tag:blogger.com,1999:blog-58215223203799878912024-03-13T17:47:47.305+01:00Shrediquette - the award-winning multirotors by William ThielickeShrediquette stands for multirotors, innovation and FPV since 2008.
William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.comBlogger125125tag:blogger.com,1999:blog-5821522320379987891.post-2213372041705317162020-04-17T21:09:00.001+02:002020-04-17T21:09:48.988+02:00My 15 inch long-range setup for 2020 (with CAD files)This is my latest 15 inch ultra-long range setup with 50 minutes flight time:<br />
<br />
<ul>
<li>Propellers: 15x5.5" Tarot with custom hub </li>
<li>Motors: T-Motor MN3110 470 kV </li>
<li>Frame: 240g custom carbon structure </li>
<li>Lipo: 2x 4S 4000 mAh SLS 20C (parallel) </li>
<li>Camera: Micro Runcam micro sparrow </li>
<li>Firmware: INAV </li>
<li>FC: Holybro Kakute F7 </li>
<li>ESC: Tekko32 F3 </li>
<li>GPS: BN-180 </li>
<li>Compass: QMC5883L </li>
<li>Receiver: FRSky R9 slim+ </li>
</ul>
<br />
<br />
Hovering flight time is 50 minutes at 8.5 Amps and 40% throttle. Current goes up to 12 A when flying 50-60 km/h. Flight characteristics are really good when tuned properly (you'll nee a HUGE D-term).<br />
<br />
<a href="https://drive.google.com/file/d/17yha0e2LghOL3-pdlMibX4C32XIU--FK/view?usp=sharing" target="_blank">Here is the CAD file of the frame.</a><br />
<br />
<b>INAV 2.4.0 PID settings: </b><br />
<span style="font-family: Courier New, Courier, monospace; font-size: x-small;">set mc_p_pitch = 85<br />set mc_i_pitch = 60<br />set mc_d_pitch = 150<br />set mc_p_roll = 85<br />set mc_i_roll = 60<br />set mc_d_roll = 150<br />set mc_p_yaw = 200<br />set mc_i_yaw = 70<br />set mc_p_level = 40<br />set mc_i_level = 10<br />set max_angle_inclination_rll = 500<br />set max_angle_inclination_pit = 500<br />set dterm_lpf_hz = 30<br />set use_dterm_fir_filter = OFF<br />set yaw_lpf_hz = 50<br />set dterm_setpoint_weight = 0.600<br />set dterm_notch_hz = 108<br />set dterm_notch_cutoff = 72<br />set rate_accel_limit_roll_pitch = 2400<br />set rate_accel_limit_yaw = 360<br />set heading_hold_rate_limit = 30<br />set d_boost_factor = 1.500<br />set d_boost_gyro_delta_lpf_hz = 40<br />set antigravity_gain = 2.000<br />set antigravity_accelerator = 5.000<br />set tpa_rate = 20<br />set rc_expo = 77<br />set roll_rate = 27<br />set pitch_rate = 27<br /><br /></span><div style="text-align: center;">
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<br />William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com0tag:blogger.com,1999:blog-5821522320379987891.post-22975605935157126672018-04-08T19:10:00.001+02:002018-04-08T19:10:15.436+02:00In-flight propulsion system test!<h2>
Idea</h2>
Ever wondered what propeller or what motor performs best for your needs? Here is a simple way to determine the performance of different propellers (or motors) directly in flight, using your multirotor, the blackbox and some math. In the past, a lot of static thrust tests have been done to determine the current, thrust and efficiency of multirotor propulsion systems. However, they don't tell you anything about the propeller or motor performance in fast forward flight. Aerodynamics in forward flight and with a non-uniform inflow of the air are very different from static measurements.<br />
My questions were:<br />
<ul>
<li><b>What propeller has the better acceleration?</b> <i>(acceleration performance of propellers is theoretically closely linked to the 'grip' during turns. Because turning is also just an acceleration, <a href="http://shrediquette.blogspot.de/2017/11/side-force-generators-detailed.html" target="_blank">see this post</a>)</i> </li>
<li><b>What propeller will reach the higher top speed? </b></li>
<li><b>And which one decelerates better when throttle is cut?</b></li>
</ul>
<br />
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<br />
<h2>
Method </h2>
My idea was to mount one kind of propellers on the left side of the multirotor, and another kind of propellers on the right side. These propellers should then be compared directly in flight. I used one of my 6 inch rigs with T2 2206 2300 kV motors (well, not the most recent stuff, but still pretty ok), and Tattu R-Line 1550 mAh 4S.<br />
<br />
This kind of relative comparison technique will eliminate disturbances caused by wind, battery performance of different packs, or even piloting error. It is a relative measure with no absolute meaning, but it allows to generate a relative ranking system of the propeller performance.<br />
<div dir="ltr">
The performance is determined by repeatedly flying three standard manoeuvres: </div>
<div dir="ltr">
</div>
<ol>
<li>Fast acceleration from static hovering to full throttle horizontal flight</li>
<li>Full speed horizontal flight</li>
<li>Braking from horizontal flight by cutting throttle quickly to zero</li>
</ol>
The flight controller will have a lot to do during these manoeuvres, as it will try to keep the flight path straight all the time. Surprisingly, it manages to do it perfectly: With a properly tuned system, you can't actually feel any influence.<br />
<div dir="ltr">
These manoeuvres will be repeated several times to get statistically significant results, and the setup of the left/right propellers will be switched to account for any asymmetries of CG, ESC or motor performance.</div>
<div dir="ltr">
After the flights, the blackbox logs will be analysed (in my case with Matlab and some custom, automated code). The mean throttle that was applied by the flight controller to each individual motor will be calculated for each manoeuvre.</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-dkvyfKnuGR4/Wqexv19kSEI/AAAAAAAAOos/LNHUxiXiQxUhfsLu-jeE09ekXEg8rki-gCLcBGAs/s1600/principle.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="767" data-original-width="1600" src="https://2.bp.blogspot.com/-dkvyfKnuGR4/Wqexv19kSEI/AAAAAAAAOos/LNHUxiXiQxUhfsLu-jeE09ekXEg8rki-gCLcBGAs/s1600/principle.jpg" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Analysis, example for the full throttle horizontal flight manoeuvre.</td></tr>
</tbody></table>
<br />
<i>That will give the following information:</i><br />
<br /></div>
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</div>
<h4>
Full speed horizontal flight</h4>
Let's assume that the two motors on the left side (with propeller type 'A') have to run at 97% throttle during this manoeuvre, while the two motors on the right side (with propeller type 'B') only run at 78% throttle. That means that type 'B' propellers have the potential to generate more thrust (in fast forward flight) than 'A'. But the flight controller needed to slow them down by 19% to keep straight flight.<b> 'B' can reach a higher top speed.</b><br />
<div dir="ltr">
</div>
<h4>
Horizontal acceleration</h4>
When 'B' has lower average throttle than 'A' during the acceleration manoeuvre, that means that 'B' could potentially accelerate even faster, but the flight controller had to slow them down. <b>'B' have better acceleration.</b><br />
<div dir="ltr">
</div>
<h4>
Horizontal deceleration / braking </h4>
When 'B' has lower average throttle than 'A' during this manoeuvre, then that means that <b>the braking force of 'B' is worse than that of 'A'.</b><br />
<b><br /></b>
<br />
<div dir="ltr">
</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-UIkOqIwEnxI/WqeUxD9hIzI/AAAAAAAAOoE/sUBSJxxzvKUVDltP1Py_6TyKTK9lA4prwCLcBGAs/s1600/matlab.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="720" data-original-width="1080" height="266" src="https://4.bp.blogspot.com/-UIkOqIwEnxI/WqeUxD9hIzI/AAAAAAAAOoE/sUBSJxxzvKUVDltP1Py_6TyKTK9lA4prwCLcBGAs/s400/matlab.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">I am using Matlab for batch processing all Blackbox data. </td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-UJV5GojcyQM/WqeU02aWjHI/AAAAAAAAOoI/5e3iu7hC7YcdHJ36BriuhJ9KMtARqIQRQCLcBGAs/s1600/sequence-overview.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="610" data-original-width="935" height="260" src="https://2.bp.blogspot.com/-UJV5GojcyQM/WqeU02aWjHI/AAAAAAAAOoI/5e3iu7hC7YcdHJ36BriuhJ9KMtARqIQRQCLcBGAs/s400/sequence-overview.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Two test sequences (green) in a Blackbox log, each consisting of acceleration, full speed and deceleration. The graph shows the pilot throttle stick position and the acceleration vertical to the propeller disk. At least 6 sequences are analysed for each propeller comparison. </td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-dYPH78XR2jE/WqeU3SmD0sI/AAAAAAAAOoM/XPRTthUOqK0aMzbdL0KnldmYWlQv3XgiwCLcBGAs/s1600/sequence%2Bdetail.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="638" data-original-width="989" height="257" src="https://1.bp.blogspot.com/-dYPH78XR2jE/WqeU3SmD0sI/AAAAAAAAOoM/XPRTthUOqK0aMzbdL0KnldmYWlQv3XgiwCLcBGAs/s400/sequence%2Bdetail.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Magnification of sequence 1, showing more detail of the three manoeuvres acceleration (red), full speed (green) and deceleration (blue). Acceleration is defined as the time span where throttle stick and Z acceleration are rising. Full speed is the time where throttle stick is maximum and Z acceleration is constant. Deceleration is when throttle stick and Z acceleration are decreasing. </td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-ylQCUhqtRrs/WqeVChdjpFI/AAAAAAAAOoU/cE3G92HXUQgr-mx53U1snF5BtQwqo_82gCLcBGAs/s1600/individual-motors.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="796" data-original-width="1077" height="295" src="https://2.bp.blogspot.com/-ylQCUhqtRrs/WqeVChdjpFI/AAAAAAAAOoU/cE3G92HXUQgr-mx53U1snF5BtQwqo_82gCLcBGAs/s400/individual-motors.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">This graph shows the individual motor throttle that is applied to each motor as an end result of the PID loop in Betaflight. It is used to calculate mean values of the left and right motor pairs for the different manoeuvres.</td></tr>
</tbody></table>
<h2>
</h2>
<h2>
... and Efficiency...? </h2>
This method can't tell you anything about the efficiency of the propellers. Efficiency is propertional to thrust times velocity, divided by PWM duty cycle (= throttle) times Lipo voltage times current draw. My method does not measure current draw. So I can't say anything about efficiency. Only brute force is what I capture. <br />
<div dir="ltr">
It also can't tell you whether your motors, Escs and lipo battery are running within their specifications with the propellers under test. This, and also efficiency, is something you have to determine with existing, traditional tests. <br />
Measuring and comparing efficiency of different propellers could be added relatively easily by using ESC current telemetry. Sponsors for suitable ESCs are welcome!<br />
<h2>
Propellers under test</h2>
<div>
I tested 9 different propeller types. Thanks to <a href="https://www.facebook.com/HeikoSchenkFPV/" target="_blank">Heiko Schenk</a> for supplying the HQ propellers!</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-hT2gmNMMq6o/WspG8oYoKgI/AAAAAAAAO80/xz03ESJzU5cs3DdHHaue2MwohOfigWNKgCLcBGAs/s1600/ubersicht-propeller.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="700" data-original-width="800" height="280" src="https://1.bp.blogspot.com/-hT2gmNMMq6o/WspG8oYoKgI/AAAAAAAAO80/xz03ESJzU5cs3DdHHaue2MwohOfigWNKgCLcBGAs/s320/ubersicht-propeller.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The propellers that I tested in flight.</td></tr>
</tbody></table>
<h2>
Results</h2>
</div>
I was testing a small selection of my favourite 5" propellers for 22XX 2300 kV motors. I also added 4 inch and 6 inch props, just to verify that my expectations do match my measurements.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-5L3ooy6SFKA/WspIfhY6EmI/AAAAAAAAO9A/SwIq8EZQ9UcpdC-OOkrXTMZS-GRhDcatwCLcBGAs/s1600/results_accel2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1051" data-original-width="1183" height="568" src="https://4.bp.blogspot.com/-5L3ooy6SFKA/WspIfhY6EmI/AAAAAAAAO9A/SwIq8EZQ9UcpdC-OOkrXTMZS-GRhDcatwCLcBGAs/s640/results_accel2.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Acceleration / turning performance. <b>LOWER</b> values represent <b>BETTER</b> acceleration</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-X5RfPc7FyhQ/WspIj8VowxI/AAAAAAAAO9E/1FivCs-z8nwCJG8_1NS9XPElw1hUCVOVACLcBGAs/s1600/results_full2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1051" data-original-width="1183" height="568" src="https://3.bp.blogspot.com/-X5RfPc7FyhQ/WspIj8VowxI/AAAAAAAAO9E/1FivCs-z8nwCJG8_1NS9XPElw1hUCVOVACLcBGAs/s640/results_full2.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Full Speed performance. <b>LOWER</b> values represent <b>HIGHER</b> full speed.</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-9e24jLUxMqQ/WspIj7-Xg2I/AAAAAAAAO9I/OepzWuiM-BMZ-5sUcBnk9HBDFgPqlYbXgCEwYBhgL/s1600/results_decel2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1051" data-original-width="1170" height="574" src="https://1.bp.blogspot.com/-9e24jLUxMqQ/WspIj7-Xg2I/AAAAAAAAO9I/OepzWuiM-BMZ-5sUcBnk9HBDFgPqlYbXgCEwYBhgL/s640/results_decel2.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Deceleration performance. <b>HIGHER</b> values represent <b>BETTER</b> deceleration.</td></tr>
</tbody></table>
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The results are pretty nice and I can now decide more easily which propellers to use for which track. However, the standard deviation of acceleration and deceleration are really high, indicating a lot of noise in the data (which makes also sense). These results have to be 'consumed with caution'.<br />
HQ 5.1x5.1 have a very good acceleration and top speed, but the deceleration is bad. So for intermediate pilots like me, it will be more difficult to fly.<br />
<div dir="ltr">
I would choose HQ 5.1x5.1 for fast tracks, and Gemfan Hulkie 5055 for more technical tracks (due to the good deceleration performance).<br />
<h2>
Can I apply these results to my 2700 kV setup?</h2>
<div>
These relative results are probably valid for all RPM, they are not limited to a small range. But you have to keep in mind that your 2700 kV setup will most likely be overloaded by high-pitch or high diameter propellers. Let's put it this way: The HQ 5.1x5.1 v1s <i>would</i> be the fastest propeller on a 2700 kV setup if it does not burn or overload the motor or deplete the battery before you finished your flight.</div>
</div>
William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com5Bremen, Germany53.079296199999987 8.801693600000021452.774353199999986 8.15624660000002 53.384239199999989 9.4471406000000222tag:blogger.com,1999:blog-5821522320379987891.post-28445021456923171662017-12-22T20:02:00.000+01:002018-01-19T19:08:33.448+01:00CFD with FPV racing dronesI am currently checking the feasibility of computational fluid dynamics with racing drones in Autodesk CFD2018. <br />
<br />
This is one of my first attempts to simulate a simple copter draft by Heiko Schenk. I am still very new to CFD, so I am looking for feedback too.<br />
<div>
<br /></div>
<div>
I am including the effect of the propeller jet (velocity distribution and swirl) and also the motor housing rotation. The flow velocities of the propellers were calculated in JavaProp (33000 RPM, 360 Watts, 30 m/s, 3 blades, 5 inch diameter).</div>
<div>
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<div>
Watch this video for more information and some results:</div>
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<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/FSaFnPVWKns/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/FSaFnPVWKns?feature=player_embedded" width="320"></iframe></div>
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William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com4tag:blogger.com,1999:blog-5821522320379987891.post-2352037110823938762017-11-28T21:47:00.000+01:002017-12-06T21:08:16.111+01:00Part 2/3: Side force generators - Forces and turningAbout a month ago, I was presenting an idea to make drones faster on race tracks: The so called <a href="http://shrediquette.blogspot.de/2017/10/side-force-generators-sfgs-in-fpv-racing.html" target="_blank">‘side force generators’ (SFGs)</a> enable racing drones to drift less during turns, making them potentially faster. The placement of the ‘wings’ is very critical and mentioned in more detail in my <a href="http://shrediquette.blogspot.de/2017/10/side-force-generators-sfgs-in-fpv-racing.html" target="_blank">earlier post on SFGs</a>. Some people tested the SFGs and confirmed the enhanced flight characteristics. Other people didn’t try and didn’t believe that SFGs could help. I must agree that the concept of the SFGs is not so easy to understand. That is why I will explain it in more detail here.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://2.bp.blogspot.com/-Tni8tcicz1c/Wh3Er8wpvvI/AAAAAAAANq4/E6uV3O5dDLkvw7kECvtoJbpKWrOvk30FQCLcBGAs/s1600/sfgs_explained.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="505" data-original-width="800" height="202" src="https://2.bp.blogspot.com/-Tni8tcicz1c/Wh3Er8wpvvI/AAAAAAAANq4/E6uV3O5dDLkvw7kECvtoJbpKWrOvk30FQCLcBGAs/s320/sfgs_explained.jpg" width="320" /></a></div>
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<div>
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<div>
Let’s start with something that everyone knows (figure 1). When you are going through a fast turn with your car, then your car needs to provide two forces to stay on the track (grey line): The ‘thrust’ (green) of your car needs to equal its aerodynamic and friction drag (yellow). When the car turns, then there needs to be a constant force towards the centre of the turn, called <a href="https://en.wikipedia.org/wiki/Centripetal_force" target="_blank">‘centripetal force’</a> (red). This force is always required to make bodies follow a curved path.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-CL5ogbpSETQ/Wh3FAbzX0YI/AAAAAAAANq8/ujf_i_kjwU0KT-JkzHgWiaEfBf9mtnHawCLcBGAs/s1600/auto2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1024" data-original-width="1024" height="320" src="https://1.bp.blogspot.com/-CL5ogbpSETQ/Wh3FAbzX0YI/AAAAAAAANq8/ujf_i_kjwU0KT-JkzHgWiaEfBf9mtnHawCLcBGAs/s320/auto2.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1: A car during a turn (top view)</td></tr>
</tbody></table>
<br /></div>
<div>
It is calculated as: <span style="font-family: "courier new" , "courier" , monospace;">F<sub>centripetal</sub> = mass * velocity<sup>2</sup> / radius </span></div>
<div>
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<div>
If it is not present (e.g. when there is ice on the road), then the car cannot follow the curved path, it will continue straight. (The centrifugal force (blue) is a pseudo force, directed away from the axis of rotation. It is not required for the explanation of turning.)<br />
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The tyres of a car (figure 2, black arrows) provide the thrust force (via friction) and the centripetal force (via cornering force). You can also get rid of the cornering force of a tyre, then you will be drifting (see animated GIF).<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-D1gRV4aIJe4/Wh3Kv5jeaeI/AAAAAAAANrs/o3zDS4rKsqwaL6nHkmnBesPYK4NI92t5QCLcBGAs/s1600/drift_grip_rc_racing.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="408" data-original-width="600" height="217" src="https://2.bp.blogspot.com/-D1gRV4aIJe4/Wh3Kv5jeaeI/AAAAAAAANrs/o3zDS4rKsqwaL6nHkmnBesPYK4NI92t5QCLcBGAs/s320/drift_grip_rc_racing.gif" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Drifting (nice, but slow) vs gripping (fast) in RC cars</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-qTal4p4q6F8/Wh3FHV5g1BI/AAAAAAAANrA/IGtK4gJptIooA5tFG9-dIFlisw2EnFWbwCLcBGAs/s1600/auto3.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1024" data-original-width="1024" height="320" src="https://1.bp.blogspot.com/-qTal4p4q6F8/Wh3FHV5g1BI/AAAAAAAANrA/IGtK4gJptIooA5tFG9-dIFlisw2EnFWbwCLcBGAs/s320/auto3.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2: Forces of the tyres (black arrows)</td></tr>
</tbody></table>
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The centripetal force is a significant force! A standard car (weight = 1500 kg) that drives at 100 km/h and follows a circular path with 16 meters diameter needs 150 kN of centripetal force (that equals 15 tons)!<br />
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An airplane works like a car when performing a turn (figure 3): Thrust (green) is generated by a propeller, it equals the total drag of the airplane (yellow). During the turn, the airplane rolls left. The wings create the centripetal force (red) via extra lift that is directed towards the centre of the turn. These two forces (thrust and centripetal force) are mostly independent from one another, because they are generated by two different parts of the airplane (propeller and wing).<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-f7CLDMd9dlQ/Wh3FxJDgXQI/AAAAAAAANrI/JXXhOX9O61sWAqyX64gtjrCbPNQC2rQSgCLcBGAs/s1600/flug2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1024" data-original-width="1024" height="320" src="https://1.bp.blogspot.com/-f7CLDMd9dlQ/Wh3FxJDgXQI/AAAAAAAANrI/JXXhOX9O61sWAqyX64gtjrCbPNQC2rQSgCLcBGAs/s320/flug2.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3: A fixed wing plane during a turn (top view)</td></tr>
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This is very different in multirotors. They do not have wings, therefore all forces during a turn need to be produced by the propellers. The only way to make a turn and to create sufficient centripetal force (red) is to rotate your nose towards the centre of the turn. This will redirect the forces of each propeller (black), resulting in sufficient centripetal force (red).<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-DEWgCGsijPo/Wh3GjcB8dyI/AAAAAAAANrQ/umJpphSaiE4XcD9D5wMMPst1QAMZWHnSwCLcBGAs/s1600/copter3.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1024" data-original-width="1024" height="320" src="https://1.bp.blogspot.com/-DEWgCGsijPo/Wh3GjcB8dyI/AAAAAAAANrQ/umJpphSaiE4XcD9D5wMMPst1QAMZWHnSwCLcBGAs/s320/copter3.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 4: A copter during a turn (top view)</td></tr>
</tbody></table>
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But redirecting the force is not the optimal solution as I will show you in the following paragraph. Up to now, we ignored gravity, as it would unnecessarily complicate things. But let us assume that we have a multirotor that is travelling straight and with <i><b>full throttle</b></i>. The pitch angle is about 70 degrees (figure 5).<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-ez6RLzOLeCA/Wh3G-Xcw18I/AAAAAAAANrY/EvueIZJ5tTwae0szQpy6Eh2PO-xICt3KACLcBGAs/s1600/copter_level_flight.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="595" data-original-width="842" height="226" src="https://4.bp.blogspot.com/-ez6RLzOLeCA/Wh3G-Xcw18I/AAAAAAAANrY/EvueIZJ5tTwae0szQpy6Eh2PO-xICt3KACLcBGAs/s320/copter_level_flight.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 5: A copter in fast flight (side view)</td></tr>
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The total force of the propellers (black) constitutes of<br />
<br />
<ul>
<li>a horizontal ‘thrust’ component (green) that equals the aerodynamic drag of the copter (yellow)</li>
<li>a vertical ‘lift’ component (blue) that equals the weight of the copter (red) </li>
</ul>
<br />
The copter now wants to start a turn. We have learned, that the copter needs to create a significant centripetal force for turning to stay on the grey path. <b>But the motors already run at <i>full throttle</i>, there is no way to generate additional centripetal force!</b> As the weight of the copter is constant, the only solution to have a ‘force buffer’ for the centripetal force is to reduce the drag of the copter. This can only be done by reducing the speed.<br />
<blockquote class="tr_bq">
When motors run at full throttle, the only way to have enough motor power to generate sufficient centripetal force is to reduce speed. You need to slow down, which is not what you want during racing (in theory, you could also reduce the weight of a copter by accelerating downwards, but this is not really a practical solution). </blockquote>
<b><u>But here is the good news:</u></b> Side force generators offer (almost) free centripetal force for everyone! The key is that they work like wings and provide high lift (per definition perpendicular to the incident flow and hence directed towards the centre of the turn) while they only have a very small amount of extra drag. The ratio of lift and drag (L/D) depends on a lot of things, e.g. Reynolds number, air foil, angle of attack and aspect ratio.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-tNK06uQhyGk/WihN5_cpP1I/AAAAAAAAN3k/rKMynA3igJA9IovYkgNt6gRzj660hsI1gCLcBGAs/s1600/copter_turn-Kopie.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1024" data-original-width="1024" height="320" src="https://2.bp.blogspot.com/-tNK06uQhyGk/WihN5_cpP1I/AAAAAAAAN3k/rKMynA3igJA9IovYkgNt6gRzj660hsI1gCLcBGAs/s320/copter_turn-Kopie.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 6: A copter in a turn equipeed with SFGs (top view)</td></tr>
</tbody></table>
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The 'wings' create lift (black arrows) towards the centre of the turn. The nose does not need to be directed towards the centre of the turn that much anymore. The propellers do not need to contribute much centripetal force, but can be mainly used to compensate the aerodynamic drag at higher speeds. The copter will fly faster - in theory and in practice.<br />
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The SFGs that I use are mounted directly in the propeller jet, that means that they can easily achieve lift coefficients of unity while the drag coefficient stays small. At elevated flight speeds, a centripetal force (= lift) of 500g can be achieved – which equals the take-off weight of standard racing drones.<br />
<blockquote class="tr_bq">
This centripetal force is offered almost for free - don’t miss it!</blockquote>
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I hope that this explanation is clear and helps to understand the benefits of SFGs, otherwise please comment and I will adjust the text. </div>
William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com4Bremen, Germany53.079296199999987 8.801693600000021452.774353199999986 8.15624660000002 53.384239199999989 9.4471406000000222tag:blogger.com,1999:blog-5821522320379987891.post-16716912064996967022017-11-13T20:09:00.000+01:002017-11-13T20:09:09.399+01:00Winter preparations: Recoil stretchThis design was just finished, I am still searching for the perfect propellers. The performance is very good already, but the props are not durable enough. The MTM is 150mm, I noticed that quads fly cleaner and with less noise when there is some extra space between the propellers.<br />
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<h3>
Here is my setup</h3>
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<ul>
<li>Recoil stretch frame, 2.5mm carbon</li>
<li>Weight without Lipo: 80g</li>
<li>Take-off weight: 135g</li>
<li>AMAX inno 1105 4000 kV</li>
<li>Emax Bullet 12A ESCs</li>
<li>Tattu 4S 450 mAh 75C</li>
<li>Runcam Swift micro NTSC, 2.1mm</li>
<li>FXT FX806T VTX, 25 mW</li>
<li>Frsky R-XSR</li>
<li>Emax femto (still my favorite FC although I haven't tried many)</li>
<li>XT 30</li>
<li>AMAX inno 3030 3-blade props</li>
</ul>
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<br />William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com3Bremen, Germany53.079296199999987 8.801693600000021452.774353199999986 8.15624660000002 53.384239199999989 9.4471406000000222tag:blogger.com,1999:blog-5821522320379987891.post-37216556879663357392017-11-08T19:47:00.001+01:002017-11-10T15:02:00.333+01:00CAD design, manufacturing + test flight of an FPV racing airplaneI wanted to create a small FPV racing aircraft that has a good performance on small racing tracks with FAI gates. So I created this bimotor airplane. The yaw control makes it very agile. I am using a flight controller with iNAV firmware to stabilize all axes.<br />
The aileron servos are much too slow (0.1s/45°), so it was hard to tune. They will be replaced now with faster ones (0.05s/60°).<br />
Propellers are 4 x4.5 inch, motors are xnova 1407 - 3100kV, Lipo is 1Ah, 4s.<br />
I like the results, and I am looking forward to fly it on race tracks with a lot of gates.<br />
Watch this video to see a timelapse of the design and milling process, followed by some inflight clips:<br />
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<br />William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com0tag:blogger.com,1999:blog-5821522320379987891.post-72467937076489962662017-10-27T22:54:00.000+02:002017-12-05T22:47:19.354+01:00Part 1/3: Side Force Generators (SFGs) in FPV Racing<b>Summary: FPV racing multirotors with side force generators (SFGs), will drift less during turns, making them potentially faster on race tracks </b><b>(watch the <a href="https://youtu.be/3DKlLZw7k7A" target="_blank">video comparison here</a>)</b><b>. But the SFGs need the be carefully placed and dimensioned, so that <i>aerodynamic centre</i> and <i>centre of mass</i> are at the same position. Otherwise it will <u>not</u> work. </b><br />
<h2>
Introduction</h2>
Recently, I was thinking about how to improve the handling of racing copters. I noticed since quite a long time, that different copters behave quite differently in fast turns: Some drift quite a lot (especially when they carry a larger battery or an action cam), others drift less. I was always preferring copters that drift as little as possible. That is also why I am trying to reduce the weight of my copters as much as feasible.<br />
The amount of drift depends on the weight of the copter and the lift and drag of the fuselage for sideways air streams (side-slip). The larger the lift and drag, the more side force the fuselage produces at a given side slip angle. <i>More weight = more drift, more side force = less drift.</i><br />
If there is only very little side force available from the copter, then you have to point the nose of the copter towards the centre of the turn ('drift') to keep the desired trajectory. This is ok and fun most of the time. But on some tracks with a lot of fast and quick turns, you will drift so much that you will be really busy with pointing the nose towards the centre of the turn.<br />
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<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-pMBjT-XPkEU/We-bEPyHKOI/AAAAAAAANQ0/zQVAtnJFv9U2nhlK4KBnB1bZzPM2LuZAwCPcBGAYYCw/s1600/side_force_generators.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1266" data-original-width="1392" height="364" src="https://2.bp.blogspot.com/-pMBjT-XPkEU/We-bEPyHKOI/AAAAAAAANQ0/zQVAtnJFv9U2nhlK4KBnB1bZzPM2LuZAwCPcBGAYYCw/s400/side_force_generators.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Drift vs. grip. Drift: the nose of the copter always has to point towards the centre of the turn to keep the desired trajectory. Grip: The copter mostly follows the direction of the nose, it doesn't slip sideways.</td></tr>
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<span style="font-size: x-small;"><br /></span>
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<blockquote class="tr_bq">
<span style="font-size: x-small;">Side note: The name 'side force generators' (SFGs) is taken from RC aircraft: SFGs are winglet-like structures at the wing tips of aerobatic RC aircraft. They are used to enhance the performance in 3D flight by enhancing the effect of the rudder. Manoeuvers that require an effective rudder (e.g. knife edge flight) highly benefit from these devices.</span></blockquote>
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<tr><td class="tr-caption" style="text-align: center;">Side force generators (red) in aerobatic RC aircraft. (image from Hacker Motor GmbH)</td></tr>
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To reduce the amount of drift during turns, you can increase the side force of your copter by enlarging the area in sideview. The people from RedBull Dr.one increased the sideview area quite dramatically (thanks, Heiko Schenk, for the image) but pilots experienced huge problems with it. The large area creates huge amounts of torque around all axes when it is not perfectly aligned with the flow (and perfect alignment will never ever happen). Then, the motors will be extremely busy to fight this torque. In the end, the RedBull fin had to be removed, because it was unflyable (well, not really a big surprise).<br />
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-m5tPGHk_kns/We-oBSWbLJI/AAAAAAAANRo/TQqta7M56AcBnwzb544cAxX-WrtUb4-8wCLcBGAs/s1600/heiko_s.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="891" data-original-width="899" height="317" src="https://4.bp.blogspot.com/-m5tPGHk_kns/We-oBSWbLJI/AAAAAAAANRo/TQqta7M56AcBnwzb544cAxX-WrtUb4-8wCLcBGAs/s320/heiko_s.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">RedBull Dr.one fin causing problems with aerodynamic torque</td></tr>
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The problem with the above fin is that the aerodynamic centre of the fin is far away from the centre of mass. Flying objects become unstable when the aerodynamic centre is in front of the centre of mass (see picture below). However, they become stable, when the aerodynamic centre is behind the centre of mass. This is the case for fixed wing airplanes. For multirotors, it is best when aerodynamic centre and centre of mass are in the same position, otherwise you will lose maneuverability.<br />
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-wxmpm3L-gX4/WfDz25uQG0I/AAAAAAAANTU/aXacnHXopbsuSXpW4lQYhfx8QTJ-axk_QCLcBGAs/s1600/Aerodynamic-stability.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="541" data-original-width="993" height="217" src="https://3.bp.blogspot.com/-wxmpm3L-gX4/WfDz25uQG0I/AAAAAAAANTU/aXacnHXopbsuSXpW4lQYhfx8QTJ-axk_QCLcBGAs/s400/Aerodynamic-stability.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Aerodynamic stability of a flying object</td></tr>
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<h2>
Enlarging the area at the correct position</h2>
There are probably many solutions to enlarge the area in sideview of a copter and keep the aerodynamic centre at the same position as the centre of mass. Here is my solution: I measured the position of the centre of mass on my copter, an then designed a simple shape with the aerodynamic centre at the correct position.<br />
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-0_9uOGUprSk/We-bDvxhTrI/AAAAAAAANQw/ESrCg8EAhZowfIJYiU-8wV42qsoijZmuQCPcBGAYYCw/s1600/Unbenannt.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="864" data-original-width="1380" height="250" src="https://3.bp.blogspot.com/-0_9uOGUprSk/We-bDvxhTrI/AAAAAAAANQw/ESrCg8EAhZowfIJYiU-8wV42qsoijZmuQCPcBGAYYCw/s400/Unbenannt.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">SFGs on one of my copter designs</td></tr>
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I was calculationg the aerodynamic centre with the copter inclined at 45 degrees (because that is the inclination it might have on average on a racetrack).<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-iBn8XdbGaTw/We-r-T3Z_HI/AAAAAAAANR0/zKGkTt0hdnIzzGvt6HBGzxUQUoxjXBmDgCLcBGAs/s1600/45deg.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="935" data-original-width="1375" height="271" src="https://4.bp.blogspot.com/-iBn8XdbGaTw/We-r-T3Z_HI/AAAAAAAANR0/zKGkTt0hdnIzzGvt6HBGzxUQUoxjXBmDgCLcBGAs/s400/45deg.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The aerodynamic centre was calculated for 45 degrees inclination.</td></tr>
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Ideally, you would calculate the aerodynamic centre of the whole copter (including the area of the frame, lipo battery, motors etc.). But I think it is ok for now to ignore the other areas (assuming that the quad was flying ok without SFGs before). I am also ignoring the effect of the propeller jet and many more aerodynamic interactions for now.</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-55tbJbC1_Co/WfD40esU0pI/AAAAAAAANTs/VD_1xMbnBsYEqfUaUayA2abA9CWb-XxjQCLcBGAs/s1600/COM%252BAC.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="702" data-original-width="804" height="348" src="https://2.bp.blogspot.com/-55tbJbC1_Co/WfD40esU0pI/AAAAAAAANTs/VD_1xMbnBsYEqfUaUayA2abA9CWb-XxjQCLcBGAs/s400/COM%252BAC.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">SFGs will only work if the aerodynamic centre coincides with the centre of mass.</td></tr>
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The location of the aerodynamic centre of SFGs can easily determined by taking 25% of the average chord length of the 'wings':<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-_C_nkWJTAZ8/We-g8pC-JII/AAAAAAAANRU/fKg-a6tteK0zyBhDN2ShmdRIYJXvk0OAwCLcBGAs/s1600/ac.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="532" data-original-width="709" height="300" src="https://1.bp.blogspot.com/-_C_nkWJTAZ8/We-g8pC-JII/AAAAAAAANRU/fKg-a6tteK0zyBhDN2ShmdRIYJXvk0OAwCLcBGAs/s400/ac.gif" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Aerodynamic centre on an airfoil</td></tr>
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For my initial tests, I was using 3D printed airfoils. Later, I was using 1 mm thick carbon plates as wings.<br />
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<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-2aGAS6pSUeE/WfD7udws95I/AAAAAAAANT4/KJF2zy6cu58wl-tkMkT56KAy2edUwZc-wCEwYBhgL/s1600/IMG_20171017_173207.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1564" data-original-width="1600" height="312" src="https://2.bp.blogspot.com/-2aGAS6pSUeE/WfD7udws95I/AAAAAAAANT4/KJF2zy6cu58wl-tkMkT56KAy2edUwZc-wCEwYBhgL/s320/IMG_20171017_173207.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The first SFG prototypes were 3D printed wings</td></tr>
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When the copter flies straight, the SFGs do not add much area and will not increase drag too much.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-M3hiVifq-N0/WfD8GZhRzZI/AAAAAAAANT8/HNXjsR1ZruE5C7pIBM5N9rTNB0CEUIgnACLcBGAs/s1600/IMG_20171017_173125.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1508" data-original-width="1600" height="301" src="https://1.bp.blogspot.com/-M3hiVifq-N0/WfD8GZhRzZI/AAAAAAAANT8/HNXjsR1ZruE5C7pIBM5N9rTNB0CEUIgnACLcBGAs/s320/IMG_20171017_173125.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Frontal area does not increase much</td></tr>
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<h2>
Flight test results</h2>
<div>
After waiting a long time for some minutes without rain, I could finally do some test flight today. I like the results. The copter drifts much less, that makes fast flying easier. As long as some throttle is applied, you will not notice any negative side effects of the SFGs. But, when you fly at full speed, then completely cut the throttle, and then apply 90° yaw, then you will hear that some motors are spinning up a little bit to compensate the aerodynamic moments. But the copter does not do any unwanted movements (if PIDs and especially the 'I' are tuned correctly).</div>
<div>
Although I have a serious lack of flying practice, I did some side-by-side comparsion on a small racetrack. With SFGs, I am almost a second faster. And also the standard deviation (how much does the lap time vary) is much lower - I think because I do less pilot errors, because it is easier to fly. Fastest lap is lmost the same. <b>BUT: On the setup without SFGs, I was skipping one gate (because of bad lighting conditions that my old CMOS cam couldn't handle). Without skipping the gate, the lap times would be worse for the setup without SFGs.</b></div>
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<a href="https://youtu.be/3DKlLZw7k7A" target="_blank">Here is the video link.</a></div>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-lidaK80cWm8/WfOTL9MW56I/AAAAAAAANXM/Eq7t8GppCPIc2s5xhHqsZ83z0r82Y0ZggCLcBGAs/s1600/racetimes.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="151" data-original-width="600" height="80" src="https://4.bp.blogspot.com/-lidaK80cWm8/WfOTL9MW56I/AAAAAAAANXM/Eq7t8GppCPIc2s5xhHqsZ83z0r82Y0ZggCLcBGAs/s320/racetimes.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Lap times on a small track</td></tr>
</tbody></table>
<div>
How about trying it yourself? You can experiment with the shape of the blades easily by 3D printing different types of 2D blades.<br />
<br />
I uploaded some of my blade holders on thingiverse, feel free to adapt them to your quad:<br />
<a href="https://www.thingiverse.com/thing:2610750">https://www.thingiverse.com/thing:2610750</a></div>
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William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com10Bremen, Germany53.079296199999987 8.801693600000021452.774353199999986 8.15624660000002 53.384239199999989 9.4471406000000222tag:blogger.com,1999:blog-5821522320379987891.post-91506079604613788322017-01-28T22:10:00.001+01:002017-01-28T22:10:53.312+01:00125mm, 125g mini brushless copterCurrently, I love to fly with my latest design, called "RECOIL": It is a very small brushless copter (125mm MTM) with a total weight (including 3S 450 mAh lipo) of 125g. It however flies like a large copter and is a lot of fun!<br />
<br />
Emax F3 femto<br />RCX H1105 5000 kV<br />Racerstar 6A<br />3x2" props<br />3S 450 mAh<br />FX806TC<br />
<br />
<a href="https://www.youtube.com/watch?v=ctqIlr-9HOk"><b><span style="font-size: large;">https://www.youtube.com/watch?v=ctqIlr-9HOk</span></b></a><br />
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<br />William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com4tag:blogger.com,1999:blog-5821522320379987891.post-74415704792140046392016-11-24T19:21:00.002+01:002016-11-24T19:21:35.082+01:00Some brushed action for the winterIt has been a while since I posted something here. It is not because my project is dead, it is more because I spent my hobby time with flying and not with making new things. The derbe evo is almost perfect and I am very happy with it, so I don't see the need to design a new frame currently. But I am currently rewriting my flightcontroller code in order to achieve a faster control loop frequency. 1000 Hz should be possible on my 8bit ATXmega32A4. I will achieve this by using integers instead of floating point variables, and by removing every unnecessary line of code.<br />
<br />
<br />
But recently, I bought an Eachine QX90 (always wanted to adapt my own flight controller for a small brushed copter, but there was not enough time...). And it flies great. I however changed it a bit, here is my setup:<br />
<ul>
<li>QX90 original FC (stock firmware, see settings in the pictures below)</li>
<li>Standard motors</li>
<li>Gemfan 65mm propellers</li>
<li>Custom frame (weight: 5.5g, see pictures below)</li>
<li>Eachine TX01 cam with dipole antenna</li>
<li>Turnigy graphene 1S 600 mAh lipo (see picture)</li>
<li>Spektrum satellite receiver (the original FRSky receiver only had 50m range, now I have >500m)</li>
</ul>
Have a look at these videos for the flight performance:<br />
<br />
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<iframe width="320" height="266" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/dRpGm2Lygmg/0.jpg" src="https://www.youtube.com/embed/dRpGm2Lygmg?feature=player_embedded" frameborder="0" allowfullscreen></iframe></div>
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<br />
Some pictures of the frame and the cleanflight settings:<br />
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William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com0tag:blogger.com,1999:blog-5821522320379987891.post-143503801618516722016-04-23T11:54:00.004+02:002016-04-23T11:54:58.896+02:00Derbe evo available on Shapeways.comHey, I decided to make the derbe evo v2 available on Shapeways.com. So I don't have to send the files manually by e-mail. You can download or order using this URL:<br />
<a href="https://www.shapeways.com/shops/shrediquette" target="_blank"><strong><span style="font-size: large;">https://www.shapeways.com/shops/shrediquette</span></strong></a><br />
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<tr><td class="tr-caption" style="text-align: center;">The fleet...</td></tr>
</tbody></table>
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William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com0tag:blogger.com,1999:blog-5821522320379987891.post-67387360505188964462016-04-08T20:22:00.000+02:002016-04-08T20:22:20.801+02:00Derbe evo - Version 2I've been flying the derbe evo for a while now, and it is very agile and fast. I had to reduce the PD parameters by 30%. This is due to the fact that the mass is closer to the centre of the copter, and that reduces the moment of inertia. I was flying a competition with the derbe evo already (Hannover Cebit FPV Cup, <a href="https://www.youtube.com/watch?v=4nyRk8Dlreo" target="_blank">here's a video</a>). Unfortunately, the derbe evo crashed very hard during the qualifying (the gates were made out of massive steel, and the video reception was very poor). I think, I was frontally hitting a metal tube, and the 3D printed frame broke (two Cobra motors also have a bent shaft - I had to replace them as I do not manage to remove the shafts).<br />
I implemented some modifications in the new version. The camera angle (wide angle lens) is now 35° (instead of 25°) to allow for higher pitch props. The 3D printed frame is thicker. And the power conncetor is now integrated in the frame. Additionally, I added a small button for the TBS unify pro to change channels comfortably.<br />
<br />
There are many competitions this year that I am planning to attend, therefore I will most likely make another derbe evo frame as backup.<br />
<br />
<ul>
<li>Flying Fischkopp vs. Kloppokopter vs. FPV Nutz (16. April 2016)</li>
<li>FPV Drone Master (30. April 2016)</li>
<li>FPV Race Friedewalde (07. May 2016)</li>
<li>Copter Clash Hannover (28. May 2016)</li>
<li>Bexbach German Master (27. August 2016)</li>
</ul>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-N9Yws-JDbYo/Vwf1cWZXIqI/AAAAAAAADH8/nwwl39yDRoIFQHZOV6gpAgsAT83CRa8Pg/s1600/IMAG3070.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://3.bp.blogspot.com/-N9Yws-JDbYo/Vwf1cWZXIqI/AAAAAAAADH8/nwwl39yDRoIFQHZOV6gpAgsAT83CRa8Pg/s320/IMAG3070.jpg" width="318" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">RGB LEDs are mandatory on some events... </td></tr>
</tbody></table>
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<tr><td class="tr-caption" style="text-align: center;">Increased camera angle. The ultra-large capacitors <br />
might keep my ESCs and motors from dying all the time <br />
(I lost 4 motors due to ESC malfunction already). I also added a <br />
pull-down resistor (10k) to the signal wire of each ESC.</td></tr>
</tbody></table>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-LD4rmM4-kUU/Vwf1aGAnxwI/AAAAAAAADH4/cycTH6Uooy8mL_RcKc3ijPYisA1Xjfrww/s1600/IMAG3072.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://3.bp.blogspot.com/-LD4rmM4-kUU/Vwf1aGAnxwI/AAAAAAAADH4/cycTH6Uooy8mL_RcKc3ijPYisA1Xjfrww/s320/IMAG3072.jpg" width="181" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Pushbutton for channel selection & integrated power plug.</td></tr>
</tbody></table>
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<br />William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com7tag:blogger.com,1999:blog-5821522320379987891.post-86315775080683179982016-02-29T23:29:00.001+01:002016-03-10T22:26:53.330+01:00First flight - derbe evoThe copter had its first flight yesterday. With the 5.5" <span style="color: black;"><a href="http://shop.graupner.de/webuerp/AI?ARTN=1351.5,5X5" target="_blank">Graupner Race-Props</a></span>, the speed is absolutely amazing - I still need to learn how to control such a fast device properly.<br />
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<b>Here is a quick + dirty video:</b><br />
<b><a href="https://www.youtube.com/watch?v=V6I8i4Hk2J0" target="_blank">https://www.youtube.com/watch?v=V6I8i4Hk2J0</a> </b><br />
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<em>And Shrediquette is still open source of course, so here are the 3D files:</em><br />
<a href="http://william.thielicke.org/multirotors/derbe_evo_v97.zip" target="_blank"><em>william.thielicke.org/multirotors/derbe_evo_v97.zip</em></a><br />
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The arms are from the Claerials HUMs quadrotor: <a href="http://claerials.com/shop/hums-ersatzarm/">http://claerials.com/shop/hums-ersatzarm/</a><br />
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<br />William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com3tag:blogger.com,1999:blog-5821522320379987891.post-11729345690030629992016-02-25T21:47:00.001+01:002016-02-25T21:47:45.434+01:00Shrediquette derbe evo: Finished, first flight this weekend (if it's not raining constantly...)The derbe evo is ready, I just need to find a suitable antenna...
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<br />William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com1tag:blogger.com,1999:blog-5821522320379987891.post-3400202550358550472016-02-23T23:45:00.000+01:002016-02-23T23:45:07.812+01:00Shrediquette derbe evo progressSome images of the assembly process...:<br />
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There is not much space inside the frame, but everything fits. The assembly also went quicker than I thought. I just need to replace all the motor shafts of the Graupner Ultra 2806 2300 kV motors (due to a hard crash), and then I am ready to go.<br />
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The take-off weight is just 447 grams.William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com0tag:blogger.com,1999:blog-5821522320379987891.post-64326328944131268872016-02-22T06:57:00.001+01:002016-02-22T06:58:34.229+01:00derbe evo FPV racing quad<div class="separator" style="clear: both; text-align: center;">
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I think I now have all the parts that I need to start assembly. The frame weight is 77 grams (without electronics).<br />
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<b>Here is the latest teaser:</b><br />
<b><a href="https://youtu.be/no3FbcdH4LE">https://youtu.be/no3FbcdH4LE</a></b>William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com2tag:blogger.com,1999:blog-5821522320379987891.post-45677544495611760792016-01-31T21:17:00.000+01:002016-02-13T11:00:25.287+01:00My next FPV racing machine...Here are some renderings of my latest frame concept. It has a very small frontal area and should reach high speeds. The diagonal motor distance is 210 mm and I will use 5.5 inch propellers (<a href="http://shop.graupner.de/webuerp/AI?ARTN=1351.5,5X5" target="_blank">Graupner Race-Prop</a> or C-prop).<br />
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William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com10tag:blogger.com,1999:blog-5821522320379987891.post-9504970781602517132016-01-11T23:30:00.000+01:002016-01-11T23:30:11.688+01:00Explanation video: FPV camera tilt compensationThis is a <a href="http://shrediquette.blogspot.de/2016/01/some-thoughts-on-camera-tilt.html" target="_blank">follow up to the previous post on tilt compensation</a>. <br />
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I made a video where I explain what FPV camera tilt compensation is needed for, how it works and how it looks like in flight:<br />
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<span style="font-size: large;"><a href="https://youtu.be/gXeaINFpvow" target="_blank">https://youtu.be/gXeaINFpvow</a></span><br />
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In FPV camera tilt compensation, control <i><b>inputs</b></i> (RC transmitter --> FC) are transformed to the local frame of reference of the <b><i>camera</i></b>.<br />
<br />The control <b><i>outputs </i></b>(FC --> motors) may additionally be transformed to the local frame of reference of the <b><i>propellers </i></b>(if e.g. the props are tilted or the FC is mounted at an angle - use parameters like 'board align' for control output transforms).William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com1tag:blogger.com,1999:blog-5821522320379987891.post-69916265182900688742016-01-07T23:51:00.001+01:002016-01-11T23:43:58.916+01:00Some thoughts on FPV camera tilt compensationAlmost every 'serious' FPV racer is tilting the FPV camera up in order to have a better image during fast flight. Angles between 10 and 35 degrees seem to be common. E.g. I am using 25 degrees. But tilting the camera with respect to the multirotors horizontal plane has a side effect on the controls (maybe you never thought about it, because you are so used to flying with this side effect).<br />
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Just to make the effect easier to visualize: Imagine you drank a beer too much and now you suddenly think you are <a class="yt-uix-sessionlink g-hovercard spf-link " data-sessionlink="itct=CC8Q4TkiEwizqaTz3ZjKAhWWkRYKHSXsByMo-B0" data-ytid="UCzOIsjoOkG1JVoPVek9cu1Q" href="https://www.youtube.com/channel/UCzOIsjoOkG1JVoPVek9cu1Q">Charpu</a>, <a class="yt-uix-sessionlink g-hovercard spf-link " data-sessionlink="itct=CC8Q4TkiEwjeg-6d3pjKAhVPABYKHZIgBv0o-B0" data-ytid="UCQEqPV0AwJ6mQYLmSO0rcNA" href="https://www.youtube.com/channel/UCQEqPV0AwJ6mQYLmSO0rcNA">Mr Steele</a> or <a class="yt-uix-sessionlink g-hovercard spf-link " data-sessionlink="itct=CC8Q4TkiEwiHubTc3ZjKAhVGChYKHVZdC-4o-B0" data-ytid="UC7gB_Nbj6RSPZTvTeNOk5jg" href="https://www.youtube.com/channel/UC7gB_Nbj6RSPZTvTeNOk5jg">Mattystuntz</a>. You mount your FPV camera with 90 degrees tilt (pointing up vertically) because your best friend told you that all the pros do it like this. In this case, your roll and yaw control will be interchanged: When you move your RC sticks to roll left, your copter will roll left, but looking through the FPV camera, it appears as if you are yawing to the left! And if you move your RC sticks to yaw left, your copter will of course yaw left, but the image from the FPV cam looks like you would roll to the right!<br />
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The strength of this effect is somewhat proportional to the camera tilt angle. But already at 25 degrees it can clearly be noticed. It doesn't really make sense to have control in the copters frame of reference when flying FPV. It does make more sense to shift the frame of reference to the FPV camera and to eliminate the effect of camera tilt: Moving the roll stick of the transmitter should roll the camera image only, it shouldn't add some undefined amount of yaw.<br />
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Luckily, it is easy to compensate these effects (you might even do this in your transmitter by adding some mixers). I however hardcoded this in my latest flightcontroller firmware. The code is like this:<br />
<blockquote class="tr_bq">
<span style="font-family: Times,"Times New Roman",serif;"><span style="font-size: small;">Roll_output = <span style="color: blue;">cos</span>(camera_tilt) * Roll_input - <span style="color: blue;">sin</span>(camera_tilt) * Yaw_input</span></span><br />
<span style="font-family: Times,"Times New Roman",serif;"><span style="font-size: small;">Yaw_output = <span style="color: blue;">sin</span>(camera_tilt) * Roll_input + <span style="color: blue;">cos</span>(camera_tilt) * Yaw_input</span></span></blockquote>
'camera_tilt' is the angle (in radians) that your FPV camera is tilted up with respect to the propeller disks. It is a constant. I am using 25 degrees of camera tilt (= <span class="cwcot" id="cwos">0.436 radians).</span><br />
<span class="cwcot" id="cwos">'Roll_input' is the roll rate that you steer with your remote control.</span><br />
<span class="cwcot" id="cwos">'Yaw_input' is the yaw rate that you steer with your remote control.</span><br />
<span class="cwcot" id="cwos">'Roll_output' is the setpoint for the multicopters roll rate.</span><br />
<span class="cwcot" id="cwos">'Yaw_output' is the setpoint for the multicopters yaw rate.</span><br />
<span class="cwcot" id="cwos"> </span><span class="cwcot" id="cwos"> </span><br />
<span class="cwcot" id="cwos">I am not familiar with other flight controllers, but I guess this feature might have been implemented already in some of them. Otherwise it really <i>should </i>be implemented...! </span><br />
<br />
<span class="cwcot" id="cwos" style="font-size: large;">Here is a video explaining the above:</span><br />
<span class="cwcot" id="cwos"><a href="http://shrediquette.blogspot.de/2016/01/explanation-video-fpv-camera-tilt.html" target="_blank">http://shrediquette.blogspot.de/2016/01/explanation-video-fpv-camera-tilt.html </a></span>William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com7tag:blogger.com,1999:blog-5821522320379987891.post-12030878493248036222015-12-30T13:14:00.000+01:002015-12-30T13:23:00.643+01:00Aerodynamics in racing multirotors! Part 2.<h2>
Introduction</h2>
In <a href="http://shrediquette.blogspot.de/2015/08/aerodynamics-in-racing-multirotors.html" target="_blank">part 1 of this article on multirotor aerodynamics</a>, some ideas on how to reduce the aerodynamic drag of racing multirotors was presented. I was also designing a tilted-body racing quadrotor called "<a href="http://shrediquette.blogspot.de/2015/09/shrediquette-derbe-almost-there.html" target="_blank">Shrediquette DERBE</a>". There were not yet any flow measurements of multirotors flying at high speeds. Therefore, I had to make quite a number of assumptions on the aerodynamics of a racing copter. This time, I am presenting some flow measurements, along with some potential optimizations for the next version of the "Shrediquette DERBE"<br />
<h2>
Methods</h2>
Recently, I had the opportunity to do some flow visualizations in a large wind tunnel at the <a href="http://bionik-bremen.de/" target="_blank">Bremen university of Applied Sciences / Dept. of biomimetics</a> (which is the place where I worked one year ago). I brought the <a href="http://shrediquette.blogspot.de/2015/09/shrediquette-derbe-almost-there.html" target="_blank">Shrediquette DERBE</a> and mounted it inside the wind tunnel. Prior to the measurements, I did some tests to determine a realistic flight speed and the appropriate pitch angle.<br />
The measurements were performed at a pitch angle of 45 degrees with the motors running at full throttle (control loops are all turned off completely). Wind speed was set to 30 m/s. The Shrediquette DERBE was equipped with Graupner C-Prop 5.5x3", 4S 75C, Ultra 2806 2300 kV.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-mfxBJXGxH3w/VoEoSQeeymI/AAAAAAAAC80/7e99GYPqcEE/s1600/IMAG2623.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="237" src="http://3.bp.blogspot.com/-mfxBJXGxH3w/VoEoSQeeymI/AAAAAAAAC80/7e99GYPqcEE/s320/IMAG2623.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">DERBE mounted inside the wind tunnel</td></tr>
</tbody></table>
The flow was visualized with a method called <a href="http://en.wikipedia.org/wiki/Particle_image_velocimetry">Particle Image Velocimetry (PIV)</a>. This allows to measure space- and time-resolved flow velocities in fluids: Some very small tracer particles are added to the air (e.g. oil droplets). These particles are illuminated by a laser in a very thin sheet. A camera is mounted perpendicular to this sheet, recording the motion of all the tracer particles. The discplacement of the particles is used to calculate the velocity of the fluid. During my PhD research, I was developing a tool (called 'PIVlab') to perform these kind of measurements within Matlab (see <a href="http://openresearchsoftware.metajnl.com/article/10.5334/jors.bl/" target="_blank">this article for more information</a>).<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-bYsO1cM1Rj8/VoErEpGdL5I/AAAAAAAAC9Q/ItBdGAr3sM0/s1600/Unbenannt.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="278" src="http://4.bp.blogspot.com/-bYsO1cM1Rj8/VoErEpGdL5I/AAAAAAAAC9Q/ItBdGAr3sM0/s320/Unbenannt.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Particle image velocimetry: Setup consisting of high-power laser, high-speed camera and particles in the fluid.</td></tr>
</tbody></table>
<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-V4xJjb2nDIA/VoEoS0Wo3FI/AAAAAAAAC9E/Xs7PX2JkJQQ/s1600/IMAG2629.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="237" src="http://4.bp.blogspot.com/-V4xJjb2nDIA/VoEoS0Wo3FI/AAAAAAAAC9E/Xs7PX2JkJQQ/s320/IMAG2629.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">PIV measurement with a laser sheet</td></tr>
</tbody></table>
Here is a short clip that shows the copter 'flying' in the wind tunnel: <a href="https://www.youtube.com/watch?v=tVVhdlqB38A" target="_blank">Youtube Video</a><br />
<br />
I measured the flow at four different locations (labelled A/B/C/D):<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-tfbVJPuqkCE/VoIz4Nd3_DI/AAAAAAAAC94/u_hEmHpwb54/s1600/liftquad1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="311" src="http://4.bp.blogspot.com/-tfbVJPuqkCE/VoIz4Nd3_DI/AAAAAAAAC94/u_hEmHpwb54/s320/liftquad1.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Top view of a multirotor. The green lines show the locations where flow velocities were determined.</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/--D482re95vg/VoJV_DfuA6I/AAAAAAAAC-Y/R8kiB-EPUEo/s1600/Ohne%2BTitel_000000.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="298" src="http://4.bp.blogspot.com/--D482re95vg/VoJV_DfuA6I/AAAAAAAAC-Y/R8kiB-EPUEo/s400/Ohne%2BTitel_000000.gif" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">This image sequence shows the laser sheet in position B.</td></tr>
</tbody></table>
<h2>
Results</h2>
The flow over the main frame is mostly horizontal - <em>hence a tilted-body concept really makes sense.</em> This concept aims to align the main frame parallel with the flow to reduce the frontal area and hence the aerodynamic drag (which is proportional to frontal area). The following image shows the flow velocities around the main frame (position A). The arrows indicate the direction, and the colors indicate the relative velocity magnitude:<br />
<span style="color: orange;"><strong>Warm colors:</strong></span> Flow > 30 m/s<br />
<span style="color: #3d85c6;"><strong>Cool colors:</strong></span> Flow < 30 m/s<br />
<strong><span style="color: #990000;">Dark red:</span></strong> shadows / no measurements possible<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-JWIj9zPovLw/VoGkd6dkwXI/AAAAAAAAC9g/lV8-FpvPdPE/s1600/center_026.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="http://1.bp.blogspot.com/-JWIj9zPovLw/VoGkd6dkwXI/AAAAAAAAC9g/lV8-FpvPdPE/s320/center_026.jpg" width="261" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">PIV measurement around the main frame (position A): The flow is mostly horizontal in this plane.</td></tr>
</tbody></table>
The flow under the propellers is actually highly assymmetric. It does not make sense to assume a constant flow velocity below the propellers. In measurement position B, the blades of the front propeller move forward, and the blades of the rear propeller move backward through the measurement plane (see the animated image sequence above). Therefore, the front propeller blades experience much higher flow velocities than the rear propeller blades. Hence, only the front propeller blades generate thrust in this plane. Furthermore, the assumption that the flow is perpendicular to the propeller disk below the propellers is only true for the regions of the propeller disk where the blades move forward.<br />
The velocities in measurement position B are shown in the following image. Note the high flow acceleration (warm colors) behind the front propeller. Also note that the rear propeller does not accelerate the flow at this measurement position - it is almost passive.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-gpa6yJj3Rx8/VoGkhALDJ7I/AAAAAAAAC9o/xrvIGSAuthQ/s1600/pos1_050_img_050.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="223" src="http://3.bp.blogspot.com/-gpa6yJj3Rx8/VoGkhALDJ7I/AAAAAAAAC9o/xrvIGSAuthQ/s320/pos1_050_img_050.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Measurement position B: Only the blades that move forward through the plane (= the front propeller) generate thrust. </td></tr>
</tbody></table>
<br />
Together with the results of the other measurement positions (not shown here), we can safely assume that only parts of the propeller (disk) generate thrust in high speed forward flight. This is very similar to the aerodynamics of large helicopters, where also the advancing and retreating blades experience very different flow velocities and generate different amounts of lift and drag). The importance of this effect (sometimes also called <a href="https://en.wikipedia.org/wiki/P-factor" target="_blank">P-factor</a>), is linked to the <a href="https://en.wikipedia.org/wiki/Advance_ratio" target="_blank">advance ratio</a> of the propeller. Earlier, I actually thought that this effect might be negligible on multirotors, but this is clearly not true. A multirotor in fast forward flight only creates noteworthy lift in the green areas shown in the following image. In the centre of the red areas, the propellers might even create additional drag:<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-UzSGhdWfKTw/VoI5DV6w6kI/AAAAAAAAC-I/qcUWSPD7n9M/s1600/liftquad2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="306" src="http://4.bp.blogspot.com/-UzSGhdWfKTw/VoI5DV6w6kI/AAAAAAAAC-I/qcUWSPD7n9M/s320/liftquad2.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Multirotor in fast forward flight: The green areas create most lift, parts of the red areas might even create drag.<br />
Note that this is only true for the propeller rotational directions shown in this image. If all propellers<br />
rotate in the other directions, then red and green areas need to be inversed.</td></tr>
</tbody></table>
<br />
<h2>
Conclusions</h2>
What does this mean for our racing multirotors? Tilted bodies make sense, as the flow is really horizontal at the main body. Vertical arms (as in the Shrediquette DERBE, see image below) are however problematic for two reasons:<br />
<ol>
<li>The flow will only be parallel to the arms at the front propellers. Because only these propellers do really accelerate the flow in fast flight. <em>Below the rear propellers (the flow is not accelerated here), the flow will actually hit the arms from the side - which causes a large drag penalty</em>.</li>
<li>Multirotors use their motors to rotate around the pitch / roll / yaw axes. The force (or better: the moment) to rotate around the roll and pitch axis is induced by generating differential thrust between opposing propellers. Very large forces can be generated around these axes. As an extreme example: If both front motors run at full throttle, and the rear motors are off, then the pitch moment (moment = radius * force) could be around M = 0.12 meters * 12 Newtons = 1.4 Nm. But the force around the yaw axis is much lower because it is induced only by the torque of the motors - not by the thrust. If we assume the propellers to have a lift-to-drag ratio of 10:1 and a diameter of 5 inch, then <em>the moment around the yaw axis is about 20 times lower than the moment around roll or pitch axes</em>. <em>Due to their orientation, vertical arms can however generate large forces around the yaw axis which can not be compensated by the small torque of the motors. In order to have a better control around yaw, it makes more sense to not rotate the arms.</em></li>
</ol>
<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-0PjCI7MAg7U/VoJjPkQqmwI/AAAAAAAAC-o/i5vfOqr5v38/s1600/Derbe-sideview.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="190" src="http://4.bp.blogspot.com/-0PjCI7MAg7U/VoJjPkQqmwI/AAAAAAAAC-o/i5vfOqr5v38/s320/Derbe-sideview.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Do vertical arms make sense...? Not really...</td></tr>
</tbody></table>
In the last weeks, I designed a standard racing quadrotor (called 'Shrediquette 0815') that I use to test the properties of 3D printed frames. I learnt how to design a very rigid and lightweight plastic frame. I will use this knowledge to improve the design of the <strong>Shrediquette DERBE II</strong>.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-CAbWE1Njxrg/VoOfzV9RLUI/AAAAAAAAC-4/pPbd1fyk4Eg/s1600/edited_1448575781702.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="279" src="http://2.bp.blogspot.com/-CAbWE1Njxrg/VoOfzV9RLUI/AAAAAAAAC-4/pPbd1fyk4Eg/s320/edited_1448575781702.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Shrediquette 0815, a standard racing quadrotor that I designed for training and to learn more about<br />
lightweight and rigid plastic construction.</td></tr>
</tbody></table>
William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com12tag:blogger.com,1999:blog-5821522320379987891.post-32984063402052237652015-10-01T13:02:00.000+02:002015-10-01T20:08:26.646+02:00How to measure top speeds of multirotorsHow fast can your multirotor fly? The simplest solution for this question would probably be to attach a GPS device (tracker / OSD) to your multirotor and to read out the maximum speed.<br />
<div>
<br /></div>
<div>
<i>But hey, this is pretty imprecise...!</i></div>
<div>
<i><br /></i></div>
<div>
GPS devices suffer from measurement noise (e.g. through signal degradation), which becomes problematic on rapidly accelerating objects like our multirotors. More advanced GPS chipsets (e.g. u-blox LEAx) have the option to choose between different filtering modes (e.g. pedestrian, car, airborne), that make some assumptions on the maximum accelerations and movements of the sensor and filter the results accordingly. That will most likely improve the accuracy of the measurements, but still noise might remain. Here is an <a href="http://www.insidegnss.com/auto/marapr15-SOLUTIONS.pdf" target="_blank">interesting article on GPS speed measurements</a>, which states that the classical methods to calculate velocities in GPS receivers have an accuracy in the order of a few meters per second, due to significant noise.<br />
<br />
I was recently attaching <a href="http://www.sm-modellbau.de/shop/product_info.php?products_id=145&cPath=15" target="_blank">a pretty good GPS logger</a> to a quadrotor (HUMs with Cobra 2204, 75C 4S 1300 mAh, C-prop 5x3). There seemed to be hardly any wind. <b>The "Top Speed" value reported by the tracker was 113 km/h.</b> But this value includes the influence of measurement noise and wind, and it is therefore not precise.<br />
<br />
The only way that I know of how to deal with these problems and how to get the <i>real</i> (air)speed out of a GPS logger is to do the following:<br />
<br />
<br />
<ul>
<li>Fly full speed at a constant height, on a straight line and against the wind for at least 300 meters. </li>
<li>Then, turn around and fly the same straight line but in the other direction. </li>
<li>Download the data from the logger and calculate the average of each of these two straight line runs (this will remove or at least attenuate noise). </li>
<li>Now, calculate the average of the two runs (this will remove the influence of wind and yield the true airspeed).</li>
</ul>
<br />
<br />
<b>The true airspeed of my copter was calculated to be 95 km/h, which is 16 % lower</b> than the maximum speed reported by the logger. And I must add that this was a day where I felt hardly any wind. Still the wind velocity was about 10 km/h according to the GPS measurements. More wind will of course make the difference even bigger.<br />
<br />
So if you hear people saying "Hey, my quadrotor is flying 150 km/h!", then be careful until you saw the measurements...<br />
<br />
<br />
<i>Today, I'll hopefully measure the top speed of my Shrediquette DERBE, let's see what comes out...!</i></div>
William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com1tag:blogger.com,1999:blog-5821522320379987891.post-21789632706409691392015-09-23T22:55:00.001+02:002015-09-23T22:55:26.112+02:00Shrediquette DERBE ... almost there...Here are some images of my racing copter. Some soldering of the ESCs etc. still has to be done. I am also waiting for some resistors and capacitors for my flight controller to arrive... But I guess the maiden flight will be this weekend :-D.<br />
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<br />William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com3tag:blogger.com,1999:blog-5821522320379987891.post-75140624034560605572015-08-31T16:03:00.000+02:002015-08-31T16:26:11.490+02:00Aerodynamics in racing multirotors!<h3 style="text-align: justify;">
Why future racing copters really should look different.
</h3>
<h3 style="text-align: justify;">
<em>by Dr. William Thielicke aka Willa aka Shrediquette</em></h3>
<div style="text-align: justify;">
<br /></div>
<h3 style="text-align: justify;">
ABSTRACT
</h3>
<div style="text-align: justify;">
<i>In this article I try to demonstrate why FPV racing multirotors need to look different. Some small modifications to the frame would (in theory…!) result in 70 % higher top speed! All that needs to be done is to align the arms parallel to the propeller flow, and to tilt the main body of the copter by about 40 degrees. I am presenting a very simple and robust racing copter design that incorporates these ideas. Furthermore, I am calculating the aerodynamic drag of different copter concepts using basic equations. The aim of this article is to make you realize the importance of aerodynamics and to stimulate people to design more innovative racing frames.</i>
</div>
<div style="text-align: justify;">
<br /></div>
<h3 style="text-align: justify;">
INTRODUCTION
</h3>
<div style="text-align: justify;">
Until recently, multirotors were mainly used as a “hovering device” and the top speed of these copters did hardly matter. Now, multirotor racing has become popular and all competitors are seeking for very fast and agile multirotors.
</div>
<div style="text-align: justify;">
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-8RxgF5ys8eo/VeILkt7e9QI/AAAAAAAAC3c/mGR8zOvwVmI/s1600/bexbach.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="121" src="http://1.bp.blogspot.com/-8RxgF5ys8eo/VeILkt7e9QI/AAAAAAAAC3c/mGR8zOvwVmI/s400/bexbach.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">FPV racing in Bexbach, Micha vs. Willa</td></tr>
</tbody></table>
</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Apparently, the aerodynamics of multirotors have been neglected in the past (with a very few exceptions), but aerodynamics actually become very important at increasing flight velocities. Just as a quick example with numbers that are realistic for copter racing: A quadrotor that weighs 0.7 kg and flies at a pitch angle (alpha) of 45 degrees has an aerodynamic drag that is also 0.7 kg (about 7 N) – which is clearly very significant. A large portion of the force that is generated by the motors is therefore just “wasted”! If this drag could be somehow reduced, then a racing copter could fly a lot faster (or it could fly longer at the same speed).</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-npUEgJBBpXU/VeIL8We-M9I/AAAAAAAAC3k/XyMPJYo_gNg/s1600/Kr%25C3%25A4fte.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="http://2.bp.blogspot.com/-npUEgJBBpXU/VeIL8We-M9I/AAAAAAAAC3k/XyMPJYo_gNg/s320/Kr%25C3%25A4fte.jpg" width="297" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Forces acting on a constant-speed multirotor at 45° pitch angle. Drag is important.</td></tr>
</tbody></table>
</div>
<h3 class="MsoNormal" style="margin: 0cm 0cm 8pt; text-align: justify;">
<o:p></o:p> </h3>
<h3 class="MsoNormal" style="margin: 0cm 0cm 8pt; text-align: justify;">
AERODYNAMICS OF A RACING COPTER
</h3>
<div style="text-align: justify;">
The real flow of the air around a full multirotor has not yet been measured to the best of my knowledge. But it is very likely, that the flow around the multirotor can be divided into two distinct parts: The flow around the arms, and the flow around the main body: Directly under the propellers, the flow is pretty fast (between 100 and 200 km/h in racing copters) and it is pretty much perpendicular to the propeller disks. Just as in this picture showing the flow of a large propeller:
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<tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-kMt8nm9Q36k/VeINYabryQI/AAAAAAAAC3w/-txTIZWSEsc/s1600/heli.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-kMt8nm9Q36k/VeINYabryQI/AAAAAAAAC3w/-txTIZWSEsc/s1600/heli.jpg" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Usually, the flow is perpendicular to the propeller disk. <br />
The faster a propeller turns in relation to the flight speed ("advance ratio"), <br />
the more constant is the angle of the flow.</td></tr>
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The flow that is hitting the main body or frame is mostly horizontal, as it is hardly influenced by the propellers: It is mainly exposed to the flow velocity that results from forward flight (I however really need to verify these assumptions in a windtunnel or with in-flight measurements, I'll do that asap and report the results here).</div>
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<tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-U5DGL9Z9g2U/VeIN8gD97_I/AAAAAAAAC34/EnGwEfCzsJs/s1600/prelude_Vergleich-Copter.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="226" src="http://3.bp.blogspot.com/-U5DGL9Z9g2U/VeIN8gD97_I/AAAAAAAAC34/EnGwEfCzsJs/s320/prelude_Vergleich-Copter.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Simplified model of the main flow components on a quadrotor.</td></tr>
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HOW TO ENHANCE AERODYNAMICS?
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It would make a lot of sense to reduce the drag of the arms below the propellers, and to reduce the drag of the main body of the racing copter. My first and simple idea to achieve this was to tilt the motors forward, and to design an aerodynamic canopy. These ideas were implemented in the <a href="http://shrediquette.blogspot.de/p/shrediquette-gemini.html" target="_blank">“Shrediquette Gemini</a>” in 2013 (which was later produced by <a href="http://team-blacksheep.com/products/prod:gemini" target="_blank">Team-Blacksheep</a>).
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<tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-2Qh5fw7EWoo/UTW5A5uJMsI/AAAAAAAACyg/earRQX9SUhE/s1600/IMAG0129.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="128" src="http://2.bp.blogspot.com/-2Qh5fw7EWoo/UTW5A5uJMsI/AAAAAAAACyg/earRQX9SUhE/s320/IMAG0129.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Shrediquette GEMINI / TBS Gemini</td></tr>
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<a href="http://shrediquette.blogspot.de/2013/03/wind-tunnel-test-data.html" target="_blank">Some force measurements in a wind tunnel</a> revealed that these two features reduced the drag of the copter by 14 – 40% (depending on the pitch angle).
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My next idea was to tilt the body instead of the propellers. The goal was to align the body with the oncoming, horizontal flow, which will significantly reduce the aerodynamic drag. If the arms are aligned parallel to the propeller flow (= perpendicular to the propeller disk), the drag will be further minimized. <a href="http://shrediquette.blogspot.de/2014/07/hexo-autonomous-aerial-cam-kickstarter.html" target="_blank">My HEXO+ design</a> (which was used in a Kickstarter project too) realized the idea of a tilted body.
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-39P_pEYhpUQ/VeIO_vKf-4I/AAAAAAAAC4E/1AU7fNN28w0/s1600/hexo%252Bflow.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="http://4.bp.blogspot.com/-39P_pEYhpUQ/VeIO_vKf-4I/AAAAAAAAC4E/1AU7fNN28w0/s400/hexo%252Bflow.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The HEXO+, a larger and modified variant of the Gemini</td></tr>
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<a href="http://2.bp.blogspot.com/-evE3tME9fKE/U8OQpkZQ4bI/AAAAAAAACUA/1_gIG2_hxKc/s1600/render-NLAF0040.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://2.bp.blogspot.com/-evE3tME9fKE/U8OQpkZQ4bI/AAAAAAAACUA/1_gIG2_hxKc/s320/render-NLAF0040.jpg" width="320" /></a></div>
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The tilted body concept was subsequently ported to my next frame, the “Shrediquette QRC5” FPV racing copter:</div>
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<tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-Mg2Cl8hAW4U/VUmmMbCDq6I/AAAAAAAACq4/qAYqW6pp3wo/s1600/qrc5.4.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="213" src="http://3.bp.blogspot.com/-Mg2Cl8hAW4U/VUmmMbCDq6I/AAAAAAAACq4/qAYqW6pp3wo/s320/qrc5.4.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The QRC5 FPV racing quadrotor</td></tr>
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Recently, I realized that a frame like the QRC5 is not crashproof enough for everyday FPV racing. Therefore I recently finished a “classical” FPV racing copter design that incorporates the idea of a tilted body and arms that are aligned parallel to the propeller flow. The “Shrediquette DERBE” is probably as crashproof and light as conventional racing copters, but it has much less aerodynamic drag. <br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-nJrzlS6KFUo/VeLVIVS-kCI/AAAAAAAAC4s/kUjsrnSMkEc/s1600/Derbe-sideview.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="177" src="http://1.bp.blogspot.com/-nJrzlS6KFUo/VeLVIVS-kCI/AAAAAAAAC4s/kUjsrnSMkEc/s320/Derbe-sideview.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The main body of the Shrediquette DERBE is tilted by 40 degrees.</td></tr>
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The following image nicely illustrates the two main sources of drag as introduced earlier, and how drag is minimized in the Shrediquette QRC5 and the Shrediquette DERBE. The idea is to minimize the frontal area of the copter at typical pitch angles (about 50 degrees in FPV racing), and to minimize the area under the propellers.
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-q5mZCZTCZ_Y/VeIRHWdK0wI/AAAAAAAAC4Q/sxiTCjS_5IQ/s1600/Vergleich-Copter.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="256" src="http://1.bp.blogspot.com/-q5mZCZTCZ_Y/VeIRHWdK0wI/AAAAAAAAC4Q/sxiTCjS_5IQ/s400/Vergleich-Copter.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Three different concepts: Comparison of frame area (green) <br />
and area of the arms under the propeller (blue).</td></tr>
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CALCULATING THE BENEFIT OF ENHANCED AERODYNAMICS
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The aerodynamic effects and the performance of these different frame concepts can be approximated by applying some relatively basic equations. I did the calculations in Matlab <a href="http://william.thielicke.org/multirotors/copterspeed.m" target="_blank">(source code here)</a> with a numerical, iterative method. I am sure there’s an analytical way to solve the equations, but rearranging these equations would take me much more time than just letting Matlab do all the work for me…
Here is how the aerodynamic drag, and the top speed of three different copters (standard, QRC5, DERBE, each with the same motors, propellers and weight) are calculated. The numbers that I am using a suitable for MN1806 2300kV motors with 4S and 5x4” propellers:
The most difficult part of the calculations is to approximate the thrust that is produced by the motors. Thrust decreases linearly with flight speed (if the rotational speed of the motors would be constant) until it goes down to zero at some flight speed. Thrust at different flight speeds is not so easy to measure, therefore I am using an equation that seems to fit experimental data from a wind tunnel reasonably well. I am however planning to do real windtunnel measurements of the propeller performance in forward flight very soon.
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<tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-9CDBcYv91K8/VeISgGyPueI/AAAAAAAAC4c/Xz7neeOhCzA/s1600/Thrust-speed.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="250" src="http://1.bp.blogspot.com/-9CDBcYv91K8/VeISgGyPueI/AAAAAAAAC4c/Xz7neeOhCzA/s320/Thrust-speed.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Thrust of 5" propellers vs. flight speed.</td></tr>
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Furthermore, I am assuming the flow to be perpendicular to the propeller disk below the propellers. The main body of the copter experiences flow that is purely horizontal in this simplified calculation.
The copter is set to a pitch angle (alpha) of 1 degree and full power is applied to the motors. The horizontal drag of the main body is calculated from the dorsal and frontal area of the main body at alpha, together with a drag coefficient of 1 (which is a reasonable approximation for a classical racing copter frame) and a horizontal velocity.
Additionally, the drag of the arms needs to be calculated and subtracted from the available total thrust: The flow velocity in the jet of the propeller is (based on the equations already mentioned above) approximated to be about 150 km/h and independent of the flight speed. A drag coefficient of 1.5 is assumed. To give a number already: The drag that is created by the arms of the “standard racing copter” at full throttle is 6 Newtons (about 0.6 kg)! This is equal to the static thrust of one motor…!
With the remaining thrust, I am calculating the horizontal and the vertical force component at the current pitch angle of 1 degree.
Now, the horizontal velocity is increased step by step until the drag equals the horizontal force component. If this is the case, then the pitch angle is increased by one degree and the calculation starts from the beginning. At each increase of the pitch angle, I am checking whether the vertical force component is larger than the weight of the copter (as a side note: I am completely ignoring the vertical velocity of the copter as I am only interested in the final solution where drag equals horizontal force AND weight equals vertical force).
At a certain pitch angle, the vertical force is not larger than the weight anymore. At this point, the calculation stops and both the pitch angle and the velocity of the copter are printed. </div>
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Here are the results:
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<td align="center" bgcolor="#67f957" valign="middle" width="227"> </td>
<td align="center" bgcolor="#67f957" valign="middle" width="227"><em>Standard racer</em></td>
<td align="center" bgcolor="#67f957" valign="middle" width="227"><em>Shrediquette QRC5</em></td>
<td align="center" bgcolor="#67f957" valign="middle" width="227"><em>Shrediquette DERBE</em></td>
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<td align="center" bgcolor="#67f957" valign="middle" width="227">Max. tilt angle [deg]</td>
<td align="center" bgcolor="#67f957" valign="middle" width="227">38</td>
<td align="center" bgcolor="#67f957" valign="middle" width="227">29</td>
<td align="center" bgcolor="#67f957" valign="middle" width="227">34</td>
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<td align="center" bgcolor="#67f957" valign="middle" width="227">Top speed [km/h]</td>
<td align="center" bgcolor="#67f957" valign="middle" width="227"><strong>107</strong></td>
<td align="center" bgcolor="#67f957" valign="middle" width="227"><strong>178</strong></td>
<td align="center" bgcolor="#67f957" valign="middle" width="227"><strong>170</strong></td>
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The numbers for the “standard racer” seem pretty realistic, although I am quite sure that the top speed is always overestimated. It is very likely that there are additional sources for drag on a copter that were ignored in my simplified assumptions, and that the hypotheses on thrust vs. flight speed could be improved. However, I am doing the same errors in the calculations of all three copters, therefore the above results represent the correct trend: Aerodynamic designs fly much faster and at lower pitch angles. These two factors a highly relevant in FV multirotor racing and in the future, more attention should be paid to designing simple aerodynamic copters like the Shrediquette DERBE. Furthermore, I will be experimenting with optional airbrakes in the first prototype. These will be deployed at very low throttle and when the throttle is quickly reduced (hence reacting to the derivative of throttle). In my imagination, this could really help on tight racetracks, as it enables the pilot to brake without having to change the pitch angle (which would take more time and also results in a camera that points to the sky).
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A few renderings of the Shrediquette DERBE (more soon):</div>
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<a href="http://1.bp.blogspot.com/-HquaNsd3nxM/Vd93SuGR_lI/AAAAAAAAC3M/IAOk4yyMFag/s1600/DERBE-keyshot.52.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="213" src="http://1.bp.blogspot.com/-HquaNsd3nxM/Vd93SuGR_lI/AAAAAAAAC3M/IAOk4yyMFag/s320/DERBE-keyshot.52.jpg" width="320" /></a></div>
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I just received all parts and really quickly snapped the parts together. Everything seems to fit really well :-D</div>
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<a href="http://4.bp.blogspot.com/-7DRtz1GmW7A/VeRjwouWUfI/AAAAAAAAC48/6XCSqG_JQxo/s1600/IMAG2551.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="244" src="http://4.bp.blogspot.com/-7DRtz1GmW7A/VeRjwouWUfI/AAAAAAAAC48/6XCSqG_JQxo/s320/IMAG2551.jpg" width="320" /></a></div>
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William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com19Bremen, Deutschland53.079296199999987 8.801693699999987152.774354699999989 8.1562466999999863 53.384237699999986 9.4471406999999878tag:blogger.com,1999:blog-5821522320379987891.post-69300746715696457592015-08-26T00:38:00.001+02:002015-08-27T22:54:59.323+02:00Tilted body race quad update 2All carbon parts are milled, the 3D printed parts are ordered, and motors + ESCs arrived. I can start to assemble soon :-D.<br />
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One thing that is new (except for the aerodynamic concept) are the airbrakes. I don't know yet how good they'll work and if they might introduce too much moments around some axis. But I think that they might be advantageous in racing tracks with a lot of tight turns. They'll be extended if the throttle is quickly reduced (hence reacting to the derivative of throttle).<br />
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Here are some renderings of the latest iteration:<br />
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<tr><td class="tr-caption" style="text-align: center;">DERBE airbrakes</td></tr>
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William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com7tag:blogger.com,1999:blog-5821522320379987891.post-63883107479412417472015-08-12T23:56:00.000+02:002015-08-12T23:56:03.228+02:00Tilted body race quad update 1Here are some more renderings of my latest project. I'll write an article on multirotor racing aerodynamics soon, then you'll hopefully agree that this design makes sense ;-D
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<br />William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com1tag:blogger.com,1999:blog-5821522320379987891.post-36944645651814327492015-07-25T22:32:00.000+02:002015-07-25T22:32:18.675+02:00Working on a new tilted body racing frame....I am working on a new racing frame with good aerodynamic properties. The intention is to make it crash proof and easy to repair too. I think this concept (a mixture between QRC5 and other standard racing frames) might work pretty well. More details soon!<br />
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William Thielickehttp://www.blogger.com/profile/01217178163189555726noreply@blogger.com0