I Made an Airplane Out of a Circle

Every airplane needs the same four things

Eric says it in the video almost in passing: “even though this thing looks ridiculous, it still needs basics — lift, stability, control and power.” That isn’t a throwaway line, it’s the entire design brief for every aircraft ever built. A 747 and a foam pancake are solving the same four problems with wildly different budgets. So that’s how this page is organised: four problems, in the order they have to be solved, with the circle as the worked example.

1. Lift: how a flat circle holds itself up

A wing works by throwing air downward. Every second it flies, the wing grabs a mass of air and pushes it down, and Newton’s third law does the rest — that air pushes the wing up by exactly as much. You’ll also hear lift explained through pressure, with the air over the top moving faster and its pressure dropping so there’s more push underneath than above. Both are true. They’re the same flow described from different ends.

Nothing in that requires a teardrop-shaped airfoil. A flat plate tilted into the wind deflects air down, so a flat plate is a wing. Almost every foam-board plane on this site flies on flat plates. A proper curved airfoil simply does the job more efficiently and stalls more gently — an optimisation, not an entry requirement.

The one equation, in plain English

Lift = ½ × air density × speed² × wing area × lift coefficient. Four dials, and you only get to turn three of them:

• Speed matters most, because it’s squared. Double the speed, four times the lift.
• Area is a straight multiplier. Twice the wing, twice the lift.
• Lift coefficient is how hard the wing is working, set mostly by angle of attack.
• Density is the weather’s business, not yours.

A circle wins on the second one, and it wins big.

Area is the circle’s superpower

This one is 30 inches across, so its area is π × 15² — 707 square inches, or 4.9 square feet. Now put it next to the two other 30-inch planes on this site, both of which have exactly the same span:

Same span, and the circle carries about three times the trainer’s wing and three and a half times the slow flyer’s. It fits in the same box on the bench and it is a fundamentally bigger wing.

Wing loading is weight divided by area, and it is the single most important number in how an airplane behaves. Three times the area for a similar weight means roughly a third of the loading, which means a much slower flying speed. At the same weight and the same lift coefficient, stall speed scales with the square root of wing loading, so a third of the loading is about 42% slower through the air.

Slow is what makes a twenty-minute build survivable: everything happens at a pace a human can react to, and when it does hit the ground it arrives with a fraction of the energy.

That’s the real answer to “how does this thing fly?” It isn’t that a circle is a clever wing. It’s that a circle is an enormous wing.

What the loading actually works out to

Eric hasn’t put this one on a scale, so here is the conversion rather than a claim. Divide the weight by 4.9 square feet:

The useful thing about that table is that the conclusion doesn’t depend on guessing the weight. Anywhere in that range, the circle is flying at less than half the slow flyer’s loading and under a third of the trainer’s — and the slow flyer is a plane built specifically to fly slowly. A foam pancake thrown together in twenty minutes has a lighter wing loading than the airframe designed for it.

The number that defines every circle: aspect ratio 1.27

Aspect ratio is span² divided by area — long and skinny scores high, short and stubby scores low. For a circle the span is the diameter D and the area is πD²/4, so the aspect ratio works out to 4/π. The D cancels completely. Every circular wing ever cut, at any size, has an aspect ratio of about 1.27.

Three things follow from sitting at the bottom of that chart:

• It flies nose-high. A stubby wing builds lift more slowly as you increase the angle, so it needs a bigger angle of attack to hold the same weight.
• It doesn’t really stall. Instead of the airflow letting go all at once and the nose dropping, a wing this stubby keeps making lift to a very high angle and simply mushes downward. Much harder to get into trouble — and much harder to make it go anywhere once it’s slow.
• It is draggy, though not for the reason most people assume.

The surprise: being stubby costs less than you’d think

Induced drag is the price you pay for making lift — the energy left behind in the swirling air coming off the edges of the wing. The usual shorthand is that low aspect ratio means terrible induced drag. Look at the actual relationship, though:

Induced drag = weight² ÷ (½ × density × speed² × π × span² × efficiency)

Read the bottom of that fraction again. Span, squared. Not area, not planform, not aspect ratio. What decides the bill is how wide a slice of air you spread the downwash across. A circle 20 inches across and a conventional wing 20 inches across, carrying the same weight at the same speed, leave behind roughly the same swirl and pay roughly the same induced drag.

So where does the circle actually lose? Profile drag — skin friction and form drag — which does scale with area. Three times the area is about three times that penalty. The circle buys its lift bargain with surface, not with swirl.

One genuinely odd fact

The textbook ideal lift distribution for a simple wing is elliptical; it’s the reason a Spitfire’s wing is shaped the way it is. Measure a circle’s chord — the front-to-back distance — at each point across the span, and the distribution you get is exactly elliptical. It is the same planform as a Spitfire, squashed from an aspect ratio of about 5.6 down to 1.27.

The catch is that the theory calling elliptical “ideal” assumes a long, slender wing. At 1.27 those assumptions come apart, the flow around the rim goes thoroughly three-dimensional, and real efficiency falls short of what the maths promises. It’s still a pleasing coincidence: the dumbest-looking wing on the internet shares its planform with one of the most admired.

What the folded-up rim is doing

Eric folds the edge of the disc up “to give it some shape.” Two separate things are happening there.

Structure, mostly. A flat sheet of foam is floppy — it bends easily about any line you draw across it. Fold the edge up and you’ve created a flange, and a flange resists bending enormously better, because you’ve moved material away from the axis it would bend around. It’s why you curl a floppy slice of pizza before you bite it, and why a paper plate has a rim. The foam didn’t get stronger; the geometry did.

Aerodynamics, as a bonus. An upturned lip is a small endplate running the whole way around, getting in the way of air trying to spill from the high-pressure underside to the low-pressure top. It also gives the outer edge a hint of dihedral, which helps in roll.

2. Stability: why it doesn’t tumble like a thrown plate

The frisbee question

A frisbee is a wing, and a thrown frisbee is stable — but not the way an airplane is. A frisbee is a gyroscope: it spins fast, and spinning things resist being tipped over. Stop the spin and a frisbee tumbles instantly.

This plane doesn’t spin. So every bit of its stability has to come the airplane way, and that means fixing three separate axes.

Pitch: the axis that decides whether it flies at all

All the lift on a wing can be summed into one force acting at one point, called the aerodynamic centre. If the centre of gravity sits ahead of that point, the airplane is stable in pitch: let the nose rise and the extra lift, acting behind the CG, pushes it back down. Put the CG behind it and every little disturbance grows instead of fading. Nose-heavy flies badly. Tail-heavy doesn’t fly.

The tail earns its keep twice. It adds a surface a long way behind the CG, which damps pitching motion, and it drags the whole airplane’s neutral point rearward, which widens the range of CG positions you’re allowed to use.

On this plane the heaviest single item is the battery, and Eric mounted it so it slides fore and aft. That’s the balance control. The relationship is the same one that decides a 54-pound airplane: the CG moves by the mass you shifted, times how far you shifted it, divided by the total weight. On something that weighs a few ounces, an inch of battery travel is a lot of centre of gravity. (For the same arithmetic at the other end of the scale, see what nine pounds of nose ballast cost the 20-foot plane.)

Yaw: the fin as a weathervane

“A nice little big rudder so it will help it track straight.”

Put a vertical surface behind the centre of gravity and you’ve built a weathervane. Let the nose swing left and that fin is suddenly meeting the air at an angle, which generates a sideways force on the tail and swings it back into line. The strength of the effect is simply the fin’s area multiplied by how far behind the CG it sits.

A circle has almost no side area behind the CG to begin with, and the motor pod sticking out in front actively works against you — side area ahead of the CG is destabilising in yaw, because it pulls the nose further into any swing. So the fin isn’t decoration. Without enough of it the plane hunts from side to side, which is the “confused paper plate” the video warns about.

Roll: what those edge fins actually do

This is the part everybody asks about — the small vertical surfaces standing up near the outer edge. They’re doing three jobs at the same time.

• Endplates. The whole reason a wing has induced drag is that air escapes around the edge from the high-pressure side to the low-pressure side. On a normal wing that’s a small fraction of the span. On an aspect-ratio-1.27 disc, almost the entire wing is edge, so anything that gets in the way of that spill is worth more here than it would be on any conventional plane. A standard rule of thumb puts the gain in effective aspect ratio at roughly twice the endplate’s height as a fraction of span — which is why quite small fins are worth their weight.
• Roll stability. A vertical surface standing above the wing catches air from the side during a sideslip, and because it’s above the centre of gravity that push rolls the airplane away from the slip. It’s the same self-righting effect a high wing gives a trainer, and it quietly turns an uncommanded slip into a wobble that fixes itself.
• Damping. Any surface out at the rim has to drag through the air before the plane can rotate, which slows down roll and yaw rates. That’s a lot of what “more stable in the air” actually feels like on the sticks.

3. Control: what the servos are really doing

A control surface is a shape-changer

A control surface is a hinged flap on the back of a fixed surface. Deflect it downward and the whole surface behaves as though it had more curvature built into it, so it makes more lift in that direction. That extra force, acting at some distance from the centre of gravity, rotates the airplane. Every control on every aircraft is that same idea:

• Elevator, on the tail: stick back, elevator up, the tail gets pushed down, the nose comes up.
• Rudder, on the fin: pushes the tail sideways, which points the nose the other way.
• Ailerons, one on each side: one up and one down together, making a rolling couple.

Force times distance. That’s the entire language of control.

Why this thing is so twitchy

“This thing flips, spins and turns way faster than I expected. Actually kind of scary for something I built in 20 minutes.”

That’s geometry, not luck. On a circle the tail bolts straight onto the back of the disc, so the distance from the centre of gravity to the tail is short — and two different things depend on that distance in two different ways. Control power scales with the arm. Pitch damping scales with the arm squared. Halve the distance and you halve the control authority, but you quarter the damping.

So you get an airplane that responds immediately and then keeps on going, because there’s very little behind it to settle the motion down. Add a tiny, light airframe — which means very little rotational inertia to overcome — and quick, under-damped and slightly alarming is exactly the flight behaviour you should expect.

Linkages are gearing

The servo never touches the control surface. A pushrod runs from an arm on the servo to a horn on the surface, and that pair of levers is a gear ratio you choose when you build it:

• Move the pushrod to a hole further out on the servo arm → more throw, less force, coarser resolution.
• Move it further out on the control horn → less throw, more force, finer resolution.

Getting this wrong is the most common reason a new plane feels awful. Too much throw makes it uncontrollably sensitive; too little and it won’t turn. Slop is the other one — any free play in the linkage shows up as a dead zone right around centre, exactly where you need precision most.

What “after some trim” actually fixed

“It’s a little rocky, but after some trim it starts flying way better than expected.”

Trim is a permanent offset added to a surface’s neutral position. If the plane climbs with the stick centred, a few clicks of down trim redefine what “centred” means. Doing it from the transmitter takes a second in the air; doing it by shortening or lengthening the pushrod is the permanent fix, and it’s the right one if you’re holding more than a handful of clicks. A plane that needs a lot of trim is telling you something about its centre of gravity or its surface alignment, and trim only hides the message.

4. Power: motor, ESC, servos, battery

The brushless motor

A brushless outrunner is two parts: a fixed core of copper windings in the middle (the stator), and a rotating can carrying permanent magnets around the outside. “Outrunner” means the outside is what spins. There are no brushes and no commutator, so nothing rubs and nothing wears out.

Two numbers matter on the label. Kv is revolutions per volt with no propeller fitted — a 1000Kv motor on an 11.1-volt pack wants about 11,100 rpm unloaded, and rather less once a propeller is fighting it. Watts is how much power it can turn into thrust before it starts cooking itself. The mental model worth keeping: voltage buys rpm, current buys torque. Fit a bigger propeller and you’ve asked for more torque, so it draws more current at the same voltage.

What the ESC is actually doing

The electronic speed control has the hardest job on the airplane, and it’s really doing three at once.

• It makes three-phase power out of DC. The battery supplies steady direct current. A brushless motor needs its three wires energised in a rotating sequence to drag the magnets round and round — six switching steps per electrical revolution, thousands of times a second.
• It works out where the rotor is, without a sensor. At any instant one of the three wires isn’t being driven, and the passing magnets induce a small voltage in it called the back-EMF. The ESC watches that idle wire, spots the moment the voltage crosses zero, and uses it to time the next switch. That’s why a brushless motor stutters and cogs at very low rpm — there isn’t enough back-EMF yet to steer by. It’s also why swapping any two of the three motor wires reverses the motor: you’ve reordered the sequence.
• It sets the throttle by chopping, not by resisting. It doesn’t dim the power through a resistor and waste the difference as heat. It switches the supply fully on and fully off thousands of times a second and varies the proportion of on-time. Half throttle is roughly half the effective voltage, so roughly half the rpm. Switching rather than resisting is the reason an ESC can be small, cheap and barely warm.

And there’s a fourth job it does quietly: the BEC, a little step-down converter that makes a clean 5 volts or so for the receiver and the servos out of the full pack voltage. It’s the part builders forget about until it runs out — on the 20-foot plane, an 8-amp BEC is the best explanation we have for why it stopped responding.

Inside a servo

A servo is a tiny closed-loop position controller in a plastic box. Open one and you find four things: a small DC motor, a gear train, a potentiometer geared to the output shaft, and a control board.

The receiver sends it a pulse about fifty times a second, and the width of that pulse is the command: 1.0 millisecond for one end of travel, 1.5 for centre, 2.0 for the other end. The board compares that command with what the potentiometer says the output shaft is actually doing, and drives the motor in whichever direction closes the gap. When the two agree, it stops. That loop never stops running, which is why a servo pushes back if you try to move the surface by hand.

Three practical consequences:

• Torque is quoted in ounce-inches or kilogram-centimetres, always at a stated voltage. More volts means more torque and more speed, up to whatever the servo is rated for.
• A buzzing servo is a warning. It means the servo can’t reach the position it’s been told to hold, usually because a linkage is binding. It will keep drawing current trying, get hot, and eventually strip a gear.
• 9-gram servos are the standard for foam planes this size, and two or three of them make up an entire control system.

The battery

Lithium-polymer cells are 3.7 volts nominal each, so “3S” means three in series, about 11.1 volts. Capacity is in milliamp-hours — the size of the tank. The C rating is how fast the pack can safely be emptied: multiply C by capacity to get the maximum current it will stand.

On an airplane this light the battery is also the heaviest single object on board, which is exactly why it’s sitting on rails. It’s the fuel tank and the balance weight at the same time.

The numbers on this power system

The parts list is a 2208-class motor at 2300Kv, a 5-inch prop, a 30 A ESC and a 3S 1300 mAh pack. Run that through the arithmetic above and a few things fall out.

• Around 25,500 rpm unloaded. 2300Kv × 11.1 V is 25,530 rpm with nothing on the shaft, and nearly 29,000 on a freshly charged pack. A propeller pulls that down, but this is a high-rpm setup by any standard.
• Theoretical pitch speed somewhere between 60 and 90 mph, depending on the prop’s pitch, once you allow for the rpm a 5-inch prop actually lets the motor reach. The airframe wants to fly at a small fraction of that, so the prop spends its life working a long way from its best operating point. Plenty of thrust, poor propulsive efficiency — a trade nobody minds on a plane like this.
• 333 watts is the ceiling, because 30 A through a 3S pack is 333 W and the ESC is the part that decides. It won’t pull all of that with a 5-inch prop, but even a third of it is more than 100 watts for an airframe weighing well under a pound and a half. A trainer flies on 50–70 watts per pound. This is nowhere near that number.
• The pack has to be at least a 23C pack to feed that ESC at full throttle: 30 A divided by 1.3 Ah is 23C. Most 1300 mAh 3S packs are rated well above it, but it is worth checking before you buy the cheapest one.
• 14.4 watt-hours in the tank. 11.1 V × 1.3 Ah. Held at the ESC’s limit that is 2.6 minutes; at a realistic third-throttle cruise it is nearer 8, and you would plan to land on 80% of it. Call it five or six minutes of actual flying.

And here is the whole airplane in one sentence. It has the wing loading of a slow flyer and the power loading of an aerobat. Those two facts, sitting in the same airframe, explain everything Eric says about how it flew: it floats, because there is an enormous wing under almost no weight — and it snaps, because there is a lot of power, almost no rotational inertia, and a very short tail arm behind it. “Flips, spins and turns way faster than I expected” isn’t surprising at all once the numbers are on the table. It’s the only way a plane with this combination could possibly behave.

One more detail worth noticing: the prop is tiny relative to the plane — 5 inches across a 30-inch span, where a conventional 30-inch build swings 8 or 9. A small fast prop makes its thrust by throwing a little air very quickly instead of a lot of air gently, which is efficient at speed and wasteful when slow. On a wing this big, a bigger, slower prop would be the efficient choice. It would also make the plane a great deal less exciting.

Why a 20-minute circle outflies plenty of careful builds

Everything on this page converges on one number: wing loading. A circle is very nearly all wing. Spread the weight over that much area and it flies slowly, and slow forgives almost everything — a centre of gravity that isn’t quite right, a rough launch, control throws that are too big, and a landing that’s more of an arrival. The airplane has time to be wrong and recover. So do you.

It’s the same reason the first-plane guide here is a 30-inch foam trainer and not a scale warbird. For a first flight, loading beats craftsmanship every single time.

So what shape is too dumb to fly?

The video ends by asking, and the engineering answer is that shape is very nearly free. What an airplane genuinely demands is a short list:

1. Enough area to carry the weight at a speed you can cope with.
2. A centre of gravity ahead of the aerodynamic centre.
3. Something behind the CG to keep it pointed forward.
4. Enough thrust to beat the drag of whatever you’ve made.
5. Surfaces that can produce a force somewhere other than at the CG.

Satisfy those five and something that looks completely absurd will fly. Miss the second one and the most beautiful wing you have ever built will not leave the ground.