In previous posts, trying to calculate the power requirements for electric motors and batteries was causing me some confusion. However, my attention turned to hydraulic motors and more recently a larger prototype so I never answered the questions I’d identified.

Before it completely disappears into the ether, I thought it wise to clear up some of the confusion I’d been having:

## What are Volts, Amps and Watts anyway?

I’ve heard of volts and amps being described in plumbing terms before where volts is the water pressure and amps is the amount of water passing through. A Watt is a measurements of their combined power, and as an aside, an Ohm is a measure of how much resistance there is, or in plumbing terms, the width of the pipe.

For some unknown reason, my brain has never been able to adopt this plumbing analogy but whilst writing this post I came across this picture on gineersnow.com which suddenly enabled me to make sense of it.

I guess I’m just a visual learner. Anyway, back on topic…

## Relationship between Watts, Volts and Amps

The relationship between Watts, Volts and Amps is really quite simple. If a Watt is the combined power of Volts and Amps then the following must be true:

Watts = Volts x Amps

Volts = Watts / Amps

Amps = Watts / Volts

This is useful to know because it allows you to calculate the current-draw of a motor.

Let’s say we have a 100w motor running off a 12v battery. To work out the current draw we divide 100 by 12 which gives us a current draw of 8.3a.

We can then use this to work out how long a battery will last. Battery capacity is measured in AH (amp/hour). To work out how long a battery will last, you divide the AH by the current draw. So if I had a 12v 50ah battery to power my 100w motor, then the battery would last 6 hours (50ah / 8.3a = 6.02).

It is a little more complicated than this though. A battery’s AH rating is usually measured over a 20 hour period. What this means is that the 50ah battery is able to provide 2.5amps (50 / 20) per hour continuously over a 20 hour period before the voltage starts to drop. However, just like the petrol in a car; the faster you go, the more you use. This means that I would actually drain my example battery in under 6 hours.

Having said that though, the motor won’t always be drawing full power so it could well last for more than 6 hours. So as I say, it is a little more complicated when you start to consider the variables, but understanding the relationship between watts, volts and amps does give us a rough idea.

This is the primary reason why I started building the larger prototype listed above; to give some real world experience of putting these calculations into practice.

## Power Distribution

In my previous posts, one of the things that was holding me back is understanding how power is distributed between motors and therefore how much battery power I’d need.

To put this into context, let’s say the wheelchair needed a 1000w motor to get it up Snowdon. If I used a 12v battery the current draw would be 83a (1000 / 12). Finding a 12v battery that would last more than an hour would be difficult. Instead what you can do is use a 48v battery – 1000 / 48 = 20.8. At 20 amps, you’re more likely to find a battery that will do the round trip.

A question that I wasn’t previously able to answer though is what happens when you add more motors? If one motor needs 20a, does that mean six motors (one for each wheel) needs 120a (6 x 20)? If this was the case then finding a suitable battery would be difficult to say the least. Luckily, and thanks to CBenson over at RobotShop.com, I can now put this question to rest and say that this isn’t the case.

If I’ve calculated that a 1000w motor will get the wheelchair up the hill, then this is the combined power required. If I use 6 motors, then they will only need to produce 166.6w each (1000 / 6). This means that with a 48v battery, they have a current draw of 3.5a each.So in total, they have a combined current draw of 20a, just the same as one motor would.

As has always been the case with calculating power requirements for this project though; it isn’t as simple as this.

## Wiring Motors in Series/Parallel to Affect Torque

Something else I’ve come across which is worth mentioning is what happens when you change between wiring motors in series or parallel.

On the Endless-Sphere forum, DrkAngel said:

Motor : 24V 10A = 1x speed 1x torque

Motors in series: 24V 10A / 2 motors 12V 10A per motor = .5x speed 2x torque

Motors in parallel: 24V 10A / 2 motors 24V 5A per motor = 1x speed 1x torque

What this means is that you can double the motors’ torque by wiring them in series. To put this into context and refering to my previous example; if I had two 1000w motors wired in series, I would have an overall power of 2000w. However, the consequence of this is that the current draw is doubled from 20a to 40a.

Whereas if I had two 1000w motors wired in parallel, I would still only have a combined power of 1000w but the current draw would be the same as if I had only one motor at 20a. Effectively this would give me six-wheel-drive without any additional power consumption.

In light of the above, it would appear that I’d want to wire the motors in series. The reason being that in my calculations I’m using the average gradient of the mountain to work out how powerful the motors need to be. In reality though, the mountain will be steeper in parts than others so at times, more torque will be required. Wired in parallel, although there is no increase in current, you’re never going to be able to get more than 1000w of power.

Wired in series, although the required amps increases, if each of the six motors drew 20a then the total current draw would be 120a giving me 6000 watts of power, in reality, the wheelchair won’t often need that much power so the current draw will be much smaller for the most part.

It will be interesting to get the next prototype working and to conduct some experiments to see how well this theory translates to the real world…

*update* Actually, now I come to think of it (two days after originally posting) I realise that I will neither be wiring the motors in series nor in parallel as I want each motor to be driven independently, for those sticky situations where you only want power to one particular wheel.