**Power Systems — Using Performance Graphs**

RC Heli Pilot Staff July 9, 2015 Gas Powered Thoughts

*By Lucien Miller*

Picking out a power system for a multirotor aircraft can be a bit overwhelming for pilots that are new to this segment of the hobby. Trying to figure out what motor, prop, ESCs and battery to use can be a difficult task without the proper documentation. Fortunately, many of the better motor companies are now providing prop charts and performance data graphs for their motors that make this process much easier. Unfortunately, if you do not know how to read the data from these charts, they are of little help. In this installment of Multirotor Flight, we will go through a step-by-step approach to explain what is represented in these data charts, and how to use that data to select a power system.

For the sake of this example, let us assume that we have a 500mm quad frame that should weigh about 56 ounces, or 3 1/2 pounds, ready to fly including all the electronics and a 3-cell 5000mAh LiPo battery. In order to be able to hover, the combined thrust of all four motors needs to be equal to the weight of the craft. In this case, the multirotor weighs 56 ounces and we have four motors, so each motor needs to make 14 ounces of thrust, since 4 x 14 equals 56.

When selecting motors for a multirotor, the total thrust that the motors are capable of producing needs to be at least double the weight of the craft to allow excess power for climb and maneuvering. For decent flight times, your motors should put out three times more thrust than the craft weighs, and for racing, you may want to go to four or five times the weight of the craft when calculating total thrust. In this example, we will use a motor that puts out three times the thrust at full throttle that we need to hover.

Fig. 1

Many motor manufacturers have prop charts available for their motors. These charts show the full throttle performance of the motors with a variety of props. While this data is not sufficient to calculate flight times or motor performance, it does provide enough information to select a motor for a multirotor. As we said earlier, each motor in our example quad needs to produce 14 ounces of thrust in a hover. If we want a 3:1 power-to-weight ratio for our machine, then each motor should be capable of producing 3 x 14 or 42 ounces of thrust at full throttle. Figure 1 shows an excerpt of the prop chart for a Cobra CM 2217-20 motor. If you look at the line for the APC 12×4.5-MR prop, you will see that this combination produces 41.2 ounces of thrust at full throttle when run at 11.1 volts, which is what you can expect from a 3-cell LiPo battery. Since this value is extremely close to our desired thrust of 42 ounces, this motor and prop look like a good combination to use.

Once we have selected a motor, the ESCs must be chosen. Even though most of a multirotor’s time is spent running in the 40 to 60 percent throttle range, you still need to size the speed controllers for the maximum rated current of the motor to be able to handle the full throttle bursts you will experience from time to time during flight. The Cobra CM-2217-20 motor has a max current rating of 20 amps, so that is the absolute minimum size ESC that should be used. It is always a good idea to use ESCs that are a size bigger than actually needed, as this gives a bit of a buffer zone to ensure they are never overworked. Because of this, ESCs in the 25 to 30 amp range would be a perfect fit for this power system.

Now that the motor, prop and ESC have been chosen, it is time to use the motor performance graphs to see exactly the power needed to fly our quadcopter. Different companies provide slightly different performance data in their charts, but since we are using the Cobra motor in this example, we will use the charts published on their website. Each motor and prop combination has a set of four data charts available for download.These charts provide Prop Thrust vs. Throttle, Motor Current vs. Throttle, Propeller RPM vs. Throttle and Prop Efficiency vs. Throttle.

Fig. 2

The data for these performance graphs comes from the prop chart shown in Figure 2. This chart shows the performance of the motor and prop, running at 11.1 volts, over the entire range of operation from 10 to 100 percent throttle in 10 percent increments. Since multirotors spend most of their time in a hover, where the motors are only putting out 40 to 60 percent throttle, the middle area of these curves is most important to us.

Fig. 3

Figure 3 shows the first curve that we will look at, the Propeller Thrust vs. Throttle Position graph. This graph will tell us how much throttle will be needed to produce the required thrust for hovering flight in our quadcopter. Once we know the throttle level required, that value will be used to read the other graphs. Earlier, we determined that each motor needed to make 14 ounces of thrust. So Step 1 of the process will start at the 14-ounce point on the left side of this graph. A line is drawn straight to the right from the 14-ounce point until it intersects the blue curve on the graph. From this point, for Step 2 another line is drawn straight down from the intersection point to the Throttle axis. This second line is a little to the left of the 50 percent throttle point, so we will call it 49 percent throttle. Now we know that in a hover, our motors will be running at 49 percent throttle to produce 14 ounces of thrust to maintain a stable hover.

Fig. 4

Fig. 5

Fig. 6

To find out how much current our motors will pull in a hover, we need to look at the next graph, Motor Current vs. Throttle Position, which is shown in Figure 4. To use this graph, we start at the bottom at the 49 percent throttle position and draw a line straight up until we intersect the blue curve. This is shown as Step 3. Then a second line is drawn straight left from the intersection point until it reaches the Motor Current axis. In this case, the line ends up halfway between the 3 amp and 4 amp lines, which is 3.5 amps of current. This is the current that each motor will pull from the battery during hovering flight. Since we have four motors on our quadcopter, the total current used will be 3.5 x 4 or 14 amps.

Next, if you desire, you can find out how fast the props will be spinning with the Propeller RPM vs. Throttle Position graph shown in Figure 5. Once again we start at the 49 percent throttle point at the bottom of the graph and draw a line straight up until it intersects the blue curve. From that point, a second line is drawn to the left until it intersects the Propeller Speed axis. In this example, the line is just a little bit below the 4,000 rpm line, or approximately 3,950 rpm.

Finally, as a double check that you drew the lines correctly on the first two graphs, the Propeller Efficiency vs. Throttle Position graph shown in Figure 6 can be used. If you start at the bottom of this graph at the 49 percent throttle point, and draw a line up until it intersects the blue curve, and then draw a second line to the left, the line hits the Prop Efficiency axis half way between the 10.0 and 10.5 lines, or approximately 10.25 grams of thrust per watt of input power. To use this data, we must first convert the weight of our quadcopter from pounds to grams. Since there are 454 grams to the pound, if you take 3.5 pounds x 454 you get 1,589 grams. To calculate the power required, we then divide the weight of our multirotor by the prop efficiency to see how many watts of power are needed in a hover. 1,589 divided by 10.25 is equal to 155 watts. Since we have a 3 cell LiPo battery, which puts out 11.1 volts, to calculate the current used you take 155 divided by 11.1, and that equals 14 amps for all four motors combined. This is the same value that we got from the Motor Current vs. Throttle Position graph earlier, so we know that the math is right!

Now that we have all this data, what can be done with it? We know that our 56-ounce machine will require 14 amps of current from the battery to stay in a stable hover, and we will be at 49 percent throttle to achieve this. From this information we can calculate flight time, based on our battery size. Most LiPo batteries have their capacity stated in milliamp hours or mAh. In this example, we are using a 3-cell 5000mAh battery. For doing flight time calculations, it is best to have the battery capacity stated in Amp-hours. This is pretty easy to do, since there are 1000 mA to the Amp, our 5000mAh battery can also be called a 5Ah battery.

Before we calculate flight times, a brief discussion of the terms “C” and “C-rate” are in order. Battery discharge is commonly measured in multiples of C, which stands for the Capacity of the battery. By definition a 1-C discharge rate will drain a battery completely in one hour. A 2-C discharge rate will drain the battery in half an hour or 30 minutes. A 3-C discharge rate will drain the battery in 1/3 of an hour or 20 minutes, and so on. To calculate how long our battery will last in our quadcopter, we need to determine the C-rate of discharge.

Earlier we calculated that our total current draw from all four motors in a hover was 14 amps. Since our battery capacity is 5Ah, the C-rate of discharge is 14 divided by 5 or 2.8-C. Since the discharge of a battery is always expressed with C being the one hour rate of discharge, which is also 60 minutes, to calculate the discharge time you simply take 60 minutes and divide it by the C-rate of discharge. In this case, 60 divided by 2.8 is equal to 21.4 minutes. Now remember, this is the time to completely drain the battery, which is something you NEVER want to do with LiPo batteries. You should always leave 20 percent of the energy in the pack at the end of the flight to prevent damaging the cells. This means that we should never use more than 80 percent of the total battery energy. To correct the flight time to use only 80 percent of the battery capacity, take 21.4 x 0.8 and you will get 17.1 minutes.

Unfortunately we are not quite finished yet. These calculations that were done so far assume that our quadcopter is in a stationary, stable hover. Any time you maneuver a multirotor of any kind, one or more of the motors needs to speed up to provide the force to move the craft to a new location. Any time a motor spins faster it uses more current, and that will cut into your flight time. Just how much this cuts into the flight time depends on the flying style and the weather conditions. If you are doing basic aerial photography work, with a minimal amount of maneuvering, taking 75 percent of the calculated flight value is a good starting point. With our 80 percent battery use time of 17.1 minutes, if this value is multiplied by 0.75 you get 12.8 minutes.

Fig. 7

Other considerations include wind conditions during the flight. If you are doing aerial photography, and there are winds blowing steady at 15 mph, the extra work that the motors must do to keep the multirotor in one place can dramatically cut your flight times, sometimes by as much as half. If you are doing pylon racing or FPV racing, and your motors are running up at 75 percent throttle or higher, the current draw can be three to four times higher than it is in a hover, and this would reduce the flight time down to as little as four or five minutes. To monitor actual battery voltage, and to make sure that you never over-discharge your batteries, a small battery alarm device, such as the one shown in Figure 7 can be used. These plug into the balance lead of your LiPo battery and monitor each individual cell. As soon as the voltage in any cell drops below a pre-set level, an alarm will sound to let you know it is time to come back and land.

Hopefully the preceding discussion has taken some of the mystery out of selecting a power system for your multirotor aircraft, and provided the information to properly use the performance graphs that are being provided with multirotor motors. If you have any questions or comments about this column, or have a suggestion for a topic that you would like to see covered, you can reach me at [email protected].

I Hope that you learned something new. ;-)

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