I've been spending a lot of time over the last few weeks trying to figure out the optimum battery, motor and prop configurations in my skyfun to provide the maximum range and endurance options. Operating on a limited budget, I've been trying to avoid trial and error and make the right choices based on specs.

This is not easy but I've settled on a lower kv motor than many have chosen, running a larger prop with a 3300Mah 3s battery at only 20C (lower C batteries weigh less). The motor I've chosen is a Scorpion II SII-2208, 1100kv, 130W, 45grams, 12Amps, 10 x 4.5 prop.
I'm still mulling over ESC choice.
The final choice was also based somewhat on easy availability in New Zealand (Turnigy is not widely stocked).


There are a lot of suggestions on this and other forums about motor and prop choice which is helpful but what is missing is a semi technical discussion about endurance, range and speed and how to maximize these on any given platform. In the commercial UAS and military worlds, range, endurance and speed can mean the difference between a useful platform and something that is useless. In general, many of the systems people are building here do not seem to be optimized and are achieving quite poor endurance and range.


In commercial aviation, the optimum cruise speed is not based on endurance or range but rather to minimise time. Airliners need to get to their destination in the minimum time while using the least amount of fuel possible so the optimum cruise speed is the speed that flies the fastest possible speed using the least possible fuel per hour.

UAS's are totally different, in general our missions are to fly to a destination, loiter over a target for as long as possible and then return. In this scenario, we need to maximise range for the first part of the journey and get there as efficiently as possible (minimum watts per mile). Once at the target we need to switch to an endurance mode and fly at the minimum speed possible to maximise the amount of time over the target. We then need to return home at a speed that maximises range again (this might alter if a payload is dropped).
Alternatively we might need three modes, in an emergency you might need to get to a target quickly (optimal cruise speed as per airliner), loiter for as long as possible (maximum endurance) and then return as efficiently as possible (maximum range).


I'm not much of a maths guru but using logic I figure the first and easiest step is determining the maximum endurance of an airframe which would be done by finding the minimum amount of thrust required to maintain level flight. At this point, power consumption is minimized and the endurance is maximised (while speed and range are sacrificed), this would have to assume that motor and ESC efficiency are linear (from what I have read brushless motors are more efficient in the medium power bands anyway).


At the other end of the spectrum is the maximum range which I'm a little less sure on how we calculate on a model. For this I figure we need to know about the drag characteristics of each airframe across the full range of speeds.
I also figure that to calculate the optimal cruise speed (max speed with minimal power as per airliner) we would also need to know about drag at different speeds.
Is there anyway the APM logs could be used to figure out useful drag measurements to calculate these speeds for our airframes?


Or, are these speeds the APM could actually calculate itself by performing an 'in flight calibration'?
You could define in the flight planner which portions of the journey should be for calibration and which for maximimum range, endurance or efficient speed.
The APM could then slowly adjust the crafts speed downward in the calibration phase to determine the minimum amount of power required to maintain altitude and store this as the loiter speed. It could then slowly increase the power and measure which power setting delivers the maximum range for input power and then the maximum speed that uses the least fuel per hour.


I realise that there is also windspeed which could affect these numbers, which might mean that the APM might always need to be in 'calibration mode' and once put into one of these modes, constantly optimize the power so as to deliver maximum range, endurance or minimum time depending on what you want.


Once my new motor arrives (my stock motor now barely maintains flight) I will do some testing and add to this post, but would be interested in others thoughts on this topic as there seems to be a severe lack of discussion on such a relevant topic to UAS.

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Comment by Philippe Petit on July 10, 2011 at 7:39am


very interesting, how do you want to calculate the efficiency of the props? I like the idea of experimentally determining the drag curve of a plane. I am pretty sure that this can be done with APM. To eliminate wind influences, several test would have to be done, but i think that this very well might be possible!

However dont you think that the first step for a good efficiency would be to take a glider aircraft like the easystar?

Please tell us how you get on with your props!


Comment by liululu on July 10, 2011 at 7:54am
Your test results helpful to me

Machine crow
Comment by Coby on July 10, 2011 at 8:25am


Nice post.  It's been some years since I taught this stuff, and it was for turbine aircraft/helicopters, so I am just thinking out loud a bit...


Max Endurance:  You might be able to have the APM find it by slowly increasing airspeed until it can find minimum current draw above a threshold airspeed.  It's not just min speed for level flight as that will be closer to stall speed and not equal to max endurance.  In rotary wing aircraft min speed is a hover and power required can also change in and out of ground effect.  Max endurance in the heli I flew the most was 65KIAS +/- a few knots depending on conditions.


Max Range: Draw a line from origin of power required over airspeed and tangential intersect is max range.  Resulting line has max slope.


Best Cruise: Draw a line from origin of drag over airspeed and tangetial intersect is best cruise.  Again, resulting line has max slope.


Overall these can all shift a bit based on environmental conditions such as density altitude.  I am assuming that high end UAS have these numbers calculated and empirically tested.  I think your assumptions about mission profiles are about right, although if it's a time sensitive mission the priority is speed and not best range to target. 


It might be interesting to see if someone could come up with a flight test routine for APM to fly in order to grab the data needed to compute these values.  With the pressure sensor on the APM you should be able to correct for temp and get a pretty close estimation of DA.  This starts to give the data you need for Power Available in order to compare to Power Required, which is what you need to compute things like max gross takeoff for any given day.  For the AP multirotor bubbas out there that means you know whether or not you can lift your 10lbs camera rig as part of a preflight calcuation rather than showing up to a site only to find out the DA is too high to fly the mission.  Or perhaps, if you can lift it, your DA adjusted flight time as that will also change with high DA as your Power Available and Power Required start to converge.  There may also be a need to adjust PIDs based on DA and takeoff weight, but I'll leave that for another day.


Hope that helps.  There is a need for this kind of info in order to professionalize the space a bit, but I think the priority right now is getting the stuff stable and working safely.  For my designs I am using the maximum DA I think I will see and working the motor specs from there.





Comment by Helldesk on July 10, 2011 at 1:04pm

Might be interesting to log the power draw while in flight, while flying a "calibration mission". Just back and forth some given distance, and taking the average to cancel out the effects of the wind (headwind one way, tailwind the other). Fly several of these flights at different speeds to get data points and plot a curve. Then do another few batteries' worth of station keeping at typical mission altitude(s). That ought to get us started.

Comment by Bernard Michaud on July 10, 2011 at 1:21pm

Very usefull


Comment by Toby Mills on July 10, 2011 at 1:51pm

Good point on the stall speed Coby, max endurance would have to be above stall speed in order to be stable. I wonder how much is a reasonable buffer? You would have to do an upwind and downwind run at just above stall speed to calculate a safe average speed, or even better adjust automatically in flight to avoid stall.

The other thing that I would also imagine the APM would be able to calculate is the most efficient climb rate for a given altitude. We tend to go to target altitude at full throttle but I would imagine there are a lot of variables that could make this less than optimal.

The good news is that for most of these scenarios the APM could safely ignore most of the variables. Initially it could make an assumption that motor efficienty is linear and simply use throttle setting, velocity and altitude as the variables. Ultimately it could add in the current draw as well to give a true view of power usage.

The other thing is that circling is not a particularly efficient flight pattern for loitering over a target. 

A perfect circle needs to be completed at a higher velocity than a straight line run in order to maintain altititude so is less efficient. The bigger the circle the more efficient it is, but its still not better than straight lines.

The most efficient Loiter would be to do long straight lines over a target followed by fast turns at each end, or perhaps more useful would be to fly to the opposite points of a hexagon so you cross directly over the target with many straight lines from different angles. The larger the hexagon the higher the efficiency and the higher the altitude the longer you would be in view of the target.

This would give you multiple views of the target from multiple angles with a forward facing fixed pitch camera and would also be easier to program a moving camera yolk to maintain view of a target as you would not need to constantly adjust it.

In fact there would be less need for a moving camera at all if loiters were not circular.

We could get really complicated with this stuff, but it seems that there are some simple things that could be done to significantly increase the endurance and range of our systems.

Comment by Toby Mills on July 10, 2011 at 2:10pm
Also, Phillipe, we can ignore the efficiency of the prop from a calculation perspective and it also doesn't matter which airframe you choose. The APM only needs to take into consideration the 'whole system'. The goal is not to find the most efficient airframe, the point is to automatically optimize any system (as we all have slightly different systems). You could have the most aerodynamically inefficient airframe in the world, there is still a particular speed for that airframe that will fly more efficiently than at higher speeds. The goal would be to automatically calculate it while in the air using throttle, altitude and velocity information which the APM knows already.
Comment by Philippe Petit on July 10, 2011 at 3:42pm

Hey, yes sorry i misunderstood you. I think the idea is however very good! Finding the optimal speed for different mission aspects with the APM could pay off!

However i do not agree that straight lines with sharp turns at the end will be more efficient then loitering. The sharper the turn, the more inefficient the curve is. Thus two sharp turn may cost more energy then continuous loitering.

Also I disagree that continuous wind will have effect on this measurement. With backwind for example we would have a higher ground speed, however the airspeed will remain the same. However you will need a airspeed sensor for these measurements, it will not work with GPS speed.

Determination of the Drag-velocity curve can be done offline, as the wireless connection contains everything you need. You would have to let your airplane fly several runs in straight lines, with different airspeeds (which can be set in APM). After the testflight you can read out how much throttle the autopilot used during the flight (this is also logged in the mavlink packaged), from this on you can determine the usedPower-flightvelocity curve. The only thing left to do is divide used Power by the air velocity and then you have your Drag-airspeed curve. Cool! we should actually try that out!


Comment by Ryan Beall on July 10, 2011 at 4:28pm
It is called Carson's speed!  Prof from my alma mater came up with it.
Comment by Toby Mills on July 10, 2011 at 7:27pm

Commercial airline holding patterns usually resemble long straights with reasonably sharp turns as this uses the least fuel. A very very large circle might be a little more efficient, but the circle would have to be so big you would not be close enough to your target to make it useful.

However, while this is the most efficient, I still think a hexagonal holding pattern where you cross to opposite corners of the hexagon would give the best balance between efficiency and crossing directly over the target the most number of times from multiple directions while using the least amount of energy possible.

I'm also not sure you need an airspeed sensor. For example, if you perform the above mentioned hexagonal holding pattern but maintained constant engine power then your groundspeed would alter based on the wind direction. This would allow the APM to work out the windspeed and direction. Once you calibrate and can eliminate windspeed then the APM would always know what its speed should be for a given power level. If it knows that airspeed should be 10m/s at 50% power and the groundspeed is 8m/s for this power level then that tells you the windspeed is slowing you down by 2m/s it could then decrease power accordingly to increase efficiency. If it sees it is actually travelling at 12m/s ground speed it might need to increase power slightly in order to maintain lift. If you again perform a hexagonal hold pattern then you will get different speeds going in different directions which should give you enough information to calculate the windspeed and direction and ultimately figure out what the groundspeed should be at a given power level. It just needs to know the airspeed constant for each power level.

However, I wouldn't be too concerned about wind direction as this would require a calibration for each flight, the main thing we need to know is actual airspeed at a power level which will be more or less depending on the angle of attack into the wind. If you performed a single 'calibration flight' which consisted of multiple passes in multiple directions at different power settings, then the APM would learn its airspeeds without the need for an airspeed sensor. This would also eliminate the need to know windspeed and direction and would keep everything much simpler.

Perhaps I'm missing something and oversimplifying it all though.


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