Where Does All That Power Go?

I’m estimating the electric deck motors on the robot lawn mower will use about 168A of current collectively, and at 24V that means they consume just over 4kW or 5.3hp of power. Even in a worst case scenario, saying that aloud sounds ridiculous. Really? Where is all of that power going?

Remember that power is equal to torque times angular velocity. The angular velocity of the mower blade is governed by the blade tip speed limitation of 19,000ft/min. The linear velocity of the blade can’t exceed this value. If we know the blade length, we can do the math and determine the necessary angular velocity to achieve that blade tip speed.

velocity
The maximum angular velocity of a 21in mower blade for compliance with ANSI B71.1-1990. Don’t forget the calculation between radians and revolutions.

So we have a very good handle on angular velocity. The mystery variable in the power equation is then torque. The amount of torque we need when the blade is spinning is going to determine how much power the motors are going to consume.

In my previous power calculations, I made a huge assumption:

I have no clue how much torque a mower blade needs. Let’s just use whatever my 21in Toro push mower outputs. It mows grass pretty good. Close enough.

-Me, making poor decisions

The engineer in me loves that assumption. Find the appropriate RPM, pull up the power curve for the engine and boom, there’s your torque value on a silver platter.

The problem is that the robot lawn mower and my Briggs and Stratton push mower are two different animals. I should have made this chart a long time ago, but here is the performance curves for the E30-400 electric motor compared to a Briggs and Stratton 450e gasoline engine, typical of a push mower with a 21in wide deck:

Gas Versus Electric Comparison

The chart above makes more sense when you remember that the 450e gasoline engine is paired with a 21in long blade, but the robot lawn mower has 12in blades. This is why the electric motor curves go all the way to 5,700RPM whereas the gasoline engine curves end at 3,600RPM. Their respective blade length gets you close to the allowable blade tip speed.

Remember that these curves represent the maximum torque and power created at a given speed. When you’re mowing your lawn, how often does your mower bog down? Not much, hopefully. If it’s designed well and your grass isn’t a foot tall your mower probably isn’t operating at it’s maximum torque or power.

Because you shouldn’t often need the maximum torque or power out of your mower engine, the guys that engineered them installed a cleverly designed throttle governor, which varies the amount of fuel and air fed into the engine in such a way that its speed stays in a narrow RPM band.

Instead of letting the engine spool up to the fastest speed it can achieve under a given load, the governor limits speed of the engine, and subsequent power output, making it more efficient. If you need more torque or power, it adjusts the air and fuel mixture accordingly. The governor also ensures the blade tip speed stays safe.

This is where my power calculations go off the rails. I’m using the maximum torque values from these curves (measured in laboratory conditions no less) and sizing an electric motor such that it can achieve this torque value. This is inflating the estimated current these motors will consume.

Remember the motor from the electric push mower I got off Craigslist? It doesn’t appear quite so undersized now, given that our gasoline engine is likely operating somewhere below those maximum torque and power curves.

Our E30-400 electric motor, on the other hand, has no throttle control. This makes the analysis simple: it will always be operating at the curves on the chart above. A brief look at the chart shows that it should still perform very well.

Under no load, it will spin at 5,700RPM. As the required torque increases, the motor speed will drop, but the total power output from the motor increases until the motor is spinning at 2,900RPM. At this power output, one single motor is almost generating the power created by the 450e gasoline engine. Nice!

So realistically, the 168A of current for all three motors is probably on the high side. By how much, I am unsure. But I suspect it’s a significant amount. The robot lawn mower uses three of these motors. Collectively, I would imagine they won’t need too much torque to spin through whatever resistance they encounter.

This is looking more and more like a problem best solved by experimentation, not analysis…

2 thoughts on “Where Does All That Power Go?

  1. The amount of power required by your full sized lawn mower is incredible! The tiny wire-guided consumer models are electric, but I think they all use disk mower blades (less inertia, maybe slower?) so they can run on beefy, but affordable LiPo batteries. All of the cool ride-on mower stuff you’ve linked to seems to get its operating power from gas engines, although I don’t know if they have an aux port to power the control electronics.

    This makes me wonder…would it be more affordable to get your power source from gasoline? A 10 HP vertical mower engine (maybe with an alternator to power the wheels?) might be the happy medium that gets you power and runtime! Refilling gas tanks is definitely more cumbersome than recharging batteries, and a three-blade layout from a single engine would definitely be a design challenge. But you can’t beat the price and energy density of a small engine with alternator (potentially less than your four lead batteries).

    Do you know if anyone else in the DIY autonomous lawnmower space has used gas powered engines for a mower at your scale? You seem to be stuck right in between the scales where batteries or gas engines are the obvious power source for a mobile robot.

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    1. I think a lot of my power consumption is due to the high wing angle of my blades. It’s more than 30°, and sitting on concrete the motors collectively draw ~40A. A few years back I bought a used electric push mower to take apart, and the blade angle on that mower was closer to 5°. When the blades are spinning at north of 5000RPM, the motors use a lot of power just cutting through the air. By my estimates, almost half of the 1800W it takes to power the robot.

      Disk blades are much more efficient, but I always had the impression that they can’t handle thicker turf. I also wonder how fast a mower with those blades can travel while maintaining a good quality cut. There’s definitely a design tradeoff here, and depending on your application, you may find that what I’ve designed is overkill. I chose to err on the side of aggressive cutting ability versus making a more efficient machine.

      The main reason I decided to stick with electric was just as you described: if you have to haul fuel out to the mower, is it really autonomous? I guess I am trying to make a machine that can maintenance a large area without human intervention. That may not be a 100% achievable goal, but it seems like a good one to shoot for. Having to refuel the robot is at odds with that goal. Looking way down the road, I envision a docking station of sorts that is hooked up to the power grid to recharge the machine.

      Luis Medina over at EvaTech.net has a series of radio controlled robot mowers that are just like you’re describing: a gas engine with an alternator to power the electronics. He has electric wheelchair style motors on them with a small lead acid battery, I believe. It’s definitely a viable system.

      If your looking for other folks working on autonomous lawn mowers, I’d start with Roby over at DeepSouthRobotics.com. He automated a ZTR mower using similar hardware to what I’m using here. You can find a lot of the guys working on similar projects over at discuss.ardupilot.org, just search for “mower” and they should be pretty easy to find.

      Thanks for the comment!

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