time wants; small fast ones are agile and what a racer wants. The choice of propeller size is the first real fork in a design.
Why four, and why they spin in two directions
Four is not the smallest number of rotors that can fly, but it is the smallest that can fly simply. A single rotor makes thrust but also, by reaction, tries to spin the body in the opposite direction to the blades, which is the torque a helicopter's tail rotor exists to cancel. A spinning propeller drags air around with it, and the air drags back, applying a reaction torque to the motor and hence to the frame. Left unopposed, that torque would set the whole craft rotating about its vertical axis.
The quadcopter cancels it for free by spinning two propellers clockwise and two counter-clockwise, arranged so that the two of each kind sit on opposite corners. The reaction torques then come in two equal and opposite pairs, and their sum is zero, so a quadcopter with all four motors at equal speed feels no net twist and holds its heading. This is the single most important fact about the layout, and it is why the propellers are not interchangeable: a clockwise propeller is a mirror image of a counter-clockwise one, and fitting the wrong handedness makes a motor push its air the wrong way. Getting one of the four backwards is the classic first-build mistake, and the craft answers it by flipping the instant it leaves the ground.
That the torques cancel at equal speed also hands over a control, which the next lesson develops in full. Speed the clockwise pair up and slow the counter-clockwise pair down by the same amount, and the total thrust is unchanged, the craft neither rises nor falls, but the torques no longer cancel and the machine turns on the spot. The same trick of unbalancing what was balanced, applied to thrust across the front and back or the left and right, is how it leans and flies in a direction. A quadcopter has no rudder, no ailerons and no swashplate. It has four numbers, the four motor speeds, and every motion it makes is some combination of raising all of them and tilting the balance between them.
What holds it there
Nothing in this lesson keeps the craft level on its own. Four propellers making equal thrust hold height and heading, but the balance between them is a knife edge: a breath of wind, a slightly heavier battery on one side, a motor a few per cent stronger than its neighbour, and the craft tips. A helicopter can be flown by a skilled pilot because its dynamics are slow enough for a human to correct. A small quadcopter cannot, because it tips faster than a person can react, on the order of tenths of a second. What makes it flyable is a computer reading a rotation sensor hundreds of times a second and nudging the four motor speeds to hold the craft where it was told to be. That loop, the sensor and the controller, is as much a part of why a quadcopter stays up as the propellers are, and most of the second half of this course is about it.
For now the picture is complete enough to build on. Weight sets the thrust each propeller must make, the thrust to weight ratio decides whether the craft merely hovers or truly flies, the fourth power law says a larger propeller is worth far more than a faster small one, and the two-and-two arrangement of spin directions is what lets the machine hold its heading and turn at will. The next lesson turns those four motor speeds into the three rotations a pilot actually commands.