Volts, Watts, Amps – Clearing the Confusion

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.

Still Confused by Power Requirements

I’ve posted several times now about batteries and power consumption but they’re still a cause of substantial concern.

Ultimately, I think it’s the batteries, or rather the power requirements, that are going to make or break this project.

My first calculations suggested that the wheelchair would need a 3 tonne battery, or in other words; this project is an impossible dream.

Employing a large dose of optimism I made some very arbitrary amendments to tailor the results of the calculations to make the project look possible but ever since it has been niggling away in the back of my mind.

Looking at it again, the Llanberis path has a distance of 7.23km and a total height gain of 0.966km (measurements taken from Ordnance Survey 1:25,000 map). Using trigonometry, we can work out that the average slope of the Llanberis path is 7.7 degrees:

To calculate this as a gradient, we simply divide the height by the length and then multiply by 100. (0.966 / 7.23) x 100 = 13.361%

Obviously the gradient of the path will be steeper in parts than others, but having this average should give us more accurate calculations.

To pull a 100kg weight up this slope at 5kph needs a 250w motor. That’s a far cry from the 3,000w motor I’d quoted previously.

As you double the weight though, the power requirement doubles. So a 200kg weight needs a 500w motor.

Obviously, as the power requirement for the motor increases, so does the power consumption and the weight of the required battery.

It’s clear then that power requirements, and therefore weight reduction, are going to become an important part of this project.

A 500w motor seems awfully small though when you consider that a child’s quad bike might have a 1,000w motor.

Looking at existing mobility scooters though, 500w seems very common. The only one I’ve seen which uses a larger 800w motor is this “All Terrain” Mobility Scooter:

Perhaps then a smaller motor would be sufficient? I guess there are currently too many unknowns to be able to find the right answer. With that in mind, I’m going to make a list of questions which need answering in order for me to get to the bottom of this:

Ultimately I want to know how powerful the motors need to be and which battery will provide that power?

In order to answer this question I need to know:

  1. Weight of wheelchair – impossible to say without knowing the other values
  2. Weight of passenger – 40kg approx, will need to get Ada on the scales
  3. Weight of Motor – difficult to say without answering other questions first
  4. Weight of Batteries – as above
  5. Gradient of Path – 13.361% average
  6. Steepest gradient likely to be incurred – need to take some measurements
  7. Length of path – 7.23km to the top, 14.46km return.
  8. How is power distributed between the motors – If six motors produce 500w each, does that mean you have 3,000w power?
  9. If a 500w motor needs 30 amps to get up the hill, does that mean that the six motors need 180 amps (6 x 30) or does it mean that because there are six motors all doing the work they don’t need to draw as much power and therefore they have a combined power requirement of 30 amps?
  10. On top of this I’m also going to need to know the power requirements of other devices, such as lights, battery indicators, linear actuators/hydraulics, any software controllers that might be on board, motor controllers etc.

As you can see, most of this can’t yet be answered so for the moment I’m going to concentrate on question 8 and 9. They seem like they shouldn’t bee too difficult to find the answers to and I expect they will influence the outcomes of the other questions too.

*Update* here are the answers to questions 8 and 9.

Just a dream?

So the other day I estimated that the wheelchair would need to be driven by six 3,000 watt motors. At a constant gradient of 40 degrees, to do the 18 mile round trip, the 4QD calculator suggested the motor would have a constant draw of approximately 65 Ampheres.

I have in my shed a very large 12v 120AH leisure battery which I use to power an electric outboard motor on a canoe. The 120AH rating means that with a 6 Amp draw, the battery provided 12v for 20 hours.

With the 65 amp draw of the 3000w motor, this battery would last 1.8 hours (120 ÷ 65). Let’s say it took 5 hours to reach the top, then you would need 3 of these batteries.

Of course, this is only for 12 volts. For 48 volts we’d need to multiply this number by 4. 4 x 3 = 12.

That’s 12 very heavy caravan batteries. At a guess, I’d say my 120AH battery weighs about 30kg. So overall, that’s a weight of 360kg just for the batteries.

But… Because I want to use 6 motors, does that mean I have to multiply this number by 6? If it does, then it would mean that the batteries weighed over 2 tonnes!!!

And of course, if you’re dragging a two tonne battery up the mountain then the power requirements of the motors increase and then so do the battery requirements. Perhaps then it isn’t possible, and this is why it appears something like this doesn’t already exist.

How about looking at other battery solutions?

I came across a 1.2v 500ah battery which weighs 15.9kg dry. To make a 48v battery, you would need 40 of these. 40*15.9. That’s 636kg for one motor and that’s without the battery fluid. You’d then need to multiply this by 6 which is nearly 4 tonnes and that’s before adding battery fluid.

It was starting to look like a bit of a pipe dream so I got out my map and actually measured the distance to the top of Snowdon rather than relying on secondary information. The distance to the top of Snowdon (On the Llanberis Path) is just over 7km, so a 14km round trip, which is far less than the 18 miles that I’d been using up until now. The internet lied!!!

I’ve also made a very basic estimation of the Llanberis path’s gradient. I had originally been using a value of 30 but keeping in mind that I’m sat at my desk and not out in the field, I’ve estimated it to be more like 10 degrees.

So if I took these new values, slowed down both the the acceleration and top speed, and gave the calculator what could be an unrealistic weight of 200kg, the current draw comes down to 20 Amperes. This would mean that 4 of the caravan batteries (120kg in total) in my shed would be able to get us to the top.

The problem now is that I don’t really know if I then need to multiply this by 6, so that each motor has the same battery pack.

I think the answer isn’t going to be as simple as this.

With 6 motors, individually they won’t need to draw as much power from the motors because they’ll be sharing the load. Imagine trying to push a car by yourself. Then imagine how much easier it would be if you had five more people to help.

Using this analogy, I suppose the same amount of force is required to push a car no matter how many people are pushing. Perhaps it’s the same for the motors? It doesn’t matter how many motors you use, the amount of current drawn will be the same.

I don’t know enough about electricity to be able to say if this is the case, and I imagine it’s not as linear as this, but it does at least sound logical. If this is case then it would mean that 120kg battery (or thereabouts) might get the wheelchair to the top of Snowdon. 120kg still sounds like a lot, but really it’s just four caravan batteries and this to me sounds doable. It is at least far more doable than a 3 tonne battery.

Moving forward, it’s clear that I don’t have the required underpinning knowledge to make these kinds of calculations and I think it’s therefore time to ask for some expert advice.

I think I might also have to stop feeding Ada! Or as mum suggested, ask Elon Musk for help.

Some Rough Estimations of Power Requirements

I’ve been doing some research into power requirements and to be honest a lot of the math such as calculating torque curves is going over my head. I’m sure I could get a grasp of it if I really applied myself but I think this would require considerable effort to develop the required underpinning knowledge. Fortunately I have been able to find some very useful online tools that help to make these calculations easier.

Before I go into them though, I want to share some of my sanity checks.

A typical “powerful” child’s quad bike uses a single 1000w motor. The motor is connected to the rear axle using a chain. Being able to adjust top speed/torque by changing gear ratios would be advantageous. This 1000w quad bike is faster than our needs so that same motor could be geared to give low speed torque instead.

Keeping in mind that in the video above the rider is on a flat even surface and we don’t see how long it’s taken to accelerate to this speed, it does at least give some idea of what a 1000w motor running off a 48v battery is capable of and gives us a reference point for future calculations.

The bike in the following video uses a single 3000w motor and is clearly capable to carrying the rider up hills at significant speed.

A typical Land Rover winch might have a 3,500w motor.

In all of these examples though, the power is coming from just one motor. If I stick to the rocker bogie design then the wheelchair will have six motors, so six times more power (Although it’s obviously not as simple as this as not all wheels will have equal traction etc). Given this EXTREMELY BASIC research, it would appear that 3000w or similar motor might be up to the job.

I found this very useful calculator which given a few known variables can calculate the required power output:

1. Vehicle Speed. The wheelchair needs to be able to move at a brisk walking speed of 5kph.

2.Vehicle Weight. Impossible to say at the moment. just to get a rough idea, lets go with the combined average weight of 4 UK adults. 77 x 4 = 308kg.

3.Passengers. 1 child.

4.Nominal Battery voltage. The higher the voltage given to the motor, the higher its torque. To keep the weight of the wheelchair down, I want to try and avoid going over 48v if possible and prefer to keep it even lower.

5.Weight of one battery. Difficult to say as I don’t yet know which batteries I’ll be using. For the moment I won’t add any weight here and just count it as already having been included in the overall weight.

6.Motor current on level ground. This is a difficult one as you usually cannot guess or measure it until after you’ve finished making the vehicle. The website recommends that if you’re unsure just use their value of 10 as it’s likely to be a fairly small part of the total.

7.Hill climbing ability. A rocker bogie vehicle will usually topple over on a gradient of more than 45 degrees. Ideally I’d go and measure the gradient of the Llanberis Path but for the moment I’ll use 30 degrees as an example. This is a gradient of about 55%.

8.Length of hill. It’s an 18 mile return journey but it won’t need the peak current for all of the time. If I said 15 miles then I think this is quite generous. 15 miles is 24km.

9.Acceleration. Acceleration time isn’t too important in terms of how long does it take to reach top speed. More importantly though is when it’s climbing over obstacles, how quickly can power be transferred to each wheel. I’ll experiment with this value to see what happens.
The results:

Given the values above, the calculator has suggested a motor of 2,500w. Given the earlier Youtube references as a sanity check, this seems OK.

In addition to this, changing the voltage supply and time to accelerate doesn’t make any difference to the output of the calculator in terms of which motor is needed.

The calculator doesn’t take into consideration things like friction, uneven surfaces, and weather etc, however it does assume that one motor will be carrying the full weight of the vehicle. In light of this, a 2,500w motor will probably be OK.

When I start shopping around I will consider 3000, 4000, and 5000 watt motors and if the cost isn’t too prohibitive will invest in bigger motors. However, for the moment at least I have a rough idea.

I like the simplicity of being able to a buy a motor which is already embedded into the hub of a wheel as it will make building the wheelchair far simpler. Although UK suppliers have been difficult to find, I have found this Chinese manufacturer which has a huge range to choose from.

There is also a 43 page forum thread started by the manufacturer on Endless-sphere.com.  I’ve only glanced at the discussion but comments on there seem positive. Both the Endless Sphere forum and the Chinese manufacturer look a good place to obtain some advice.

Having said this though, despite the complications of mounting a motor separately to the wheels, it does give the advantage of being able to change gear ratios and makes it possible to work with local manufacturers.

Power, Speed and Motors

One of the biggest unknowns at the moment is which motors are going to be used in the final wheelchair.

The problem is that my background is in computing not engineering and I don’t know much about motors. As an experienced walker though I can make some calculations about speed.

The average healthy person walks in the mountains at a speed of 4km per hour (2.5 mph) so there isn’t much need for the wheelchair to go any faster than this. To work out what speed the motors need to turn, I’m going to use a 12″ (30cm) wheel as an example. A 12″ wheel has a circumference of nearly 1m. To travel 4km then it would require 4,000 rotations. This tells us that this wheel would need to rotate at a speed of 4,000 rotations per hour, or 66.66 rotations per minute. If we rounded this up to 67RPM we have an idea of what speed a 12″ wheel needs to rotate in order to travel at a walking pace.

This example though presumes that the wheel turns at the same speed of the motor and doesn’t take gear ratios into account. However, even with this simplified example it becomes clear that the motor doesn’t need to operate at high speeds. What’s going to be more important is torque, but more on this in a moment.

Providing power to the motors is also a current unknown. To complete the 18 mile journey to the top of Snowdon and back at 4kmph would take about 7.5 hours (without stops). This would mean that the batteries would need to be able to supply constant power to the motors for an absolute minimum of 7.5 hours, although this doesn’t take into consideration things like terrain, angle of inclination, or wheel spinning/slipping.

Another consideration is the battery voltage. It’s a lot more complicated than this but in very general terms, the higher the voltage rating of a motor, the higher the torque. Also, as a battery’s ability to supply a higher voltage over a longer period of time increases, its size and weight also increase.

I don’t yet know what calculations I need to perform, but, I don’t think a 12v battery (similar to what you’d find in a car) will be big enough. To get enough torque out of the motors, I’d guess that we’d need at least 36 volts (3 car batteries).

If the final design employs a rocker bogie mechanism then it will likely need 6 motors (one for each wheel). 3 car batteries for each motor (18 car batteries!!!) is clearly out of the question. I think it will most likely either use one battery for the whole system, or two batteries so that there is one for each side. This could be a 48v battery overall, or 2 x 24v batteries.

At the moment I’m thinking of 12v/24v leisure batteries used in caravans and boats but there are alternatives such as the small 12v batteries you get on motorbikes (although I doubt they’d up to the job), the 48v batteries that you get on electric bicycles, and of course I should look at the batteries used on a typical wheelchair.

I don’t think it’s possible to decide on a battery until we know the power requirements of the motor though, which brings me back tot he topic of this post.


Motors are powered by magnetic fields. These magnetic fields are created by passing current through a wire. The stronger the current, the stronger the magnetic field. So as I said above, in very general terms, the higher the voltage rating of a motor, the more torque it has.

There are different types of motors such as brushed, brushless and servo motors amongst others.

According to sparkfun.com, brushed motors have the advantage of being simple to control, have excellent torque at low RPM and are inexpensive to manufacture. They sound perfect for our needs. The disadvantages of brushed motors are that the brushes can wear out over time, they generate electromagnetic noise and are usually limited in speed due to brush heating. As mentioned above though, speed isn’t an issue for us and brushes can be replaced. Noise could be an issue though as it’s going to be important not to upset other hill walkers.

Brushless motors are becoming more and more popular as they are reliable, efficient, produce high speeds, are mass produced and easy to find. They are however difficult to control without a specialised controller, and importantly they require a low starting load.

In comparison then, brushed motors are better for low speed torque, whereas brushless motors are better for high speed where torque isn’t a concern. Of the two it’s clear that a brushed motor is the more suitable.

The motor manufacturer MAHLE sell 24v DC motors with a power rating up to 3,5 kW. These motors are used in winches and the like. If they can pull a Landrover then they shouldn’t have difficulty pulling a wheelchair. However MAHLE also sell an AC induction motor which is specially designed for low-voltage applications and for use in electric vehicles. Although they use alternating current, they will still run off a direct current battery with the use of an ECU which converts DC to AC. MAHLE’s 24v AMT has a power rating of 5kw. Although I still don’t know what power rating is needed, just to give some context a child’s electric quad bike typically uses a 1kw motor.

In summary, this feels like progress towards choosing a motor and it seems the first step is to calculate torque requirements and then research AC induction motors.

This page was last updated on April 18th, 2018 by .
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