What is the relation between the motors in a quadcopter, the propellers, the battery, and flight time?

The quads in question are the Hubsan H107D and H107C.

On a 380 mAh battery, the H107D flew for a little over 4 minutes, while the H107C flew for a little over 10 minutes.  I suppose the difference is due to the FPV camera that is always on on the H107D.  There is a camera in the H107C, but it is on only if there is a microSD card installed (and I do not have one yet).

On a new 500mAh battery, the H107D flew for over 6 minutes, much as I expected given the flight time on the 380 mAh battery.  But the H107C flew for only 8 minutes on a new 500 mAh battery.  I do not understand why.

Is there a good resource that shows the math relating the key properties of the batteries, the motors and propellers in use to the flight time?  (I am no stranger to complex mathematical models; I am just a stranger to this sort of engineering.)

I haven't done enough testing to provide statistically significant results (I have 5 500 mAh batteries, supplied as an upgrade to the 380 mAh battery they come with, so I could spend weeks testing enough to get statistically significant results), but this result has me puzzled.  I know the 500 mAh battery is longer and heavier than the 380 mAh battery (but both fit the Hubsan quads I have), but should that result in such a reduction in flight time?  I thought the bigger battery should result in a longer flight time.  Did I waste my money getting the 'upgraded' batteries?

Thanks

Ted

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Hi Ted,

! The better part of an hour - lets say 45 minutes. !

In order to do that, none of the current truly small quad copters can even come close and nothing under a hundred dollars stands a chance.

45+ minutes is in our world very rarified territory and it takes truly optimized multicopters to have any chance of achieving it.

Everything needs to be optimized:

Lightest frame and big slow props on motors optimized to turn prop to provide sufficient thrust at hover weight of copter and battery just the right size and weight to be optimal with motor/props chosen.

Probably the smallest motor currently with sufficiently optimal efficiency to accomplish this time goal is the KDE 2814 515KV motor swinging 13" or 14" propellers on a purpose built carbon fiber tube frame.

And those motors alone are $72.00 each.

I am using them on a Hoverthings FLIP Pro FPV Gimbal with extended arms to take the 14" props.

This copter is definitely not optimized for maximum endurance but it is my hope to be able to accomplish near 30 minute practical flight times.

There is one other "trick" that you can use to get longer flight times and that is a straight lithium battery as opposed to LiPos. You can get 30% + more energy out of them per unit weight (but they are very limited as to maximum current output).

18650 is the correct battery designation, but this is very specialized territory.

I am using special enhanced Multistar LiPo batteries which can give about a 20% boost in performance to battery weight ratio.

Currently, the best truly small brushless quadcopter made is the BNF (Bind and Fly) Blade 200 QX (which I also have).

It sells for $230.00 and requires a Spektrum at least 5 channel receiver at around $160.00 for a DX6i.

It can manage 12 to 15 minutes of flight, a bit longer with available over sized batteries.

But third party (Phoenix) carbon fiber airframe is available for it that can accommodate larger batteries while still reducing weight and give you a longer flight time but still not much over 20 minutes.

The propellers are just too small to yield good efficiency at higher weights.

You might be able to use 18650 batteries on the CF frame version that could get around 30 minutes if you can get the max power requirements to work out though.

Basically if you want something approaching an hour you need to add a decimal point to your expected investment and double or triple the size (for now anyway).

Best Regards,

Gary 

Hi David,

So, I would infer that the benefit, or disadvantage, of the 3x blade GF5030 depends on the capability of the motor.  The chap who advised the use of the 2X GF5030 reported that it significantly improved the performance of his Blade 200 QX.  So, I guess the thing for me to do is get both and see which provides the best performance.  Right?  BTW: How did you measure the stress the propeller placed on your stock motor?  I.e. How would I tell if using it caused to much stress relative to the 2X GF5030?

I guess the take home message from what you say about propellers is that when I experiment with them, for a given motor, longer and thinner, and more flexible, is likely to be better; given that the motors on the small quads spin so fast.

So, from what you say about the V929, the V222, that I understand is to replace it, is less desirable for you because of it's more current electronics/flight control software?

My take on your assessment of 3D printing tiny parts is that you don't think the 3D printing technology is up to the task yet.  Would that be fair? 

You will have to point  me to resources that talk about the DIY methods you mention using foam, carbon and sheets of plastic.  Is it not the case that these carbon rods you mention are stronger and lighter than most other materials that  might be used for the same purpose?  How, especially, would you make a frame, on the one hand, and propellers on the other, from them?  Or can you?  I am a bit concerned, though, about manual processes as I have a neuropathy that affects my hands and feet.  In addition to perpetual pain, and inaccurate sensing of temperature (which can be dangerous when cooking or using tools that can get hot - there are people with my condition that have lost limbs from injuries due to acidents during such activities), it is difficult for me to do precision work with my hands.  That is why, for example, I appreciate computer assisted flight more than you apparently do.  And, my fall back solution to limitations to computer assistance in anything is to apply my mind to the software engineering (something I have been doing for decades in other disciplines), to see if I can make the software more effective, rather than try to force my hands to do something my neuropathy doesn't readily let them do.  If a decent FC board helps me not crash, so be it.  With my hands, that may be what it takes for me to enjoy flying.  You see now, why the idea of having a computer deal with the precision work in making small parts appeals to me.  I can wait until the technology (and materials used for printing) have improved to the point where it can handle these requirements.  In the mean time, I can either try my hand at making parts, or simply rely on parts that exist for different quads that are out there.

Hmmm, I find your take on Walkera interesting.  The only reason I have looked at them, and in fact have a couple coming, is that they were highly recommended by folk here in Canada.

I like Einstein's take on simplicity.  He said to keep things as simple as practicable, but no simpler.  He had observed that the simplest 'solutions' are often as poor as the most complex ones, and that the optimal solutions were as simple as the system considered permitted without overlooking or ignoring anything.

If I observed you and your buddies with your respective quads, what I would do is pick your brains about what you did and why, as well as analyze the properties of your respective quads, and then use that information to figure out how to make the software better.  What you would then observe is that the next generation of DJI Phantom would perform better: certainly not as well as you, given what you'd have learned during the time I did my thing, but much better than the current generation does.  And, of course, the process of miniaturization means that it is just a matter of time before all the electronics required for FC systems will fit on a PCB the diameter of a small pea (at which point the impact on weight would be negligible).

It is true that this technology carries a cost, but the fact is that computers today are much more reliable than they were when I was young; and one the size of your phone can do more than could a super computer back then.

For me, now, the joy of flying is just to be able to complete a flight without crashing into anything (I just started a coupe weeks ago). ;-)  It IS an addicting activity!

Thanks

Ted

A further thought re 3D printing,

You want maximum flight times, that means light strong frames.

3D printed frames are heavy, not very strong and excessively flexible, that is at direct odds with producing a copter with optimal flight times.

Propeller diameter is king for efficiency, the smaller the diameter the less the efficiency.

Propeller design matters a bit, but not very much in comparison to diameter.

3 Bladed props can be more efficient at carefully chosen prop speeds than equivalent diameter 2 bladed prop, but a larger 2 bladed prop will always be more efficient than any smaller prop.

Of course given relatively correct selection of pitch in both cases.

Best,'

Gary

Thanks Gary,

This is gold.

What you say is not much of a surprise.  It seemed to me that since so many quads available no have such short flight times, it must be hard to do.This is precisely WHY I want to do it.  ;-)  If it was easy, everyone would have done it by now; and in such a case, it wouldn't be worth doing as I could just buy what I wanted.

I have a math and science background, with a lot of computer programming experience, but I am brand new to the realm of robotics in general, and the science involved in developing a good multirotor copter.  I have picked up several books that introduce, in an intelligent way, the reader to robotics using Arduino boards.  Alas, I have yet to find the corresponding book(s) dealing with how to do the kind of optimization you are talking about.  Are you able to recommend a book or three that deals usefully with the science and engineering involved in designing and building a highly optimized multirotor copter?  I guess what would be very good is something that documents several projects I could build, based on what I see in the book, and which gives the current main suppliers of parts in Canada and elsewhere.  And of course, if there is open source software that can be used to do some or all of the optimization calculations, so much the better (computer code is something I can adapt to my own purposes, once I understand it).  Maybe after a few years of studying this (and experimenting as my budget allows), and with the improvements that are inevitable in the technology in this area, my objective may well be feasible: not today, but before I die.

On Amazon.com, the only Multistar LiPo battery is the 3S 5200 mAh for Walkera's Qaudcopter QR X350 Pro.  Is that the one you're using?  If so, I may be in trouble as amazon.com tells me that it does not ship to Canada.  And, Multistar LiPo batteries are completely unknown to amazon.ca.

I DO have a Blade 200QX on it's way (seemingly on a very slow boat from China).  I have some questions about it.  1) Will it work properly with the DEVO controllers that Walkera uses for their copters: If so, I should be in good shape as I will have a DEVO 4 and a DEVO 7 by the end of next month (they're coming on a slow boat from China too).  2) I have seen reviews that talk about improved performance for the Blade 200QX by replacing the original propellers by GF5030 propellers.  Do you find these reports plausible?  The link  given showed propellers with 2 blades, but searching I found also GF5030 propellers with 3 blades.  Do you have a sense as to whether such propellers would provide a benefit?  Am I likely to damage anything by trying the 3 blade propellers the same radius as the 2 blade propellers was reported on?  3) Where can I find a supplier (Canadian, or someone who ships to Canada), for the Phoenix airframe and Multistar batteries you mentioned?  What would be the largest battery you'd try for this?  Would it be feasible to just get extra spare parts for the Blade 200 QX to build up a second unit around the frame you mentioned (maybe a project for next summer)?  If so, can one just put longer arms on that Phoenix frame to accommodate bigger propellers?

Do you have a website where you document your project that you mentioned above, so I can bookmark it and see how your efforts inthis area progress?  If so, I'd love to see the URL.

Thanks

Ted

Thanks Gary,

Is it necessarily true that 3D printed frames are too heavy and flexible, or might that be an artifact of the primitive state of the technology at the moment?  Is it not possible to use such a technology to print carbon fiber or nylon frames (and using thin hollow tubes rather than solid bars - to aim for strength combined with low weight)?  If not, how are good frames made with good precision.  I fear if I tried to make a frame or body by hand, the neuropathy in my hands would prevent me from making perfectly balanced propellers or perfectly symmetric frames with absolutely correct angles between the parts of the frame.  Sadly, I no longer have the strength and dexterity in my fingers that I had when I was young, so without a computer controlled machine, some kind of robot, precision work may not be a viable option when it comes to fabricating parts (this is why 3D printing holds such an allure for me).

One question comes to mind.  If excessive flexibility can kill efficiency, there must be an upper limit on propeller diameter.  In order to accommodate a larger propeller for a given body, one might give the copter longer arms.  But if you do that, I would expect that as they are increased in length, the arms would become too flexible (or too brittle) because of their length, and may at the same time contribute too much to the total weight of the copter.  So what would the optimal ratio be between the size of the copter body and the length of the arms, and thus the diameter of the propellers?  Also, with regard to the geometry of the copter, should the arms not be long enough that the propellers do not blow down on the body, but rather beside it?  If so, perhaps the arms of a quad or a hexacopter or an octocopter ought to be roughly the same length as the radius of the propellers (just thinking that now, I checked the arms and propellers on my quads and every one of them has arms that have a length equal to the radius of the propellers).  If the efficiency of a copter is largely defined by the area covered by the spinning propellers, then perhaps a large number of smaller propellers, driven by small efficient motors, might be more efficient than a small number of larger propellers driven by large and thus heavier but perhaps more efficient motors; at least within limits.  It seems obvious comparing a quad or hexacopter with a copter with only one or two rotors, but I have my doubts about going beyond 8 arms with 8 or 16 rotors (I wonder, now, if it helps or hurts to have two or more propellers that cover overlapping areas - witness the Y6 geometry of the Walkera Scorpion, and IIRC 3DR has a Y6 hexacopter).  Thoughts?

Thanks again,

Ted

Hi Ted,

On my Quadcopters are Fun Web site there are several pages you should find useful:

http://quadcoptersarefun.com/index.html

Regarding the Blade 200QX I have an introductory page on that all by itself:

http://quadcoptersarefun.com/Blade200QX.html

For basic understanding of quadcopters the following page:

http://quadcoptersarefun.com/Quadcopters.html

And the Build a quadcopter page

http://quadcoptersarefun.com/BuildAQuadcopter.html

You might want to take a particular look at the Quadrysteria Black Mamba frame near the bottom of the above page, it is about the smallest thing that can carry a GoPro and Gimbal effectively and is very well made.

Generally for carrying a GoPro and Gimbal 8" or 9" props are about the smallest I would consider for efficiencies sake and that sets the minimum frame size. 

And for more in depth understanding of quadcopter design:

http://quadcoptersarefun.com/QuadcopterDesign.html

Best,

Gary

I am also currently constructing a smaller is better page you might find interesting:

http://quadcoptersarefun.com/SmallerIsBetter.html

Gary

Thanks Gary,

I appreciate all these links.

BTW: My Blade 200 QX finally arrived today.  Silly me, I did not order a transmitter for it when I ordered the quad itself, so that is ordered now, and will arrive probably Monday or Tuesday (I found a Canadian supplier, with branches across the country so no Canadian is very far from one of their outlets, which means shipping is inexpensive and fast, in marked contrast to most of the Asian vendors).

BTW: Had you seen this?  http://www.rcgroups.com/forums/showthread.php?t=1880665

I wonder to what extent his methods scale down to really tiny size, especially the use of carbon fibre tubes 1 mm outer diameter.  I mean he achieved a flight of over two hours.  That would be wonderful if it can be scaled down to something the size of the Blade 200QX, or smaller.  Can you image that kind of efficiency in Blade's upcoming pico?  ;-)

The key is probably the motor, finding one that is designed to be slower, but with greater torque, a matching ESC, and suitable propellers.  It is all about ratios of these things against the dimensions of the copter, and it's weight, right?  If so, then it reduces to finding a manufacturer that can provide what is needed.

For that matter, what else uses the motors in the Blade 200 QX, and what is the largest propeller (2 blade and 3 blade, or even 4 blade) that that motor, and the ESC used, can handle?  It looks to me like there is space for a 5 inch, or even a 5.5 inch propeller would fit without adjacent propellers hitting each other.  That should greatly improve efficiency over the 4 inch propellers it comes with, right?  But I do not want to burn out the motors or ESC on my first Blade 200 QX.

Cheers

Ted

Ah End of Days - been there done that.

It is actually possible to build an endurance copter with those cheap components, lots of people have done it and I have a set of those cheap RC Timer motors myself.

However, it is NOT a practical quadcopter, it handles very poorly, is very failure prone and is mostly good for hovering quietly in a very wind sheltered area for a relatively long period of time.

It is an experiment with cheap parts on a setup optimized for one thing only - holding its own self aloft in a static hover for the longest period of time.

These particular RC Timer motors are very low quality and often arrive barely or not functional and they have short service lives.

They are cheap junk really.

I have been there.

To get into the practical aspect of long endurance copters you really cannot also be about cost cutting at the same time, one or the other, not both.

A practical long endurance copter that is actually designed to fly around and do something is not the same as a record attempt copter that is only designed to move minimally while hovering quietly above the ground.

Even though my current writing is about the necessity and benefit of very small quadcopters, the fact remains that the biggest propellers spinning at the slowest speed are the most efficient - always - period.

However they also have a downside, increasing dynamic instability (especially on quadcopters) and slowness of response.

For taking videos or photos, the dynamic instability can definitely become problematic and even for basic control in gusty winds.

And the slowness of response can make the copters sluggish.

Basically a practical balance always needs to be struck.

When I started I was attracted by all the cheap parts available, now I am attracted to the best parts for the job.

In motors for instance, KDE multirotor motors generally have 3 ball bearing races with at least one larger bearing which supports the lions share of the axial load.

They are also the most efficient motors available, which is critical for the longest (practical) flight times.

Their motors are optimized both for efficiency and longevity and the motor is the core ingredient of any multicopter system.

The bottom line is if you want a practical quadcopter with exceptional longevity you really have to use the best components and that also generally means the most expensive.

This is my current main quadcopter, a Hoverthings Flip FPV Pro G with extended frame arms, KDE 2814 515KV motors, 14" props (13 are generally better for this copter), a Quattro 4 in 1 ESC and a Pixhawk flight controller with a Sony AS100V sport camera.

This represents the best components I can buy, it gets around a safe 25 minute flight time the way it is configured with the optimized low C Multistar 6600MAH LiPo battery.

Best Regards,

Gary

Thanks Gary,

I had no idea he'd made junk. I was just astonished that he'd obtained a flight time of over two hours.  I'd have thought that to get such a result, he'd have spent a fortune on really good components, as well as a lot of time designing and redesigning different aspects of it.  I had this, obviously mistaken, notion that you had to have good components and a good design to get a good result.

I guess the first question I'd have is, "Who makes the best components I can consider?"  What would be the top 3, or top 5, manufacturers of good motors, ESC's and FCs?  And does anyone make a good, small proximity sensor: something that can detect small objects a few tens of meters away, but which would allow you to mount half a dozen on a small quad, even one as big as a Blade 200 QX?  All of the proximity sensors I have found so far that could be useful are so big they'd really only be suitable on quads that are half a meter or more across.

Next, I spent much of the weekend watching reviews of RTF quads that are on the market today: mostly DJI, Walker and Blade.  I know the Blade 350 QX was junk when the first version of it was released (at least according to some, according to others, it was just the propellers that were junk), but the reviews I saw (and I watched a lot of them) report that all the problems Blade had initially were solved and that the result, with the 350QX2, compares well with the DJI equivalent.  Actually, the reviews I saw showed no significant difference between the three in the 350 class (though one professional photographer was not impressed with the gimbal on the Walkera and Blade).  granted some claimed one or another was 'better', whatever that means, but their claims were not borne out by either the video they showed or the data they presented (as if they had a religious devotion to one manufacturer or another).  But the important thing was that all three could comfortably stay aloft for 25 to 30 minutes.  Some of the tests included tests of the ability of the quads to hold position in windy weather (with gusts in excess of 25 mph in the one test I watched), and others showed rather aggressive flying.  Thus, I plan on getting both a Walkera 350 and a Blade QR 350 QX2 to study what they did (and to both learn better how to fly well and just to have fun flying - something that is so much safer with their return to home function, which, in the tests I watched, performed admirably).

One last question.  With a view toward making the frame lighter, so most of the copter's weight comes from the battery and motors, I have been looking at the feasibility of making an airframe using primarily carbon fibre tubes (motived by the observation that birds' bones are hollow).  I would drawn your attention to www.cstsales.com.  They have carbon tubes, ranging  from .07 mm outer diameter, through 1.0, 1.5, 2.0, 2.5, 3.0 mm and up.they also have carbon fibre plate, from just over half a mm think on up.  I was astonished at how light those things are.  I have also read about incredibly strong adhesives that can be used with this material.  So, I had an idea that one can make airframes for quads, hexacopters, octocopters, &c., using the tubes of appropriate lengths for the bulk of the airframe, and the carbon plates to join them, the plates would be used for motor mounts, as well as for mounts for the electronics.  I would suppose that the carbon plates used to make the motor mounts would have to be close to the thickness of the tubes, because the strength comes from the combination of the tubes, the adhesive and these plates fastened as strategic positions.  But with the use of so little material to make the airframe, the plates used to make the mounts for the electronics does not need to be so thick.  I would suppose one could use these materials to make a frame as tough as the Pheonix airframe but that weights much less.  I DID, though, find a way to use a little geometry to make the use of fittings and adapters completely unnecessary.  The ONLY things in the airframe I have conceived are the tubes, the small plates, and the adhesive.  thus, the limitations I have seen regarding use of carbon fibre tubes do not apply to this concept.  But, as a scientist, I know I  need a few experiments to see if it will work, and what it's weaknesses are.

I am not looking to make an airframe that can survive crashing from a height of 100 m full speed into an asphalt parking lot and survive.  That would be silly and unrealistic.  I am, rather, looking to see if I can make an airframe that handles as well as a Blade or Walkera quad (I have seen videos this weekend of pilots making those things do things I would be terrified to try, at least for the moment - but don't ask me to find them again as I didn't know how to save the links to the videos, links that existed only in the media player and not in the web browser), but with an airframe which is a fraction of the weight of a Pheonix airframe so that more of the weight comes from the battery and motors.

Don't get me wrong.  I will be starting with spare parts from a Hubsan to make a Hubsan, and then I will make a kit from either 3DR or DJI, or both, and maybe more than one, and then I will make one from the Pheonix airframe (and hopefully I can get all the parts as spare parts, so I don't have to buy a Blade 200 QX and rip it apart to make the one using the Pheonix airframe).  But then, what is the next step.  I am starting my research into the potential of an airframe using carbon fibre tubes, to see if I can get a copter that is lighter still.  I am just at the beginning of reading up on this, and don't expect to even begin crafting such an airframe until well into next year.

To this end, I have actually, finally, found several books, written within the past couple years, on aerodynamics, especially copter aerodynamics and UAVs.  I have my reading cut out for me. 

Regarding my experiments with carbon tubes and carbon plates, do you have a sense of what diameter tube would likely be appropriate for a quad the size of a Hubsan H107, and what would likely be appropriate for a quad the size of a Blade 200 QX?  And what thickness of carbon plate?  The 1 m tubes are all less than US$6, and the carbon plates I'd work with range in price from US$ 10 to US$ 30, so I could just experiment with them all, in different configurations, to see what is sufficiently strong.

This is very much an experimental, R&D effort, and I don't expect significant results for at least a year.  And I hate the notion of buying junk, so I would repeat my request for information about the manufacturers of good quality parts.  I do not want my experiments sabotaged by inferior parts.

Thanks for all the information you have provided.

That is a cool looking quad, though.  But it looks kind of naked.  Is it possible to put a thin shell on it without significantly adding to it's weight?  But, I guess if it is built to do serious work, it doesn't need a pretty shell.

Thanks

Ted

Hi Ted,

It was really an exercise in making a high endurance copter with (mostly) inexpensive parts, he definitely proved it could be done, but you don't really end up with a practical copter for actually doing anything.

As for motors, KDE is currently probably best with Tiger Motor (T-Motor) a strong second. There are also other good manufacturers, but those stand out and aside from supplying very well made motors they actually provide adequate operational specifications at a variety of throttle settings, prop sizes and various number of battery cells. (This is very important for figuring appropriateness for a particular platform.)

There is a lot of talk about Simon K capable ESCs being "better" but for the most part most better ESCs are of similar efficiency. I use Quattro 4 in 1 ESCs where 20 to 25 amps is an appropriate current rating and am quite happy with them. They have several advantages (no need for a power distribution board or rats nest and less interference with the flight controllers magnetometer (compass). Because of their aluminum plate they also have superior heat dissipation to most ESCs. If you need larger ESCs the KDE ones are reputed to be very good and T-motor as well. For smaller ones the better Turnigy ones from Hobbyking have proven reliable. 

Currently the proximity sensor problem isn't about the sensors at all, it is about implementation in the "autopilots" firmware.

There is some work currently with optical flow which uses a camera, but there is very little current implementation of proximity sensors for navigation.

This will change, but it is just getting started.

Sonar is not as good at this as you might hope and is very subject to noise, absorbing materials, off angle reflections and beam divergence.

And the inexpensive little angle IR led sensors are pretty much useless.

Laser range finders are starting to be used for simple altitude, and a scanned one could work pretty well for horizontal obstacle / opening detection, but it is barely getting started in firmware and is not a simple project.

The goal of this is "SLAM" simultaneous localization and mapping which permits real time path finding and following.

That is not a simple computer task and generally requires a multicore processor for reasonable implementation (and a whole lot of very high level programming).

There are major university and government projects working on this.

Best Regards,

Gary

Thanks Gary,

Now I have some companies to examine. 

If it isn't about the sensors, but rather the firmware, perhaps I can improve things.  I have been programming computers for over three decades, and that experience includes some embedded systems and precision agriculture mapping applications.   Perhaps with my software engineering experience and quantitative bent, I may be able to contribute something beneficial in that realm. 

But if that is the case, what sensors are worth examining, and what size copter would be best to carry them (ideally, if something the size of a Blade 350 QX2 or Walkera X350, or bigger, something that has an effective return home and position holding capability, so that the risk of catastrophe is minimized)?  Or is it the case that there are no sensors available that I could use? If labs are making their own, to use to test their software, it isn't feasible for me as I do not have a lab that could make a good sensor. 

But then, if it really does require a multicore processor, it will be a while before it can be deployed.  On the other hand, I can make my C++ code fly relative to commercially available competitors, so if I can code the firmware in C++, it may be feasible to make it run acceptably on at least the best of the available FC.  My ecommerce software, which I have been working on lately, is more than twice as fast as my fastest competition.  Your description of the challenges involved in SLAM just make me want even more to try, as soon as I can get/make a good working platform to run my code on.  After all, if it was easy, it wouldn't be worth my time.  ;-)

Thanks for this.  I appreciate it.

Cheers

Ted

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