Thinking about designing multirotors to optimizing flight time

Designing electric multicopters for a specific flight time is a complex multidisciplinary optimization problem. This short blog post is some of my thoughts on how to think about this problem. Obviously, there so many different ways of doing this and welcome suggestions and other constructive discussions.

From an energy conversion standpoint, multirotors is a pretty simple systems. Energy is available from the batteries which is routed via ESCs to the motor and the propeller.

The challenging part is that batteries do not always provide the same efficiency(energy). They are dependent on the power draw (watts,current). For most batteries, the higher the current you draw from the battery, the lower the total-energy available from them. This is mainly due to the internal resistance of the batteries which is pretty low (milliohms or less), but not zero. A typical characteristics of few of the different battery cells are given below. The y-axis shows the energy density (Wh/Kg) of the battery and x-axis shows the power that was drawn from one Kg of battery.

Notice how the increased drain causes the energy capacity to drop sharply for all the cells.

If we ignore the ESCs power loss characteristics, the other significant power conversion is from the electrical energy received to the motor and the thrust provided by the propeller. One intuitive way to think about this conversion is W/Kg. This is the watts input to the system for every Kg of thrust generated by the propeller.

If we ignore the motor and consider just the propeller, we can define this as

“Mechanical power (watts) supplied to rotate the propeller / Kg of thrust”.

If we consider the motor, this unit becomes “Electrical power input to the motor (watts) / Kg of thrust”.

Shown below is an “electrical watts/Kg of thrust” of various sizes of propellers tested with different motors. The x-axis shows the “electrical watts/Kg of thrust” and y-axis is the total thrust generated by the propeller. Each color shows a propeller of a particular size.

The three things to note are

• How the same propeller can have widely varying efficiency with different motors.
• How a given propeller drops its efficiency for higher thrust
• The higher efficiency of a larger propeller

Designing an optimal multirotor requires matching the characteristics of the battery to those of the motor and the propeller. Would love to discuss more about this is in a later blog

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Comment by Mateusz Sadowski on October 4, 2019 at 11:19pm

In my first internship I was testing various propeller - motor combinations to plot the thrust to power ratio. Good times!

Comment by Jim Faunce on October 9, 2019 at 10:59am

As you state, it is a complex multidisciplinary problem, with many variables.  However, assuming you want to use commercial off the shelf (COTS) components, your variables are quickly reduced.  The first thing to do is write down the requirements.  Is long flight time the only requirement?  What is the application?  How big is the payload?  Will you only be flying in perfect weather?  Does the multirotor have to handle large wind gusts?  Do you need high reliability?  What is your budget?

We did a lot of ESC/Motor/Prop testing to build and fly a 55 lb (with payload) X8 for the NIST UAS challenge.

If reliability is a big issue (Expensive payload? Flying in populated area? Flying over water?) then you might consider using 6 or 8 prop configurations.  For highest efficiency a quad with large props will be more efficient than a hex or octo that hover at the same weight.

The prop is the first thing to size.  For a guide you can look at manufacturers’ data, such as KDE at https://www.kdedirect.com/collections/uas-multi-rotor-brushless-motors

and T-Motor http://store-en.tmotor.com/ and HobbyWing https://hobbywing.com/index.php

along with several others.  Look at the performance data for different motors, as an example

https://cdn.shopify.com/s/files/1/0496/8205/files/KDE_Direct_XF_CF_... and figure out what thrust you will need for each propulsion unit (ESC, Motor and Prop) and look for the combination that will give you the best efficiency (grams/watt or lb/hp) at around 50% throttle so the UAV can be easily controlled and fly in some wind.

A few other comments.  Most ESCs have highest efficiency near full throttle, and BLDC motors hit peak efficiency at 70 to 80 % full speed (no load speed).  The new FOC ESC’s with sine-wave drive are much more efficient than the older common tarpazoidal drive ESCs.

Designing with COTS components, you should start with choosing a prop based on the full estimated weight of the UAV, then go up or down a prop size during testing.  If you are building a large UAV, consider using Lithium-Ion batteries vs LiPo.  The LiPo are most convenient and less volatile, and can handle a relatively large discharge (C rating).  The Li-Ion cannot provide as many Amps discharge, so you need to have more of them in parallel to provide the current you will need, but they have 60 to 80% more energy per kg than LiPo.  For example check out https://www.gettitanpower.com/

Comment by Bart Theys on October 10, 2019 at 12:34am

the efficiency of your propeller will not change if you take another motor, it will be the motor + ESC combination that will not have the same efficiency depending on the esc+mot+propeller combination. Propeller efficiency in hover is characterized with the propeller Figure of Merit which is Thrust^1.5 / (torque*omega*sqrt(rho*2*A_disk)).

The efficiency of your motor + ESC is torque*omega/(current*voltage). A larger propeller will, in theory, always decrease your required W/kg but in reality large propellers at very low rpm's will have a decreasing aerodynamic efficiency (the figure of merit) because profile drag becomes significant.

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