Hover At RPM 3250 With 5.47° Collective Pitch For Fuel Economy
The endurance build and extreme robotics build investigated why the prototype NACA0015 blade's PIDs and collective pitch curves can be directly transplanted into the production build with a different airfoil, as well as the subtle differences. Here, we set the pitch curve identical to the prototype build when operating the pitch curve from the common PWM signal 1000us to 2000us.
Production PIDs and pitch curves ARE the prototype PIDs and pitch curves.
Prototye rotor RPM for level hovering is 2640/minute = 44/s . Rotor diameter 0.48m , speed at 3/4 blade span is 0.48m x 3.14 x 44/s x 3/4 = 50m/s . Reynolds number is 50m/s x 18mm / 1.46 x 100000 = 62,000 . It is very well known that the highest cL/cD (numerically equivalent to fuel economy) of NACA0015 between Reynolds number 50,000 and 100,000 is at alpha 6 degrees to 6.25 degrees.

For simplicity of collective pitch angle calculation, we choose servo arm length identical to blade pitch lever length, in the prototype build, 12 mm pictured above and on the right. The Oxy2 Sport grips and the Align 250 grips have congruent geometry as shown in the picture above. When all 3 pillars of the swash plate are raised evenly, the blade lever and angle are congruent to the servo arm and angle. The angle of travel of the RF control PWM 1000-2000 µs is 83 degrees in the above picture and 84.6 degrees in another test with the avionics computer PWM 1000-2000 µs, averaging 83.8 degrees.
As tested by FlightPoint, the angle of travel of PWM 989-2011 µs is 85.4 degrees, as pictured here.
For the prototype optimal lift-to-drag ratio blade pitch 6.2 degrees, servo arms also rotate 6.2 degrees. The full range angle of the EMAX 9501 for 1000us to 2000us PWM is 83.8 degrees. 6.2 degrees / 83.8 degrees x 200 points = 14.8 points. To fit the PWM with our swash plate mixers here, we double the hovering points because most avionics computers allocate 50% swash travel for collective mixing. So, the prototype used a straight line for the collective pitch curve from 0 to 14.8x2=29.6=30 points at mid throttle stick. This angle and set point are
optimal for cruising for the production build's Joukowsky 10.5 blades. We stipulate the collective pitch to 3/4 of the throttle stick to avoid straining and overheating
motors that have mislabeled KV. We use the servo sequence, the first servo on the front, the second on the right, and the third on the left, when looking down on the craft from above the craft. With Betaflight, servo 0 and servo 1 are reserved as pan-tilt servos for camera, so, the servo numbers start from 2 for the first craft servo.
Also in the -50 mix lines, the source 0 and 1 are stabilized roll and pitch respectively. Source 7 is throttle channel 1, not an aux(source 8+). The problem of assigning collective pitch control channel to Aux is that avionics computer TPA(Throttle PID Attenuation) and TPS(Thrust PID Scaling) only corresponds to throttle, not AUX. The consideration with throttle input channel 1 in TAER being recognized as the throttle means arming for throttle position should not near 1500us to avoid stick function commands. After considering all
substitutes, the arming is set to have a large negative collective pitch for low throttle. This large negative collective pitch is set as the inverted hovering pitch angle for racing RPM, which is -23 points, or 1500-23/200*1000=1385us. The F7's min_check=1385us can mislead us to think that a hypothetical RF calls for -57 point of 1215us collective signal will be conflated to 1385us in F7 setup, but F7's signal 7 is raw RF signal, not processed nor conflated.
The relationship between servo mixer attenuation and servo/swash/pitch/DFC arm spans is illustrated here.

Because the prototype's servo mixing used standard CC3D 50%/50% collective/cylic mix when the p value was 1, the extra attenuation of production build's p value at 1.5 means the production build's collective mixing, if and we do want prototype's throttle curves reused in production build, needs to compensate the 50% mix by the factor of 1.5, 50% x 1.5 = 75%.
Because the prototype's cyclic mixing occurred with p*(d/u)=1*(1.833/0.916)=2 while production build's p*(d/u)=1.5*(2.25/1.1875)=2.842. The extra attenuation of 2.84/2 = 1.42 is compensated as 50% x 1.42 = 71%, and (50*sqrt(3)/2)% x 1.421 = 62%.
Because we compensate the mixer difference in software, the pitch curve calculation in RF hardware controller based on the 50%/50% mix does not need recalculation.
The endurance build notes show the measurements of p, d, and u, where lightweight substitutes were considered. All these production-improved settings are part of the dump_all file.
The prototype's optimal lift-to-drag ratio pitch angle doesn't mean the overall motor-propeller-battery combination is the most fuel-efficient, but just the propeller optimal. The production build is optimized for overall fuel efficiency and uses a 6.0-degree collective pitch for cruising. The production build's servo arm length is 2/3 of the grip pitch arm width, which attenuated the collective pitch by the same fraction, so the dump_all has an allocation of the swash movement needs to be exaggerated by the inverse of the fraction, 50% * 3/2 = 75%, as the following 3 lines,
smix 1 2 7 75 0 0 100 0
smix 4 3 7 75 0 0 100 0
smix 7 4 7 75 0 0 100 0
. The production build has collective pitch curve points 0, 15, 30, 45, and 45, same as the prototype build. The production build's first servo is on the back, the second servo on the left, and the third servo on the right, by the craft's own perspective.
The production build's RPM 3250 is inherited from the prototype(II) with 193mm blades of
endurance build note with 193mm x 18mm blades for neutral buoyancy at 6.2 degrees of collective pitch that is optimal for in-place hovering, which incidentally is the optimal collective pitch for cruising of the production build (19mm chord length blades) at mid throttle stick. But RPM 3250 itself is not optimal for cruising. Instead, RPM 3250 incidentally is optimal for production build neutral buoyancy at 5.47 degrees optimal collective pitch. What this means is that when the production craft reaches neutral buoyancy after takeoff (throttle stick is slightly less than mid throttle), it also reaches the optimal fuel efficiency for in-place hovering. When you raise the throttle collective pitch stick to mid-stick, the pitch is at optimal cruising fuel economy, but you need to lower the RPM to prevent climbing.
The production build is more sophisticated and conveys 2 information points: neutral hover and mid-throttle stick. The prototype conveys only 1 information point: the mid-throttle stick is neutral hover.
This concludes that RPM 3250 in the production build gives the highest fuel efficiency (numerically equivalent to cL/cD) when the production build hovers in place at alpha 5.47 degrees. The NACA0012 airfoil (equivalent to cuspid 0010.5) has the highest cL/cD from alpha 5.0 to alpha 5.5 as Reynolds number goes from 50,000 to 100,000.
Swashplate Setting
For swashplate leveling, our spool-up is performed in manual mode. If the swash banks to one side of the craft, there is no PID correction by the computer and no heavy battery or long tail lever on the sides of the fuselage to counter the tipping. Use a zip tie with the half-cut end, as shown in the below picture, to check that all 3 pillars nearly touch the servo linkage. This zip tie should only be used after checking for enough room between the swash and the hub after booting up the avionics computer.

It is well known that servos accept PWM range 1ms to 2ms, or 1000us to 2000us. But, the consensus is that manufactures specify margin of error of 150us between avionics computer and servos when viewed in BLHeli configurator. So, it is safe to give servos PWM between 1000-150=850 and 2000+150=2150. The spline count of the servo arm is 15; the servo arm travels 83 degrees for 1000us. So, each spline dial notch is equivalent of 1000.0*(360.0/15)/83.0=289us PWM change. The actual testing result is that 1 spline dial is equivalent of 310us PWM at the near center. That means that when attempting to set the high-end PWM to larger than 1660us, you could dial the arm position up 1 spline and increase PWM on top of 1660-310=1350us, which will set the high-end PWM closer to the central 1500us in the tolerated range.

When changing the servo PWM center micro-second value, the change should be multiples of 10us because it doesn't have the resolution of the full 1000 PWM points; instead, it only changes with 1/100 of the full range. Considering that the full range of the servo arm is 83 degrees, 1/100 of the range is 0.83 degrees. To center the swash plate, check the top of the blade boltings pictured on the right. Change all the 3 PWM center neutral values 10us at a time.
Indoor Hovering With RF Receiver With Proximity Cutoff
In the following video, XM+ receiver's LED starts out green, the transmitter antenna is shifted to create stronger radio coupling with the receiver at 0:01. The cutoff occurs at 0:02, the LED turns red, fail safe takes effect. The camera moves forward to zoom in to the receiver. The movement inadvertently shifts the transmitter antenna again , weakening the proximity coupling. The cutoff is released at 0:07, and LED returns to green.
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| https://archive.org/download/yt-oJo2eLmeVjw/yt-oJo2eLmeVjw.mp4 |
To avoid mid-air failure, the FrSky XM+ receiver requires putting transmitter on "range testing" mode before hovering in close proximity. This is not needed with Crossfire or R9M receiver, which does not have proximity cutff. In the prototype, the receiver sits on the pedestal as appropriate for the small, geared motor under 22mm diameter of stater, spaced across the cage. In production, when 4004 direct drive motor is used center in the cage, the receiver signal is severely jammed by the spinning motor. So, production build does not use the pedestal.
Takeoff Procedure With Safety Checks Applicable To Both Prototype And Production
Motor bolting failure in-air has the same characteristic left turn, resulting in twisted tail motor wires and missing bolts after recovering the wreckage. The tail wreckage of such a case is pictured here on the right.
The takeoff procedure for the prevention of mechanical failures follows.
1. DFC bolts marking on the installed position. Twist the tail motor and tail props to see no loose screws.
2. Plug in the craft battery. Check the rough zero pitch and level of the swashplate. If the servo arm clutch is sprained during the last mission or handling, dial it to correct it.
3. Position the craft on the takeoff surface with friction that prevents it from sliding. Remember, during the spool-up of the main rotor, there is no counter-torque compensation unless the tail yaw is applied manually. The blades should not scrape grass or thin twigs on the ground because the initial spool can bend the foldable hinges, throw the rotor off balance, and sprain the servo arms.
The following steps show the OSD percent display of channel 1 throttle in a video clip for illustration only. Our base build does not require OSD; RF control transmitter LCD is. The corresponding RF control transmitter LCD point displays are next to the OSD percent. The production build hovers at 13%, 0.7 degrees, less collective pitch than the mid-stick position, but this is within the margin of error between build variations. In particular, the half-turn of the servo linkage ball socket can cause a collective-pitch "jump" with a thread pitch of 0.35mm. Remember, helicopter linkage rod threading is often "more coarse" than "standard coarse" metric thread pitching to allow deeper thread cutting and more robustly "grab" onto the rod material. And servo PWM resolution is about 10us jumps.
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https://www.youtube.com/watch?v=rFdlgMNyZsU messed up with https://archive.org/download/yt-rFdlgMNyZsU/yt-rFdlgMNyZsU.mp4 |
4. Leave the craft and power on the RF control transmitter. The video above shows that the collective pitch changes from neutral to -4.8 degrees at 0:00 when the LCD display point of channel 1 throttle changes from 0 to -22.5. The throttle percent shown at OSD goes from 18 to 0. The 0 percentile display refers to the PWM signal at min_check from the RF transmitter, which is a negative collective pitch. The 18 percentile display refers to the actual neutral zero collective pitch at 1500us in the scale from min_check = 1386us to 2000us.
5. Arm the craft. This occurs at 0:00 of the video.
6. Spool up the main rotor slowly to the hovering RPM at 2/8 stick, as seen in the above video from 0:05 to 0:17, reaching the top red line of the soil color region in the table on the right. Slowly make the spool up so that the craft doesn't capsize due to an unbalanced rotor with folded blades. Then the craft should have no movement after the shaking because the friction of the ground overcomes the main rotor torque, and the negative pitch lift force presses down the craft firmly on the ground.
7. Switch on stabilization attitude mode with the throttle stick at 2/8 position, as seen in the above video at 0:18. The collective pitch will suddenly become positive 3.4 degrees, as shown as 14-15 LCD throttle point, also shown as 30 percent in the upper right OSD of the video. The craft will swing for a few seconds for computer stabilization to settle.
8. As shown in the video, raise the collective pitch to 3/8 stick from 0:18 to 0:24. The craft will stay on the ground.
9. Raise collective pitch toward 1/2 stick slowly; craft will reach neutral buoyancy between 3/8 and 4/8 stick and lift off at 25.5 throttle LCD display points or 39 percentiles shown in OSD, as shown in the video from 0:24 to 0:27.
10. If the drift is acceptable, raise the collective pitch to mid stick 4/8 at 29.3 throttle LCD display points, or 42 percentiles in OSD. The climb starts. At this point, the collective pitch is at the most fuel-efficient angle for level cruising as verified in the endurance build. To benefit from the fuel economy, start the forward movement of the craft to reach the optimal configuration.
Overall, the craft flies in the blue-sky region of the table on the right and stays on the ground in the green-grass region. The production build feels like a "punchy build" in flight because it has an extra 13% collective pitch beyond what's needed for hovering.
Reduce Trimming From RF Control
The Takeoff Procedure shows rolling to the right when switching to Attitude mode due to the required 4-degree tilt (align_board_roll = 4 in dump_all config) of the helicopter hovering physics. The RF control has a small right-roll trim. The rolling and self-correction don't need pilot input to correct. However, some builds may need a 5-degree tilt. If the avionics computer configuration is off and the roll trim is large, the RF control trim will cause more rolling than shown in the video and can be a risk for tip-over.
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| https://archive.org/download/yt-sz0uScNMNcA/yt-sz0uScNMNcA.mp4 |
Accidental Manual Spool-Up Mode
The negative collective pitch of the spool-up mode with tailspin somehow results in near-perfect craft inversion. In the footage on the right, the accident occurred at 0:05 during hovering with a hovering throttle (collective pitch) in attitude mode. The recovery is flipping the mode switch to attitude mode, keeping the same throttle (collective pitch) at a hovering level. The altitude drop from the corrective action of flipping the switch to attitude mode to stabilizing altitude is 6 meters.
Failsafe Setup
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| https://archive.org/download/yt-CMaeS6-ue3M/yt-CMaeS6-ue3M.mp4 |
With all-default settings, when more than 0.15 seconds of RF signal loss, the procedure of DROP the craft enters. The craft will drop to the ground if nothing else happens. When the RF signal resumes, the first 0.05 seconds of the signal is considered dirty and discarded. If the failsafe sets arming status to disarmed, it would require lowering channel 1 to lower than min_check when flipping on the rearming switch. So we set the arming status to armed during a failsafe. So the craft recovered successfully without the main rotor's slow spool-up nor flipping any switch on the RF control transmitter, as tested in the first video footage, which disconnected the ribbon cable between the RF control transmitter and the TBS Crossfire Mini module.
Summary RF Control Setup
In gyro-only mode, the accelerometer is not used, and the outer loop calculation of PID in avionics software is zeroed, so the RF control's trim from the transmitter handset is inappropriate. And so, the roll and pitch RF control mixer should have 2 separate pages for each axis, one with trim, another without trim.
To summarize, with
all substitutes rejected, the montage of 25 screens of created/edited pages are here below. Navigate-thrugh pages without needing to modify the page are skipped here.
Balance The Rotor Or Tip Over On Takeoff
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| https://archive.org/download/yt-gnn21smGVrQ/yt-gnn21smGVrQ.mp4 |
As seen in the video explanation on the right, vibration can result in seemingly deliberate mechanical movement that produces erroneous attitudes by the micro-electro-mechanical gyroscope during takeoff.
The building step of
trimming the feathering shaft discovered that the feathering shaft slop contributes the most to a rumbaling unbalanced rotor. When the slop is larger than 0.2 mm, the infinitesimal imbalance shifts the feathering shaft to either side of the blades after spooling up, and the direction of the shift is unpredictable and only observed after spooling down. When the feathering shaft's centering slop is less than 0.2 mm, the balanced rotor with smooth hissing can easily be achieved with thin, clear tape squares of 1cm sides.
So, what happens if the rotor has longitudinal off-balance by more than 1/100th of a gram in the field? In the videos below on the left, with perfect balancing, the PIDs are 2 notches lower than required because the swash slop is 10mm, the largest. The dive loses its heading hold about 2 seconds before punch-up at 0:11, but video stabilization patches up the insufficient PIDs below on the right.
Make Rotor Stiffness Consistent And Balanced For Stable Video
A prototype with overly loose grips that draped before turning the craft to the side 90 degrees, as the video below on the left shows, was recorded to have off-standard PID settings, as in the video below on the right.
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| https://archive.org/download/yt-O2LQsu6K7kk/yt-O2LQsu6K7kk.mp4 |
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| https://archive.org/download/yt-JVFXiyKf_lg/yt-JVFXiyKf_lg.mp4 |
For consistency, we set the drape at 90 degrees as the "standard" because we don't have a consistent gauging method.
When blades are overtightened slightly, the mast bumping is noticeable as shown in the following video comparison table.
| Stuck Blades At 90+ Degrees | Blades Drape At 90 Degrees |
Raw video has mast bumpings during a dive
 | | https://archive.org/download/yt-TzO3nS1PzLs/yt-TzO3nS1PzLs.mp4 |
Post-stabilization cannot fix the mast bumping
 | | https://archive.org/download/yt-Ck6FwZm7tF8/yt-Ck6FwZm7tF8.mp4 |
| Immediately after loosening the bolting
 | | https://archive.org/download/yt-s21TtDi5prM/yt-s21TtDi5prM.mp4 |
Post-stabilization results in undetectable bumping
 | | https://archive.org/download/yt-qu236OOzPag/yt-qu236OOzPag.mp4 |
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Change Rotor RPM With Locale/Weather
According to the NASA education page screenshot below on the left, density affects blade lift linearly; in the screenshot below on the right, the lift is proportion to RPM to the square power. Using binomial approximation, blade airspeed RPM should be adjusted by half the percentage of air density change with weather reports.
Overclocking RPM can cause craft instability and/or vibration because the avionics computer PID gain is tied to rotor angular momentum and proportional to rotor RPM.
Our reference condition is the middle of the Fahrenheit scale of 0-100, 50 degrees Fahrenheit, 10C temperature for RPM 2643 at 27 throttle points in the -100-to-100 points scale of the 1000us-2000us PWM signal range. Weather, temperature, and pressure can change air density from normal conditions by 11%. For example, a typical winter temperature weekly low of -10C produces air density 293.0/(293-20-10)=1.11 times the reference air density around Boston suburbs. Barometric pressure generally does not affect air density as much as temperature; for example, a 13% pressure change from 30 inHg to anything below 26 inHg would approach world records for the eyes of an intense cyclone. On the other hand, locale consideration for elevation, many cities above the elevation of 3000 feet, such as Tucson, northeast of Los Angeles County, El Paso, Denver, can reduce air pressure by 11% by altitude. However, the simple square relation doesn't consider turbulence effects with Reynold's number, and the simple square relation consistent for both drag and lift in response to blade speed change would contradict the deviation of Cl/Cd ratio curves when Reynold's number changes. The effect of blade speed is more powerful than the second power proportion because the higher the blade speed, the higher Reynold's number and the higher the Cl/Cd ratio. So, we will use a spreadsheet table on the right for RPM adjustment, approximating the blade speed effect to the 2.5th power.
AI Shahed Tracking/Intercepting
The converged_aiot executable in the converged_aiot.tar.gz package uses the very popular christianrauch/msp to command Betaflight on roll/pitch/yaw setpoints. Currently, it sets the roll/pitch/yaw attitude to a fixed continued navigation path before engaging the autopilot/navigator, while the video streaming continues in a separate thread in the main program.
TODO: With the publicly available Shahed loiter munition YOLO model, similar to https://zir-system.com/en/product/automatic-guidance-module-zir-ai-betaflight/, we need to integrate converged_aiot's fcu_thread with detected object screen coordinates to steer the craft with the setRPYT() function accordingly.
Engineering page here.