Physics of Drones

[sar104]

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.

I've been thinking about this some more, so that's a timely post. It definitely removes the clearly incorrect element of the previous version - the treatment of horizontal and vertical forces as independent scalar quantities. The fundamental difference remaining between the author's method and mine is indeed the calculation of power expended, but not just for the reason that you mention.

I did use the standard relationship (P² ∝ F³), and I think the main problem with that is that the implicit assumption is that the speed of the incident air is small compared to the exhausted air. In other words the relationship is not airspeed independent and so it will become increasingly incorrect as airspeed increases. I've been worrying about that off and on, because I think that implies that my power estimate will be too low at higher speeds.

The author still separates the calculation of power to hover (from rate of change of kinetic energy of the air) and to overcome horizontal drag (the product of force and distance). That seems inelegant - why not simply calculate total rate of change of kinetic energy of the air to achieve the total required thrust and get power directly? I'll try that for comparison.

The obvious question is why do most of the reports of testing still suggest that the optimal airspeed is rather higher than 10 m/s? The assumption that we both made, that lift is negligible, may be part of the answer. DJI's specifications clearly indicate that maximum flight time is not at hover, but at around 7 m/s. One answer here is some careful still-air flight measurements, which I keep meaning to find time to do.

One last question - are you actually the author of this analysis? The discussion would be much simpler if that's the case.

 

[sar104]

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 "tiltmeter" is the 3-axis accelerometer package.

 

[Talisker]

Yes, electronic tiltmeters have been around for quite a while. I first came across Rank, Taylor & Hobson's "Talyvel" in a workshop context in the 1970s but they weren't even new then. They were much easier to use than the traditional accurate spirit level, and more sensitive. The Wikipedia article on tiltmeters highlights that today's versions on circuit boards are examples of microelectromechanical systems (MEMS) and they can have more than enough precision for drones. They are used by civil engineers, geophysicists and I guess can be found in many balancing devices. If I were designing a drone I'd put one in but whether DJI have is a question I can't answer. 'Inclinometers' are a variant but I usually associate that name with devices to measure larger angles than are needed to establish a level.

 

[Karlos-Kydd]

Yes, electronic tiltmeters have been around for quite a while. I first came across Rank, Taylor & Hobson's "Talyvel" in a workshop context in the 1970s but they weren't even new then. They were much easier to use than the traditional accurate spirit level, and more sensitive. The Wikipedia article on tiltmeters highlights that today's versions on circuit boards are examples of microelectromechanical systems (MEMS) and they can have more than enough precision for drones. They are used by civil engineers, geophysicists and I guess can be found in many balancing devices. If I were designing a drone I'd put one in but whether DJI have is a question I can't answer. 'Inclinometers' are a variant but I usually associate that name with devices to measure larger angles than are needed to establish a level.

OK that further explains "tilt-meters" but here's one big problem --- if a Phantom tilts forward by 5 degrees as it accelerates forward --- the resulting forward acceleration pushes the tilt-meter back to center position and this tells the IMU the Phantom is once again level, when it is actually not.

And so the conundrum continues ....

 

[sar104]

Yes, electronic tiltmeters have been around for quite a while. I first came across Rank, Taylor & Hobson's "Talyvel" in a workshop context in the 1970s but they weren't even new then. They were much easier to use than the traditional accurate spirit level, and more sensitive. The Wikipedia article on tiltmeters highlights that today's versions on circuit boards are examples of microelectromechanical systems (MEMS) and they can have more than enough precision for drones. They are used by civil engineers, geophysicists and I guess can be found in many balancing devices. If I were designing a drone I'd put one in but whether DJI have is a question I can't answer. 'Inclinometers' are a variant but I usually associate that name with devices to measure larger angles than are needed to establish a level.

The DJI aircraft all use MEMS IMU modules comprising 3-axis accelerometers and 3-axis rate gyros, with separate magnetometer(s). Some of the models use two IMUs and two compasses for redundancy, while some just have one.

 

[With The Birds]

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.

There are two monumental flaws in your assumptions here that are easily addressed without resorting to mathematics.

1) the return to home speed required to achieve maximum distance for a given battery usage is not 10m/s- it is significantly higher. This is demonstrated by actual real world performance of the phantom AC’s. A quick read of the various distance threads will clear this up for you if you don’t believe SAR’s calculations.

2) if you look at a phantom in stationary hover you will rarely see it level (all rotors on same horizontal plane). Almost always it will be tilting to counteract prevailing air movement. There is significantly more to it then a “tilt meter”. The IMU in the phantoms contains both accelerometers and gyroscopes to determine movement further assisted by the compass to determine heading. And yes this is further complemented by the GPS system.

 

[Talisker]

2) I'm sure the IMU works very hard to keep the bird steady both when hovering and moving but accelerometers measure only change in speed and gyros measure change in orientation. Both position and orientation need something to define their zeros so that the changes can be applied to a known starting point. The good question was 'how does the drone know what 'level' is?', level being the starting point from which to measure tilts. My suggestion was that if I were designing a drone I'd put in an electronic tiltmeter, effectively to reference 'level' given by gravity. Once the gyros have a reference, then it's over to them to keep track of orientation changes. Hardly a 'monumental flaw' in reasoning. What DJI do is unlikely to be a commercial secret. How they do it is another matter!

1) The power estimates given were specifically for steady conditions with no constant corrections for wind fluctuations and other real-world effects. These are likely to make the optimum return-to-home speed dependent on conditions and, likewise, the distance achieved for a given expenditure of battery energy condition dependent. The matter could be easily resolved if battery current were available as well as battery voltage. Then the usage power curve with speed could be seen unambiguously and all would be revealed, with no guesswork needed. It would be useful to know why DJI have set the RTH speed at about 10 m/s and it is at least interesting that the simplified treatment given comes up with a similar figure.

 

[sar104]

2) I'm sure the IMU works very hard to keep the bird steady both when hovering and moving but accelerometers measure only change in speed and gyros measure change in orientation. Both position and orientation need something to define their zeros so that the changes can be applied to a known starting point. The good question was 'how does the drone know what 'level' is?', level being the starting point from which to measure tilts. My suggestion was that if I were designing a drone I'd put in an electronic tiltmeter, effectively to reference 'level' given by gravity. Once the gyros have a reference, then it's over to them to keep track of orientation changes. Hardly a 'monumental flaw' in reasoning. What DJI do is unlikely to be a commercial secret. How they do it is another matter!

Accelerometers do not only measure change in speed - they also measure acceleration due to gravity, both magnitude and direction. As I said earlier - they are the "tilt meter" that you keep referring to. No other instrumentation needed. There is absolutely no mystery to any of this.

 

[sar104]

2)

1) The power estimates given were specifically for steady conditions with no constant corrections for wind fluctuations and other real-world effects. These are likely to make the optimum return-to-home speed dependent on conditions and, likewise, the distance achieved for a given expenditure of battery energy condition dependent. The matter could be easily resolved if battery current were available as well as battery voltage. Then the usage power curve with speed could be seen unambiguously and all would be revealed, with no guesswork needed. It would be useful to know why DJI have set the RTH speed at about 10 m/s and it is at least interesting that the simplified treatment given comes up with a similar figure.

Battery voltage, current and power are all available in the DAT files. This just needs some careful tests to generate the necessary data. I'll do it.

 

[Karlos-Kydd]

Accelerometers do not only measure change in speed - they also measure acceleration due to gravity, both magnitude and direction. As I said earlier - they are the "tilt meter" that you keep referring to. No other instrumentation needed. There is absolutely no mystery to any of this.

That's essentially the problem --- the acceleration can be in any axis and thus the accelerometer doesn't know whether it's gravity or forward/backward or upward/downward acceleration.

And still no simple explanation for how a Phantom knows what level is .....

 

[N017RW]

That's essentially the problem --- the acceleration can be in any axis and thus the accelerometer doesn't know whether it's gravity or forward/backward or upward/downward acceleration.

And still no simple explanation for how a Phantom knows what level is .....

Have you looked/researched?

You seem to want to be spoon fed.

 

[Karlos-Kydd]

Have you looked/researched?

You seem to want to be spoon fed.

There is no "spoon feeding" in here --- unless it's for me to inform you that Phantom Pilots is supposed to be a helpful forum where members of a certain knowledge set help others of a different knowledge set understand a confusing topic about Phantoms.

So please focus on your own "research" --- let the others in here like me stimulate a healthy discussion about complex drone physics and flight controller mechanisms. How a drone always knows what level should be is a core mechanism for stable flight. And yet hardly anyone in here understands how it works. Shouldn't be that difficult.

 

[N017RW]

I see why you are having a hard time.

I’d wager many have given up on you.

The IMU contains multiple 3-axis sensors which are fused together to report the forces acting on it. Since it’s attaced to the drone and oriented to report them in unison it can inform the flight controller as to its orientation in free space and it can then make the required controls to the motors to execute the operator’s commands. With no command input it will maintain a level attitude.

Just like you use your 5 senses to evaluate your surroundings.

By researching it beyond this site you may find an explanation that better suits your level or means of understanding.

Cheers

 

[Karlos-Kydd]

The IMU contains multiple 3-axis sensors which are fused together to report the forces acting on it. Since it’s attaced to the drone and oriented to report them in unison it can inform the flight controller as to its orientation in free space and it can then make the required controls to the motors to execute the operator’s commands. With no command input it will maintain a level attitude.

Yes, the 3-axis accelerometer is known by most of us in the drone world. But it doesn't clearly explain how the IMU uses the 3-axis accelerometer to know it's orientation in space in order to know it's deviation from level in the horizontal plane. For example, if a Phantom has a forward pitch of 5 degrees as it accelerates forward, the 3-axis accel. will send inputs to the IMU to let it know the bird is forward pitched by 5 degrees and thus will up-pitch the camera by 5 degrees to maintain a stable video angle to the ground. But if the Phantom encounters a headwind and reduces the forward acceleration to zero and the bird hits a constant velocity, common sense would say the camera should pitch down by 5 degrees since it thinks the Phantom is once again level and not moving in the horizontal plane, when it reality it's still pitched forward by 5 degrees flying into the headwind but not accelerating and the camera does not change it's angle to the horizontal plane. How does the IMU know this?

 

[N017RW]

IMU also contains a gyro(s).

 

[N017RW]

IMUs commonly contain accelerometers, rate gyros, barometers, and some may also contain the magnetometer.

This is the sensor fusion I mentioned earlier.

Then there is some software and motor controllers all doing their part.

 

[TurnerConstruction]

Very cool. Thanks forsharingi

 

[Andy9]

I think that most of us don't need the detailed physics for the explanation how drones know what is the level position. They do it and do it fine and for most of us that is enough. I'm not an expert in physics but I can understand that putting the drone on the perfectly level desk or whatever the accelerometer should then show zeros in all three axes.
About the energy consumption which enables the maximum distance (or minimum consumption per defined distance), which was the original question, I can make a simple estimation with the car analogy. My car has the max. speed of 220km/h. The most economic speed (the min. gasoline consumption per km) is around 90km/h (tested many times). This is not much under the median value of 110km/h.
As the physics works for all things in the world in the same manner, you can apply this for drones too. Not very precise but very useful for drone flyers.

Sorry in advance if this is too simplified for somebody.

 

[bsartist]

I think that most of us don't need the detailed physics for the explanation how drones know what is the level position. They do it and do it fine and for most of us that is enough. I'm not an expert in physics but I can understand that putting the drone on the perfectly level desk or whatever the accelerometer should then show zeros in all three axes.
About the energy consumption which enables the maximum distance (or minimum consumption per defined distance), which was the original question, I can make a simple estimation with the car analogy. My car has the max. speed of 220km/h. The most economic speed (the min. gasoline consumption per km) is around 90km/h (tested many times). This is not much under the median value of 110km/h.
As the physics works for all things in the world in the same manner, you can apply this for drones too. Not very precise but very useful for drone flyers. This values are displayed all time of the flight.

Sorry in advance if this is too simplified for somebody.

Where I think the car analogy falls short is that it doesn’t require energy to simply hold it up at, say, zero velocity. So my intuition leads me to believe that the slower you go with a drone the longer you stay aloft and the more that component of energy use comes into play. So my intuition tells me that the faster I get home, the less energy is spent defying gravity.

Of course I must emphasize *intuition* because I realize that other factors may outweigh this such as drag caused by higher forward speeds and such.

 

[sar104]

Where I think the car analogy falls short is that it doesn’t require energy to simply hold it up at, say, zero velocity. So my intuition leads me to believe that the slower you go with a drone the longer you stay aloft and the more that component of energy use comes into play. So my intuition tells me that the faster I get home, the less energy is spent defying gravity.

Of course I must emphasize *intuition* because I realize that other factors may outweigh this such as drag caused by higher forward speeds and such.

Correct - that is the basic reason that the car analogy is completely inapplicable. But it's not the only factor - drag increases with the square of the airspeed, and so faster is not necessarily better, and so the discussion is a good example of why intuition is not going to get you to the right answer.

I think that most of us don't need the detailed physics for the explanation how drones know what is the level position. They do it and do it fine and for most of us that is enough. I'm not an expert in physics but I can understand that putting the drone on the perfectly level desk or whatever the accelerometer should then show zeros in all three axes.
About the energy consumption which enables the maximum distance (or minimum consumption per defined distance), which was the original question, I can make a simple estimation with the car analogy. My car has the max. speed of 220km/h. The most economic speed (the min. gasoline consumption per km) is around 90km/h (tested many times). This is not much under the median value of 110km/h.
As the physics works for all things in the world in the same manner, you can apply this for drones too. Not very precise but very useful for drone flyers.

Sorry in advance if this is too simplified for somebody.

A more detailed explanation that takes into account at least all the first order factors is already in this thread, and your attempt to ignore the physics and come up with a completely different answer is really not going to work. The fact that the most economical speed for your car is near (well actually it really isn't that near at all) half its top speed is complete happenstance - there is no systematic relationship at work there.