Exercises

Stall speed 30.1km/h, wing loading 52.9g/dm², aspect ratio 6.15. The area is the mean of the two chords times the span: (300 + 220)/2 × 1,600 = 416,000 mm², which is 41.6 dm². Wing loading follows directly. For the stall speed the sheet uses 1.215, not 1.35 — it takes ten per cent off for a finite wing before it goes near the square root. Use 1.35 raw and you get about five per cent less stall speed than the aeroplane has.

Stall speed 33.0km/h, up from the 30.1km/h of the standard day — about ten per cent. Reynolds number 202k, down from 240k, which is nearer sixteen. Stall speed goes as the inverse square root of density, so a given density loss costs it half as much in proportion. Reynolds number carries the density directly and the viscosity, which rises with temperature — a hot day pushes it down twice. Humid air is lighter than dry air at the same pressure, so the humidity is working the same way as the heat, not against it.

All-up 2,100g, of which structure is 52.5% and energy 16.6%. The structure share is higher than the figure quoted for full-size aircraft, and that is not an error: a full-size aeroplane spends a third of its mass on fuel and payload, and a model carrying neither gives that share to structure. The areal density behind it is compiled from build practice, not measured — if you have ever weighed a wing, that number beats it.

Wing loading 55.6g/dm², giving 39.6dm² of wing, and 286W installed. The wing loading comes from the stall requirement — it is the only boundary that caps wing loading rather than demanding power, which is why the design point sits against it. The sheet names the binding boundary for the power, and it will not be cruise: cruise is the cheapest thing this aeroplane ever does.

0.0313 against a guess of 0.040, with add-ons contributing 20.8% of the total. A component build-up lands below measured drag, reliably, and more so at model scale — it counts the surfaces it knows about and misses the gaps, the antennas, the tape and the roughness. Treat the answer as a floor. Note also where the add-ons sit: the landing gear is usually a fifth of the total, and the legs cost more than the wheels.

125,101, and it would need 72km/h to reach 200,000. The density is down and the viscosity is up, and the Reynolds number carries both, so it falls faster than the density does. Down here the difference matters: below about 200,000 a laminar separation bubble is what decides the polar, and published section data mostly stops applying.

Best glide 1:10.7 at 39km/h, minimum sink 0.89m/s. Add the ballast and the ratio is 1:10.7 — it has not moved at all. Weight appears in neither lift coefficient, so it cancels out of the glide ratio entirely. Both speeds and the sink rate go as the square root of weight, so the heavier aeroplane glides exactly as far, arrives sooner, and cannot stay up in weak lift. That is the whole argument for water ballast in a competition glider.

Density 1.0169kg/m³, density altitude 1,897m, kinematic viscosity 18.985×10⁻⁶ m²/s. Lighter. Water vapour is less dense than the nitrogen it displaces, so a muggy day costs density on top of what the heat has already taken — the intuition that humid air feels heavy is about how it feels, not what it weighs. Density altitude is not a height you are at: it is the altitude in the standard atmosphere where the air is this thin, and the aeroplane behaves as though it were up there.

Cruise 42W, power loading 130W/kg, endurance 56min. Cruise is a steady, cheap condition; climb is not, and the motor is sized by the climb with a margin on top. Sizing a motor on cruise power is one of the most common ways to end up with an aeroplane that flies level perfectly well and cannot go up. Note too that the endurance is a steady cruise on eighty per cent of the pack — no climb, no circuit, no reserve.

Cruise 70.2%, climb 56.1%, static thrust 1,199g. Efficiency is a property of the operating point, not of the propeller: pushing hard at low speed throws air backwards fast and the kinetic energy in that wake is lost, while cruising gently throws it back slowly and wastes much less. Static thrust comes from a figure of merit rather than the disc model, because at zero advance the blade is stalled and the disc model runs well over. The gap between the two efficiencies is the error a single fixed figure carries on Sheets 04 and 06.

Climb current 19.6A, sag 0.20V, ESC headroom 104%. P over the nominal 14.8 V gives 19.3 A, which is close here — but only because this pack is large and loafing. The pack sags as it works, so the voltage it delivers depends on the current it is delivering, and the current is the smaller root of a quadratic rather than a division. Put the same aeroplane on a tired 3S 1300 and the two answers separate completely.

Neutral point 42.5% MAC, static margin 15%, MAC 262mm. The average chord here is 260 mm and the MAC is not that: the mean aerodynamic chord weights each strip of wing by its own chord, so a tapered wing's MAC always exceeds the arithmetic mean. It is the length everything else is measured in — tail volume, neutral point and static margin all quote it — so getting it wrong moves the centre of gravity of the whole aeroplane. The neutral point is where stability runs out; the centre of gravity belongs ahead of it by the margin.

Weathercock 0.0585Cnβ, dihedral effect -0.1147Clβ, balance 1.96−Clβ/Cnβ. A fuselage in a sideslip is a badly shaped wing with its lift pointing sideways, and most of it sits ahead of the centre of gravity where that lift is destabilising — it gives back 24% of what the fin produces here. The balance is the ratio that decides the character: fin-dominant spirals, roll-dominant Dutch rolls, and pleasant aeroplanes sit between one and three.

Aileron servo 1.45kg·cm, roll helix 0.166pb/2V, roll rate 294°/s. Chord enters the hinge moment twice — once through the area and once as the moment arm — so half again on the chord is roughly double the torque, not half again. It also grows as the square of the airspeed, so a surface sized at cruise is undersized in a dive. Roll helix rather than roll rate is the headline because helix is a property of the aeroplane and rate is proportional to speed.

Take-off roll 18m, over the obstacle 32m, field needed 80m. Add the payload and the roll goes to 32m and the field to 90m: close to double the take-off run for under a quarter more mass, because the roll goes roughly as the square of the weight. The obstacle costs more than the roll because the climb angle comes from what thrust is left after drag at 1.2 times the stall, and on a model that is not much. The field length is the greater of take-off and landing, since the strip has to serve both.

Loiter 41.1min, payload ceiling 572g, mission needs 15.3Wh. Energy is usually not the binding ceiling and it is not here: stall speed grows as the square root of weight, so at some payload the cruise speed falls inside 1.3 times the stall and the aeroplane stops being flyable before the pack stops paying. The sheet takes the lower of the two ceilings and says which one bound. And none of this includes wind — add ten per cent before believing it on the day.

Nose wheel carries 15.3%, tip-back 25.3°, turnover 43.3°. The answer to the last part is the track, and almost nobody guesses it: the turnover lever depends on the nose wheel distance and the track, not on where the mains sit fore and aft. Widening the track grows the lever while the centre of gravity height does not move, which is the only free improvement available. Note also that a nose wheel below its load band and an aeroplane that will sit on its tail are the same defect said twice.

Still air it needs 18.9Wh and could loiter 36.4min. In the wind it needs 21.2Wh and the loiter falls to 33.3min. The legs do not cancel. The power to hold an airspeed does not change with the wind — the aeroplane cannot tell — but you spend longer in the slow leg than in the fast one, so the round trip always takes longer than still air, by 1/(1−(w/V)²). At 20 against 45 that is 25% more time in the air and 25% more energy out of the pack. The intuition that the headwind home is paid for by the tailwind out is the most expensive one in this list.

It wants 39km/h at release, it drops 0.1m, and the throw costs 48.4J. No — it is what most hand launches of anything heavy are. The aeroplane leaves your hand not flying and the propeller has to get it to flying speed before the ground arrives; held at maximum lift the wing carries most of the weight while it does, so the fall is small. Throw it slower and the fall grows fast: at 20 km/h it becomes 1.5m, which is more height than a launch from shoulder height has. The number that decides a launch is not the margin over the stall — it is how far it falls collecting one.

Best glide is at 30km/h, the speed to fly is 51km/h, and the cycle averages 31.5km/h across the ground. You are not trying to go furthest per metre of height. You are trying to get there soonest, and height thrown away flying fast is height the next thermal gives back at 2 m/s. Expect a stronger climb and it pays to fly faster still: at 4 m/s the speed to fly is 63km/h for 40.6km/h across the ground. Expect nothing and the whole thing collapses back to best glide, which is what the rest of the sheet is about.

Switched off it needs 15.1Wh and loiters 29.2min. With the camera running it needs 18.2Wh and loiters 22.3min — a quarter gone, not a tenth. A continuous draw is charged twice. It takes its watts out of the pack during the climb and the cruise, which is the tenth you expected, and then it raises the burn rate for every minute of loiter that is left, from 44 W to 54 W. The second charge is the larger: of the minutes lost, about a quarter is the transit energy and three quarters is the higher rate. Nothing about the aeroplane changed — it is the same airframe, the same weight and the same drag. A payload is two bills, its mass and its watts, and on an aircraft that exists to carry a sensor the watts are frequently the larger of the two.

Design load factor 5.0g, cap area 13.2mm², tip deflection 45mm. The deflection is reported for a spar sized exactly to strength, and it is usually more than a builder would accept — which is the sheet telling you that stiffness, not strength, is the binding requirement. Check the load factor against what you entered, too: the sheet takes the largest of your manoeuvre limit and two gust cases, and on a model the gust case often wins, because the gust increment goes inversely with wing loading and a model's is a tenth of a light aircraft's.

Rectangular it is 29.9N·m and needs 15.8mm² of cap. Tapered it is 28.1N·m and 11.2mm². The lift is the same; what moved is where it acts. This sheet uses Schrenk's approximation — the average of an elliptical load and one shaped like the planform — so a constant-chord wing carries its lift at 0.462 of the semi-span and a 0.5 taper at 0.434. The moment is that distance times the load, so tapering the wing shortens the lever without shortening the wing. It is the one change that reduces the root moment without reducing the lift, and it is why almost every wing that has to carry something is tapered. The cap area falls further than the moment did, and that is a second effect worth seeing: tapering at constant area makes the root chord deeper, and cap area goes inversely with spar depth. Taper buys you both at once.