In respect to post #17, what is minimized is the energy required to travel a given distance, not power (which is a rate of energy production). The article does find the speed that minimizes the sum of both the energy required to keep the drone aloft while covering this distance and the energy required to move the drone horizontally. The distance chosen is 1 metre but the same result is true for any distance. The result looks plausible to me.
Physics of Drones
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Energy per unit distance and power per unit speed are the same quantity. Looking again the author did attempt to minimize that quantity, but with the function (45/v + 0.0235v²). That's a simplification that calculates the total power as the sum of the powers of two independent horizontal and vertical motor thrusts. That's not correct because the power dissipated by the motors goes is proportional to total motor thrust raised to the power of 3/2, not to the linear sum of the vertical and horizontal components of thrust raised to that power.
Using my nomenclature, as previously, the correct form for total power, combining the force required to keep the aircraft up (its weight) and the force required to overcome drag as a result of horizontal velocity (equation [4] derived in post #6) is:
P = (M²g² + k₁²u⁴)^(3/4)/√k₂
JSR's form for power, expressed in similar terms but with lift and drag as independent, is:
P = (Mg)^(3/2)/√k₂ + k₁u²
Using the values from JSR's article for consistency, k₁ = 0.0235 and k₂ = 0.878. Plotting those functions against velocity:
Those result the same power at hover - as expected - but a quite different relationship between power and velocity as the aircraft moves. The much more rapid increase in power predicted by the oversimplification of the motor thrust into two separate forces and then adding the powers is the reason for JSR's optimal velocity for distance being much lower. Plotting that explicitly in terms of velocity per unit power (distance per unit energy) shows the two different maxima of around 10 m/s with JSR's method and nearer 20 m/s with my combined derivation.
Conclusion - JSR's method seems incorrect - you cannot separate forces and then independently calculate powers and add them. That is also consistent with the observation that the larger value for optimal velocity is consistent with observed results. Please critique if you spot any errors.
You guys might find this relevant.
Ideal forward speed for max. distance on a charge?
Ideal forward speed for max. distance on a charge?
That's consistent. The calculations do indicate a maximum in the curve but, given that it is at or above 30 mph, it's not surprising that many people have come to the conclusion that as fast as possible is best.
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I find these types of detailed scientific discussions fascinating. I took 3 semesters of physics in college and it was challenging but great stuff to learn that will reap dividends your entire life. Certainly helped me understand how a quadcopter works.
I wish someone would kickstart a thread like this about how a drone knows what level is? It's essential for any modern drone to always know what level is so that it can maintain a static hover as well as make the camera gimbal work correctly. But how does a drone always know what level is? And please don't respond by saying "IMU" or "accelerometers". I know those are the key components involved, but that's like saying somebody asks you how a car moves down the road and you say "engine" or "transmission". Not very helpful and insightful.
I wish someone would kickstart a thread like this about how a drone knows what level is? It's essential for any modern drone to always know what level is so that it can maintain a static hover as well as make the camera gimbal work correctly. But how does a drone always know what level is? And please don't respond by saying "IMU" or "accelerometers". I know those are the key components involved, but that's like saying somebody asks you how a car moves down the road and you say "engine" or "transmission". Not very helpful and insightful.
Its absolute orientation reference in terms of pitch and roll is the 3-axis accelerometer package in the IMU. That measures acceleration along the 3 principle axes of the aircraft (x - front/back, y - right/left, z - down/up). If the aircraft is level in a hover then a_x and a_y will be zero while a_z should be -9.8 m/s² (-1 g).
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Yes but that only applies to a static hover. What about when the Phantom is flying upwards and to the right? Now you have acceleration not only from gravity but also upward acceleration and lateral acceleration. Very confusing to see how a 3-axis accelerometer makes sense of it all.
The dynamic orientation is handled by a process referred to as sensor fusion. The IMU has fast (200 Hz) data from the 3-axis accelerometer and 3-axis rate gyros, together with slower data (various rates) from the 3-axis magnetometer, barometer, GPS position and GPS velocity streams. The IMU determines initial orientation (pitch, roll and yaw) from the accelerometers and magnetometers, and represents that in quaternion form. After that, it uses the rotation data from the rate gyros to update the orientation quaternion and linear acceleration data from the accelerometers to update its velocity. Both those are modified at low gain by the slower ongoing data from the magnetometers, GPS and barometer to counter the effects of drift and bias in the fast (first derivative wrt time) data using a method such as the Kalman filter or equivalent.
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LOL --- do yourself a favor and don't ever teach physics to high school or college students. You spout a lot of fancy jargon but that makes it nearly impossible to understand the fundamentals of what's trying to be conveyed.
The big monkey wrench in your argument is that the Phantom is perfectly capable of maintaining a static hover in an underground cave where it can not receive GPS data. So according to your hypothesis, the bird would quickly crash since it's receiving no "slow data" stream from the GPS receiver.
No need to toss out meaningless terms like "quaternion" and "Kalman filter" when the basic premise is flawed.
OK - it's kind of difficult to explain this if you are totally unfamiliar with even the basic concepts of flight control. You mentioned that you had at least studied physics and so I made the (obviously incorrect) assumption that you would be capable of looking up any key terms that you didn't know. But if you think that quaternions and the Kalman filter are simply jargon and you can't be bothered even to figure out what they mean, then you may as well give up right now.
Your snarky response notwithstanding, I'll address your point about lack of GPS. Firstly - I'm not making an "argument" - I'm describing a perfectly well understood flight control process. Secondly, if you read what I wrote you will see that GPS provides a low gain modification to position and velocity, not to orientation (attitude). Orientation is determined by the rate gyros, accelerometers and magnetometers. So, in a cave, it has everything that it needs to hold attitude. Position is another issue - it will drift unless it has vision positioning turned on and surfaces that it can detect.
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I kinda have to be snarky if you make a post with "quaternions" and "Kalman filters" and expect most of us to understand what you're talking about.
As far as being "totally unfamiliar with the basics of flight control", that is a rather pugnacious and condescending statement. Most of us in here are familiar with the "basics" of flight control or else we'd all be crashing our Phantoms every day. You move the left stick up and the bird goes higher, you move the right stick up and the bird moves forward laterally.
What I'm seeking is a good explanation of how a Phantom always knows what level is --- a thorough description that falls between total noob beginner "never had physics in high school, bud" and highly advanced aerodymanics and flight control mechanics like they would be discussing in a NASA brainstorming room with senior rocket engineers. Is that too much to ask? Anyone?
The "basics of flight control" is not "how to use the sticks to fly a Phantom". What I wrote above describes the very basic concepts of how sensor-fusion (combining data from multiple sensors) flight control works. It's not rocket science. If that simple use of rate gyros and accelerometers to track orientation doesn't help then I cannot imagine what will. If the idea of a quaternion is too advanced then just regard it as a 3-D orientation description that is more complete and tractable in equations than pitch, roll and yaw. I included that term, together with the Kalman filter, as the names of the schemes that I had already described in fairly simple terms in case you (or anyone else) wants to research them further. Obviously you don't, so I won't waste any more of my time or yours.
But feel free to keep demanding explanations and then insulting the resulting attempts - I'm sure that will work out splendidly for you.
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Like I already said, you have a detailed understanding of flight controls but no simple idea on how to convey that to the Phantom-Pilot audience. Simply saying "go look up the terminology and concepts" is not very helpful in a discussion board meant to help members better understand how to use their Phantoms and know how they work. A physics professor can't just walk into a lecture hall and say "Maxwell's equations" and "vector mechanics" and then walk out, claiming that they are too difficult to explain and the students will just have to "look it up". Like I already said, don't attempt to be a teacher because your skills in that area are sorely lacking LOL.
I think your pitching too high here SAR- feed him the ball bearing on the plate analogy- or perhaps a mercury tilt switch for the IMU and move on. You ate wasting your time here.
I know - I've put him on ignore. I was suckered into trying to give an explanation by his comments about enjoying technical discussions. If I pitched it too high at first then he had the option of asking me to simplify it further, but instead chose to accuse me of spouting jargon, getting it wrong, and being a lousy teacher. Kind of amusing and definitely rather ironic. I don't think he is actually here to learn anything - I think he's just trolling for a fight.
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LOL "mercury switch in the IMU" --- please tell me you aint this clueless about drone technology!
I made no attempt, nor do I feel inclined now to tell or otherwise demonstrate to you what my level or cluelessness or perhaps some more advanced level of knowledge might be. My post was addressed to SAR and merely my suggestion that he was likely wasting time and energy.
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You're just wasting electrons. Probably spewed a couple pounds of CO2 into the atmosphere pushing those wasted electrons.
The whole essence of my posts is to foster a lively and detailed discussion about how a Phantom knows what level is --- because that is essential to maintaining a stable hover and also allows the camera gimbal to operate correctly. Posting a snooty response about "go look up quaternions and Kalman filters" does NOT foster that type of interesting discussion. Just makes one look like a snooty geek who can copy-paste fancy words.
Returning to the original piece that kicked off this thread (http://homepages.abdn.ac.uk/nph120/meteo/DroneFlight.pdf) version 2 has appeared that does not make the assumptions highlighted in post 22. There is some difference in the power figures from the earlier version but the return to home speed comes out slightly slower than with the assumptions. In round figures it's still about 10 metres per second, in close agreement with DJI's settings. My reading is that sar104's figures seem to be based on a relationship between thrust and power that is true for a hovering drone but not true for a drone in motion.
The question about how the drone knows it's level is interesting since the software processing gyros and accelerometers needs to be given starting positions to work out changes in position and orientation. I don't know the answer but can only assume there is an electronic tiltmeter within, perhaps something like a miniature pendulum with a means of detecting a tilt signal when the drone is inclined very slightly to the suspended 'bob' . Tiltmeters can be made incredibly sensitive. In short, if this is true then gravity determines the level, just as with a spirit level but with different technology.
The question about how the drone knows it's level is interesting since the software processing gyros and accelerometers needs to be given starting positions to work out changes in position and orientation. I don't know the answer but can only assume there is an electronic tiltmeter within, perhaps something like a miniature pendulum with a means of detecting a tilt signal when the drone is inclined very slightly to the suspended 'bob' . Tiltmeters can be made incredibly sensitive. In short, if this is true then gravity determines the level, just as with a spirit level but with different technology.
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"Electronic tiltmeter" sounds interesting but is there really such a thing? I've never heard of it. Please post some reference links about them.
For the past 5-6 years as consumer drones have been getting more and more popular --- I find it amazing that nobody has explained in simple terms how a Phantom knows what level is and the mechanisms it uses to maintain level. It's fundamental to making a Phantom fly stable in the sky and also how the camera gimbal produces stabilized video while the drone is moving erratically in the air. Yet I've searched YouTube and Google for the past couple years and still can not find a clean and simple explanation for how this is accomplished. Truly one of the great mysteries of modern electronics!
