I love this topic! Maybe it's my background in aeronautical engineering, but I love propellers and motors and all the good things that happen when you put them together. In the world of aquatic vehicles, the combination of a motor and propeller is often called a "thruster." Over the years, one of the most commonly-asked questions I've gotten about thrusters is why they look so different: why does an ROV thruster have a small, stocky propeller inside a nozzle, while a long-endurance ASV has what appears to be a miniature airplane propeller? And if you're building your own thruster, how in the world do you choose among the many hundreds of available motors? By the end of this Tech Tip, you'll be able to answer these questions.

What we learn here about thruster performance applies equally to ASVs/USVs, ROVs, and AUVs. For that matter, almost everything discussed here will also apply to airplanes (UAVs, if you aren't sick of acronyms yet), drones, helicopters, or anything else with a motor and a propeller. That's the beauty of propellers: for the most part, they don't care much whether they're working in water or in air. For the motor side of the equation, we are going to narrow the focus a bit to discussing brushless DC motors only, but that will cover a large segment of autonomous vehicle applications.

I've put together a very handy spreadsheet if you want to perform your own thruster calculations. It allows you to compare different motors, choose the right propeller diameter, and predict the overall performance of your thruster system. The graphs shown below come from this spreadsheet.

## What's your goal?

In thruster design, you really can't have it all. You can't have a thruster that produces tons of thrust at a low speed and also works efficiently at high speed. So you have to decide what's most important to you. At which operating condition do you want your thruster to be optimized? If you're designing a long-endurance solar-powered ASV, you probably want to optimize your thruster for efficiency at "cruise" speed, perhaps 2 or 3 knots. On the other hand, an ROV thruster needs to develop as much thrust as possible at zero forward speed, with less regard for efficiency. So begin by deciding what's important to you, then keep reading.

## Motor choice

As stated above, we'll assume that you're going to use a brushless DC motor in your thruster. Brushless motors will generally be more efficient and more durable than brushed motors. Brushed motors are cheaper since they don't need a motor controller (also known as Electronic Speed Control, or ESC), but the cost of ESCs has come down so much that there's really no reason to go brushed anymore.

Any manufacturer of decent-quality brushless motors will publish the three parameters that you need to determine the performance of the motor. These three parameters are:

Io: the "no-load current." This is how much current is required to spin the motor with zero external load on the motor. Motors have both mechanical friction as well as magnetic effects that require a certain amount of electrical current to make the motor spin even when there is no external load on the motor. The no-load current captures these various effects. It's not really a precise parameter, because the amount of current needed to spin the motor depends a bit on the RPM. But we have to work with what we've got, and usually manufacturers only give us one value of Io, often without even telling us what RPM it was measured at. Don't worry though, it'll be close enough. You want Io to be as low as possible.

Rm: the "winding resistance" or "motor resistance." This is pretty simple: it's the resistance of the windings of the motor. Just hook a multimeter up to any two of the three wires coming out of the motor and measure the resistance. That's Rm. Resistance means wasted energy, so you want Rm to be as small as possible.

KV: the "speed constant." Technically, the KV tells you how much back-EMF the motor generates for a given RPM. But to keep things simple, we usually use a different, less-precise definition: KV is approximately how fast the motor will spin at a given input voltage, assuming no external load. The units are RPM/volt. So if the motor has a KV of 1000 and you run it at 12 volts, it will spin close to 12,000 RPM (again, assuming no external load). If you put a load on it, it'll spin somewhat slower than that. Usually you want the KV to be as low as possible. Why? Because large, slowly-spinning propellers are more efficient than small, fast-spinning propellers. More on propeller design later.

Now, if you actually start comparing brushless motors, you'll run into a few disturbing realities. The first is that physically smaller motors tend to have higher KVs, and we want our KV to be as low as possible. So if you want your thruster motor to be compact, there will be a limit to how low the KV can be. The second is that motors with low KVs tend to have a high Rm. This is because, to make a low-KV motor, they put in a large number of loops of thin wire in the windings. A lot of thin wire equates to a lot of resistance. Basically, there are some physical laws getting in the way of us having everything we want.

One way of getting around some of these problems is to use a gearbox. A gearbox will essentially turn a high-KV motor into a low-KV motor. However, it takes up more space, costs more money, reduces the efficiency of the system, and adds another possible failure point. Some commercially-available thrusters use gearboxes and some don't. There's no consensus either way, so a gearbox is definitely worth careful consideration.

Either way, as a first cut, you should find two or three of the lowest-KV motors that will physically fit your application, and pick the one with the lowest Io and Rm values. Pay attention to the rated wattage of the motor as well. If the motor is advertised as a 100-watt motor and you want to run it at 200 watts, proceed with caution. It may be possible, but be careful. Similarly, if the motor is rated at 1,000 watts and you want to run it at 100 watts, there's a good chance that the motor is bigger than it needs to be for your application, and thus less efficient than other, smaller motors. So use the rated power of the motor as a general guide as to whether the motor is a good match for your application.

## Calculating motor performance

Given the three parameters discussed above, you can find the current, voltage, and power draw of a motor using the equations below. Start by assuming the RPM and required power output of the motor, P_out (also known as shaft power).

motor current I = Io + P_out / (RPM / KV)

motor voltage V = RPM / KV + I * Rm

motor input power P = I * V

If you don't know the exact RPM or power output, you can make the following approximations:

RPM = KV multiplied by the approximate voltage that you want to operate at

P_out = The drag on your vehicle (in Newtons) multiplied by the vehicle speed (in m/s) divided by the propeller efficiency (assume 0.7 for propeller efficiency).

Note that none of these equations include the efficiency of the motor controller (ESC). A good ESC might reach about 90% efficiency. If you want to account for the power draw of the ESC, just divide the motor input power by 0.9 to approximate the total system power.

You'll quickly discover that there are numerous inter-dependencies between the motor, the propeller, and the vehicle. In other words, you won't be able to choose the right motor without knowing what propeller you're using, you won't be able to choose the propeller without knowing what motor you're using, you can't choose either motor or propeller without knowing the drag of your vehicle, and so on. Therefore, it becomes an iterative process involving a lot of compromise (like pretty much everything else in engineering). Fortunately, if you have your calculations organized in a spreadsheet and just start playing with it, a good answer will eventually materialize.

## Propeller choice

Similar to brushless motors, propellers can be defined by a few basic parameters or coefficients. In the case of propellers, the two most important are the "thrust coefficient" and "power coefficient." The both depend on the "advance ratio," which is basically the ratio of the forward speed of the vehicle to the rotational speed of the propeller. There's a lot of good information on the internet about these parameters and how to use them (I am not going to reproduce the equations here, just google it if you're interested).

Unfortunately, it's very rare for propeller manufacturers to publish thrust and power coefficients for their propellers. The only one that I know of that publishes this information is APC, a manufacturer of propellers for R/C airplanes. If you're building a long-endurance ASV or AUV, there's a good chance that one of APC's propellers would work in your application (not saying they would be the best, just that they might work). If you're building an ROV, you're probably going to want a different kind of propeller. In that case, you will have to perform some serious analysis in order to get the data you want. That analysis is way beyond the scope of this Tech Tip, but don't despair -- we can still make some useful conclusions about propellers.

First of all, let's consider the diameter of the propeller. If you're going after efficiency (perhaps for a long-endurance ASV or AUV), you want the diameter to be as large as possible. This has to do with the difference between momentum and energy. As we learned in high school physics class, the momentum of an object depends on the speed of an object, but the energy depends on the speed squared. The thrust produced by a propeller is simply the change in momentum of the water flowing through the propeller. Therefore, just like momentum, thrust depends on the change in speed of the water, but the energy consumed by the propeller depends on the speed of that water squared. So if you want to get high thrust and low energy usage, you want the propeller to take a large amount of water and accelerate it only a little bit instead of taking a small amount of water and accelerating it a lot. This implies a large propeller with two slender blades, just like an airplane propeller.

There are plenty of considerations other than just efficiency, though. For example, you might not have room for a large propeller. Or your motor might not be capable of swinging a large propeller slowly. Or you simply might not care about energy usage, like if you have an ROV that gets power through its tether, or if you have an ASV that is only going to run for a few hours at a time and has plenty of battery capacity. In these cases, your propeller will typically be smaller in diameter, with three or four relatively fat blades. It will look more like a ski boat propeller.

Now let's talk about propeller pitch. The pitch is how many inches (or centimeters) the propeller would move forward in one rotation if it were moving through a soft solid, like wood. Propellers with lower pitch are better for producing static thrust (static thrust is the thrust produced when the vehicle is not moving forward). Higher-pitched propellers are better producing thrust at higher speed.

To illustrate, I've plotted the thrust coefficient, power coefficient, and efficiency for a low-pitched propeller (APC 9x3, which has a 9-inch diameter and a 3-inch pitch) and for a high-pitched propeller (APC 8x8, which has an 8-inch diameter and 8-inch pitch). Notice first that the efficiency of the low-pitched propeller peaks at an advance ratio of 0.36, while the efficiency of the high-pitched propeller peaks at an advance ratio of 1.07. If you remember that advance ratio is the ratio of the speed of the vehicle to the tip speed of the propeller, it should be evident that the higher-pitched propeller will do better at higher vehicle speeds.

Also notice that the higher-pitched propeller reaches a max efficiency of 0.9, while the lower-pitched propeller only maxes out at 0.4. I'm actually VERY suspicious of that value of 0.9. That's a terribly high efficiency for any propeller. I guess the lesson here is to take everything with a grain of salt until you've proven it to be true. Nevertheless, the point remains: higher-pitched propellers will tend to have higher maximum efficiencies, but that high efficiency can only be attained with the vehicle moving through the water at a relatively high speed.

You may wonder why the efficiency of both propellers goes to zero at an advance ratio of zero. This is because efficiency is defined as the thrust of the propeller multiplied by the forward speed of the vehicle, divided by the power input required to spin the propeller. If the forward speed of the vehicle is zero, then efficiency is zero by definition. Sometimes you'll see thruster manufacturers expressing efficiency as the thrust produced divided by the electrical power input. This is not a terribly scientific definition of efficiency, but it is quite practical, since it quantifies the "efficiency" of the motor/propeller combination in the static thrust condition.

Now look at the trends in the power coefficient (red). Notice that for the high-pitched propeller, the power coefficient skyrockets at low advance ratios (low vehicle speed). This is most likely because the propeller blades are stalling because of their high pitch, causing a huge amount of drag on the blades. Again, this propeller is not meant to operate efficiently at low speed.

In summary, if you want to produce a lot of static thrust without using a lot of power, go with a low-pitched propeller, where the pitch is typically half of the diameter or less. If you're more interested in efficiency at higher speeds, use a high-pitched propeller, where the pitch is roughly equal to the diameter. And, by the way, when we're talking about "higher speeds," that might be only 1 knot. It doesn't take much forward speed to get out of the sweet spot of a low-pitched propeller and into the sweet spot of a high-pitched propeller.

## Nozzle, shroud, duct, or nothing at all

Now that you have some idea of what your propeller should look like, you have to decide whether to put it inside a nozzle (or shroud or duct, same thing). The nozzle has a couple of purposes. First, it keeps your fingers out of the propeller and potentially keeps debris out of the propeller (although be careful here... it could also trap debris in the propeller, depending on the situation). Second, a nozzle can increase the thrust of the propeller, especially if the propeller is of the small-diameter type with fat blades. There is some science behind designing nozzles properly, so if you embark on this, either do the research or try to copy someone else's nozzle design.

In general, ROVs should have nozzles on their propellers. Indeed, I'm not aware of a single commercially-available ROV thruster that doesn't have a shroud. ASVs or AUVs that are designed for long endurance probably should not have nozzles on their propellers. In those cases, a nozzle would just reduce efficiency.

## Putting it all together

Analyzing a motor in isolation is fairly simple and analyzing a propeller in isolation is fairly simple, but figuring out the best motor/propeller combination can get complicated. I use this spreadsheet that combines the motor and propeller equations to yield an overall system efficiency for a given operating point. By playing around with different motors and propellers, eventually a winning combination surfaces.

One of the first tasks in finding this winning combination is to find the right propeller diameter. As discussed before, larger, slower-spinning propellers are generally more efficient, but you have to take the motor efficiency into account as well because the motor's sweet spot may not match the propeller's sweet spot.

The graphs to the right show the power draw of a certain motor/propeller system as a function of propeller diameter. Three different motor choices are shown, and there is an underlying assumption of a certain amount of thrust at a particular speed. The actual values aren't important for this discussion, but the trends are.

Look at the graph of power draw. Now that we've combined the propeller and motor calculations, it isn't just a simple matter of "larger propeller is better." For the Maxon 634043 motor (blue), that seems to be the case, but for the other two motors, there is a steep increase in power draw as the propeller diameter gets above 6.5 inches. Those motors are not designed to handle the lower speeds required to spin the larger propeller efficiently.

Power draw is obviously very important, but we also have to consider operating voltage. Looking at the second graph, we can see that the Cobra CM-4510-40 motor wants to operate at a very low voltage at this particular operating point (it has a much higher KV than the other two motors). In practice, this means that you either have to supply it with a low voltage in the first place or operate it with the motor driver (ESC) at partial throttle. Both of these approaches can reduce efficiency or cause other problems (for instance, most ESCs simply won't operate below about 5 volts).

In this instance, the Maxon 634043 with a 8 or 9.5-inch propeller seems to be a good choice from the standpoint of power draw. If you add in the constraint of operating voltage, though, you may want to use a 6.5-inch propeller in order to keep the system voltage up.

One last set of graphs and then I'll finish up...

Once we've optimized the motor and a propeller for a given operating point, we can examine the performance of this motor/propeller combination in a wide range of conditions. These last two graphs show the total power draw of two motor/propeller systems as a function of thrust, at different vehicle speeds. This is useful if you don't know exactly how much drag your vehicle will produce (and therefore how much thrust is needed) or if you want to see how power draw depends on vehicle speed.

The Maxon 634043 motor is used in both graphs, but the propeller in the first graph is a 9x3 while the propeller in the second graph is an 8x8. By now you should know to expect better performance from the 9x3 at low speeds and better performance from the 8x8 at higher speeds. Sure enough, that is exactly what the graphs reveal.

The first graph, with the 9x3 propeller, is very straightforward: all the lines indicate that more thrust requires more power (seems reasonable) and the trends with vehicle speed show that more speed requires more power (also reasonable).

The second graph is a lot more interesting. We still see that, at any given vehicle speed (on any given line on the graph), more thrust requires more power. But if you compare the different vehicle speeds (different lines), you can see that it is NOT necessarily true that more speed requires more power. For instance, at a thrust of 8 newtons, it actually requires less power to go 1.0 m/s than it does to go 0.0 or 0.5 m/s. This may seem counterintuitive, but it is real. As noted above, the blades of a high-pitched propeller can be partially or fully stalled at low speeds. Thus, for a given amount of thrust, this motor/propeller may actually require more power at lower vehicle speeds.

## Summary

Hopefully by now you know what to look for in a motor and propeller for your vehicle. All of these concepts become much easier to grasp with practice, so get started! Download the spreadsheet and give it a spin. In a future Tech Tip, I'll build on this discussion by sharing some tips about how to physically build a thruster.