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.
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 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
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.
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.
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.
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.
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.
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.
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.