## Using Performance Graphs

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, ESC’s 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 Li-Po battery. In order to be able to hover, the combined thrust of all 4 motors needs to be equal to the weight of the craft. In this case, the multirotor weighs 56 ounces and we have 4 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 3 times more thrust than the craft weighs, and for racing, you may want to go to 4 or 5 times the weight of the craft when calculating total thrust. For the sake of this example, we will use a motor that puts out 3 times the thrust at full throttle that we need to hover.

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 to 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 Li-Po battery. Since this value is extremely close to our desired thrust of 42 ounces, this motor and prop looks like a good combination to use.

Once we have selected a motor, the ESC’s must be chosen. Even though most of a multirotors time is spent running in the 40 to 60% 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 ESC’s that are a size bigger than actually needed, as this give a bit of a buffer zone to ensure they are never overworked. Because of this, ESC’s 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 4 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.

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% throttle in 10% increments. Since multirotors spend most of their time in a hover, where the motors are only putting out 40 to 60% throttle, the middle area of these curves is most important to us.

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% throttle point, so we will call it 49% throttle. Now we know that in a hover, our motors will be running at 49% throttle to produce 14 ounces of thrust to maintain a stable hover.

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% 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 half way 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 4 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% 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 4000 RPM line, or approximately 3950 RPM.

Finally, as a double check that you drew the lines correctly on the first 2 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% 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 1589 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. 1589 divided by 10.25 is equal to 155 watts. Since we have a 3-cell Li-Po 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 4 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% throttle to achieve this. From this information we can calculate flight time, based on our battery size. Most Li-Po batteries have their capacity stated in milli-amp hours or mah. In this example, we are using a 3-cell 5000 mah 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 5000 mah battery can also be called a 5 Ah 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 1 hour. A 2-C discharge rate will drain the battery in ½ of 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 4 motors in a hover was 14 amps. Since our battery capacity is 5 Ah, 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 1-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 Li-Po batteries. You should always leave 20% 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% of the total battery energy. To correct the flight time to use only 80% 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 need 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% of the calculated flight value is a good starting point. With our 80% battery use time of 17.1 minutes, if this value is multiplied by 0.75 you get 12.8 minutes.

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% throttle or higher, the current draw can be 3 to 4 times higher than it is in a hover, and this would reduce the flight time down to as little as 4 or 5 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 Li-Po 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.

## Multirotor Maintenance

Multirotor aircraft are relatively low-maintenance models by design. Unlike helicopters, which have a large number of moving parts such as swash-plates, gears, pulleys, pushrods, blade holders and thrust bearings to name a few, conventional multirotors are rather simple machines with very few moving parts. The standard quad or hex configuration multirotor has just 4 or 6 rotating propellers which provide all the flight control. Because of the simplicity of multirotors, pilots often see them as “maintenance-free” models, but this can lead to problems down the road, and cause costly in-flight failures which could have been easily avoided. In this installment of Multirotor Flight, we will take a look at some of the important aspects of routine multirotor maintenance, and how this can prevent costly damage to your model.

Any multirotor that has an even number of motors requires nothing more than the spinning props to provide all of the models flight control. With half of the props spinning clockwise and the other half spinning counter-clockwise, the motor torques cancel each other out and the craft can be stable in yaw in a hover. With tri-copter designs, two of the motors can cancel out each others torque, but the third motor will require a tilt servo to provide torque cancellation and yaw control. Since the majority of multirotors in use today are either quad or hex configurations, we will concentrate on those in this discussion. Everything covered here does also apply to tri-copter designs, you just have the added complexity of the tilt mechanism and its control servo and associated pushrods.

One of the most important things to watch for in a multirotor, and often the most neglected, is the condition of your propellers. In multirotors, everything happens in the props. By constantly changing the speed of the motors, and thus the RPM of the props, multirotors maintain controlled flight and amazing maneuverability. Props should always be checked for balance before they are installed onto any multirotor. If the prop is out of balance you can bring it into balance by carefully scraping away material on the heavy blade, or by adding tape to the light blade to bring the prop into balance. Running out of balance props can cause issues with control stability and can lead to failure of the flight controller board.

Even with experienced pilots, a multirotor will occasionally make a rough landing and flip over causing the props to strike the ground. If this is done in tall grass, chances are you will not suffer any prop damage. However, you should always inspect your multirotor carefully any time a prop strikes the ground. One of the worst possible things to happen to a multirotor is to have an in-flight prop failure. This is especially true if you throw one blade off of a prop and have the other one left intact. In a quad, the loss of a prop results in an uncontrollable flight situation that will cause the machine to fall out of the sky and hit the ground. In most hex models, proper tuning of the flight controller will allow for flight with an inoperative motor. The flight controller senses the loss of thrust from the inoperative motor and compensates for it by slowing down the motor directly opposite it. The craft can then continue to fly like a quad on the four remaining motors and make it back to the takeoff point safely. On the other hand, if you lose a prop blade on a motor, and the motor continues to run, the vibration caused running with just one prop blade can be extremely high. In some cases, the vibration can be so bad that the solid state MEMS gyros in the control board can no longer function properly and the craft can completely lose control.

If your model ever does flip over at the end of a flight, the props can sustain hidden internal damage that may not cause a failure right away. This is especially true of plastic props and fiber reinforced plastic props. Figure 1 shows some of the types of internal stress damage to look for on plastic props. If you look closely at this prop you can see a white line that has formed at the right edge of the hub where it meets the blade. This is the type of damage you can see after a multirotor flips over on a landing. A prop like this will continue to operate fine for several flights, but eventually it will fail and the prop blade will tear off at the hub leaving a horribly out of balance condition on that motor. You can also see some lighter discoloration of both blades on this prop as indicated in the photo. Whenever a prop shows a lightening of the color, it means that the plastic itself has stretched, and the glass fibers in the prop have torn loose from the surrounding plastic. This substantially weakens the prop and will cause a failure later on during a flight. If you ever see a prop that shows this type of discoloration, do not fly the multirotor before replacing the prop!

Another common type of prop damage comes from incidental contact with objects during a flight. With the extreme FPV type of flying that is common now, people are flying very close to buildings, fences, trees and other obstacles. While this makes for extremely exciting flights, and great flight videos, it can be tough on the props if you bump into things during the flight. When doing this type of flying, you should always inspect the props after every flight. Figure 2 shows a prop that has come into contact with a few obstacles during a flight, and shows a few battle scars to prove it. The scratches on this prop create areas of stress concentration that can later lead to in-flight failures. The ground off tips of the prop can cause the prop to go out of balance and put a lot of vibration into the airframe. This vibration can cause screws to loosen up in the frame over time and also damage the sensors in the gyros and accelerometers on your flight controller board. If any of your props look like the one shown here, replace them before flying again.

Another area that should be looked at from time to time is the tightness of your prop retaining nuts. Figure 3 shows a typical motor and prop combination with a prop washer and prop nut holding the propeller in place. Because the motors in multirotor are constantly speeding up and slowing down, the changing torque forces can cause a prop to slip on the prop adapter and cause the prop nut to loosen over time. The prop nut only has to loosen up about ¼ of a turn to allow the prop to slip on the motor, and then you can lose control of the model. This is especially true with wood props. Because of the open cell nature of wood, these types of props will crush slightly over time and cause the prop nut to loosen up. Many times at the end of a days flying, we will take a prop off a motor and put the nut on just finger tight, and then get distracted and forget to tighten it up all the way. If this happens, it is pretty likely that the prop will spin off on the next flight and cause a crash. If you carry a small 4-way wrench in your tool box, it is very quick and easy to check the tightness of your prop nuts before each days flying, and make sure that nothing has worked lose over time.

While we are talking about props, one thing that is very important to check for is interference between the prop washer and the prop itself. On many Slow-Fly style props, the blades have a lot of pitch near the hub and sweep up above the front edge of the prop hub. When the prop washer is put onto the motor shaft the prop washer can hit the blades of the prop before it touches the prop hub. The left side of Figure 4 shows this very clearly. When a prop washer hits the prop in this way, the edges of the prop washer can cut into the prop and cause a weak spot in the prop blade. This will cause a crack to start to form in the prop and can lead to an unexpected blade failure several flight down the road. The good news is that most prop washers have a taper cut into one side of them, and by flipping the prop washer over, as seen in the right side of Figure 4, the prop washer will hit the hub of the prop first and clear the blades quite nicely.

By following these suggestions, and keeping a close eye on your propellers, you can avoid a lot of problems with your multirotors. Now that we have covered all of the prop maintenance basics, let’s move on to the multirotor frame.

Most multirotor frames are held together with a series of nuts, bolts and screws. The motors are also attached to the frames with some type of mounting screw. With 4 or more motors running at various speeds all the time, you can induce some rather strong harmonic vibrations into your multirotor frame if all the props are not balanced properly. These vibrations can cause screws to vibrate loose on frame arms or motors, and eventually lead to catastrophic failures.

Figure 5 shows a typical small multirotor frame that is held together with socket head screws. When building frames of this type, always use a drop of medium (blue) thread locking compound on each and every screw as the frame is put together. This will lock the screws into place and prevent them from backing out later on during a flight. The same holds true for your motors when they are mounted to the frame. By using thread locking compound on your motor mount screws, you will ensure that a motor does not loosen up in flight and cause problems for you down the road. Always remember that thread locking compound is much like CA glue, it cures in the absence of oxygen and is a one-time use product. If you ever have to take your frame apart later for repairs, you will need to re-apply the thread locking compound to each screw as you put the frame back together.

Quite often, motor lead extensions are used on multirotors when the speed controllers are mounted in the center frame. This adds extra connectors that need to be plugged in and can be failure points if not monitored. If you are adding motor lead extensions to a motor, it is a good idea to add an extra piece of heat shrink tubing over the bullet connectors where they plug together. This provides an extra layer of insulation to avoid electrical shorts, and prevents the wires from pulling apart inside the arms of your multirotor if you ever have to pull a motor off to change a motor mount.

With these few simple maintenance tips, you can ensure that you get many hours of safe, trouble-free operation from your multirotor, and protect the investment that you have made in your equipment. Always remember to fly safe, and drop by next time for another installment of Lucien’s Corner.

## Maximizing Flight Time

Once pilots get their multirotors operating well, and start actually doing things with it other than tearing holes in the sky, one of the first hurdles faced is increasing the available flight time. Most pre-packaged, ready-to-fly multirotor models come with a battery pack that will only last from 8 to 10 minutes of normal flying. For many, this is long enough, but for others that wish to do aerial photography, survey work or other professional type applications, there is always a desire to extend the flight times. Getting flight times in the 20 to 30 minute range is achievable with many multirotors that are available today, but there is a bit more to it than simply strapping more batteries on the model. In this months installment of Multirotor Flight we will take a look at how to maximize the efficiency of the multirotor power system in order to get the longest possible flight times.

First and foremost, there are a few basics about flight that must be considered. Number one is the fact that “Lighter Always Flies Better”. This is especially true in multirotors since the weight of the machine takes a certain amount of power to hold in the air. Heavier machines require more power and therefore they will have shorter flight times than lighter machines.

The second major thing to consider is the fact that larger props are more efficient than smaller props at converting rotational energy into thrust. This is because larger props can move larger volumes of air more efficiently.

The third thing to consider is slower turning props are more efficient at creating thrust that faster turning props. Props are essentially little wings going round and round generating lift. Basic aerodynamic principles show that the drag on a wing increases exponentially as speed increases, and this is the same with props. Props that are spinning faster have greater drag losses than slower spinning props, and this robs a model of flight time.

Finally, the efficiency of the motors and speed controllers themselves will play a role in the overall efficiency of the power system and can have a big impact on the flight time of a multirotor. Now that each of the components of the efficiency equation have been introduced, let’s take a closer look at each one and how it affects the overall flight time of multirotor aircraft.

Weight is always a factor in considering flight times for electric powered models of any kind. Design engineers will always say, “Design an aircraft to fly, not to survive a crash”. There is always a trade-off between structural strength and weight when designing aircraft. All aircraft must be built strong enough to survive any of the forces they will see in the air, but also be able to handle a bit of “hanger rash” and the occasional not-so-perfect landing without falling apart. Modern carbon fiber composites, light-weight aluminum alloys and molded plastic parts work together in many multirotor frames available today providing an airframe that is not only strong, but also light weight. The best starting point to maximize flight times is to use as light a frame as you can to get the job done.

Another consideration in the weight part of the equations is the total weight of the power system. Careful attention needs to be paid when selecting motors to make sure they are matched to the power that is actually needed to do the job. If a machine needs motors capable of producing 200 watts each, and larger motors capable of producing 400 watts are used, the total weight of the multirotor will be higher than necessary and this will require more power to keep the craft flying. Always remember, lighter always flies better, and also longer!

Next let’s take a look at how propellers factor into the flight time and efficiency of multirotor power systems. Larger props will always be more efficient than smaller props, because they move a larger column of air downwards as the props rotate. From 7th grade geometry class, we all know that the area of a circle is equal to Pi times the radius squared. For a 10 inch diameter prop, the cross sectional area of the column of air moved down by the propeller is equal to 3.14159 x 5 x 5 or 78.5 square inches. If you go to a 14 inch prop, then the area is equal to 3.14159 x 7 x 7 or 153.9 square inches or roughly double that of the 10 inch prop. With the larger 14 inch prop, you only have to move the air downward at half the speed to move the same volume of air compared to the 10 inch prop. Since less energy is required to accelerate the air, less current is pulled from the battery and flight time increases.

Prop efficiency is commonly expressed in the number of grams of thrust created per watt of power consumed by the motor, such as 8.5 g/W. The higher this number is, the more efficient the prop is at converting the rotational energy of the motor into thrust. Figure 1 shows a chart of the efficiencies of several different size props running on the same motor. Each of these props is spinning at an RPM that produces 500 grams of thrust. As can be seen from the data, the larger props turn at a lower speed to generate the thrust AND require less power to do so. When you take the grams of thrust created, and divide that by the number of watts used by the motor, you get the efficiency factor of that prop at one specific thrust value.

From this data, you can quickly see how prop diameter affects flight time. If you had a quadcopter that weighed 2000 grams (4.4 pounds) you would need to make 500 grams of thrust from each motor to hold the craft in a stable hover. From the chart you can see that the 10 inch props have an efficiency of 9.08 grams per watt while the 14 inch props have an efficiency of 11.55 grams per watt. This is an increase in efficiency of 27%, so all other things being equal, switching from 10 inch props to 14 inch props would give you an increase in flight time of 27%. Of course, this is assuming that the motors are actually capable of running the larger props without exceeding the maximum current rating of the motor. In some cases, it is necessary to use a lower Kv motor to have the torque needed to spin the larger prop without exceeding the motors maximum current recommendations.

If this data is taken one dimension further, we can see how rotational speed affects the efficiency of propellers. Props act much like wings from an aerodynamic standpoint. The parasitic or skin friction drag of any wing increases as a function of the square of the speed. Because of this, if a prop is rotating at twice the speed, the drag is 4 times higher. Figure 2 shows a set of data collected with a brushless motor running on 4 Li-Po cells with an APC 12×4.5 Multirotor prop. This table shows the performance of the motor over its full range of operation at throttle settings from 20% up to 100% throttle. From this chart, if a graph is created that plots prop efficiency versus throttle position the data set will look like the one shown in Figure 3. From this graph, if the machine is hovering at 50% throttle the efficiency of the props is approximately 8.2 grams per watt. At 40% throttle this value increases to about 9.3 grams per watt, and at 60% throttle it decreases to 7.2 grams per watt. If your multirotor is heavier, not only do you have to generate more lift to keep it flying, the props are also less efficient at producing thrust, so you get hit even harder on the current draw from the battery. On the other hand, if your machine is lighter, you need less power and the props are working more efficiently which contributes to longer flight times.

The final part of the equation is the actual power system itself. Higher quality motors that are made with better grades of materials will be inherently more efficient than cheaper motors using inferior components. If you have one motor that has an efficiency of 80% compared to another motor that has an efficiency of 90% there is a huge difference between the two. At first glance some will say that one motor is 10% more efficient that the other. The truth is that one motor is twice as efficient as the other! If you look at the inefficiency of the motors, the 80% efficient motor is 20% inefficient and the 90% efficient motor has an inefficiency of only 10%. The inefficiency is what causes the losses in the motor. The motor that is 80% efficient has double the losses of the motor that is 90% efficient, and will cost you flight time across the board.

The other thing to consider in power systems is the voltage that the motors are running at. The electrical losses in a power system are directly related to the current flowing through the system. From Ohm’s law we know that power is equal to voltage times current. Voltage can also be expressed as current times resistance, so if we substitute this for voltage, power can also be expressed as current times current times resistance, which is commonly called “I-Squared-R”. This is why electrical losses in a system go up as a function of the square of the increased current.

When we consider total power in a system, we normally figure Volts x Amps. In a 3-cell power system (11.1 volts) if we are pulling 20 amps all together, the total power is 222 watts. In a 6-cell power system (22.2 volts) we can get the same power from only 10 amps. If the wiring in a power system had a resistance of 0.1 ohms, the total power losses in the 3-cell system would be 20 x 20 x 0.1 or 40 watts. In the 6-cell system, the power losses would be 10 x 10 x 0.1 or only 10 watts. This is why higher voltage power systems are inherently more efficient. In this example switching the power system from 3-cells to 6-cells cuts the electrical loses by 75%!

Batteries are another important consideration when calculating flight times on multirotors. In many cases, the batteries make up the highest percentage of the payload weight of the craft. Quite often, pilots make the mistake of thinking that adding a second battery will double the flight time. This is incorrect for 2 reasons. First, when a second battery is added, the overall weight of the aircraft increases, and this requires more power to hold the craft in a hover all the time. The other thing that people forget to consider is the fact that the props also operate less efficiently at the higher loading, so the efficiency takes a double hit! In most cases, adding a second battery will not double the flight time, but will instead give a 70 to 75% increase in flight time. Each additional battery has a smaller impact in the increase of flight time, and eventually a point is reached where adding another battery will actually decrease the flight time due to the high weight and lack of efficiency in the power system.

When all of these different aspects are combined, it is possible to double the flight time of a multirotor by simply optimizing every part of the power and propulsion system. Putting all of these different considerations together, you will get the longest flight times from a multirotor if you start with the lightest airframe possible, use the largest props that will fit on the frame and power them with high quality, low Kv motors, using higher voltage battery packs. Hopefully this information will help to get the power system in your multirotor optimized for the longest possible flight times and allow you to get the maximum benefit from your multirotor power system.

## The ABC’s of PID’s

If you have ever worked with any open-source multirotor controller boards in the past, then you have probably needed to tune the PID settings in the feedback loops a few times. For some, these settings make perfect sense, but for most, they are a complete mystery that seemingly requires the combined skills of a computer programmer and an electrical engineer to figure out. In this installment of Multirotor Flight, we are going to take a look at control feedback loops, the PID settings that adjust them, and how they all work together to make a multirotor aircraft controllable.

All closed loop control systems are designed to keep a specific device, or system of devices, operating at a pre-determined setpoint. Whether it is the thermostat on the wall that controls the temperature of your home, the cruise control in your car that keeps it traveling down the highway at a specific speed, or the gyro sensors in your multirotor that keep it level when you let go of the controls, all closed loop systems rely on PID settings to keep the system in equilibrium. Understanding PID settings, and how they affect the response of closed loop systems, will help out greatly in understanding how to properly tune a multirotor aircraft flight controller.

So what are PID’s? Some people refer to them as “pid” settings, said like the word “kid”, while others will refer to them as 3 individual letters, calling them “P-I-D” settings. While either one works, the letters do mean something. The letter “P” stands for “Proportional Control”, the letter “I” refers to “Integral Control” and the letter “D” stands for “Derivative Control”. Any of the readers that remember taking a calculus class in high school or college are familiar with the terms Proportional, Integral and Derivative, and when talking about PID settings, these terms do have similar meanings. To understand PID settings, we need to discuss each of these terms in brief detail in order to see how each one affects the control of our multirotor aircraft.

In every closed loop control system there are three terms that must be considered: A particular variable, a desired setpoint and an error value. When talking about multirotors, the variable could be the roll angle, with a desired setpoint of 0 degrees, or altitude with a desired setpoint of 50 feet above the ground. The error value only exists if the variable is NOT at the desired setpoint. To clarify this a little more, here is an example. If you are looking at the roll axis in a multirotor, and at one instant in time, the frame is rolled 4 degrees to the right, then the variable is Roll, the desired setpoint is 0 degrees, and the error value is 4 degrees. The purpose of the control loop is to sense the 4 degrees of error in roll, and then tell the system what to do in order to put the multirotor frame back to the desired set-point, which would be 0 degrees, or level, for a hover.

Figure 1 shows a block diagram for the operation of a typical PID closed loop control system. Starting at the left side of the diagram, we have two values that are compared against one another, namely, the desired Setpoint value and the current Output value of the system. Any difference or “error” between these two values is then fed into the 3 sections of the PID control loop for processing. In any PID control loop, the “P” term is related to the present error, the “I” term is related to the accumulation of past errors, and the “D” term is related to prediction of future errors. The corrections that are generated by each of these three sections are then added together to form a total correction value, which is finally fed into the Process section of the control loop.

For a multirotor controller, the process section creates each of the control pulse signals that get sent out to the speed controllers, which then drive the motors in the aircraft. Finally, the props that are attached to the motors provide the corrective forces needed to move the multirotor back to the desired setpoint. The output from the gyro sensors in the multirotor controller are looped back and compared once again to the setpoint value, and the entire process starts all over. This control loop runs continuously, hundreds of times per second, trying to keep the multirotor level when no control input is made, or moving the multirotor to a new attitude whenever a control input is given.

When all three sections of the PID control loop work together, and are properly tuned with respect to one another, you get a system that responds incredibly well to the constantly changing environment that is inherent in multirotor flight. The truly amazing thing is that there are multiple PID loops in a multirotor controller, all running together at the same time! Each axis of flight requires a separate control loop that is driven by the various sensors. Pitch, Roll, Yaw, Altitude, Heading, and Position are all continuously monitored and maintained at some specific set point as directed by the internal sensors, or to new set points as commanded by the pilot. When you stop and think about it, multirotor controllers do a lot of stuff that we simply take for granted!

Now that we have a basic understanding of what each of the P-I-D terms means, and how they relate to one another, let’s look at each one in a little more detail to get a better understanding of how they actually work. As we said earlier, the P part of the PID loop stands for Proportional Control. Like the name suggests, proportional control responds proportionally to the amount of error in the system. If there is a small error in the system, then the feedback loop will generate a small force to correct it back to the desired setpoint. If there is a large error detected, then a large force will be applied to correct the system back to the desired setpoint.

This process can be pictured easily from the standpoint of driving a car down a highway. If you are driving down a straight section of highway and your car is drifting slightly to the right, you will turn the steering wheel just a few degrees to the left to get the car headed back to its desired path. If the car is drifting very quickly to the right, then you would turn the steering wheel a lot more to the left to make the correction. When setting the Proportional part of a PID loop, the idea is to apply the proper amount of correction force to get the system back to the desired setpoint. With the P value set too high, the system will overcorrect and can oscillate back and forth around the desired setpoint, and with too low of a P value, the system will slowly wander towards the setpoint, without ever getting there.

The second part of the PID control loop, the “I” component, is the Integral control. Back from the calculus days you may remember that if you integrate a mathematical formula, you get the area under the curve, which is the accumulation of a value over time. The purpose of the Integral component of the PID control loop is to respond to how the error occurs over time. If something happens to push the system out of equilibrium, and the Proportional part of the control loop is taking too long to respond, the Integral part of the loop will add in more corrective force to bring the system back into equilibrium quicker. If the gain is set too high, too much correction will be applied and the system will oscillate back and forth around the desired set point. If the gain in the Integral portion of the control loop is set too low, it will take a long time for the system to get exactly back to the desired set point, and will always drift slightly one direction or the other.

The third and final part of the PID loop is the Derivative control. If you remember from calculus, if you take the derivative a formula, you get the slope of the curve, which is an indication of how rapidly the value is changing. Likewise the “D” portion of the PID settings, or Derivative Control, responds to how quickly the error value is changing. For our multirotors, if a machine is in a hover, and gets hit by a huge gust of wind that rapidly flips it up on its side, you want the corrective forces to be applied quickly, and in a large enough amount to bring the frame back to a level state. So while the Proportional control gives a lot of corrective force if the frame is displaced a large amount, the Derivative Control will add in additional corrective force if the movement happens quickly. When adjusting the Derivative portion of the PID loop, if you have too much gain, the response will happen too quickly, and correct too much, causing the machine to overshoot past the desired “level” point which can lead to oscillation, and if you do not have enough gain, the response will be sluggish and not respond quickly enough.

With any PID control system, you can tune the performance to meet the type of flying that you are doing and the mass of your specific airframe. When the parameters are set up perfectly, you will always have a small amount over correction in the system that dampens our after 1 or 2 small oscillations. This is great for an aerobatic machine where you want quick, crisp controls. However, for a big camera rig multirotor, you would want a much smoother response and set the gains a little lower.

Figure 2 shows the response characteristics of 4 different amounts of gain in a PID control loop with respect to time. The origin of the graph indicates a current steady state of control, the thin gray line represents the new desired setpoint value, and each of the colored lines represents how the system gets from the current value to a new desired setpoint value with respect to time. Curve A, the red line, shows the response of a system with not enough gain. On this curve it takes a long time for the system to respond to the change, and it never quite gets all the way there. In a multirotor this would create a very sluggish feel to the controls, a machine that wanders around a lot and has very slow response to external forces that disrupt the position of the craft.

Curve B, the green line, represents what is known as Critical Gain. This is the condition that gets you to the new set point as quickly as possible, but without overshooting past the desired setpoint. This would be an ideal condition for a large camera platform multirotor where you want smooth steady response, without any jerkiness in the controls.

Curve C, the blue line, represents a system that has a little too much gain, but is still stable. This system gets you to the new set point as quickly as possible while remaining stable, but with this much gain in your control system, you will actually go a little past the desired set point, which is called overshoot, and then wobble a tiny bit back and forth before settling on the new desired setpoint. This amount of gain would be good for an aerobatic type multirotor, where you want the response to be as quick as possible, and you do not mind if it overshoots and wobbles a tiny bit from time to time.

Finally, Curve D, the orange line, shows a system that has way too much gain and cannot stabilize itself. In this condition, the corrections happen too fast and are too great to ever allow the multirotor to level out. A multirotor that is set up like this will never stabilize, and will do the “Hula Dance” or “Toilet Bowl” maneuvers all the time. In extreme cases the oscillations will actually get greater and greater with each cycle until the machine becomes completely uncontrollable and smashes into the ground. If you ever increase the gain in one of the PID loops and the machines starts oscillating right after takeoff, set it back down immediately! If you continue flying, you will probably regret it.

Most flight controller boards come with some PID values preset in them, which are usually pretty safe and slightly conservative. If you want to fine tune the settings a bit to suit your flying style, then by all means do it. There are a few things you should always remember when setting PID settings though. First, only vary one setting at a time. If you do change more than one setting at a time, you never know which one is actually causing the changes you see. Second, it is best to move in small steps, no more than about 10% of whatever the current value is. For example, if you have an I setting of 0.050 in a control loop, and want to raise it, try 0.055 first, then 0.060, then 0.065 and so on. If you try changing a setting too much at once, you can end up with a completely unstable controller that destroys your multirotor. Third, when you find a set of variables that works well for you, WRITE THEM DOWN! Files get easily overwritten, so if you have a combination that works well, keep a little logbook with your PID settings written down in it so you can refer back to them later on if you need to.

Each and every flight controller board has its own unique set of PID settings, so you will have to do a little research, check the on-line forums, and generally ask around to find good starting points for your PID settings. From there, you can fine tune the values to get the board to meet the requirements of your particular frame and flying style. Hopefully this has helped you understand the mystery of PID settings, and enable you to try fooling around with them yourself.

## Multirotor DIY

Like many other segments of the RC Hobby, after building a few kits, some people like to try designing and building their own models from scratch. Modelers have been doing this for decades with fixed wing aircraft by scratch building from plans, building their own designs or kit-bashing and modifying existing designs. When it comes to helicopters, because of the complex mechanics that are used in them, unless you own, or have access to, a machine shop, it is pretty tough to design and build your own models. Multirotors on the other hand, are more like aircraft in this respect, and do offer modelers the option of quickly and easily designing and building their own multirotor aircraft. For modelers on a tight budget, scratch building can often be a good way to get into multirotors for a minimum investment. In this installment of Multirotor Flight, we will take a look at some of the different options that are available, as well as some general rules of thumb for designing and building your very own multirotor aircraft.

Virtually all multirotors share the same common group of electrical components. These components include a flight controller board, a battery, motors, speed controllers and props. The multirotor frame basically serves as a way to mount these components together in a specific alignment, with the motors spaced far enough apart so the props can rotate freely. This basic arrangement can take the form of a Tri-copter, Quad-copter or Hex-copter platform, and each type has its specific benefits. The most common and simplest of these configurations is the Quad-copter platform, so we will focus our attention on that design for now.

The cool thing about multirotors is that you can use virtually anything to build the frame, as long as it is light enough to be carried by the thrust of the propellers. People have actually taken 4 motors and mounted them to the corners of a Fed-Ex shipping box and built a multirotor from it! Obviously this is not a very efficient design, because over 1/4 of the prop arc on each motor is blocked by the corners of the box, but it does show how simple a quad can be built.

When considering quad frames, there are basically three different types, the X-style, where all the motors are spaced equally from a central body as shown in Figure 1, a Spider style, which is shown in Figure 2, and an H-style, which is shown in Figure 3. The Spider style frame is most commonly used for FPV or aerial photography, since this design provides a way to mount a camera out ahead of the front props to eliminate them from the view of the camera. The commonality of all three of these designs is that the four motors basically form a square, with the electronics mounted somewhere in the middle.

The frame itself can be constructed from a wide variety of materials including wood, plastic, metal, fiberglass, carbon fiber or any combination of these materials. An extremely simple and inexpensive frame can be constructed by taking a wooden yard stick from a home improvement store, cutting it in half, and epoxying the two pieces together into an X shape. The motors can be attached to the ends of the arms with wood screws, and the remaining electronics can be mounted with hook and loop fastener or double sided servo tape. Other wood designs can be constructed from 3/8” to 1/2” square pine or spruce stock combined with 1/8” plywood for motor mounts and center plates. Figure 4 shows an example of this type of frame with a small plastic food storage box added to the center to house all of the electronics.

Lightweight metal is also a good material to make rugged, easy to assemble frames. Most home improvement stores carry 3 foot, 4 foot and 8 foot lengths of square aluminum tubing in several sizes, and this can be used to assemble multirotor frames. Center plates and motor mounts can be fabricated from either sheet aluminum or fiberglass G-10 or FR4 material, and everything can be held together with sheet metal screws or pop rivets. These types of frames are extremely crash resistant, and are easy to fabricate with common hand tools. Figure 5 shows an example of a typical metal quad-copter frame.

Once you have your frame materials picked out, the actual design is only limited by your imagination, but remember, for best operation you do want the motors to end up in as close to a square pattern as possible. Once you pick a frame shape, you need to decide on a frame size. For multirotors, the frame size is usually listed as the center to center distance in millimeters between two motors on opposite corners of the frame. Most commercially available flight controller boards are designed to work best with mid-size multirotors with a frame size of between 400mm and 800mm. For a first try at scratch building, something in the 500mm to 600mm size is a great place to start.

Once you decide on a frame size, the next thing you want to do is select the proper motors for your quad. In any quad design, you want to make sure that you have enough power to fly properly and efficiently. In order for any multirotor to fly well, you need to have a thrust to weight ratio of at least 2 to 1. If your machine weighs 40 ounces ready to fly, including batteries and all payloads, then you want to make sure that the combined thrust of all the motors at full throttle is at least 80 ounces. At this point you may ask, “How do I know how much thrust my motor will produce?” If you purchase good name-brand motors that have published propeller data charts, this is easy. You simply look up a motor and prop combo, and see how much thrust it produces. If you choose motors with no test data from the manufacturer, then you have to take an educated guess as to the thrust they will produce.

When picking out motors, low Kv models that spin larger props are always more efficient and quieter than higher Kv motors spinning smaller props. For the best thrust efficiency, you should use the largest prop your motors can safely run. Most mid-sized multirotors run well on 3-cell Li-Po batteries, and motors with Kv values in the 800 to 1000 RPM/volt range do very well on 3 cells. If you want to use a 4-cell Li-Po battery, then motors with a Kv value in the 650 to 800 range would work best.

Here are a couple examples of how much thrust you can get with different size motors. Running on 3 Li-Po cells, a motor with a stator size of 2212 or 2213 and a Kv value of around 950 will produce 24 ounces of thrust from a 9×4.7 prop, and would work on a quad that weighs up to 48 ounces. A 2215 to 2217 size motor with a Kv of around 950 will produce around 35 ounces of thrust from a 10×4.7 prop, and would work on a quad that weighs up to 70 ounces. It is OK to have greater than a 2 to 1 thrust to weight ratio on your model, it will just result in longer flight times due to more efficient operation, but do not take this to extremes. If you get much more than a 3 to 1 thrust to weight ratio, the extra available power can result in difficulty in tuning the PID settings or gain settings in your flight controller board due to the high amount of thrust that is available.

To calculate how much power you need for flying a multirotor, a good rule of thumb is 60 watts per pound to maintain a stable hover. This lets you know approximately how much total power you will need, and gives a starting point for picking out motors and calculating flight times. If you have a machine that weighs 3 pounds, ready to fly with batteries, then you will need approximately 180 watts of power in a hover. If you have 4 motors on your multirotor, then each one will be producing 180/4 or 45 watts of power. If you are running a 3-cell battery pack, which produces around 11.1 volts under load, then each motor will pull 45/11.1 or 4.05 amps of current.

The 60 watts per pound rule can also be used to calculate flight times. In this example, 180 watts divided by 11.1 volts gives a total current draw of 16.2 amps and this value can be used to get a rough flight time calculation based on the size of your battery pack. For the sake of this example, let’s assume that you have a 3-cell 3300mah battery pack for your model. Since a 3300mah battery can also be called a 3.3 Ah battery, a 16.2 amp current draw is equal to a discharge rate of 16.2/3.3 or 4.9C. From earlier columns you may remember that flight time can be calculated by taking 60 minutes, and dividing that by the C-rate of discharge. Using this formula, 60/4.9 is equal to 12.25 minutes. This formula assumes full discharge of the pack, which you really never want to do. You should always leave 20% of the energy in a battery pack at the end of each flight, so if you take 80% of the calculated flight time of 12.25 minutes you get 9.8 minutes of flight time from the 3300mah 3-cell Li-Po battery.

Once the motors and props have been selected, the next item to pick is the speed controller. All of the speed controllers in a multirotor should be identical to one another. They should be the same brand, the same size and have the same firmware. Using different brand speed controllers mixed together can make it very hard for the flight controller to do its job properly. When sizing speed controllers for multirotors, it is a good idea to have the speed controllers be able to handle double the full throttle current of your motors and props that you are using. If you have motors that draw 9 amps at full throttle, use 20 amp speed controllers. If you have motors that pull 14 amps at full throttle, then use 30 amp speed controllers.

There are several reasons for over-sizing the speed controllers. First and foremost is reliability. If a speed controller never sees more than half of its rated current, the chance of having an in-flight failure is practically zero. In multirotors, especially quads, the loss of power to one motor will always result in a crash, so you want to make sure that the motors stay running! Another big reason to over-size your speed controllers is cooling. In many cases, the speed controllers are mounted in the center of the frame, often under a cover or inside a radio equipment box where they get little or no air flow for cooling. If you run the speed controllers at less than 50% power at all times, they will run cool enough to be able to operate with little or no airflow across them.

Finally, the last piece of equipment you will need for your project is the flight controller board. This is where the do-it-yourself idea can be taken to extremes if desired. If a modeler is adept in soldering and building electronic circuits, then a flight controller board can also be fabricated from scratch by starting with an Arduino board, or other microprocessor development board, and adding all the sensors themselves. Going this route would only be for the truly hard-core electronics buff, sine it does require a completely different set of skills and electronic knowledge to pull off successfully. For most people, buying an off the shelf, fully assembled Flight Controller is really the only way to go.

When picking a Flight Controller, there are a lot of options available over a wide range of prices. As it is with most things, you get what you pay for, and this is especially true when it comes to flight controllers. A quick look at eBay or overseas online stores will uncover dozens of different Multi-Wii based controller board clones, some for under \$20.00. Figure 6 shows a typical Multi-Wii type flight controller board that is available for about \$35.00 on line. This is an area where spending a little extra money will pay for itself in the long run. Many of the cheaper boards do not come with software pre-loaded, and require some knowledge of computer coding in order to get them to operate correctly. Many have very basic computer interfaces, or rely on interfaces from open source projects to operate and program the controller boards. Some of the higher priced flight controllers, such as the DJI Naza series, come with all the software pre-loaded and feature a polished, easy to use computer interface that makes setting up the board a very simple procedure. For first time scratch builders, you should probably stick with a board that you are already experienced with that already works reliably, since that is one less thing that you will have to worry about when setting up and flying your model.

Whether you are on a tight budget, and want to build a multirotor as cheaply as possible, or have some radical new design that you want to build and see if it will actually fly, scratch building can be a very fun process, and offer a new challenge for multirotor pilots. By taking the time to figure out a few basic design rules, a successful project can be easily realized. One of the coolest things about scratch building is the sense of pride that you have at the flying field when someone asks you, “What multirotor kit is that?”, to which you can proudly reply, “It is not a kit, it is my own design!”