# Choosing Multicopter Motors

by Alf | February 20, 2014 | (23) Posted in How To

REVISION 1 - 14 MARCH 14: After noticing some discrepencies with either very large or small setups, I revisited the equation. Now, you can input Thrust-to-Weight (T:W) ratio to obtain the result. I also included, as discussed below, an estimate of endurance, as well as calculating ESC and battery rating requirement.

Changes to the original article will be marked by an indent.

The situation

I was working on an academic paper looking at integrating various sensors on a multicopter while optimizing endurance and I soon discovered that selecting motors for a multicopter was not an easy task. All I had was community-based info, which I knew my prof would frown upon. So, I sat down and over many hours created a spreadsheet that would calculate, based on weight and props data, the KV required to reach maximum endurance. Below, I will explain how to use it, and I welcome feedback in making this tool better, so that we can all enjoy flying instead of scrolling down pages of motors.

Of note, I also know many use e-calc, but the issue I have is being forced to go through each motor one-by-one before finding the right solution instead of knowing what to look for. Also, not having access to the calculations does not allow to verify how the results are obtained.

The file

The file is a fairly simple spreadsheet. I am leaving it completely editable for you to see the math behind it and tweak it as you wish.

1. AUW calculator

The spreadsheet is divided into sections, which should be filled somewhat chronologically. The first two is where the magic happens, while the last two are your legend and some common conversions to save you the round trip to Google.

The first section is the 'AUW (All-Up-Weight) Calculator', which allows you to enter the weights of specific components. The legend at the bottom explains the color and font coding. To get started, I personally like to populate the components name. This way you can easily go back later. Then fill in the frame weight (in grams), the weight of a single battery, motor, and ESC (in grams), and some miscellaneous weights to account for your electronics, hardware, added landing skids, etc. Now, I know you don't know what the motor and ESC weigh as that's what we're trying to figure out. This is why selecting a motor can be so daunting. The problem is circular, and the only way out is to use some assumptions to get in the ballpark. Using the quad example, we will start with 75g for the motor and 25g for the ESC, and we'll come back to polish it. The table will automatically calculate weights for multiple components using 4x for quads, 6x for hexa, and 8x for octo.

2. Efficiency Calculator

This section will allow you to add a few more details and try to optimize your solution.

Setup

First, beside '# rotor', indicate the number of rotors the copter will have. Then using the 'Propeller Correction Factors' table, find the value associated to the prop you are planning on using. The table has some of the most common brand name props but a rule of thumb is E-props are 1.0 to 1.3, multi-rotor props are 1.3 to 1.5, and slow-fly are 1.6 to 1.9. This number will have a significant impact on the solution, so don't skip it. The table also indicates the max manufacturer recommended RPM, which will recalculate as you change the Prop Diameter, make sure to confirm the prop is safe for your application.

Battery

Now, indicate the battery voltage you are planning to use beside 'Batt', which 3S in the example below gives us 11.1V. Then indicate the number of batteries you will have onboard beside '# Batt'. Notice that when changing the number of batteries, the AUW table automatically updates. Using the updated weight, fill in the 'Mass' value using kg. Almost there!

Then, input the battery capacity. This will be used for endurance calculations later. Notice that the calculator also provides a required C rating based on the expected power consumption. The rating accounts for a 20% margin of error.

Propeller

Based on your frame size, you should have an idea of the maximum or recommended prop size for it. The example here is a DJI FW450, which commonly uses 10in props with a 3S setup. The value is added beside 'Prop D'. Then, fill in 'Prop Pitch'. If you are unsure, use a value between 3.8 and 5 to start.

Thrust-to-Weight

The table now allows you to choose your Thrust-to-Weight (T:W) ratio. A T:W of 3 is often used as good. If you are planning on adding equipment on the platform, you may wish to give yourself some room by increasing either the AUW or the T:W. The calculator will then provide both a total and a single motor thrust requirement. The required RPM and Output KV is also provided.

Required Motor

Finally, the motor efficiency is placed beside 'Efficiency'. 80% is a good assumption for now. This value is usually difficult to find, especially for budget motors. A rule-of-thumb is 70% for budget motors, 80% for average, and 85-90% for high-end.

Press Enter and Voila! beside 'Req Nom KV' is the nominal KV value you will require, aka the KV number written on the motor.

Notice it will also provide an estimated power requirement for the motor to turn the prop at max throttle, and an ESC rating which automatically accounts for a 20% margin.
Lastly, the estimator provides data for both 100% throttle and hover conditions. P-out being the power required to turn the prop at the calculated RPM, P-in being a function of motor efficiency, and an estimate of current either per motor or the total consumption.
The endurance calculator results will vary and is meant only as an indicator. First impression is that it may be slightly optimistic.

You found a motor that matches the Required Nominal KV value from the spreadsheet. What now? You will be able to replace assumptions with reality, which will in turn change the Req Nom Value. Remember the circular problem from above; well this is most likely your last lap.

• Update the motor and ESC weight in the AUW table, and make sure to update the Mass in the calculator. Update the Efficiency if you have one. The Req Nom KV changed.
• Change Prop Correction Factors and Pitch Prop to see which brand and/or prop dimensions will get you back to the selected motor. Make sure that the Prop Pitch is actually available from that brand.
• Make sure the motor and ESC you found is powerful enough to turn that prop.

At this point, you should have a decent solution. It is okay to be within 50 to 100KV of the answer.

The last thing to do is to consider what you will be using it for especially if your applications will vary greatly in AUW. Just make sure the motors will be powerful enough to change props to suit the new application.

Conclusion

This is a theoretical model to optimize endurance. I have only verified it against the example shown, DJI FW450 with TBS 900KV and ESC with 10x4.5 APC MR. So far, the hover is between 50-55% throttle depending on 1x or 2x2200mAh 3S batteries with a measured 5500RPM, using both a tachmeter and ESC logging, while Max RPM was measured at 8200RPM . The latter is within 150RPM of the predicted RPM, which in my mind is negligeable and seem to prove the model.

Please leave a comment below with your results or if you have tested a different setup. Don't be afraid to point out errors or failures, I'm here to learn and hopefully improve the tool.

Cheers,

ALF

MT Alex on February 28, 2014
Very nice piece of work! You may want to edit your article to remove the bottom half, which is a duplicate of the top.
Alf on February 28, 2014
Done, not sure what happened. Cheers.
ikem on February 28, 2014
Plugged in everything, and guess what.. i get a 922KV and i have 920kv's on there! Nice calc!
Alf on March 6, 2014
Is that on the Titan or a different setup?
ikem on March 7, 2014
On the TITAN
ScottyZ on February 28, 2014
Fantastic! Thank you very much.
Techno16 on February 28, 2014
Please make one of these wonderful charts for tricopters!
Alf on February 28, 2014
I will update the AUW table to include a Tri. In the mean time, if you already have a weight, you can simply change the '# rotor' to 3. The result will then be for a tricopter.
Alf on March 1, 2014
Revised file added at the end of the article including an AUW table for tricopters. Cheers.
sickwayne on February 28, 2014
This is really wonderful. What is the "prop correction factor", what do you use it for, and how did you calculate it for the different props. I am curious as to how your spreadsheet will handle the input of new props.
Really nice job!
Alf on February 28, 2014
Disclaimer: The 'prop correction factor' is a mathematical concept which pushes the limit of my aerodynamics understanding.

It is a dynamometer measured value of an actual prop thrust that is applied inside the equation over a theoretical value to account for specific propeller characteristics. An analogy would be the shape of an airfoil and its effect on lift. In effect, the propeller is a spinning airfoil and therefore specific blades will produce various levels of thrust despite having the same length and pitch.

Therefore, changing the value from an APC E of 1.3 to an APC SF of 1.9 lowers the required KV with the caveat that using the SF with 900KV and a 3S will exceed the RPM limit of the prop (8000RPM when 6500RPM limit). This could have structural and aerodynamic implications.

Something not mentioned yet is that it also applies to 3- and 4-blade. I have values for a few other brands which were less common for quads, and almost none for the chinese ones. If you would like to get a specific one, just reply and I'll go hunt for it. Cheers.
ghostrider03z on February 28, 2014
Awesome article.
I got to admit, 1400kv motors give so much dang power at the cost of flight time. Lower kv motors are the way to go.
twitchythumbs on March 1, 2014
I'll bet there are many out there, including myself, who have unwittingly been flying multirotors on a 3S setup and exceeding the maximum recommended RPM of our commonly used SF props. Since the factor of safety used to set recommended maximums is always conservative, and since clearly the props can endure spinning faster than this value (I've never had one fail in normal or high-speed flight), my question is this: What are the affects on the system by over-spinning these props? I've got to think that it greatly reduces motor efficiencies and probably introduces deformation and vibrations that also affect performance. I just don't know how to quantify those losses, especially with regard to the efficiencies. Do you have any idea about this? Thanks.
Alf on March 1, 2014
My understanding is that you will mainly exceed flutter speed which results in significant torsional and flexural forces being applied on your blades (google Tacoma Narrows Bridge). Flutter is a function of airspeed, airfoil shape, and Angle of Attack (AoA also known as prop pitch in RC). Usually, the higher the lift and the lower you will reach flutter speed. A SF has lots of lift and will reach it at lower RPM. So flutter will induce a significant amount of stress on your prop which may lead to breakage and remember that lack of evidence is not evidence so I would be wary regardless of past experience. Furthermore, most propellers airfoil shape, often seen in NACA numbers, will vary from end-to-end to take advantage of the travelling speed of each section (tip goes faster than center at given RPM).

So the answer is yes it is quantifiable but you will need a few hours to a day punching numbers to figure it and at the end probably a wind tunnel to verify. The quick answer is that although motor efficiency will for the most part be unchanged you may see not only less lift from your prop but potentially a decrease. In other words, there will be no differences between 90% throttle and 100% despite the motor turning faster. Wasted energy. From a motor point of view the impact will be vibration related with possible earlier onset of wear in bearings.

Evidence of flutter may be a change in the prop sound beyond a certain throttle setting. If you fly fpv you may experience more jello at higher speeds. Your flight controller may have more noise from vibration resulting in poorer controllability at high speed.

At the end it will depend on your setup and type of flying. If you spend a lot of time at 100%. There would be better options out there. If not it may very well work as casual flying would nit exceed max RPM. I hope this answers your question. Cheers.
twitchythumbs on March 1, 2014
Thanks for the response, Alf. What you say certainly makes sense, and I would say that video data I've shot backs it up pretty well. I think the moral of the story is that when I really need the performance, I'll put on a set of Graupners or even carbon props, but for normal, everyday, line-of-sight flight, I'll stick with the lower cost SF props.
MIDNCOCO on March 3, 2014
Alf,

Great Calculations. I would recommend you expand on this to also in battery information for flight time and a calculated performance ratio. Since you have the KV of the motor you can also include battery size and C rating this will give you flight time. You can also take it a set further in include a throttle range. Assumes linear throttle programing you can generate a Max efficency plot or flight time for a given throttle range. You can also include performance as well with the ratio of thrust to weight. Typically a 3:1 should be your target. here is the link to my paper to help with your research.

http://www.flitetest.com/articles/tricopter-design-part-4-the-paper
Alf on March 4, 2014
Great ideas. I was thinking to start from prop size to power requirement and move to W-in from there. This way it allows one more piece of information toward selecting the motor. You are right though, it would be simple to add battery size and rating from there based on the average motor efficiency and a simple ohm's law application.

I will have to think about the efficiency plot. My understanding is that despite linear throttle programming, actual power consumption is not and the slope is often offset to include no-load current. Also, motors efficiency often decline while throttle increases. Therefore, I'm wary to include it as a valid prediction.

On a side note, I read your paper and it is a thorough holistic look at tri design. I noticed on page 26 you did not include plastic as one of the materials. Would you agree that it would fall between wood and AL, probably closer to wood? If so, it is also interesting to see that for most 500-sized multicopter and below applications, material selection is negligible from a vibration point of view. Did you assess the general impact of different prop length and pitch on the results?
MIDNCOCO on March 4, 2014
I understand about the linear relationship being slightly not linear. For you data points it would be best as a linear approximation as you can see from my wind tunel test. The linear relation would be that of voltage and RPM, while the AMPs would be more curvey and would give and exponet fit line when you plot out power. I find that "Pump Laws" are a pretty good represenation of what you would find. For the material I wanted to use 10mmx10mm cube rods to compare each and at the time I was not able to find G10 plastic. With the different plastics on the market it would be hard to say where it all falls in relation to the others. I would disagree that vibes would be negligible, this would be the case of the 450 size motor that I used, but is is dependant of the motor. As for the impact of prop length and pitch, i looks at the efficiency for the number of blades and only asset maxiumizing the speed and generating the most amount of lift. The prop length and pitch assumed to be balanced and only increased the ampliude of the vibrations while keeping the motors vibrational signature. If not then this process would have been go beyond my scope that I wanted to research.
Alf on March 4, 2014
Voltage and RPM makes sense. I'll try to come up with it when I have a sec.

I guess my previous comment led to some confusion. By 500-sized, I really meant 500mm sized as the arm length would be less than 250mm and therefore below the curve.

Thanks for the input and response, a great paper once again.
frugalflyer on March 4, 2014
Unfortunately I am unable to access your spread sheet as Microsoft insist on attempting to sell me a newer version of Office. Can you make it available for older versions? I have 2000
Alf on March 4, 2014
I will do so later, but in the mean time you can also download Open Office at https://www.openoffice.org/download/index.html. It's free and handles just about everything Microsoft Office can.
Alf on March 4, 2014
New file uploaded for 97-2003. Cheers.
frugalflyer on March 6, 2014
Thanks. I/we oldies appreciate your work.
anddy103 on March 4, 2014
Is it possible to do this for a tricopter?
Alf on March 4, 2014
Absolutely. Download the updated file at the bottom of the article. It will have the AUW table for a tricopter. Use the calculated weight as per the explanations making sure to change '# rotor' to 3. Cheers.
anddy103 on March 5, 2014
thanks

Alf on March 11, 2014
Revision 1 is out. I spun the equation on it's head and got more consistent results across the range of multicopter sizes based on user desired thrust-to-weight ratio. The file also includes an estimator and now provides motor power, ESC rating, and battery C rating. Cheers
Bala on March 21, 2014
@Alf.. A really wonderful article... I'm currently building a quadcopter as my final year project. Is it possible for you to send/share the formula and its references to me by any chance? I have been trying to explore a lot on this topic. Your calculations are actually impressive. I hope you can help me out designing my copter mathematically.. :)
Alf on March 22, 2014
@Bala. I would be happy to help, but I believe you may be well ahead of me if you are in final year and what I could provide would most likely fall short of you expectations. The goal of my paper was on autonomous indoor navigation and mapping with only a small part being copter design as a proof of concept. Therefore, the math behind it is fairly simplistic. Still, the formulas should be visible by clicking on the 'output' cell if you wish to look at them.

I have edited the article to include MIDNCOCO's article under 'related'. His paper is impressive and thorough, and will most likely give you the necessary info to get started.

Good luck in the last stretch! Cheers
Bala on March 26, 2014
Thanks a lot... The article was really informative... :)
jeffstreet on April 14, 2014
@Alf Thanks for building and posting this. It's super useful.

I fixed a few typos and made a couple formatting tweaks. Can I send you the updated version? (I don’t see a way to send it on this site, so it’s posted as a Google Doc here: https://docs.google.com/spreadsheets/d/1qW8ddgzoDMM1Orw1CgpyT3pagm6uTuS5Z6zCzRHqrf8 )
Alf on April 18, 2014
@jeffstreet you're welcome. Thanks for the typos, there is always a few despite my best effort. I like what you did with the spreadsheet and the feel of it. I work on a large screen so I considered breaking it down into sheets, but I preferred seeing everything at once. In my next update I will post your link in the article. Cheers
jeffstreet on April 18, 2014
@ Alf
Cool. If you'd like the project to live as a Google Sheet, I'd be happy to give you editing permissions. Just send a request via the Share button.
Alf on April 18, 2014
@jeffstreet. Thanks for the offer, but I'm happy if you want to make it your own. The goal is to help people build by removing some of the guessing game. Therefore, the math is free ;)
Cheers
Drfreaky on April 18, 2014
How do you calculate the start hover throttle in %?
Alf on April 18, 2014
Hi Drfreaky. The calculator provides a hover RPM which is based on a T:W of 1.2:1 in order to give a more conservative number, which my own tests seem to support as accurate.

When it comes to calculating the actual throttle %, I wouldn't know how, but I doubt you can apply a generic formaula to a specific setup mostly because a motor efficiency is not linear and will vary from motor to motor. It should hover around the 50% mark. In my case the hover was at 54% which using a throttle curve on my transmitter I brought down to be at mid-stick.

Drfreaky on April 20, 2014
Alf,

Another question is about the C rating for the battery, when doing calculation ive got an answered of 3C...is this the required Minimum C rating for buying batteries? Or discharging rate? Anyhow awesome calculator...
Alf on April 20, 2014
Hi Drfreaky,
It is possible depending on your setup. The value calculated is the minimum C rating required. So, assuming a quad, if your setup requires 10A total, or 2.5A per motor, and you use a 10,000mAh battery, you would only need a 1C battery (i.e. a 35C battery would have 35x more discharge rate ability than needed). Doubling or halving either of those should have a similar effect on C rating requirement. Note the calculator adds 20% for a safety margin.

Cheers
Drfreaky on April 20, 2014
Meaning to say that it is still safe to use a battery with a high mah eg:-10000mah @ 30c discharge rate?
Alf on April 20, 2014
Absolutely fine. It simply means the batterry could handle a 300A discharge (10,000mAh × 30C = 300A) and all you need is 30A for your setup.
Runaway on May 12, 2014
@Alf,
First off, let me say thanks for such a great tool. I've been using it on a balsa-quadcopter I built and the numbers seem to match up almost identically.

I'm studying engineering, so I decided to try and figure out the math behind your spreadsheet. Is there any chance you could explain where the constants you use come from? Specifically two in the calculations for required RPMs: (.0981 and 3.29546).

Any help or resources you could point me to would be awesome.
Thanks
Runaway on May 12, 2014
Actually, nevermind, I was able to figure them all out.
For anyone else interested, the derivations are explained here: http://electricrcaircraftguy.blogspot.com/2014/04/propeller-static-dynamic-thrust-equation-background.html#.U3Fci_ldWac

Alf on May 13, 2014
@Runaway,
I'm glad I can help. The source you found is more in depth and thorough than the one I did. I'll have to read it when I have a sec.

Cheers
JeremyK on October 24, 2014
@Alf,
I just found your spreadsheet and think it's a great resource. I would like some clarification on the required RPM field. Does the equation produce an RPM with or without a load? It's my understanding that kV ratings are for unloaded motors, and the Nom kV is found using the required RPM field. I just wanted to verify I was interpreting the RPM value correctly.
Thanks!
Alf on October 24, 2014
@JeremyK,

- Required (T6): is the RPM at which the motor needs to turn in order to produce the required thrust.
- Required kV (T7): is the actual kV value obtained from dividing the 'Required RPM' (loaded) by your voltage.
- Efficiency (T8): is were you can capture the expected drop between nominal (unloaded) and actual (loaded) kV. This one is though to find. Usually, 80%+ for good motors, less for budget ones.
- Req Nom kV (T9): is the nominal (unloaded) kV value of your motor which is the advertised.

Cheers
AkshayBudhiraja on October 29, 2014
@Alf,

Let me start by saying that this is a great resource! I was wondering if you could help me out for figuring the prop-correctional value for a three-blade prop, more specifically a 5030 3-blade prop? Is there any other information you would need to specify the correctional factor?

Thanks!
Alf on October 30, 2014
@AkshayBudhiraja,
Thanks for the comment. To answer your question, I do not have specifics for 3- or 4-bladed props and unfortunately, unless it is physically tested, you won't know for sure. What I can tell you is a ballpark value. It should range from approx. 1.40 to 2.05. The lower value would be for a really thin, cheap, and fleamsy prop, while the upper one would be for highest quality material (think carbon) slowfly type. My best guess for a starting point would be 1.6-1.7, but results may vary.

Cheers,
Alf
mturneruk on November 10, 2014
Amazing Work. I have just used your spreadsheet to calculate everything for my new Scratch Built X8 Multirotor Made entirely from light ply and CNC machine!
However the suggested flight times appear to be way out, or i am doing something wrong.

I was expecting at least above 10 minutes and ended up hitting Low Voltage Cutoff. Luckily i got away with no damage.

I am running....
8 Motors in a 4 up 4 down X config
3s 2p 3000mah. E.g. (6000mah)
8 * 4.5 Props.
AUW : 1.95KG
1200KV Motors (was expecting the AUW to be slightly higher).
Spreadsheet now suggests nearer 1100KV based on 1.95KG.

Any ideas on what is wrong here ?
Thanks....
Martin Bristol UK...
Alf on November 15, 2014
Hi Martin,
Sorry for the delay in replying. I think you are pushing the limits of the calculator ;)

First, the stacked setup will influence the flow of air around the lower props decreasing their effectiveness. Something the model does not account for. No doubt you will have found during your research some will use a different sized prop under to mitigate this loss.

Secondly, with the above taken in consideration, the further down we get into the math the more the errors add up. For a conventional quad setup, I get results pretty close to the calculator for endurance at the various throttle settings. I am glad nothing bad happened with your shorter than expected flight times. Lastly, other factors to keep in mind are weather conditions, controller logic, ESCs efficiency,... therefore, I don't think we'll ever get to the perfect answer. Testing with various size and types of props would be your best bet at this point. You can measure your battery voltage every minute to assess your endurance keeping in mind that flying around will consume more than in the hover.

All that being said, I wouldn't worry to much about the motors, the additional 100kv is not that far off, and in the case of an X8 may actually compensate for some of the lost thrust.

I hope this helps.

Cheers,
Alf