Four designs taken through every sheet in the order a study is done. Every number on this page came out of the sheets themselves — the page is generated from a run, not typed up afterwards, so it cannot quote a figure the site does not produce. The prose is mine; the arithmetic is the site's.
They are here for two reasons. One is that a method is easier to learn from a worked example than from sixteen sheets in isolation. The other is that carrying one design all the way through is the only way some faults appear at all: the run that produced this page found that span efficiency was not travelling between the five sheets that use it, and every sheet was individually right.
The four, side by side
| What | Sheet | Trainer | FPV | Survey UAV | Glider |
|---|---|---|---|---|---|
| Wing area wanted | 06 | 37.4 dm² | 32.0 dm² | 52.9 dm² | 23.4 dm² |
| Power to install | 06 | 251 W | 205 W | 365 W | 151 W |
| Weight built up | 05 | 2,107 g | 1,631 g | 3,186 g | 1,356 g |
| Stall speed | 01 | 28.8 km/h | 31.4 km/h | 30.2 km/h | 24.1 km/h |
| Aspect ratio | 01 | 5.54 | 5.11 | 11.30 | 11.05 |
| Static margin | 03 | 12% | 12% | 12% | 12% |
| CD0, built up | 07 | 0.0375 | 0.0300 | 0.0209 | 0.0212 |
| Cruise power | 04 | 49 W | 57 W | 46 W | 13 W |
| Prop efficiency | 08 | 70.2% | 72.0% | 70.9% | 74.5% |
| Usable pack energy | 09 | 29.3 Wh | 26.0 Wh | 118.4 Wh | 19.5 Wh |
| Design load factor | 10 | 5.0 g | 5.0 g | 5.0 g | 5.5 g |
| Lateral balance | 12 | 2.22 | 2.66 | 4.79 | 5.90 |
| Ground it needs | 13 | 68 m | 70 m | 91 m | 87 m |
| Leaves the ground at | 13 | 33 km/h | 40 km/h | 35 km/h | 28 km/h |
| Best glide | 14 | 9.2 | 7.4 | 15.8 | 18.8 |
| Loiter available | 16 | 29.0 min | 19.9 min | 140.2 min | 84.8 min |
A club trainer
High wing, tricycle undercarriage, built-up balsa and film, flown off mown grass. The aeroplane the rest of the site defaults to.
Built-up balsa, film covered, a box fuselage, four standard servos and a fixed tricycle undercarriage, off a 60 m strip of mown grass.
The constraint diagram is the honest place to start, because it is the only sheet that takes requirements and returns an aeroplane rather than the other way round. Asked for a 2.4 kg trainer it wants 37.4 dm² of wing and 251 W out of the pack, and it says the climb requirement is what sets the power — not the cruise, which is the usual case and the usual surprise.
The first disagreement is the useful one, and this study now goes round it. The brief assumed 2,400 g. Building the weight up group by group from the wing area, the build method and the pack, Sheet 05 arrives at 2,107 g — 12 per cent under the assumption. Take that as the new mass and every sheet is re-run against it; the loop closes in two passes, and the table below is the whole of it.
Why it closes so fast is worth understanding. Sheet 05's answer does not depend on the mass you assumed at all — it depends on the wing you are building, the way you are building it, and what you are putting in it. So the second pass confirms the first rather than refining it. That is a property of this weight model rather than a general truth: let the wing move as well and the loop takes eleven passes and lands somewhere else entirely, which is run out in full further down this page.
The second check is the drag, and this one now agrees. Sheet 07 builds parasite drag up component by component — a box fuselage 1,100 mm long, a film-covered wing sitting on top of it with a blunt root join, three wheels and three legs hanging in the airflow — and gets CD0 0.0375 against the 0.040 the design assumed, 6 per cent under. That is inside the tolerance the sheet argues with, and it is the first version of this study where it was: until the trainer was told it had a tricycle undercarriage and a blunt wing root, the build-up came out 24 per cent under its own assumption and the sheet said so. The disagreement was the study's, not the aeroplane's.
Most of it is unremarkable, which for a trainer is the point: it glides 1:9.2, stalls at 28.8 km/h, gets off grass in 16 m and loiters 29.0 minutes. Nothing about it is clever.
Two things are marginal, and both of them only appeared once the aeroplane was described on the ground. This is the only one of the four with an undercarriage and a strip, so it is the only one where Sheets 13 and 15 are answering a real question — and they both answer back. It does not fit the field. It gets off in 16 m and needs 68 m — all of it the landing, which rolls 40 m with no brakes and takes 68 m once the approach over a three-metre hedge is counted. The 60 m strip the study gave it is enough to leave and not enough to come back to. Take-off is not what sizes a club field.
The other is the ailerons. A quarter-chord aileron over the outer half of each wing, throwing 20°, rolls it at 295°/s — a helix angle the sheet calls very quick, which is not what a first aeroplane wants. And Sheet 15 puts 15.3% of the weight on the nose wheel against a sound band of 8 to 15 per cent, so it is a shade nose-heavy on the ground: it will steer well and it will not like a bad landing. Neither is a fault in the design. Both are the study's own numbers meeting a sheet that had something to say about them.
Round the weight loop
| Pass | Mass assumed | Sheet 05 builds | Apart by |
|---|---|---|---|
| 1 | 2,400 g | 2,107 g | -12.2% |
| 2 | 2,107 g | 2,107 g | agreed |
What the sheets objected to
- Sheet 11, controls — How fast it rolls
- Sheet 13, field performance — Verdict
- Sheet 14, glide polar — It stalls before it reaches minimum sink
- Sheet 15, landing gear — What the nose wheel carries
- Sheet 16, mission energy — It stalls before it reaches minimum power
Every figure, sheet by sheet
The whole run for the settled aeroplane, sheet by sheet in the order the study was done: what each sheet was typed, what reached it from the sheet before, and every figure it returned — not only the ones the prose above argues with. Both tables export as CSV.
What each sheet was told
| Sheet | Name | Typed into it | Arrived from the sheet before |
|---|---|---|---|
| 06 | Constraint diagram | All-up weight 2107 g · Maximum lift coefficient 1.215 · Parasite drag coefficient 0.040 · Span efficiency 0.78 | nothing; this is where the study starts |
| 05 | Weight budget | Wing area 43.4 dm² · Cells in series / capacity 3 · Pack capacity in milliamp hours 3300 mAh · Build method Built-up balsa, film covered · Fuselage and gear, against wing structure 0.75 · Servo size class Standard, 45 g · Servos — how many, what size 4 · Payload 0 g · Tail area, as a share of the wing 22 % | 11 carried, new or changed here: Oswald span efficiency 0.78, all-up weight 2107 g, wing area 37.445 dm², aspect ratio 5.54, finite-wing max lift 1.215, parasite drag coefficient 0.04, cruise speed 43 km/h, electrical power at cruise 52.142 W, electrical power in climb 250.821 W, field elevation 0 m, relative humidity 0 % |
| 01 | Wing sizing | All-up weight, ready to fly 2107 g · Wingspan, tip to tip 1550 mm · Root chord 280 mm · Tip chord 280 mm | 13 carried, new or changed here: all-up weight 2107.176 g, wing area 43.4 dm², cells in series 3, pack capacity 3300 mAh |
| 02 | Airfoil choice | nothing; everything it needed had arrived | 19 carried, new or changed here: all-up weight 2107 g, aspect ratio 5.536, span 1550 mm, root chord 280 mm, tip chord 280 mm, mean aerodynamic chord 280 mm, Reynolds at cruise 245320.7, 2D section max lift 1.35 |
| 03 | Balance and tail | Span 1550 mm | 20 carried, new or changed here: mission key sport |
| 07 | Drag build-up | Wing reference area 43.4 dm² · Category you would otherwise have picked Sport, fixed gear — 0.040 · Wing thickness to chord ratio 12 % t/c · Exposed wing, less what the fuselage covers 92 % · Surface finish Film covered, smooth and taut · Wing–fuselage junction Blunt junction, or strut braced · Tail area as a percentage of wing area 22 % of wing · Tail mean chord 150 mm · Tail thickness to chord ratio 9 % t/c · Fuselage length 1100 mm · Fuselage width 100 mm w · Fuselage height 130 mm h · Cross section Square-sided box · Number of wheels 3 · Wheel diameter 60 mm ⌀ · Wheel width 20 mm w · Number of gear legs 3 · Exposed leg length 120 mm · Leg thickness 5 mm thick · Everything else 2 cm² drag area · Surface and excrescence markup 15 % | 22 carried, new or changed here: section pitching moment -0.08, tail arm, quarter chord to quarter chord 760 mm |
| 04 | Power and endurance | All-up weight, ready to fly 2107 g · Wing area 43.4 dm² · Maximum lift coefficient 1.215 · Parasite drag coefficient 0.040 · Span efficiency 0.78 · Cell count 3 · Capacity 3300 mAh | 22 carried, new or changed here: parasite drag coefficient 0.03751 |
| 08 | Propeller | Cells in series 3 | 23 carried, new or changed here: parasite drag coefficient 0.04, cruise speed 40.313 km/h, electrical power at cruise 49.045 W, electrical power in climb 247.724 W, propeller efficiency at cruise 0.65 |
| 09 | Battery | Cells in series 3 · Pack capacity 3300 mAh | 26 carried, new or changed here: propeller efficiency at cruise 0.702, static thrust 10.682 N, pitch speed 83.23 km/h, propeller diameter 254 mm |
| 10 | Structures | All-up weight, ready to fly 2107 g · Wing area 43.4 dm² · Wingspan 1550 mm · Root chord 280 mm · Tip chord 280 mm · Maximum lift coefficient 1.215 | 26 carried, none of it changed |
| 11 | Controls | All-up weight 2107 g · Wing area 43.4 dm² · Wingspan 1550 mm · Root chord 280 mm · Tip chord 280 mm · Maximum lift coefficient 1.215 · Design speed for control loads 90 km/h · Aileron chord as a percentage of wing chord 25 % chord · Maximum aileron deflection 20 ° · Aileron inboard station 50 % semi · Aileron outboard station 95 % semi · Tailplane area as a percentage of wing area 15 % of wing · Elevator chord as a percentage of tail chord 40 % chord · Maximum elevator deflection 25 ° · Fin area as a percentage of wing area 7 % of wing · Rudder chord as a percentage of fin chord 45 % chord · Maximum rudder deflection 30 ° · Control horn length 12 mm · Servo arm length 18 mm · Hinge gap Open gap — pin hinges, visible daylight | 26 carried, none of it changed |
| 12 | Lateral stability | Wing area 43.4 dm² · Wingspan 1550 mm · Root chord 280 mm · Tip chord 280 mm · Fin area as a percentage of wing area 7 % of wing | 26 carried, none of it changed |
| 13 | Field performance | All-up weight 2107 g · Wing area 43.4 dm² · Wingspan 1550 mm · Maximum lift coefficient 1.215 · Parasite drag coefficient 0.040 · Span efficiency 0.78 · How the aeroplane leaves the ground Off wheels, from a strip · Field length available 60 m · Obstacle height 3 m obstacle · Headwind 0 m/s · Braking / ground lift coefficient No brakes · Lift coefficient on the ground 0.35 | 30 carried, new or changed here: fin area, share of the wing 7 %, fin arm, quarter chord to quarter chord 780 mm, fin aspect ratio 1.6, weathercock stability, fin less what the fuselage takes 0.052 |
| 14 | Glide polar | All-up weight 2107 g · Wing area 43.4 dm² · Wingspan 1550 mm · Maximum lift coefficient 1.215 · Parasite drag coefficient 0.040 · Span efficiency 0.78 · Headwind 0 m/s | 30 carried, none of it changed |
| 15 | Landing gear | All-up weight 2107 g · Undercarriage Tricycle — nose wheel · Centre of gravity height above the ground 95 mm high · Horizontal distance from the centre of gravity to the main axle 45 mm · Horizontal distance from the centre of gravity to the nose or tail wheel 250 mm · Track, the distance between the main wheels 260 mm track · Main wheel diameter 60 mm wheel · Thrust line height above the ground 165 mm high · Side area seen from the side 10 dm² · Height of the centre of the side area 130 mm high | 30 carried, none of it changed |
| 16 | Mission energy | Weight without payload 2107 g empty · Wing area 43.4 dm² · Wingspan 1550 mm · Maximum lift coefficient 1.215 · Parasite drag coefficient 0.040 · Span efficiency 0.78 · Cells in series 3 · Pack capacity 3300 mAh · Wind speed 0 km/h · Avionics and payload electrical draw 3 W | 30 carried, none of it changed |
Every figure the sheets returned 89
| Sheet | Name | Figure | Value | What it means here |
|---|---|---|---|---|
| 06 | Constraint diagram | Wing loading | 56.3 g/dm² | stall limited |
| Wing area | 37.4 dm² | for 2,107 g | ||
| Power loading | 119 W/kg | Climb sets this | ||
| Electrical power | 251 W | from the pack | ||
| With 15% margin | 288 W | motor to install | ||
| Wing cube loading | 9.2 | Sport | ||
| 05 | Weight budget | All-up weight | 2,107 g | 74.3 oz |
| Empty, no payload | 2,107 g | 0 g of payload comes out of the all-up above | ||
| Wing loading | 48.6 g/dm² | 15.9 oz/ft² | ||
| Wing cube loading | 7.4 | Sport | ||
| Structure | 56.8% | 1,197 g | ||
| Energy | 12.4% | 36.6 Wh | ||
| 01 | Wing sizing | Wing loading | 48.5 g/dm² | 43.4 dm² of wing carrying 2,107 g |
| Wing cube loading | 7.4 | Sport — the number to compare designs of different sizes on | ||
| Stall speed | 28.8 km/h | clean and level; fly the approach at 37.4 km/h or above | ||
| Aspect ratio | 5.54 | Conventional — taper 1.00, mean aerodynamic chord 280 mm | ||
| Reynolds no. | 245k | Comfortable — at the mean chord and a typical cruise — the number Sheet 02 filters on | ||
| 02 | Airfoil choice | this sheet prints no figures of its own | ||
| 03 | Balance and tail | Neutral point | 39.8 % MAC | 111 mm aft of the mean chord's leading edge |
| Static margin | 12 % | sport — anywhere from 25% to 30% MAC will fly; forward is heavier on the elevator and steadier | ||
| Mean aero chord | 280 mm | 388 mm out from the centreline, where to measure it | ||
| Tail volume V_H | 0.488 | In band — flying designs of this kind land between 0.4 and 0.6 | ||
| 07 | Drag build-up | CD0 | 0.0375 | at 43 km/h |
| Flat plate equivalent | 162.8 cm² | the hole it punches | ||
| Before markup | 0.0326 | 15% added | ||
| Wing Reynolds | 228,965 | workable | ||
| Add-ons | 23.3% | 38.0 cm² of it | ||
| Your guess was | 0.040 | 6% under | ||
| 04 | Power and endurance | Cruise power | 49 W | 26 W of it reaches the air; the rest is the propeller and motor |
| Best glide | 9.2 : 1 | at 37 km/h, where the two drags are equal | ||
| Top level speed | 86 km/h | 3.0× the stall, and where the two power curves cross | ||
| Power loading | 135 W/kg | Trainer — 61 W/lb, sized for 5.0 m/s of climb with 15% in hand | ||
| Endurance | 36 min | at cruise; the pack is 12% of the all-up weight | ||
| 08 | Propeller | Cruise efficiency | 70.2% | 251 g thrust |
| Climb efficiency | 55.6% | 1,003 g thrust | ||
| Static thrust | 1,089 g | at 198 W | ||
| Pitch speed | 83 km/h | 52% slip at cruise | ||
| Tip Mach | 0.36 | clear | ||
| Advance ratio | 0.29 J | P/D 0.60 | ||
| 09 | Battery | Cruise current | 4.4 A | 1.3C |
| Climb current | 22.7 A | 6.9C of 30C | ||
| Sag in climb | 0.17 V | to 10.9 V | ||
| Usable energy | 29.3 Wh | of 36.6 Wh | ||
| Pack mass | 262 g | 140 Wh/kg | ||
| ESC headroom | 76 % | over climb draw | ||
| 10 | Structures | Design load factor | 5.0 g | the limit you set |
| Manoeuvre speed | 64 km/h | 40 mph · below this you stall before you break | ||
| Dive speed | 74 km/h | 46 mph · the right-hand edge of the envelope | ||
| Root bending, ultimate | 27.8 N·m | 246 lb·in at 5.0g × 1.50 safety factor | ||
| Cap area needed | 13.1 mm² | 0.020 in² · Spruce, each of two caps | ||
| Tip deflection | 45 mm | 1.77 in · 5.8% of semi-span | ||
| 11 | Controls | Aileron servo | 2.40 kg·cm | 33.3 oz·in · mini, 20 g |
| Elevator servo | 2.50 kg·cm | 34.7 oz·in · mini, 20 g | ||
| Rudder servo | 1.79 kg·cm | 24.8 oz·in · micro, 9 g | ||
| Roll rate | 295 °/s | at 90 km/h | ||
| Roll helix | 0.160 pb/2V | very quick | ||
| Time to 45° bank | 0.15 s | at the steady rate — the real one is longer | ||
| Elevator authority | -0.92 CLt | the download it makes at full throw · tail volume of 0.407 on a 760 mm arm | ||
| Crosswind it can hold | 15 km/h | 4.1 m/s · full rudder holds 23° of sideslip on a 37 km/h approach | ||
| Balance point can go to | 1 % MAC | at or ahead of the leading edge — the elevator is not your forward limit | ||
| 12 | Lateral stability | Weathercock | 0.0519 Cnβ | sound |
| Dihedral effect | -0.1155 Clβ | sound | ||
| Balance | 2.22 −Clβ/Cnβ | balanced | ||
| Fin volume | 0.0352 Vv | Sheet 03 checks this against its own band | ||
| Fuselage takes | 26 % | of what the fin produces | ||
| Effective dihedral | 6.0 ° | geometry, wing position and sweep together | ||
| 13 | Field performance | Take-off roll | 16 m | 54 ft |
| Over the obstacle | 32 m | clearing 3.0 m at 11.1° of climb | ||
| Lift-off speed | 33 km/h | stall 29 · approach 37 | ||
| Landing roll | 40 m | no brakes | ||
| Landing over it | 68 m | approach at 6.2° | ||
| Ground needed | 68 m | longer than your 60 m | ||
| 14 | Glide polar | Best glide ratio | 1:9.2 | at CL 0.74, where the two drags are equal |
| Speed for it | 37 km/h | sinking 1.12 m/s | ||
| Minimum sink | 0.98 m/s | at the stall, not at the ideal speed | ||
| Down from 100 m | 921 m | in still air, at best glide | ||
| Longest it can stay up | 102 s | gliding down from 100 m at minimum sink | ||
| Circling at 30° | 1.05 m/s | 13 m radius · 10 s a circle | ||
| 15 | Landing gear | Nose wheel carries | 15.3 % | 3.15 N · sound is 8–15% |
| Each main carries | 8.76 N | 893 g · 42.4% of the weight | ||
| Tip-back angle | 25.3 ° | wants more than 15° | ||
| Turnover angle | 43.3 ° | under the 63° limit, by 19.7° | ||
| Propeller clearance | 38 mm | 15% of diameter · strikes at 16° of roll | ||
| Blows over at | 66 km/h | crosswind, parked · 18.4 m/s | ||
| 16 | Mission energy | Mission needs | 15.1 Wh | 41% of the pack nameplate |
| Pack gives you | 29.3 Wh | 36.6 Wh nameplate · 100% at this load · 80% discharged | ||
| Margin | 48 % | of the energy you allowed yourself | ||
| Loiter you can do | 29.0 min | you asked for 10 | ||
| Payload ceiling | 337 g | the cruise reaches 1.3 × stall before the pack runs out | ||
| Time in the air | 19 min | 5.3 km flown · cruise at 1.34 × stall | ||
An FPV platform
Pod and boom, camera in the nose, four cells, flown fast. Draggier than it looks and heavier than it needs to be, which is the character of the type.
Foam board, a pod rather than a box, mini servos, 120 g of camera and video transmitter, thrown by hand at 28 km/h and belly landed.
This is the design that came back cleanest, and the reason is instructive: almost nothing about it is ambitious. A short, thick wing at aspect ratio 5.11, a lot of assumed drag, a modest pack. Sheets that flag marginal designs have little to say about a design that is not trying anything — until they are told what shape it is, and then three of them do.
It pays for that in the one number FPV pilots care least about and should care more about: it glides 1:7.4, the worst of the four by a wide margin. With the motor off, from 100 m, that is about 740 m of ground covered. A trainer manages 920 m and the survey aircraft nearly 1580 m. Drag you accepted for a camera pod is drag you fly home on when the motor stops.
It is also the only one of the four that was guessed nearly right: the brief assumed 1,600 g and Sheet 05 builds 1,631 g, 2 per cent over — near enough that the loop closed on the pass straight after. Foam board is a forgiving thing to estimate.
It is thrown, and the sheet has two things to say about that which sound like opposites. The first is that the throw is short: it wants 40 km/h at release, 1.2 times the stall, and a hand gives it 28. The second is that the aeroplane does not much care — under the stall the propeller takes it from there, and it falls 0.2 m in the 0.5 s that takes. Both are true and the second is the one you feel. The 1.2 is a margin for a gust and a fumble; two-tenths of a metre is what your hand actually has to be above the grass. A sheet that printed only the first would have told you not to fly an aeroplane that flies.
Two of the three are about the pod. Sheet 12 finds the fuselage giving back 46% of what the fin produces — a body 110 mm wide and 120 mm deep, most of it ahead of the centre of gravity, is a badly shaped wing with its lift pointing sideways, and past about 45 per cent the sheet stops calling that a modest share. A camera pod is not free in yaw either, and the fix is more fin rather than more arm. Sheet 11 is the lighter complaint: quarter-chord ailerons at 22° on a 1.2 m wing roll it at 606°/s, which is a great deal of roll rate for a camera platform.
The drag is where the brief and the build-up part company. Described to Sheet 07 — a foam-board pod 900 mm long, taped seams, no undercarriage because it is hand launched, and 6 cm² of camera, antenna and horns — it builds up CD0 0.0300 against the 0.058 its category assumes, 48 per cent under. That is the largest disagreement on this page and it is worth sitting with rather than splitting the difference. The category figure is what the type is known for; the build-up is what this description of it comes to. Between them sits everything an FPV model carries that nobody lists: a camera bump rather than a camera in the nose, a GoPro on the top, exposed servo arms, wire looms, a battery hanging under. The sheet is not saying the assumption is wrong. It is saying the aeroplane you described is not the aeroplane the assumption is about.
Cruise takes 57 W and the pack gives 26.0 Wh, so the mission sheet allows 19.9 minutes on station. That is a real FPV sortie, and every figure in it rests on the drag rather than the battery — which is why the paragraph above matters more than it looks.
Round the weight loop
| Pass | Mass assumed | Sheet 05 builds | Apart by |
|---|---|---|---|
| 1 | 1,600 g | 1,631 g | +1.9% |
| 2 | 1,631 g | 1,631 g | agreed |
What the sheets objected to
- Sheet 07, drag build-up — It reads low
- Sheet 11, controls — How fast it rolls
- Sheet 12, lateral stability — The fuselage is the opponent
- Sheet 13, field performance — What the launch has to do
- Sheet 13, field performance — Verdict
- Sheet 14, glide polar — It stalls before it reaches minimum sink
- Sheet 16, mission energy — It stalls before it reaches minimum power
- Set aside: Sheet 15. Sheet 15 asks about an undercarriage, and this aeroplane has none. What that sheet returns for it is in the trail below, and it is the sheet answering a question this aeroplane does not ask.
Every figure, sheet by sheet
The whole run for the settled aeroplane, sheet by sheet in the order the study was done: what each sheet was typed, what reached it from the sheet before, and every figure it returned — not only the ones the prose above argues with. Both tables export as CSV.
What each sheet was told
| Sheet | Name | Typed into it | Arrived from the sheet before |
|---|---|---|---|
| 06 | Constraint diagram | All-up weight 1631 g · Maximum lift coefficient 1.10 · Parasite drag coefficient 0.055 · Span efficiency 0.75 · Launch Hand launch or bungee | nothing; this is where the study starts |
| 05 | Weight budget | Wing area 28 dm² · Cells in series / capacity 4 · Pack capacity in milliamp hours 2200 mAh · Build method Foam board or Depron, flat plate · Fuselage and gear, against wing structure 0.55 · Servo size class Mini, 20 g · Servos — how many, what size 4 · Payload 120 g · Tail area, as a share of the wing 20 % | 11 carried, new or changed here: Oswald span efficiency 0.75, all-up weight 1631 g, wing area 32.016 dm², aspect ratio 5.54, finite-wing max lift 1.1, parasite drag coefficient 0.055, cruise speed 43 km/h, electrical power at cruise 51.436 W, electrical power in climb 205.231 W, field elevation 0 m, relative humidity 0 % |
| 01 | Wing sizing | All-up weight, ready to fly 1631 g · Wingspan, tip to tip 1200 mm · Root chord 250 mm · Tip chord 220 mm | 13 carried, new or changed here: all-up weight 1630.929 g, wing area 28 dm², cells in series 4, pack capacity 2200 mAh |
| 02 | Airfoil choice | nothing; everything it needed had arrived | 19 carried, new or changed here: all-up weight 1631 g, wing area 28.2 dm², aspect ratio 5.106, finite-wing max lift 1.215, span 1200 mm, root chord 250 mm, tip chord 220 mm, mean aerodynamic chord 235.319 mm, Reynolds at cruise 225034.164, 2D section max lift 1.35 |
| 03 | Balance and tail | Span 1200 mm | 20 carried, new or changed here: mission key sport |
| 07 | Drag build-up | Wing reference area 28 dm² · Category you would otherwise have picked Foamboard, exposed hardware — 0.058 · Wing thickness to chord ratio 10 % t/c · Exposed wing, less what the fuselage covers 88 % · Surface finish Foamboard, open structure, tape seams · Wing–fuselage junction Clean junction, no fillet · Tail area as a percentage of wing area 20 % of wing · Tail mean chord 130 mm · Tail thickness to chord ratio 8 % t/c · Fuselage length 900 mm · Fuselage width 110 mm w · Fuselage height 120 mm h · Cross section Streamlined pod · Number of wheels 0 · Wheel diameter 60 mm ⌀ · Wheel width 20 mm w · Number of gear legs 0 · Exposed leg length 120 mm · Leg thickness 5 mm thick · Everything else 6 cm² drag area · Surface and excrescence markup 20 % | 22 carried, new or changed here: section pitching moment -0.08, tail arm, quarter chord to quarter chord 760 mm |
| 04 | Power and endurance | All-up weight, ready to fly 1631 g · Wing area 28 dm² · Maximum lift coefficient 1.10 · Parasite drag coefficient 0.055 · Span efficiency 0.75 · Cell count 4 · Capacity 2200 mAh | 22 carried, new or changed here: wing area 28 dm², parasite drag coefficient 0.03003 |
| 08 | Propeller | Cells in series 4 | 23 carried, new or changed here: finite-wing max lift 1.1, parasite drag coefficient 0.055, cruise speed 46.408 km/h, electrical power at cruise 57.356 W, electrical power in climb 211.151 W, propeller efficiency at cruise 0.65 |
| 09 | Battery | Cells in series 4 · Pack capacity 2200 mAh | 26 carried, new or changed here: propeller efficiency at cruise 0.72, static thrust 9.603 N, pitch speed 110.97 km/h, propeller diameter 254 mm |
| 10 | Structures | All-up weight, ready to fly 1631 g · Wing area 28 dm² · Wingspan 1200 mm · Root chord 250 mm · Tip chord 220 mm · Maximum lift coefficient 1.10 | 26 carried, none of it changed |
| 11 | Controls | All-up weight 1631 g · Wing area 28 dm² · Wingspan 1200 mm · Root chord 250 mm · Tip chord 220 mm · Maximum lift coefficient 1.10 · Design speed for control loads 120 km/h · Aileron chord as a percentage of wing chord 25 % chord · Maximum aileron deflection 22 ° · Aileron inboard station 45 % semi · Aileron outboard station 95 % semi · Tailplane area as a percentage of wing area 14 % of wing · Elevator chord as a percentage of tail chord 40 % chord · Maximum elevator deflection 25 ° · Fin area as a percentage of wing area 6 % of wing · Rudder chord as a percentage of fin chord 45 % chord · Maximum rudder deflection 30 ° · Control horn length 10 mm · Servo arm length 15 mm · Hinge gap Sealed — tape, or a hinge with no through-gap | 26 carried, none of it changed |
| 12 | Lateral stability | Wing area 28 dm² · Wingspan 1200 mm · Root chord 250 mm · Tip chord 220 mm · Fin area as a percentage of wing area 6 % of wing | 26 carried, none of it changed |
| 13 | Field performance | All-up weight 1631 g · Wing area 28 dm² · Wingspan 1200 mm · Maximum lift coefficient 1.10 · Parasite drag coefficient 0.055 · Span efficiency 0.75 · How the aeroplane leaves the ground Hand launched · Speed at release 28 km/h · Field length available 60 m · Obstacle height 3 m obstacle · Headwind 0 m/s · Braking / ground lift coefficient No brakes · Lift coefficient on the ground 0.35 | 30 carried, new or changed here: fin area, share of the wing 6 %, fin arm, quarter chord to quarter chord 780 mm, fin aspect ratio 1.6, weathercock stability, fin less what the fuselage takes 0.041 |
| 14 | Glide polar | All-up weight 1631 g · Wing area 28 dm² · Wingspan 1200 mm · Maximum lift coefficient 1.10 · Parasite drag coefficient 0.055 · Span efficiency 0.75 · Headwind 0 m/s | 30 carried, none of it changed |
| 15 | Landing gear | All-up weight 1631 g | 30 carried, none of it changed |
| 16 | Mission energy | Weight without payload 1631 g empty · Wing area 28 dm² · Wingspan 1200 mm · Maximum lift coefficient 1.10 · Parasite drag coefficient 0.055 · Span efficiency 0.75 · Cells in series 4 · Pack capacity 2200 mAh · Wind speed 0 km/h · Avionics and payload electrical draw 8 W | 30 carried, none of it changed |
Every figure the sheets returned 89
| Sheet | Name | Figure | Value | What it means here |
|---|---|---|---|---|
| 06 | Constraint diagram | Wing loading | 50.9 g/dm² | stall limited |
| Wing area | 32.0 dm² | for 1,631 g | ||
| Power loading | 126 W/kg | Climb sets this | ||
| Electrical power | 205 W | from the pack | ||
| With 15% margin | 236 W | motor to install | ||
| Wing cube loading | 9.0 | Sport | ||
| 05 | Weight budget | All-up weight | 1,631 g | 57.5 oz |
| Empty, no payload | 1,511 g | 120 g of payload comes out of the all-up above | ||
| Wing loading | 58.2 g/dm² | 19.1 oz/ft² | ||
| Wing cube loading | 11.0 | Sport | ||
| Structure | 48.1% | 784 g | ||
| Energy | 14.3% | 32.6 Wh | ||
| 01 | Wing sizing | Wing loading | 57.8 g/dm² | 28.2 dm² of wing carrying 1,631 g |
| Wing cube loading | 10.9 | Sport — the number to compare designs of different sizes on | ||
| Stall speed | 31.4 km/h | clean and level; fly the approach at 40.9 km/h or above | ||
| Aspect ratio | 5.11 | Conventional — taper 0.88, mean aerodynamic chord 235 mm | ||
| Reynolds no. | 225k | Comfortable — at the mean chord and a typical cruise — the number Sheet 02 filters on | ||
| 02 | Airfoil choice | this sheet prints no figures of its own | ||
| 03 | Balance and tail | Neutral point | 53.7 % MAC | 126 mm aft of the mean chord's leading edge |
| Static margin | 12 % | sport — anywhere from 39% to 44% MAC will fly; forward is heavier on the elevator and steadier | ||
| Mean aero chord | 235 mm | 294 mm out from the centreline, where to measure it | ||
| Tail volume V_H | 0.893 | Large — flying designs of this kind land between 0.4 and 0.6 | ||
| 07 | Drag build-up | CD0 | 0.0300 | at 43 km/h |
| Flat plate equivalent | 84.1 cm² | the hole it punches | ||
| Before markup | 0.0250 | 20% added | ||
| Wing Reynolds | 192,428 | workable | ||
| Add-ons | 7.1% | 6.0 cm² of it | ||
| Your guess was | 0.058 | 48% under | ||
| 04 | Power and endurance | Cruise power | 57 W | 30 W of it reaches the air; the rest is the propeller and motor |
| Best glide | 7.4 : 1 | at 39 km/h, where the two drags are equal | ||
| Top level speed | 84 km/h | 2.5× the stall, and where the two power curves cross | ||
| Power loading | 149 W/kg | Trainer — 68 W/lb, sized for 5.0 m/s of climb with 15% in hand | ||
| Endurance | 27 min | at cruise; the pack is 14% of the all-up weight | ||
| 08 | Propeller | Cruise efficiency | 72.0% | 261 g thrust |
| Climb efficiency | 61.5% | 822 g thrust | ||
| Static thrust | 979 g | at 169 W | ||
| Pitch speed | 111 km/h | 58% slip at cruise | ||
| Tip Mach | 0.48 | clear | ||
| Advance ratio | 0.25 J | P/D 0.60 | ||
| 09 | Battery | Cruise current | 3.9 A | 1.8C |
| Climb current | 14.4 A | 6.5C of 30C | ||
| Sag in climb | 0.14 V | to 14.7 V | ||
| Usable energy | 26.0 Wh | of 32.6 Wh | ||
| Pack mass | 233 g | 140 Wh/kg | ||
| ESC headroom | 178 % | over climb draw | ||
| 10 | Structures | Design load factor | 5.0 g | the limit you set |
| Manoeuvre speed | 74 km/h | 46 mph · below this you stall before you break | ||
| Dive speed | 85 km/h | 53 mph · the right-hand edge of the envelope | ||
| Root bending, ultimate | 16.4 N·m | 146 lb·in at 5.0g × 1.50 safety factor | ||
| Cap area needed | 8.7 mm² | 0.013 in² · Spruce, each of two caps | ||
| Tip deflection | 30 mm | 1.18 in · 5.0% of semi-span | ||
| 11 | Controls | Aileron servo | 2.16 kg·cm | 30.0 oz·in · mini, 20 g |
| Elevator servo | 1.66 kg·cm | 23.0 oz·in · micro, 9 g | ||
| Rudder servo | 1.05 kg·cm | 14.5 oz·in · micro, 9 g | ||
| Roll rate | 606 °/s | at 120 km/h | ||
| Roll helix | 0.190 pb/2V | very quick | ||
| Time to 45° bank | 0.07 s | at the steady rate — the real one is longer | ||
| Elevator authority | -0.92 CLt | the download it makes at full throw · tail volume of 0.452 on a 760 mm arm | ||
| Crosswind it can hold | 19 km/h | 5.2 m/s · full rudder holds 26° of sideslip on a 43 km/h approach | ||
| Balance point can go to | -5 % MAC | at or ahead of the leading edge — the elevator is not your forward limit | ||
| 12 | Lateral stability | Weathercock | 0.0414 Cnβ | sound |
| Dihedral effect | -0.1101 Clβ | sound | ||
| Balance | 2.66 −Clβ/Cnβ | balanced | ||
| Fin volume | 0.0390 Vv | Sheet 03 checks this against its own band | ||
| Fuselage takes | 46 % | of what the fin produces | ||
| Effective dihedral | 6.0 ° | geometry, wing position and sweep together | ||
| 13 | Field performance | Release speed needed | 40 km/h | 1.2 × the 33 km/h stall · you throw at 28 |
| It drops first | 0.2 m | thrown under the stall, so it falls 0.2 m in the 0.5 s it takes to reach it | ||
| Energy in the launch | 49.3 J | what your arm has to put in, at 28 km/h | ||
| Landing roll | 49 m | no brakes | ||
| Landing over it | 70 m | approach at 7.9° | ||
| Ground needed | 70 m | to land, which is all it needs · you have 60 m | ||
| 14 | Glide polar | Best glide ratio | 1:7.4 | at CL 0.82, where the two drags are equal |
| Speed for it | 38 km/h | sinking 1.44 m/s | ||
| Minimum sink | 1.30 m/s | at the stall, not at the ideal speed | ||
| Down from 100 m | 742 m | in still air, at best glide | ||
| Longest it can stay up | 77 s | gliding down from 100 m at minimum sink | ||
| Circling at 30° | 1.39 m/s | 17 m radius · 11 s a circle | ||
| 15 | Landing gear | Nose wheel carries | 15.3 % | 2.44 N · sound is 8–15% |
| Each main carries | 6.78 N | 691 g · 42.4% of the weight | ||
| Tip-back angle | 25.3 ° | wants more than 15° | ||
| Turnover angle | 43.3 ° | under the 63° limit, by 19.7° | ||
| Propeller clearance | 38 mm | 15% of diameter · strikes at 16° of roll | ||
| Blows over at | 58 km/h | crosswind, parked · 16.2 m/s | ||
| 16 | Mission energy | Mission needs | 17.0 Wh | 52% of the pack nameplate |
| Pack gives you | 26.0 Wh | 32.6 Wh nameplate · 100% at this load · 80% discharged | ||
| Margin | 35 % | of the energy you allowed yourself | ||
| Loiter you can do | 19.9 min | you asked for 10 | ||
| Payload ceiling | 261 g | the cruise reaches 1.3 × stall before the pack runs out | ||
| Time in the air | 18 min | 5.4 km flown · cruise at 1.32 × stall | ||
A long-endurance survey UAV
Four and a half kilograms, high aspect ratio, a big four-cell pack and a camera, flown for as long as it will stay up.
Moulded composite, a slim oval fuselage polished all over, mini servos, 300 g of survey camera, no undercarriage, and off a catapult at 45 km/h because 3.2 kg is past what an arm does.
The brief is endurance and the aeroplane delivers it: 140.2 minutes of loiter, which is the two-hour sortie the brief asked for, on 118.4 Wh of pack. It glides 1:15.8 and cruises on 46 W.
It is also the design the sheets argue with most, and every objection is about the same thing. Stretching to aspect ratio 11.30 on a 4.5 kg airframe moves several numbers at once, and four sheets notice independently: Sheet 01 questions the planform, Sheet 03 says the fin is too small, Sheet 10 raises stiffness as a question separate from strength, and Sheet 12 says twice over that it will not track straight — its lateral balance comes out at 4.79, past the 3.0 where a long wing and a small fin start wallowing in Dutch roll.
None of those is a calculation error and none is fatal. They are the price of the span, and they all have the same fix: more fin. The sheet that says the fin is too small and the sheet that says it will not track straight are describing one problem from two directions, which is what a set of sheets that check each other is supposed to do.
The catapult is the one thing on this aeroplane nothing objects to. At 3.2 kg it is past what an arm does, so it leaves a line at 45 km/h against the 35 the sheet asks for — and with 5.6 N of thrust over drag at that speed it climbs away at 10.4°. The launch costs 248.9 J, which is a bungee pulling about 25 N through ten metres: a stretch, not a machine. Of the four designs this is the only one that reaches the air with no sheet complaining about how.
The largest correction of the four is here. The brief assumed 4,500 g; built up from a moulded composite airframe with a slim fuselage, Sheet 05 says 3,186 g — 29 per cent under. On an endurance design that correction matters more than anywhere else, because loiter power goes as the three-halves power of weight: taking 29 per cent off the mass takes about two-fifths off the power it takes to stay up. Every figure on this page is from the settled aeroplane, not the assumed one.
Round the weight loop
| Pass | Mass assumed | Sheet 05 builds | Apart by |
|---|---|---|---|
| 1 | 4,500 g | 3,186 g | -29.2% |
| 2 | 3,186 g | 3,186 g | agreed |
What the sheets objected to
- Sheet 01, wing sizing — Planform
- Sheet 03, balance and tail — Fin too small
- Sheet 07, drag build-up — It reads low
- Sheet 10, structures — Stiffness is a separate question
- Sheet 11, controls — The crosswind the rudder can hold
- Sheet 12, lateral stability — Does it track straight
- Sheet 12, lateral stability — The balance is the point
- Sheet 14, glide polar — It stalls before it reaches minimum sink
- Sheet 16, mission energy — It stalls before it reaches minimum power
- Set aside: Sheet 15. Sheet 15 asks about an undercarriage, and this aeroplane has none. What that sheet returns for it is in the trail below, and it is the sheet answering a question this aeroplane does not ask.
Every figure, sheet by sheet
The whole run for the settled aeroplane, sheet by sheet in the order the study was done: what each sheet was typed, what reached it from the sheet before, and every figure it returned — not only the ones the prose above argues with. Both tables export as CSV.
What each sheet was told
| Sheet | Name | Typed into it | Arrived from the sheet before |
|---|---|---|---|
| 06 | Constraint diagram | All-up weight 3186 g · Maximum lift coefficient 1.30 · Parasite drag coefficient 0.030 · Span efficiency 0.85 | nothing; this is where the study starts |
| 05 | Weight budget | Wing area 60 dm² · Cells in series / capacity 4 · Pack capacity in milliamp hours 10000 mAh · Build method Moulded composite — carbon or glass sandwich · Fuselage and gear, against wing structure 0.5 · Servo size class Mini, 20 g · Servos — how many, what size 4 · Payload 300 g · Tail area, as a share of the wing 18 % | 11 carried, new or changed here: Oswald span efficiency 0.85, all-up weight 3186 g, wing area 52.918 dm², aspect ratio 5.54, finite-wing max lift 1.3, parasite drag coefficient 0.03, cruise speed 43 km/h, electrical power at cruise 64.643 W, electrical power in climb 365.066 W, field elevation 0 m, relative humidity 0 % |
| 01 | Wing sizing | All-up weight, ready to fly 3186 g · Wingspan, tip to tip 2600 mm · Root chord 250 mm · Tip chord 210 mm | 13 carried, new or changed here: all-up weight 3186.117 g, wing area 60 dm², cells in series 4, pack capacity 10000 mAh |
| 02 | Airfoil choice | nothing; everything it needed had arrived | 19 carried, new or changed here: all-up weight 3186 g, wing area 59.8 dm², aspect ratio 11.304, finite-wing max lift 1.215, span 2600 mm, root chord 250 mm, tip chord 210 mm, mean aerodynamic chord 230.58 mm, Reynolds at cruise 211632.393, 2D section max lift 1.35 |
| 03 | Balance and tail | Span 2600 mm | 20 carried, new or changed here: mission key sport |
| 07 | Drag build-up | Wing reference area 60 dm² · Category you would otherwise have picked Sport, no exposed gear — 0.032 · Wing thickness to chord ratio 12 % t/c · Exposed wing, less what the fuselage covers 94 % · Surface finish Moulded composite, polished · Wing–fuselage junction Filleted, mid or shoulder wing · Tail area as a percentage of wing area 18 % of wing · Tail mean chord 170 mm · Tail thickness to chord ratio 9 % t/c · Fuselage length 1500 mm · Fuselage width 120 mm w · Fuselage height 140 mm h · Cross section Oval or circular · Number of wheels 0 · Wheel diameter 60 mm ⌀ · Wheel width 20 mm w · Number of gear legs 0 · Exposed leg length 120 mm · Leg thickness 5 mm thick · Everything else 4 cm² drag area · Surface and excrescence markup 10 % | 22 carried, new or changed here: section pitching moment -0.08, tail arm, quarter chord to quarter chord 760 mm |
| 04 | Power and endurance | All-up weight, ready to fly 3186 g · Wing area 60 dm² · Maximum lift coefficient 1.30 · Parasite drag coefficient 0.030 · Span efficiency 0.85 · Cell count 4 · Capacity 10000 mAh | 22 carried, new or changed here: wing area 60 dm², parasite drag coefficient 0.02095 |
| 08 | Propeller | Cells in series 4 | 23 carried, new or changed here: finite-wing max lift 1.3, parasite drag coefficient 0.03, cruise speed 40.758 km/h, electrical power at cruise 45.716 W, electrical power in climb 346.139 W, propeller efficiency at cruise 0.65 |
| 09 | Battery | Cells in series 4 · Pack capacity 10000 mAh | 26 carried, new or changed here: propeller efficiency at cruise 0.709, static thrust 13.351 N, pitch speed 110.97 km/h, propeller diameter 254 mm |
| 10 | Structures | All-up weight, ready to fly 3186 g · Wing area 60 dm² · Wingspan 2600 mm · Root chord 250 mm · Tip chord 210 mm · Maximum lift coefficient 1.30 | 26 carried, none of it changed |
| 11 | Controls | All-up weight 3186 g · Wing area 60 dm² · Wingspan 2600 mm · Root chord 250 mm · Tip chord 210 mm · Maximum lift coefficient 1.30 · Design speed for control loads 95 km/h · Aileron chord as a percentage of wing chord 22 % chord · Maximum aileron deflection 18 ° · Aileron inboard station 55 % semi · Aileron outboard station 92 % semi · Tailplane area as a percentage of wing area 12 % of wing · Elevator chord as a percentage of tail chord 40 % chord · Maximum elevator deflection 22 ° · Fin area as a percentage of wing area 6 % of wing · Rudder chord as a percentage of fin chord 45 % chord · Maximum rudder deflection 28 ° · Control horn length 12 mm · Servo arm length 18 mm · Hinge gap Sealed — tape, or a hinge with no through-gap | 26 carried, none of it changed |
| 12 | Lateral stability | Wing area 60 dm² · Wingspan 2600 mm · Root chord 250 mm · Tip chord 210 mm · Fin area as a percentage of wing area 6 % of wing | 26 carried, none of it changed |
| 13 | Field performance | All-up weight 3186 g · Wing area 60 dm² · Wingspan 2600 mm · Maximum lift coefficient 1.30 · Parasite drag coefficient 0.030 · Span efficiency 0.85 · How the aeroplane leaves the ground Bungee or catapult · Speed at release 45 km/h · Field length available 100 m · Obstacle height 3 m obstacle · Headwind 0 m/s · Braking / ground lift coefficient No brakes · Lift coefficient on the ground 0.35 | 30 carried, new or changed here: fin area, share of the wing 6 %, fin arm, quarter chord to quarter chord 780 mm, fin aspect ratio 1.6, weathercock stability, fin less what the fuselage takes 0.028 |
| 14 | Glide polar | All-up weight 3186 g · Wing area 60 dm² · Wingspan 2600 mm · Maximum lift coefficient 1.30 · Parasite drag coefficient 0.030 · Span efficiency 0.85 · Headwind 0 m/s | 30 carried, none of it changed |
| 15 | Landing gear | All-up weight 3186 g | 30 carried, none of it changed |
| 16 | Mission energy | Weight without payload 3186 g empty · Wing area 60 dm² · Wingspan 2600 mm · Maximum lift coefficient 1.30 · Parasite drag coefficient 0.030 · Span efficiency 0.85 · Cells in series 4 · Pack capacity 10000 mAh · Wind speed 0 km/h · Avionics and payload electrical draw 12 W | 30 carried, none of it changed |
Every figure the sheets returned 89
| Sheet | Name | Figure | Value | What it means here |
|---|---|---|---|---|
| 06 | Constraint diagram | Wing loading | 60.2 g/dm² | stall limited |
| Wing area | 52.9 dm² | for 3,186 g | ||
| Power loading | 115 W/kg | Climb sets this | ||
| Electrical power | 365 W | from the pack | ||
| With 15% margin | 420 W | motor to install | ||
| Wing cube loading | 8.3 | Sport | ||
| 05 | Weight budget | All-up weight | 3,186 g | 112.4 oz |
| Empty, no payload | 2,886 g | 300 g of payload comes out of the all-up above | ||
| Wing loading | 53.1 g/dm² | 17.4 oz/ft² | ||
| Wing cube loading | 6.8 | Trainer | ||
| Structure | 38.0% | 1,210 g | ||
| Energy | 33.2% | 148.0 Wh | ||
| 01 | Wing sizing | Wing loading | 53.3 g/dm² | 59.8 dm² of wing carrying 3,186 g |
| Wing cube loading | 6.9 | Trainer — the number to compare designs of different sizes on | ||
| Stall speed | 30.2 km/h | clean and level; fly the approach at 39.2 km/h or above | ||
| Aspect ratio | 11.30 | Sailplane — taper 0.84, mean aerodynamic chord 231 mm | ||
| Reynolds no. | 212k | Comfortable — at the mean chord and a typical cruise — the number Sheet 02 filters on | ||
| 02 | Airfoil choice | this sheet prints no figures of its own | ||
| 03 | Balance and tail | Neutral point | 40.7 % MAC | 94 mm aft of the mean chord's leading edge |
| Static margin | 12 % | sport — anywhere from 26% to 31% MAC will fly; forward is heavier on the elevator and steadier | ||
| Mean aero chord | 231 mm | 631 mm out from the centreline, where to measure it | ||
| Tail volume V_H | 0.430 | In band — flying designs of this kind land between 0.4 and 0.6 | ||
| 07 | Drag build-up | CD0 | 0.0209 | at 43 km/h |
| Flat plate equivalent | 125.7 cm² | the hole it punches | ||
| Before markup | 0.0190 | 10% added | ||
| Wing Reynolds | 188,553 | workable | ||
| Add-ons | 3.2% | 4.0 cm² of it | ||
| Your guess was | 0.032 | 35% under | ||
| 04 | Power and endurance | Cruise power | 46 W | 24 W of it reaches the air; the rest is the propeller and motor |
| Best glide | 15.9 : 1 | at 34 km/h, where the two drags are equal | ||
| Top level speed | 95 km/h | 3.3× the stall, and where the two power curves cross | ||
| Power loading | 125 W/kg | Trainer — 57 W/lb, sized for 5.0 m/s of climb with 15% in hand | ||
| Endurance | 155 min | at cruise; the pack is 33% of the all-up weight | ||
| 08 | Propeller | Cruise efficiency | 70.9% | 234 g thrust |
| Climb efficiency | 52.4% | 1,306 g thrust | ||
| Static thrust | 1,361 g | at 277 W | ||
| Pitch speed | 111 km/h | 63% slip at cruise | ||
| Tip Mach | 0.48 | clear | ||
| Advance ratio | 0.22 J | P/D 0.60 | ||
| 09 | Battery | Cruise current | 3.1 A | 0.3C |
| Climb current | 23.8 A | 2.4C of 30C | ||
| Sag in climb | 0.24 V | to 14.6 V | ||
| Usable energy | 118.4 Wh | of 148.0 Wh | ||
| Pack mass | 1,057 g | 140 Wh/kg | ||
| ESC headroom | 68 % | over climb draw | ||
| 10 | Structures | Design load factor | 5.0 g | the limit you set |
| Manoeuvre speed | 65 km/h | 40 mph · below this you stall before you break | ||
| Dive speed | 75 km/h | 47 mph · the right-hand edge of the envelope | ||
| Root bending, ultimate | 69.3 N·m | 613 lb·in at 5.0g × 1.50 safety factor | ||
| Cap area needed | 36.7 mm² | 0.057 in² · Spruce, each of two caps | ||
| Tip deflection | 141 mm | 5.54 in · 10.8% of semi-span | ||
| 11 | Controls | Aileron servo | 1.28 kg·cm | 17.7 oz·in · micro, 9 g |
| Elevator servo | 2.28 kg·cm | 31.6 oz·in · mini, 20 g | ||
| Rudder servo | 1.92 kg·cm | 26.6 oz·in · mini, 20 g | ||
| Roll rate | 129 °/s | at 95 km/h | ||
| Roll helix | 0.111 pb/2V | lively | ||
| Time to 45° bank | 0.35 s | at the steady rate — the real one is longer | ||
| Elevator authority | -0.81 CLt | the download it makes at full throw · tail volume of 0.396 on a 760 mm arm | ||
| Crosswind it can hold | 7 km/h | 2.0 m/s · full rudder holds 11° of sideslip on a 38 km/h approach | ||
| Balance point can go to | 7 % MAC | forward limit, elevator on the stop at the stall · Sheet 03 sets the aft one | ||
| 12 | Lateral stability | Weathercock | 0.0280 Cnβ | weak |
| Dihedral effect | -0.1339 Clβ | sound | ||
| Balance | 4.79 −Clβ/Cnβ | roll-dominant | ||
| Fin volume | 0.0180 Vv | Sheet 03 checks this against its own band | ||
| Fuselage takes | 22 % | of what the fin produces | ||
| Effective dihedral | 6.0 ° | geometry, wing position and sweep together | ||
| 13 | Field performance | Release speed needed | 35 km/h | 1.2 × the 29 km/h stall · you throw at 45 |
| Out of your hand | +5.6 N | accelerating away at 10.4° of climb | ||
| Energy in the launch | 248.9 J | a bungee pulling 24.9 N through 10 m | ||
| Landing roll | 44 m | no brakes | ||
| Landing over it | 91 m | approach at 3.7° | ||
| Ground needed | 91 m | to land, which is all it needs · you have 100 m | ||
| 14 | Glide polar | Best glide ratio | 1:15.8 | at CL 0.95, where the two drags are equal |
| Speed for it | 34 km/h | sinking 0.60 m/s | ||
| Minimum sink | 0.54 m/s | at the stall, not at the ideal speed | ||
| Down from 100 m | 1,583 m | in still air, at best glide | ||
| Longest it can stay up | 187 s | gliding down from 100 m at minimum sink | ||
| Circling at 30° | 0.58 m/s | 13 m radius · 10 s a circle | ||
| 15 | Landing gear | Nose wheel carries | 15.3 % | 4.77 N · sound is 8–15% |
| Each main carries | 13.24 N | 1,350 g · 42.4% of the weight | ||
| Tip-back angle | 25.3 ° | wants more than 15° | ||
| Turnover angle | 43.3 ° | under the 63° limit, by 19.7° | ||
| Propeller clearance | 38 mm | 15% of diameter · strikes at 16° of roll | ||
| Blows over at | 81 km/h | crosswind, parked · 22.6 m/s | ||
| 16 | Mission energy | Mission needs | 16.7 Wh | 11% of the pack nameplate |
| Pack gives you | 118.4 Wh | 148.0 Wh nameplate · 100% at this load · 80% discharged | ||
| Margin | 86 % | of the energy you allowed yourself | ||
| Loiter you can do | 140.2 min | you asked for 10 | ||
| Payload ceiling | 509 g | the cruise reaches 1.3 × stall before the pack runs out | ||
| Time in the air | 20 min | 5.3 km flown · cruise at 1.36 × stall | ||
A thermal glider
Two metres, light, clean, launched on a motor and then flown on lift. The design where every gram is argued over.
Built-up balsa, film covered, a slim pod and boom, micro servos, a small climb motor, no undercarriage, thrown by hand at 26 km/h.
It glides 1:18.8 and sinks least of the four, which is the whole brief in two numbers. It also never touches the ground to leave it: this is the design where a take-off roll was always a fiction, and the sheets now say so rather than computing one.
Thrown at 26 km/h against the 28 the sheet asks for, it leaves the hand with 4.3 N in hand and climbs at 18.9° — the steepest of the four, and the reason is the wing: light, large and already flying. The launch is the easy part. Coming down is not: it needs 87 m to land over a three-metre hedge, more than the 60 m strip the study gave it, because a wing that does not want to stop flying does not want to stop flying on the approach either.
The interesting finding is structural. The design set a limit load factor of 5.0 g, and Sheet 10 came back with a design load factor of 5.5 g — the sheet took the gust case instead, because a sharp-edged gust on a large, light, high-aspect-ratio wing beats the manoeuvre the pilot would fly. On a glider the spar is sized by weather, not by the pilot. That is the single most useful thing this study produced and it is invisible unless you run the sheet.
This is the one the loop moved the wrong way. The brief assumed 1,300 g and Sheet 05 came back with 1,356 g — 4 per cent over, the only design of the four that turned out heavier than it was meant to be. A two-metre wing is a lot of area to cover, and area is what the weight model charges for. The wing loading it settles at is still the lowest of the four, which is the answer to whether it will still soar.
The drag is the clearest thing this study has to teach, and it took getting it wrong first. Sheet 07 now returns CD0 0.0212 against the 0.025 category nearest the brief's assumption — 15 per cent under. In the previous version of this page it came out above the assumption, the only design of the four that did, and the page named that as the study's own fault: Sheet 07 was running its default box fuselage and fixed undercarriage under a two-metre soarer, because nobody had told it otherwise. Told instead about a 70 mm pod, a thin section and no wheels at all, it comes back where a soarer belongs. An input you did not set is still an input. The sheet was never wrong; it was answering a question about a different aeroplane.
The fin is the one thing this study would change. Five per cent of the wing on a two-metre span leaves the weathercock stiffness weak and the lateral balance at 5.90, well past the 3.0 where roll starts to dominate yaw: plenty of dihedral effect, not enough fin to answer it, which is the recipe for a wallowing Dutch roll and a spiral that tightens on its own. Sheet 12 says it twice, in two different numbers. The soarer's slim pod does not help — it takes 39% of what the fin makes. The wing that makes it soar is the wing that makes it unstable, and the fin is where you pay for it.
Loiter comes out at 84.8 minutes, but that number should be read carefully: this aeroplane is not meant to hold height on the motor, it is meant to be launched and then to find lift. What the mission sheet is really telling you is how many launches the pack is good for.
Round the weight loop
| Pass | Mass assumed | Sheet 05 builds | Apart by |
|---|---|---|---|
| 1 | 1,300 g | 1,356 g | +4.3% |
| 2 | 1,356 g | 1,356 g | agreed |
What the sheets objected to
- Sheet 01, wing sizing — Planform
- Sheet 07, drag build-up — It reads low
- Sheet 10, structures — The gust beats your limit
- Sheet 10, structures — Stiffness is a separate question
- Sheet 11, controls — The crosswind the rudder can hold
- Sheet 12, lateral stability — Does it track straight
- Sheet 12, lateral stability — The balance is the point
- Sheet 13, field performance — What the launch has to do
- Sheet 13, field performance — Verdict
- Sheet 14, glide polar — It stalls before it reaches minimum sink
- Sheet 16, mission energy — It stalls before it reaches minimum power
- Set aside: Sheet 15. Sheet 15 asks about an undercarriage, and this aeroplane has none. What that sheet returns for it is in the trail below, and it is the sheet answering a question this aeroplane does not ask.
Every figure, sheet by sheet
The whole run for the settled aeroplane, sheet by sheet in the order the study was done: what each sheet was typed, what reached it from the sheet before, and every figure it returned — not only the ones the prose above argues with. Both tables export as CSV.
What each sheet was told
| Sheet | Name | Typed into it | Arrived from the sheet before |
|---|---|---|---|
| 06 | Constraint diagram | All-up weight 1356 g · Maximum lift coefficient 1.25 · Parasite drag coefficient 0.022 · Span efficiency 0.90 · Launch Hand launch or bungee | nothing; this is where the study starts |
| 05 | Weight budget | Wing area 40 dm² · Cells in series / capacity 3 · Pack capacity in milliamp hours 2200 mAh · Build method Built-up balsa, film covered · Fuselage and gear, against wing structure 0.35 · Servo size class Micro, 9 g · Servos — how many, what size 4 · Payload 0 g · Motor / ESC / propeller and spinner 90 g motor · Speed controller mass in grams 25 g ESC · Propeller and spinner mass in grams 25 g prop · Tail area, as a share of the wing 16 % | 11 carried, new or changed here: Oswald span efficiency 0.9, all-up weight 1356 g, wing area 23.424 dm², aspect ratio 5.54, finite-wing max lift 1.25, parasite drag coefficient 0.022, cruise speed 43 km/h, electrical power at cruise 23.012 W, electrical power in climb 150.876 W, field elevation 0 m, relative humidity 0 % |
| 01 | Wing sizing | All-up weight, ready to fly 1356 g · Wingspan, tip to tip 2100 mm · Root chord 210 mm · Tip chord 170 mm | 13 carried, new or changed here: all-up weight 1356.331 g, wing area 40 dm², cells in series 3, pack capacity 2200 mAh |
| 02 | Airfoil choice | nothing; everything it needed had arrived | 19 carried, new or changed here: all-up weight 1356 g, wing area 39.9 dm², aspect ratio 11.053, finite-wing max lift 1.215, span 2100 mm, root chord 210 mm, tip chord 170 mm, mean aerodynamic chord 190.702 mm, Reynolds at cruise 139793.457, 2D section max lift 1.35 |
| 03 | Balance and tail | Span 2100 mm | 20 carried, new or changed here: mission key sport |
| 07 | Drag build-up | Wing reference area 40 dm² · Category you would otherwise have picked Clean built-up glider — 0.025 · Wing thickness to chord ratio 9 % t/c · Exposed wing, less what the fuselage covers 95 % · Surface finish Film covered, smooth and taut · Wing–fuselage junction Filleted, mid or shoulder wing · Tail area as a percentage of wing area 16 % of wing · Tail mean chord 130 mm · Tail thickness to chord ratio 8 % t/c · Fuselage length 1200 mm · Fuselage width 70 mm w · Fuselage height 95 mm h · Cross section Streamlined pod · Number of wheels 0 · Wheel diameter 60 mm ⌀ · Wheel width 20 mm w · Number of gear legs 0 · Exposed leg length 120 mm · Leg thickness 5 mm thick · Everything else 1 cm² drag area · Surface and excrescence markup 12 % | 22 carried, new or changed here: section pitching moment -0.08, tail arm, quarter chord to quarter chord 760 mm |
| 04 | Power and endurance | All-up weight, ready to fly 1356 g · Wing area 40 dm² · Maximum lift coefficient 1.25 · Parasite drag coefficient 0.022 · Span efficiency 0.90 · Cell count 3 · Capacity 2200 mAh | 22 carried, new or changed here: wing area 40 dm², parasite drag coefficient 0.02123 |
| 08 | Propeller | Cells in series 3 | 23 carried, new or changed here: finite-wing max lift 1.25, parasite drag coefficient 0.022, cruise speed 33.211 km/h, electrical power at cruise 12.953 W, electrical power in climb 140.816 W, propeller efficiency at cruise 0.65 |
| 09 | Battery | Cells in series 3 · Pack capacity 2200 mAh · Speed controller, continuous rating 25 A | 26 carried, new or changed here: propeller efficiency at cruise 0.745, static thrust 7.33 N, pitch speed 83.23 km/h, propeller diameter 254 mm |
| 10 | Structures | All-up weight, ready to fly 1356 g · Wing area 40 dm² · Wingspan 2100 mm · Root chord 210 mm · Tip chord 170 mm · Maximum lift coefficient 1.25 | 26 carried, none of it changed |
| 11 | Controls | All-up weight 1356 g · Wing area 40 dm² · Wingspan 2100 mm · Root chord 210 mm · Tip chord 170 mm · Maximum lift coefficient 1.25 · Design speed for control loads 110 km/h · Aileron chord as a percentage of wing chord 20 % chord · Maximum aileron deflection 15 ° · Aileron inboard station 55 % semi · Aileron outboard station 95 % semi · Tailplane area as a percentage of wing area 11 % of wing · Elevator chord as a percentage of tail chord 45 % chord · Maximum elevator deflection 25 ° · Fin area as a percentage of wing area 5 % of wing · Rudder chord as a percentage of fin chord 45 % chord · Maximum rudder deflection 30 ° · Control horn length 10 mm · Servo arm length 15 mm · Hinge gap Sealed — tape, or a hinge with no through-gap | 26 carried, none of it changed |
| 12 | Lateral stability | Wing area 40 dm² · Wingspan 2100 mm · Root chord 210 mm · Tip chord 170 mm · Fin area as a percentage of wing area 5 % of wing | 26 carried, none of it changed |
| 13 | Field performance | All-up weight 1356 g · Wing area 40 dm² · Wingspan 2100 mm · Maximum lift coefficient 1.25 · Parasite drag coefficient 0.022 · Span efficiency 0.90 · How the aeroplane leaves the ground Hand launched · Speed at release 26 km/h · Field length available 60 m · Obstacle height 3 m obstacle · Headwind 0 m/s · Braking / ground lift coefficient No brakes · Lift coefficient on the ground 0.35 | 30 carried, new or changed here: fin area, share of the wing 5 %, fin arm, quarter chord to quarter chord 780 mm, fin aspect ratio 1.6, weathercock stability, fin less what the fuselage takes 0.022 |
| 14 | Glide polar | All-up weight 1356 g · Wing area 40 dm² · Wingspan 2100 mm · Maximum lift coefficient 1.25 · Parasite drag coefficient 0.022 · Span efficiency 0.90 · Headwind 0 m/s | 30 carried, none of it changed |
| 15 | Landing gear | All-up weight 1356 g | 30 carried, none of it changed |
| 16 | Mission energy | Weight without payload 1356 g empty · Wing area 40 dm² · Wingspan 2100 mm · Maximum lift coefficient 1.25 · Parasite drag coefficient 0.022 · Span efficiency 0.90 · Cells in series 3 · Pack capacity 2200 mAh · Wind speed 0 km/h · Avionics and payload electrical draw 1 W | 30 carried, none of it changed |
Every figure the sheets returned 89
| Sheet | Name | Figure | Value | What it means here |
|---|---|---|---|---|
| 06 | Constraint diagram | Wing loading | 57.9 g/dm² | stall limited |
| Wing area | 23.4 dm² | for 1,356 g | ||
| Power loading | 111 W/kg | Climb sets this | ||
| Electrical power | 151 W | from the pack | ||
| With 15% margin | 174 W | motor to install | ||
| Wing cube loading | 11.9 | Scale/Warbird | ||
| 05 | Weight budget | All-up weight | 1,356 g | 47.8 oz |
| Empty, no payload | 1,356 g | 0 g of payload comes out of the all-up above | ||
| Wing loading | 33.9 g/dm² | 11.1 oz/ft² | ||
| Wing cube loading | 5.4 | Trainer | ||
| Structure | 62.3% | 846 g | ||
| Energy | 12.9% | 24.4 Wh | ||
| 01 | Wing sizing | Wing loading | 34.0 g/dm² | 39.9 dm² of wing carrying 1,356 g |
| Wing cube loading | 5.4 | Trainer — the number to compare designs of different sizes on | ||
| Stall speed | 24.1 km/h | clean and level; fly the approach at 31.3 km/h or above | ||
| Aspect ratio | 11.05 | Sailplane — taper 0.81, mean aerodynamic chord 191 mm | ||
| Reynolds no. | 140k | Transitional — at the mean chord and a typical cruise — the number Sheet 02 filters on | ||
| 02 | Airfoil choice | this sheet prints no figures of its own | ||
| 03 | Balance and tail | Neutral point | 55.8 % MAC | 106 mm aft of the mean chord's leading edge |
| Static margin | 12 % | sport — anywhere from 41% to 46% MAC will fly; forward is heavier on the elevator and steadier | ||
| Mean aero chord | 191 mm | 507 mm out from the centreline, where to measure it | ||
| Tail volume V_H | 0.779 | Large — flying designs of this kind land between 0.4 and 0.6 | ||
| 07 | Drag build-up | CD0 | 0.0212 | at 43 km/h |
| Flat plate equivalent | 84.9 cm² | the hole it punches | ||
| Before markup | 0.0190 | 12% added | ||
| Wing Reynolds | 155,943 | workable | ||
| Add-ons | 1.2% | 1.0 cm² of it | ||
| Your guess was | 0.025 | 15% under | ||
| 04 | Power and endurance | Cruise power | 13 W | 7 W of it reaches the air; the rest is the propeller and motor |
| Best glide | 18.8 : 1 | at 29 km/h, where the two drags are equal | ||
| Top level speed | 90 km/h | 3.8× the stall, and where the two power curves cross | ||
| Power loading | 119 W/kg | Trainer — 54 W/lb, sized for 5.0 m/s of climb with 15% in hand | ||
| Endurance | 90 min | at cruise; the pack is 13% of the all-up weight | ||
| 08 | Propeller | Cruise efficiency | 74.5% | 85 g thrust |
| Climb efficiency | 55.4% | 690 g thrust | ||
| Static thrust | 747 g | at 113 W | ||
| Pitch speed | 83 km/h | 60% slip at cruise | ||
| Tip Mach | 0.36 | clear | ||
| Advance ratio | 0.24 J | P/D 0.60 | ||
| 09 | Battery | Cruise current | 1.2 A | 0.5C |
| Climb current | 12.8 A | 5.8C of 30C | ||
| Sag in climb | 0.10 V | to 11.0 V | ||
| Usable energy | 19.5 Wh | of 24.4 Wh | ||
| Pack mass | 174 g | 140 Wh/kg | ||
| ESC headroom | 95 % | over climb draw | ||
| 10 | Structures | Design load factor | 5.5 g | the gust, not the limit you set |
| Manoeuvre speed | 53 km/h | 33 mph · below this you stall before you break | ||
| Dive speed | 61 km/h | 38 mph · the right-hand edge of the envelope | ||
| Root bending, ultimate | 25.9 N·m | 229 lb·in at 5.5g × 1.50 safety factor | ||
| Cap area needed | 16.3 mm² | 0.025 in² · Spruce, each of two caps | ||
| Tip deflection | 109 mm | 4.30 in · 10.4% of semi-span | ||
| 11 | Controls | Aileron servo | 0.69 kg·cm | 9.5 oz·in · micro, 9 g |
| Elevator servo | 2.10 kg·cm | 29.1 oz·in · mini, 20 g | ||
| Rudder servo | 1.14 kg·cm | 15.8 oz·in · micro, 9 g | ||
| Roll rate | 161 °/s | at 110 km/h | ||
| Roll helix | 0.096 pb/2V | sport | ||
| Time to 45° bank | 0.28 s | at the steady rate — the real one is longer | ||
| Elevator authority | -0.98 CLt | the download it makes at full throw · tail volume of 0.438 on a 760 mm arm | ||
| Crosswind it can hold | 7 km/h | 1.8 m/s · full rudder holds 12° of sideslip on a 31 km/h approach | ||
| Balance point can go to | -3 % MAC | at or ahead of the leading edge — the elevator is not your forward limit | ||
| 12 | Lateral stability | Weathercock | 0.0225 Cnβ | weak |
| Dihedral effect | -0.1325 Clβ | sound | ||
| Balance | 5.90 −Clβ/Cnβ | roll-dominant | ||
| Fin volume | 0.0186 Vv | Sheet 03 checks this against its own band | ||
| Fuselage takes | 39 % | of what the fin produces | ||
| Effective dihedral | 6.0 ° | geometry, wing position and sweep together | ||
| 13 | Field performance | Release speed needed | 28 km/h | 1.2 × the 24 km/h stall · you throw at 26 |
| Out of your hand | +4.3 N | accelerating away at 18.9° of climb | ||
| Energy in the launch | 35.4 J | what your arm has to put in, at 26 km/h | ||
| Landing roll | 31 m | no brakes | ||
| Landing over it | 87 m | approach at 3.1° | ||
| Ground needed | 87 m | to land, which is all it needs · you have 60 m | ||
| 14 | Glide polar | Best glide ratio | 1:18.8 | at CL 0.83, where the two drags are equal |
| Speed for it | 29 km/h | sinking 0.43 m/s | ||
| Minimum sink | 0.38 m/s | at the stall, not at the ideal speed | ||
| Down from 100 m | 1,882 m | in still air, at best glide | ||
| Longest it can stay up | 263 s | gliding down from 100 m at minimum sink | ||
| Circling at 30° | 0.41 m/s | 9 m radius · 8 s a circle | ||
| 15 | Landing gear | Nose wheel carries | 15.3 % | 2.03 N · sound is 8–15% |
| Each main carries | 5.63 N | 575 g · 42.4% of the weight | ||
| Tip-back angle | 25.3 ° | wants more than 15° | ||
| Turnover angle | 43.3 ° | under the 63° limit, by 19.7° | ||
| Propeller clearance | 38 mm | 15% of diameter · strikes at 16° of roll | ||
| Blows over at | 53 km/h | crosswind, parked · 14.7 m/s | ||
| 16 | Mission energy | Mission needs | 4.8 Wh | 19% of the pack nameplate |
| Pack gives you | 19.5 Wh | 24.4 Wh nameplate · 100% at this load · 80% discharged | ||
| Margin | 76 % | of the energy you allowed yourself | ||
| Loiter you can do | 84.8 min | you asked for 10 | ||
| Payload ceiling | 217 g | the cruise reaches 1.3 × stall before the pack runs out | ||
| Time in the air | 23 min | 5.3 km flown · cruise at 1.31 × stall | ||
What happens if you let the wing move too
Every study above holds the wing it was given and iterates the mass alone. Sheet 06 is asked what area the requirements want, its answer is read, and then the study carries on with the wing in the brief. This section does the other thing: the same trainer, the same requirements, but Sheet 06's answer is taken as the next wing — the span held, the chords scaled to hit the area — and round again until both the mass and the area stop moving.
It takes eleven passes. Not two, and the reason is visible in the table: the two variables take turns. A pass that settles the mass leaves the area wrong; taking the new area unsettles the mass; and each round closes a little over two-fifths of what is left rather than all of it. That is what a loop with two variables in it does, and it is the difference between a study you can do in an afternoon and one you leave running.
| Pass | Mass assumed | Sheet 05 builds | Apart by | Wing flown | Sheet 06 wants | Apart by |
|---|---|---|---|---|---|---|
| 1 | 2,400 g | 2,107 g | -12.2% | 43.4 dm² | 42.7 dm² | -1.6% |
| 2 | 2,107 g | 2,086 g | -1.0% | 42.7 dm² | 37.4 dm² | -12.4% |
| 3 | 2,107 g | 1,925 g | -8.6% | 37.4 dm² | 37.4 dm² | agreed |
| 4 | 1,925 g | 1,925 g | agreed | 37.4 dm² | 34.2 dm² | -8.6% |
| 5 | 1,925 g | 1,828 g | -5.0% | 34.2 dm² | 34.2 dm² | agreed |
| 6 | 1,828 g | 1,828 g | agreed | 34.2 dm² | 32.5 dm² | -5.0% |
| 7 | 1,828 g | 1,776 g | -2.8% | 32.5 dm² | 32.5 dm² | agreed |
| 8 | 1,776 g | 1,776 g | agreed | 32.5 dm² | 31.6 dm² | -2.8% |
| 9 | 1,776 g | 1,749 g | -1.5% | 31.6 dm² | 31.6 dm² | agreed |
| 10 | 1,749 g | 1,749 g | agreed | 31.6 dm² | 31.1 dm² | -1.6% |
| 11 | 1,749 g | 1,734 g | -0.9% | 31.1 dm² | 31.1 dm² | agreed |
What it converges to is not the aeroplane in the brief. The wing comes down from 43.4 to 31.1 dm² — a 200 mm chord instead of 280, which is 31.0 dm² once the chord is rounded to the millimetre the sheets are given — and the mass with it, to 1,734 g. Everything gets better: it needs less power, glides further and loiters 42.0 minutes against 29.0.
| What | Wing held | Wing let go |
|---|---|---|
| All-up weight | 2,107 g | 1,734 g |
| Wing area | 43.4 dm² | 31.0 dm² |
| Aspect ratio | 5.54 | 7.75 |
| Wing loading | 48.5 g/dm² | 56.4 g/dm² |
| Wing cube loading | 7.4 | 10.1 |
| Stall speed | 28.8 km/h | 31.0 km/h |
| Wing Reynolds | 245k | 189k |
| Power to install | 251 W | 208 W |
| Best glide | 9.2 | 10.9 |
| Loiter | 29.0 min | 42.0 min |
| Take-off roll | 16 m | 18 m |
And it is no longer a trainer. Wing cube loading goes from 7.4 to 10.1 and the aspect ratio from 5.5 to 7.8: a smaller, faster, slipperier aeroplane that lands quicker and forgives less. Nothing went wrong. The loop converged on the requirements it was given, and none of them said "docile". The brief did — in the word trainer, which is not a number and so is not in the loop.
That is the argument for holding the wing, and it is why the four studies above do. A conceptual design loop is not an optimiser: it is a way of finding out whether the aeroplane you have in mind is consistent with itself. Let every variable go and it will happily walk to an aeroplane nobody asked for, one defensible step at a time.
What these studies do not settle
Each design is specified four ways over. The figures that characterise it — weight, span, chords, area, maximum lift, drag, span efficiency, cells and capacity. How it is built: the method, the fuselage share, the servos, the payload. Its body: the fuselage, the finish, the wing root, the tail and the undercarriage Sheet 07 skins. And its controls: aileron chord, deflection and span stations, elevator and rudder, the horn and the arm, and whether the hinges are sealed. The trainer adds a fifth, its undercarriage and its strip, because it is the only one that uses them. Everything a sheet is not told, it assumes — and every assumption left in these studies is named below rather than left for you to find.
What is left is not a missing input but a mismatch, and it is down to one sheet. Three of these four aeroplanes are thrown or catapulted and land on their bellies. Sheet 15 asks what their nose wheel carries, and for those three the answer is about an aeroplane that does not exist; its warnings are listed under each study as set aside rather than as findings, and the figures behind them are left in the trail where you can see them.
Sheet 13 used to be in that sentence and is not any more. It models the launch now — what the throw has to do, how far the aeroplane falls before it is flying, and the energy a catapult has to put in — so it answers all four: the launch for the three that are thrown, a take-off run for the one with wheels to do it on. That is the second time this page has turned a set-aside into a finding by making the sheet ask the right question, and it is the more useful direction than excusing the answer.
An earlier version of this page took a different approach and excused five warnings by name, on the grounds that they fired on all four aeroplanes. That was over-reaching. Two of the five were the stall notes on Sheets 14 and 16, which were never artefacts of anything: a wing that cannot reach the lift coefficient for minimum sink is a finding about the wing, and the sheet says so in as many words. Naming a whole sheet inapplicable to a particular aeroplane is a claim that can be checked; naming a warning generic is a claim that it is somebody else's problem.
The drag was the last of those gaps, and closing it did not tidy the answers up. Until this revision each design stated its aerodynamics and its build but not its body, so Sheet 07 ran the same trainer-shaped box under all four. Each now describes its fuselage, its finish, its wing root, its tail and its undercarriage, and all four build-ups moved — but only two moved towards the category the brief assumed:
| Design | Before | Now | Against the category |
|---|---|---|---|
| Club trainer | 0.0303 | 0.0375 | 24% under → 6% under |
| FPV platform | 0.0373 | 0.0300 | 36% under → 48% under |
| Survey UAV | 0.0278 | 0.0209 | 13% under → 35% under |
| Thermal glider | 0.0327 | 0.0212 | 31% over → 15% under |
The trainer came into agreement and the glider turned the right way round — both of them had been carrying a body that was not theirs. The other two went further from their category, and that is the honest result rather than a fault: a polished moulded airframe with no undercarriage, and a taped foam pod that is hand launched, really do have less skin and fewer holes than the types they belong to are known for. A category figure is the average of every aeroplane of that kind, including the ones with wheels, wire and a camera bolted on top. Describe an unusually clean one and the build-up should come out under it. What the sheet is comparing is not right against wrong; it is a description against a reputation.
One thing the four say together, now that each of them has a tail. Sheet 03 sets the aft limit on the balance point — the neutral point, less the static margin — and Sheet 11 now sets the forward one, which is a question about whether the elevator can hold the nose up at the stall. On all four designs the forward limit lands at or ahead of the leading edge: 1% of the mean chord on the trainer, 7% on the survey aircraft, and ahead of the nose on the other two. On a model the elevator is almost never what limits how far forward you can balance, which is the opposite of full-size practice, where the forward limit is usually set by the elevator in the flare. The reason is throw: 25° of elevator on a tail that is a fifth of the wing is an authority no certificated aeroplane has. What limits a model is the aft end — stability — and that is Sheet 03's number, not this one.
And the rudder says the same thing the fin sheet has been saying. Sheet 11 now asks what crosswind each aeroplane's rudder can hold on the approach. The trainer manages 15 km/h and the FPV 19, which is more wind than either would be flown in. The survey aircraft and the glider manage seven — about two metres a second, which is an ordinary afternoon. Both of them were already flagged by Sheet 12 for not tracking straight, and this is the same shortage of fin seen from the other end: a long wing raises the fin volume's denominator and the dihedral effect at once, so the span that makes these two efficient is the span that makes their fins too small. Two sheets, one fix, and neither of them would have told you on its own.
Nothing about the sheets changed in any of this. The study started telling them what it was asking about, and two of the four answers got further from what it had assumed. That is the direction of travel a study should expect.
These do go round the weight loop. Each design is run through all sixteen sheets, Sheet 05's built-up mass is taken as the next assumption, and the whole set is run again until the two agree to within one per cent. Every figure on this page is from the settled aeroplane. The pass-by-pass table under each design is the working, and the corrections are large: the survey aircraft came down by nearly a third, the trainer by an eighth, and the glider went up.
Two things that loop taught us about these studies rather than about the aeroplanes. The first is that it closes in two passes, because this weight model does not depend on the mass you assumed — only on the wing, the build and the contents. Let the wing move as well and it takes eleven, which is no longer arithmetic on this page but a run: it is the section above.
The second is that the first attempt at it was wrong, and usefully so. The four designs specified their aerodynamics and left the build to the sheet's own defaults, so the loop was arguing with a trainer's construction whatever the aeroplane was: it settled the two-metre soarer at 1,908 g, which is not a soarer. Each design now states how it is built, and that is the line under its brief.