# Varying PMDC motor shaft rpm, how does it affect efficiency?

I am working on a project to harvest electrical power from a rowing machine by connecting a permanent magnet DC motor to the flywheel of the rower. However, my knowledge of electrical motors, and especially using them as generators to convert mechanical energy to electrical energy, is limited at best, non-existent at worst.

I'm trying to figure out how I will be able to vary the level of resistance felt by the user. My current plan is to attach a couple of different sized sprockets to the flywheel of the rowing machine and the shaft of the motor and make use ratios between their diameters, similar to what you'd find on a bicycle with gears. I am aware that by doing this, the shaft of the motor will be spun at different speeds for a given force applied to the rowing machine.

My question is this: By spinning the motor at different speeds as planned, what will the affect be on the efficiency of the motor? For example, by operating below the rated wattage, or very close to it, would I expect a lower/higher efficiency, i.e., less electrical energy out per unit mechanical energy that goes in? If there are any resources i could be pointed to that could explain this to me id be MASSIVELY grateful.

Also, any advice on suitable rating for the motor in question would be a huge help. I'm looking at an average sustained mechanical power input to the rowing machine of approximately 80 watts, with maximum as high as 700 watts (only for very short instants during the beginning of each rowing cycle)

Apologies this is very long and painfully under/mis-informed, very new to this.

This can be approached from a few different angles and solved in a few different ways.
If it were me, I wouldn't worry too much about the RPMs affecting the efficiency.
I would rather be concerned with the way to control the mechanical load and at the same time produce a useful output for charging a battery at varying input voltages.
Some rowing machines use a car alternator attached to a large resistor (250-300W) and control the load by controlling a much smaller current of the rotating electro-magnet.
Since you want to actually harvest the energy instead of just dissipating it, a permanent magnet generator (motor) would be better than a generator/alternator using some electricity itself.

The question is where and how do you want store or use this energy?
- If storing it in a battery, a Li-Ion type would be the best because it can absorb the energy the fastest and most efficiently, AND because it is easy to maintain for its long service life - all you have to do is make sure it stays within certain voltage boundaries.
The simplest way would be to measure the voltages at various speeds (what are the minimum and maximum voltages produced by the motor/generator) and use a DC-DC converter with constant voltage and constant current output (CV/CC DC-DC converter).
You would need to modify the converter by simply using an external potentiometer and wire it in the place of the constant current trimmer. Adjusting the constant current value would provide a relatively constant and consistent variable load (it would change only slightly, up to 5-7% depending on the Li-Ion battery voltage at the moment). Furthermore, you need to provide a large load resistor in case the battery is full and can't take any more charge.
And then you need to control and balance all that. It's not easy.

STEP 1 would be to determine the RPM range your rowing machine will give to your motor/generator. This will help you in more closely determining the motor you need, but is not the only piece of information required for it.
STEP 2: The power of your motor. If an average power generated by a rower is about 150W, and the maximum a man can generate is 200W, you could use a 150-200W motor, even if a person generates 300W in peaks, because an electric motor can usually take twice as much load for short amounts of time (up to few minutes).
Actually, when I think about it, it's better to get a more powerful motor (like 400-1000W) because it would be more durable for the same load (especially if it's Chinese-made, as their ratings are usually exaggerated).
STEP 3 is to determine the size of the battery in Watt-hours (Wh) and this depends on the average amount of power generated and the maximum length of time expected to be generating it (plus the reserve capacity for the time you will not use the battery and it would get overcharged if you continue using the machine).
Let's say you will produce around 200Wh, so you need a 200Wh Li-Ion battery just to cover 1 hour of exercise. Ignoring the losses, we could use ~4V Li-Ion cell of 50Ah capacity. To extend its lifetime and to make sure it can always take all of the power generated, we should only use 50% of its rated capacity, so we should go with at least 100Ah on a single cell (it's hard to overdo it with a Li-Ion battery capacity). If you won't spend that energy immediately, you should at least double it to 200Ah.
STEP 4: Based on the power capacity (in Wh) and the voltage we need for an inverter, we can choose the voltage or how many cells we need in series.
Let's say the inverter will use 12V at its input. Now we pick a 12V (3-cell) lithium battery whose capacity is 200Wh/12V=17Ah (rounded up). We can simply use a 20Ah battery of 12V, since it will loose its capacity over time.
STEP 5: Choose motor based on its voltage. This should be selected so the voltage is sufficient at the lowest RPMs but not too high at the highest RPMs for our battery-charging DC-DC converter.
STEP 6: Choose a DC-DC converter of sufficient power (always go for a more powerful one than needed). To make sure it can cover up for the power peak of 300W, it should be capable of transferring at least 300W.

To be continued...

– Rob
Apr 13, 2020 at 20:37
• I will keep editing my answer with more information as I go, but I will need your input as to what kind of information do you need exactly. Apr 13, 2020 at 20:40
• Thanks for the reply! I am planning to store the energy in a battery. So by applying a greater force to the handle of the rowing machine, and in turn applying a greater torque to the shaft of the motor spinning it at a faster rate, would i expect the amount of electrical energy generated per unit mechanical energy to increase? (IE Efficiency increases) and if i was to look for a suitable Permenant magnet generator (motor), would you be able to advise what specifications/ratings would i need to look for?
– Rob
Apr 13, 2020 at 20:46
• I wouldn't expect the efficiency to vary significantly. Apr 13, 2020 at 20:49
• If you give me a place where you plan to buy such motor/generator, I might be able o help you choose. I am not sure about its voltage rating yet. The size (voltage and Ah rating) of the battery would have to be determined around the same time. Then you would have to find a suitable (and powerful) DC-DC converter which can be modified/controlled to suit your needs. Apr 13, 2020 at 20:54

You can use the measured chart of the specific motor, the efficiency won't be much different in generator mode. If the charts aren't available, then you need a measuring setup to make your own measurements.

80W nominal power with peaks of 700W is an utopia. All parts have to withstand this power surge, pretty expensive and useless.

• "80W nominal power with peaks of 700W is an utopia" - the flywheel should absorb most of the peak power. Apr 13, 2020 at 21:31