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.

Download here: Multicopter Motor Selector

or: Multicopter Motor Selector - Excel 97-2003 compatible

**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.

**3. Polishing your results**

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

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Really nice job!

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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.

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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.

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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.

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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

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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?

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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.

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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

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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 )

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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.

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Cheers

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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.

I hope this answer your question. Cheers,

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Thanks for the reply,

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...

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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

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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

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For anyone else interested, the derivations are explained here: http://electricrcaircraftguy.blogspot.com/2014/04/propeller-static-dynamic-thrust-equation-background.html#.U3Fci_ldWac

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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

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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!

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The fields are as follow (spreadsheet cell in bracket):

- 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.

I hope this answers your question,

Cheers

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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!

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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

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However the suggested flight times appear to be way out, or i am doing something wrong.

Your spreadsheet suggested I should get a 22 minute hover, however I got about 6.

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...

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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

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Your values support those that I've gotten from eCalc as well as are similar to actual numbers from builds. Keep up the good work.

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