# Power Consumption Revisited

I think I may have incorrectly estimated my power needs for the mower. A key assumption I’ve been making is that the motor will generally need to be capable of generating ~5ft-lbf of torque during maximum operation. I’m not sure this is really true though.

Do We Really Need 5ft-lbf of Torque?

The 5ft-lbf of torque figure comes from taking a typical gasoline push mower engine and looking at the gross torque output of the engine. But one variable I forgot to consider is that the torque curves I looked at are associated with an engine typically used with an 18in to 21in blade. Our mower uses a 12in blade.

Intuitively, the torque we need to cut through grass is going to be positively correlated to the amount of grass we’re trying to cut at once. So a smaller cutting blade should require less torque than a larger blade. There’s less grass for the blade to run into, sapping momentum from the rotating blade.

I have no idea what the relationship between blade length to required torque looks like. I am going to assume it is linear for simplicity, but I have no clue if this is a good assumption. The torque you need is also going to be related to the quantity of grass clippings circulating around under the deck impacting the blade. Good luck modeling that.

Given the smaller blade size, let’s say you only need 60% of that 5ft-lbf torque value, so 3ft-lbf or 2.2N-m of torque. That’s the ratio between a 20in blade and a 12in blade.

How Much Current Does the Motor Draw at 3ft-lbf of Torque?

The performance curves for the E30-400 motor say that the motor consumes 56A of current at 3ft-lbf of torque. I think this is a more accurate number for current draw from the motor.

How Much Power Does the Motor Consume at 3ft-lbf of Torque?

Another mistake I made was pulling power numbers off this chart thinking they were power supplied to the motor, not shaft power output by the motor.

This is an important distinction, because no motor is 100% efficient. The input power should be the power supply voltage of 24V times the current consumed at a given point on the curves. At 3ft-lbf of torque, it’s (56A)(24V) = 1344W.

This jives with the chart above, because shaft output power at 3ft-lbf or 2.2N-m of torque is about 1040W. That would imply an efficiency of (1040W)/(1344W) = 77%. The chart says the motor is about 75% efficient at this torque, pretty close to this estimation.

So under maximum operating conditions, each motor should consume 56A of current and 1344W of power. The three motors collectively consume 168A of current and 4062W of power.

Is That a Good or a Bad Number?

The 168A number is acceptable because it is right at the limit of what the Mauch current sensor can handle. It’s rated for 200A of current and that leaves us 32A of current for drive motors and miscellaneous control electronics, which should be enough.

So assuming our three mower deck motors consume 56A, our two drive motors consume 12A and our control electronics consume 5A of current, you could have a maximum of 197A drawn from the batteries. Very little margin, but I think it should be okay because…

Maximum Versus Typical

One additional thing I’d like to mention is that I think these are maximum power consumption numbers. Previously I referred to them as typical power consumption numbers.

Do you need 3ft-lbf of torque while mowing the entire time? I doubt it. The calculations above prove that if our electric motors need to operate at 3ft-lbf of torque, they should be able to do it. Operating at 3ft-lbf of torque drops the rotation speed down to 4500RPM which results in a blade tip speed of 14100ft/s, which is a little lower than I’d like but should work.

Run Time Recalculated

Turns out I also miscalculated how battery charge adds when batteries are connected in parallel versus series. In series, battery voltage adds. In parallel, charge (your amp hours) add. Previously I assumed your total charge is the sum of each individual battery charge.

Since we have two sets of batteries connected in series, and then in parallel, our equivalent battery is 24V, 70Ah. This makes sense because I think the Ryobi lawn mower is advertised at 24V, 70Ah too. It’s the same battery set up, apparently.

If we were to run all three deck mowers with a load of 3ft-lbf torque on them, it would take (70Ah)/(197A) = 21 minutes to completely drain our batteries (again, assuming that’s even possible to do, in reality it isn’t).

At half this torque value, total current consumption would be 28A for each deck motor, resulting in 113A total. That results in (70Ah)/(113A) = 37 minutes of run time. The E30-400 motor consumes 29A of current at peak efficiency, so I’m hoping that I’ve sized these motors for the sweet spot of their performance.

If you were to bump up the battery size used on the mower to four 50Ah batteries, run time would be (100Ah)/(113A) = 53 minutes. Doing this would add 34lb to the mower, which would show up in the current consumed by the drive motors.

Thoughts

Even though I have more confidence in these numbers being correct, they’re still disappointing. I would like to shoot for a minimum 2 hours of run time. The only two ways I can think of to get there:

1. More efficient motors and electronics.
2. Larger batteries.

Using BLDC motors would increase our efficiency, but they cost 4 times the brushed DC motors I intend to use. Reduced run time is an acceptable trade off to save \$700 in my opinion.

Larger SLA batteries start getting pretty ridiculous beyond the four 35Ah’s I’m using currently. The battery bay has to grow to accommodate the larger batteries, and that pushes the wheels out, increasing the wheel base and negatively affecting vehicle performance.

Additionally, the added weight makes me wonder if the 0.125in sheet metal battery bays are sufficient to support the weight of the batteries. Two 50Ah SLA batteries weigh 64lb. I’d probably want to reinforce it just to make sure.

We could switch to some Lithium Ion batteries, but here the cost is at least as bad as switching to BLDC motors.

If you were to make a composite battery out of 18650 cells equivalent to the four 35Ah SLAs I’m using currently, it would cost just shy of \$1,000 in 18650 cells alone. And that doesn’t even include labor to build the battery and a fancy charging system to go with it.

I found some guys that make custom 18650 batteries, and maybe they can do it for cheaper. I’m starting to understand why Tesla’s use lithium ion technology. If you need a boat load of power and have any kind of space or weight constraint, you kind of have to. Unfortunately, I drive a 2003 Honda Accord, not a Tesla Model X and so the mower project can’t afford some legit lithium ions.

I may have to get used to about 30 minutes of run time.

# Power Consumption

I decided to make the autonomous lawn mower fully electric for one big reason: If a person has to walk out to the mower with a gas can and refill the tank, is it really autonomous?

Ideally, you want the mower to do it’s job without any human intervention. If you have a gas engine, no matter how you cut it fuel has to be delivered to the mower in some fashion. With an electric design, you can have the mower automatically dock with a charging station when the battery gets low. No human required.

So from the get-go I have been trying hard to make the mower electric. I am encouraged by some electric riding mowers out there that use SLA batteries as their power supply. I like SLA batteries because they contain a lot of energy and are fairly cheap. Minimizing battery weight and volume isn’t a huge constraint for this project, thankfully.

Because these electric riding mowers cut grass and carry a ~200lb person on the mower, I have been operating under the assumption that as long as our batteries are larger capacity than those on this riding mower, we should be okay. That Ryobi mower features a battery bank that consists of four 12V, 25Ah SLA batteries.

I am beginning to question that assumption…

Power Consumption

Sizing the batteries ultimately depends on how much power the mower needs. The deck motors take the lion’s share of power consumption. Previously I estimated the mower would require motors that can output at least 5ft-lbf of torque to cut through thick grass based on typical gas engine torque output.

Examining the torque curves for the E30-400 motor I selected for our design shows that at 5ft-lbf or 3.7N-m torque, the motor consumes 1400W of power. If you assume all three motors pull this level of power, the deck motors collectively consume 4200W.

The drive I’m using on the mower design are stolen from the wheel chair. I suspect they are rated for 500W but I am not sure. The gearbox on them ensures they will generally be operating in an efficient area of their torque curves, so I am going to consume both motors consume 250W, and collectively consume 500W between the two motors.

The control electronics are almost negligible compared to the power consumed by the motors, but I will budget 100W for all the other little things on the mower, just to be safe.

That brings the total estimated power the mower needs during operation to 4200W + 500W + 100W = 4800W.

Battery Capacity

The batteries I’ve selected are four 12V, 35Ah SLA batteries. If you assume we intend to discharge these batteries 100% (and that doing so was physically possible), you could obtain (4)(12V)(35Ah) = 1680Wh of energy. If we were to draw 4800W of energy from these batteries, we would drain them in (1680Wh)/(4800W) = 21 minutes. Yikes.

But it gets worse. Because we’re pulling so much power out of these batteries, it looks like you have to discount the total amount of energy you can get out of them. I’m not entirely sure what that calculation looks like, but from the SP12-35 datasheet, it looks like a 1hr discharge rate only allows you to get 21.8Ah of charge out of each battery. That’s only 60% of the 20hr rate of 35Ah. I could be wrong about this interpretation of the datasheet, please correct me if I am mistaken.

Some Thoughts

Do the motors really draw that much power? Holy moly I hope not. At their most efficient, the motors draw 500W of power. Running the calculations above with this number gives you a run time of 48 minutes. Still not great.

The reality is somewhere between those two extremes. Taking the average of the two gives 35 minutes of run time. I was hoping for something more in the neighborhood of 2 or 3 hours. Going up to some 12V, 50Ah batteries could give us some extra oomph, but I don’t think it will be 3 hours of oomph.

Please let me know if these numbers seem way off base, it’s my best swag at them I can come up with. The last thing I want is a mower that can only cut grass for 10 minutes.

# Progress

I’ve started doing some wiring diagrams for the robot lawn mower, as the mechanical portion is fairly well defined. However, there are a few things I’m still not sure about:

1. Will four 12V 35Ah SLA batteries will provide the energy needed to run the mower?
2. Should the battery bays be replaced with some off the shelf enclosures?
3. Is there a better way to do the deck height adjustment mechanism?
4. Are the motors sized appropriately, both for speed and torque?
5. Is a pulley quick disconnect bushing really the best way to attach the cutting blade to the motor shaft?
6. The sheet metal used on the weldments is 0.1875in thick aluminum. That is expensive and probably too stout. It should be changed to 0.125in thick.

I’m chasing my tail with these questions above, so I will take some time off from modeling the mechanical side of the mower and work on wiring for a while. Hopefully things will be more clear when I revisit these issues later.

# E30-400 Motor Evaluation

The electric mower motor I got off craigslist had a 12in blade on it. That motor was rated for 24V, 4300RPM, 1.3N-m. I suspect it was pretty undersized for doing any real grass cutting, but whoever manufactured it had to size it at least somewhat appropriately.

Our three blade mower design has 12in blades on it. So in theory, any motor larger than the craigslist motor should be sufficient. But because I’m a perfectionist, I don’t want to just barely exceed these parameters. I want to knock them out of the park.

For the same torque values as the craigslist motor, the E30-400 motor will rotate at about 5000RPM, consuming 700W while operating at about 77% efficiency. That translates to a blade tip speed of 15700ft/min, or 80% of the maximum allowable tip speed.

At the same speed as the craigslist motor, the E30-400 outputs about 2.8N-m of torque. That’s more than twice what the craigslist motor is rated for. Not bad.

The best part? Three of these guys only cost \$354.41. And that’s after shipping, with insurance. The holy grail indeed.

# Mower Design: How Many Blades

There are a lot of variables to play with as we design the prototype autonomous mower from scratch:

1. The deck dimensions and shape are entirely up to us.
2. We get to choose the number of blades.
3. The size of the blades.
4. How the blades are driven: direct drive, through a pulley, chain, or timing belt.
5. What standard lawn mower components we attempt to use.

This is not an exhaustive list, but these are the main variables I find myself tweaking as I try to optimize the design.

We have a lot of freedom to do whatever we want because we are custom making the mower deck. But this also creates a lot of questions. As we discussed previously, the deck geometry and the number of blades used on the mower lock down several of these variables. So before we go any further, I want to go into detail the advantages and disadvantages of a design with one, two, and three mower blades.

The single blade design has one huge advantage: one blade, one motor. The motor can even be coupled straight into the blade if it is sized appropriately. This could minimize cost and complexity in a big way for our design.

Unfortunately, it also creates some disadvantages that aren’t immediately obvious:

1. A single blade design results in the longest wheelbase, which will adversely affect the agility of the mower.
2. It also results in the largest mower deck. That means it will be heavy and expensive compared to alternatives.
3. The largest blade you can get is ~30in. So in addition to the negative performance and cost impact from the points above, you can only achieve a cutting width of ~30in with this design.
4. And on top of all these issues, you also have to go with a minimum 3kW BLDC motor and controller to get the power you need to rotate the blade. That’ll set you back close to \$700 after everything is said and done.

Yikes. Turns out a single blade actually creates more problems than it solves. If our target cutting width was in the neighborhood of 20in, this would be the way to go. But since we’re aiming for closer to ~36in, this design is unacceptable.

The two blade design solves a lot of the issues that the single blade design faces. The deck length and resulting wheelbase are considerably smaller, and because there are two blades that need to be driven, two smaller, cheaper motors could be used. Or alternatively, you could use one large motor and have a pulley drive system transmit power to each blade.

The biggest drawback with a two blade design is related to geometry. In the picture above there are two dashed circles showing the path the tip of each blade with follow as it rotates. See how they overlap? If we leave the design as shown in that picture, the blades will crash into each other during operation. If space them apart, the grass between them doesn’t get cut.

There are two possible solutions to this issue:

1. Use a chain or timing belt to link the two blade spindles together. This will ensure they are synchronized through their rotation paths and won’t crash.
2. Separate the blades so their paths don’t intersect, but angle the deck. As the mower travels, it won’t leave a small tract of uncut grass.

Using chain isn’t a good option to synchronize the rotation of the two blades in my opinion. The blade drive system needs to be designed for shock loading, and also to minimize vibration for the Pixhawk. Chain doesn’t help any in this realm. It also creates maintenance issues, although those are secondary concerns. I suspect this is why V belt is used on commercial mowers most commonly, not chain.

A timing belt is a better solution, but this forces us to find a way to integrate timing belt sprockets into our design, which will invariably result in some expensive fabricated adapters to link an off the shelf timing belt sprocket to the mower spindle. So it’s a better solution than chain, but has it’s own set of problems. So option 1 is out.

Option 2 is an elegant solution, and you see it on commercial mower decks that feature two blades quite often. However, the tradeoff is that you increase the length of the deck because you are essentially moving one blade further forward than the other. See the picture below to see what I’m getting at.

Dimensionally, option 2 results in the same wheelbase as a single blade design, but with the headache of two motors. It may even be longer than a single blade design, because the swivel caster assembly on the front needs clearance to swivel.

Plus it just looks funky. So a two blade design is out, too.

Initially I was hesitant to even consider a three blade design because of the number of parts it will require. Three blades, three spindles, three pulleys, a belt to connect all of the spindles, or three motors to direct drive the blades.

To complicate matters, the smaller the blade length, the faster it needs to rotate to achieve good grass cutting velocity. We previously discovered that a 21in blade requires 3500RPM in order to achieve a blade tip speed of 19000ft/min. For a 12in long blade, that number jumps to more than 6000RPM.

This is a problem because most DC motors don’t operate at those speeds with any significant amount of torque. In fact, most of the motors I’ve seen have no-load speeds listed far below 6000RPM. That’s the bad news with a three blade design.

The good news? Other than these blade drive system constraints, the three blade design is geometrically very efficient. It results in the smallest wheelbase, and because it is triangular in shape, you get bonus clearance for the front casters to swivel. It requires the least amount of material to fabricate. That means cheap and lightweight.

The blades are separated by a small amount but because the center blade is slightly more forward than the outer two, you still get 100% cut coverage, similar to the angled two blade design.

The three blade mower design is by far the most efficient, and I like the way it looks, too. The only hurdle to making it works is finding a motor that won’t break the bank, but still get us close to the 6000RPM requirement for a 12in blade. If we can find a motor that works with this design it will by far be the best one of the three. Does such a motor exist?

The Holy Grail of DC Motors

We had previously considered BLDC motors to give us the power and efficiency we need to spin the cutting blade. But unfortunately that power and efficiency comes at a cost: BLDC motors require a controller to run them.

So even if you find a fairly cheap BLDC motor that meets your needs, tack on 50% of the motor price for the controller. Need three motors? Looks like you need three controllers, too. And the space to mount them somewhere. I’m sure they make combo controllers out there, but I can’t find them.

The other problem with these controllers is that you’re paying for a ton of features you don’t even need. Most are designed for electric scooters. I don’t need the ability to go in reverse, or to vary the speed. I just need a motor to spool up and stay there. With typical BLDC motor controllers, you get a bunch of these features, and boy do you pay for them.

So while BLDC motors fit our application requirements, they are costly. Ideally we’d like to use a simple brushed motor that operates at the speed and torque we need. Turn it on with a \$3 relay. Keep it simple.

In my adventures across the interwebs, I had trouble finding anyone who makes a brushed motor that runs close to 6000RPM with significant amounts of torque, that also costs less than \$400.

But that was before I found the folks out at AmpFlow. They make a really nice set of brushed, DC motors in the speed and torque range we need. They also appear to be US based, which is a plus. They post torque values in oz-in and dimensions in inches. And they have torque curves for their products. All around, these guys are awesome.

Next time I’ll go over the specifications for the E30-400 DC motor, which I think is perfect for this application.

# Selecting a Motor

As I mentioned previously, I need to find a motor manufacturer that posts more than a picture of their product on an electric bike. I need torque curves and CAD models. I am surprised at how few of these manufacturers exist, or at least have websites that I can find. Maybe I just don’t know how to search for them.

Part of the problem is that I’m looking for a motor that has power output on the level of a small riding lawn mower. Finding smaller BLDC motors has been pretty easy, but finding something that operates efficiently at lawn mower speeds while still outputting decent torque has been challenging. Also, it has to cost no more than a few hundred dollars, because I’m cheap and I need some money left over for an RTK GPS module down the road.

So I’m starting out from behind the 8-ball to begin with. I wasn’t sure such a motor existed until I found the folks at Golden Motor. These guys are a little sketchy, and they need to hire a web designer from the 21st century. But they appear to have a wide selection of motors in some pretty epic sizes, with fairly comprehensive performance data, too.

But before we go looking at individual motors, let’s review our requirements.

Motor Requirements

At the moment I am leaning toward a single mower blade design. I’ve learned the hard way that complexity is not your friend, and simple designs are generally more robust.

To maximize the deck width, I am considering a 30in long blade. A 30in blade needs to rotate no faster than 2400RPM to be safe. Riding mowers with one single 30in cutting blade are equipped with engines that output about 10ft-lbf of torque.

The plan currently is to have four 12V 35Ah sealed lead acid batteries wired in series to power the motor. So it must be rated for 48V.

Evaluating the BLDC-108 Motor

This is a 1500W motor that Golden Motor makes. It’s also the only one that doesn’t have  a nice chart for all the relevant performance parameters, but they did give an excel spreadsheet with several data points. I graphed the data and here’s what it looks like.

The efficiency of the motor is greater than 85% between 1 to 3.5ft-lbf torque with a maximum efficiency of 88% at 3325RPM and 2.6ft-lbf torque. The motor consumes about 40A of current at the torque shown on the chart.

To achieve the maximum safe blade rotation speed of 2400RPM, we need to use two pulleys of different diameters on the motor shaft and the blade spindle. Taking the maximum speed the motor operates at of 4072RPM and dividing it by 2400RPM gives us the pulley ratio we’ll need, which in this case is 1.7.

If we use the motor with a pulley ratio of 1.7, we could obtain 5.9ft-lbf of torque at 1800RPM. Reducing the speed increases the torque.

1. The torque is a little on the low side, even after you factor in the pulley ratio. I suppose you could go with a higher pulley ratio, but that reduces your speed even further, which I’m told affects the quality of your grass cut.
2. I like that the current draw is only 40A. With four 35Ah batteries, you could in theory get 3.5 hours of operating time, neglecting current consumption from other electronics and motors. I like that number.
3. The picture on the website is nothing like the CAD model you can download. So that’s something I’ll need to investigate if this is the motor I choose.

The motor is priced at \$142 with \$60 for shipping. BLDC motors require a separate motor controller, so that will be another \$95 with \$30 for shipping. So a system built around this motor will cost a total of \$327. Not horrible. I wish I knew why the shipping was so high…

Next time I’ll evaluate the 3000W HPM3000B motor.

# More Mower Musings

I’ve had some more time to think about our mower blade and the system that will be required to power it. To summarize what we discovered last time:

1. A 21in blade is the maximum size we can use.
2. A larger mower will be more efficient in general because a smaller portion of the mower width will be used to overlap the previous pass.
3. Typical brushed DC motors are probably not a great way to power the blades.

I think I need to retract statement (1) above. It turns out there are larger blades out there, the only caveat is that they have to be rotated at a slower angular velocity to maintain a blade tip speed of less than 19,000ft/min.

Using the math I outlined previously, a 30in blade needs to be rotated at just over 2,400RPM to achieve a blade tip speed of 19,000ft/min. This turns out to be a good thing too, because this slower speed can be achieved by using different sized pulleys on the drive motor and spindle, which will allow us to trade higher RPMs for more torque, which will be needed with a larger blade.

I was really hoping to avoid a mower with two blades for a few reasons:

1. Complexity: two blades means two spindles, some idler pulleys, and more moving parts.
2. Blade interference: the travel paths of the two blades need to overlap a little so you don’t miss any grass, forcing us to make sure the blades don’t get out of sync and crash into each other
3. Vibration: I imagine two blades will result in more vibration, but this is speculation.
4. Real estate: the mower deck needs to also house (4) 12V 35Ah batteries and a bunch of control boxes. Two spindles and a large belt with idler pulleys eat this space up really quick.
5. Robustness: More parts means more opportunities for failure.
6. Cost: More parts means more cost.

So seeing as we can use one blade while still achieving a cut width of about 30in, I think this is the preferable solution. There are mowers out there that use 30in blades, but the torque required for such a blade size is pretty high. This mower is equipped with a Briggs and Stratton engine that outputs 10.5ft-lbf of torque at 2,400RPM.

Keep in mind that’s engine torque output, not torque at the rotating blade, but that still means our electric motor needs to output at least 5.25ft-lbf at 4,800 RPM (see the pulley ratio math below). I’m guessing that will be a difficult number to achieve.

Motor Alternatives

Regarding (3) above, I think a brushless DC motor may be the way to go. I found this motor on an electric scooter parts store which seems promising, but I need to see a torque to RPM curve to be sure. Coincidentally, that motor is rated for 4800RPM, which results in a pulley ratio of about 2:1. Not bad.

On the down side though, most of those motors are designed to be used with sprockets and chain, which isn’t a great idea for mowers. There’s a reason mowers use pulleys and V belts. I suspect it is because they allow for a more fluid transmission of torque to the blade and also slippage if the blade hits something rigid, resulting in less strain on the drive motor or engine.

This will mean I’ll probably need to fabricate a custom drive pulley to adapt to the motor shaft and accommodate the V belt required by the blade spindle.

What Do The Other Engineers Think?

This is the 21st century. Has anybody designed an electric mower with similar parameters to the ones we’re looking at here? Turns out the answer is yes. The specs for the Ryobi RY48110 riding mower:

1. Looks like they’re using a few 12V 25Ah lead acid batteries for power.
2. They use two BLDC motors directly connected to the cutting blade.
3. Deck width is 38in which would imply a ~19in blade length.

Funny story, if you pull up the parts list and google their replacement motor part, you come up with this motor rated at 48V, 32A, 1800W, 4500RPM. So we’re at least in the neighborhood.

1. They’re using this motor to drive a ~19in blade. We’re looking at using a motor that is actually rated at 1600W to drive a blade that’s more than 50% larger. Not good.
2. Direct drive is interesting, it’s definitely simpler. I would be interested to see what kind of connection hardware they use.
3. A 19in blade implies a maximum blade tip speed of 3800RPM. The motor is rated for 4500RPM. I wonder if the mass of the blade results in a equilibrium rotation speed of about 3800RPM. If not, the mower isn’t in compliance with ANSI B71.1-1990.
4. How do the two motors stay in sync? I wonder if the blade paths overlap or if there is some kind of chain or belt between them to maintain their angular offset.
5. Being BLDC motors, I also wonder what the controller looks like. I imagine it shoots for a fixed rotation speed. I would be interested to know what that rotation speed is.
6. The Cadillac version of this electric riding mower only offers 100Ah of charge at 48V. That’s only 4.8kWh of energy. Our system with four 12V 35Ah batteries can store up to 6.72kWh of energy. This is interesting because not only does the riding mower need to cut grass, but it also has a possible 250lb person it’s driving around too. So I think we’re on the right track as far as power requirements go.

In Summary…

1. I need to get some torque speed curves for these motors. Otherwise we’re just guessing about motor capability here.
2. I think our power system is appropriately sized based on the RY48110 specifications.
3. Torque output is still the big unknown here. The RY48110 gives us a baseline to work from though.
4. It looks like BLDC motors are going to be the device that powers our blade, seeing as the folks at Ryobi arrived at the same conclusion we did.

# Mower Musings

One of my goals for this winter is to design the prototype autonomous lawn mower. The rover V2 is coming along nicely, and while I have a few systems left to work on, the big ones are already implemented and working. So I spent some time this week thinking about the thing that makes a mower a mower: the cutting blade.

A few months ago I purchased a small electric push mower off Craigslist. It had a DC motor and a 12in cutting blade that I disassembled for the mower project. I figured the “cutting grass” problem is essentially already solved and that there’s no sense in reinventing the wheel. But now that I’ve done some thinking, I’m not sure this problem is as simple as it seems.

Eventually I will attempt to integrate an RTK GPS system on the mower. Depending on who you ask, you’ll find that RTK GPS systems are accurate to about +/-1in. For the rest of this post I will be talking in terms of accuracy relative to the base receiver. Absolute positioning with any degree of accuracy is another can of worms altogether.

What +/-1in means is that at any given time, the mower could be 1in to the right, or 1in to the left of its reported position. Let’s say it’s 1in to the right while it’s mowing a row in your lawn. That +/-1in means when it doubles back for the next pass, it could be off by 1in in the other direction. Basically, +/-1in means there could be up to a 2in gap between passes.

So we will need to overlap passes by some amount. You would normally do this anyway if you were mowing your lawn manually. I overlap passes with my push mower by about 4in when I’m mowing my lawn to make sure I don’t miss anything, and we’ll want the robot mower to do this too to maintain a quality lawn cut. So we’ll need at least 6in of overlap: 2in to account for RTK GPS drift and 4in to account for normal overlap.

The issue I’m trying to highlight here is that the narrower your mower, the more critical it will be that it is positioned accurately. You can’t tolerate much drift because you’ll start missing passes if you’re mislocated by any amount. And to overlap such that you don’t miss passes requires overlap equal to 50% of your blade width, which is very inefficient.

This is why (in my opinion) RTK GPS works pretty seamlessly on big agricultural equipment. Those tractors and combines are a whole order of magnitude larger than our mower. They’re also out in big open fields with great GPS reception, but that’s a rabbit hole for another post.

So Pick the Biggest Blade Size, right?

Well, sort of. If you do much searching, you’ll find that the biggest blade you can get your hands on is about 21in. There’s a good reason for this: mowers cut best when the blade rotates at near-ballistic speeds, and if you make a blade much larger than 21in and then rotate it at 3600RPM, anything it hits turns into a piece of shrapnel. Not to mention what could happen if the blade itself shatters. Go look up some lawn mowing accident videos to see what I mean.

In my reading, I found that our friends at the American National Standards Institute (ANSI B71.1-1990) did some testing and recommended manufacturers keep the blade tip speed below 19,000ft/min, or 216mph. That’s linear velocity, not angular velocity. Remember that angular velocity is equal to linear velocity divided by the radius through which it rotates.

So How Fast Should We Spin the Blade?

So knowing that we want a big blade size and that we want to achieve a blade tip speed of just shy of 19,000ft/min, we can calculate the required angular velocity.

Knowing the angular velocity, we can now calculate the required power if we know the torque the mower blade will experience spinning through thick grass. Unfortunately, that’s a very difficult figure to arrive at. So instead of doing some convoluted math to estimate the torque to cut through grass, we’ll just take the gross torque ratings listed by the folks out at Briggs and Stratton, as their mowers generally cut through grass with no problem.

This engine is one of their lower end models. Briggs and Stratton advertises gross torque at 2600RPM, so for this engine it would be 4.5ft-lbf of torque. If we take 5ft-lbf of torque as the required torque to cut through grass, we can estimate the power we’ll need for an angular velocity of 3450RPM.

Does the Craigslist Motor Cut It?

Electric motors aren’t like gasoline engines. Their torque to RPM curves are much simpler. With no load attached to the armature, the motor will spin very fast while outputting very little torque. If you apply a small load to the motor, the angular velocity will decrease slightly and torque will increase slightly. If you keep doing that until the motor stops turning, you’ll arrive at the stall torque. This is the maximum torque the motor can output.

So electric motor torque to RPM curves are linear. To draw them, you only need three pieces of information: the angular velocity and torque at a given point on the curve and the no load angular velocity. Using that information, you can draw a line for the torque curve.

The table here indicates the no load speed is 4300RPM and gives an operating point of 0.96ft-lbf (1.3N-m) of torque at 3700RPM. From this information you can find the stall torque and the maximum power the motor can output.

The manufacturer says that the rated power for the motor is 500W, but from my calculations I’m not sure that’s true. However, I am very surprised that the calculated power is this low. It’s very possible I have no clue what I’m doing here with these calculations. If that is the case, please call me out on it.

A motor that gets even close to the power levels we need would have to be a 2500W motor. We have a 24V power system, and we need the motor to spin at 3600RPM minimum. Doing a brief web search for those terms doesn’t come up with many promising alternatives. I’m not sure motors with those parameters are practical or even exist, at least in the PMDC variety.

So What Have We Learned?

I can think of a few things:

1. If RTK GPS is our positioning technology, we’re going to want to make the mower as wide as we reasonably can.
2. To keep our mower safe, the blade tip speed needs to be no faster than 19,000ft/min.
3. Mower blades don’t come much larger than 21in long, so if we want a deck bigger than that we’ll be adding complexity to our design.
4. We’re going to need a boat load of power to spin that 21in blade at power levels generated by gasoline engines.
5. A permanent magnet DC motor may not be the way to go given these constraints.

I hope these musings about the mower make sense. I am always open to opinions and criticism about the evidence above, and what conclusions should be drawn from them.

Brushless DC motors, on the other hand…