Preface – I wrote this piece to capture my thought processes. It is meandering. I have not rewritten any section, even though Scotch played a part in the authoring of much of the red text section and looking back over it, it could definitely use a rewrite. Which I am not going to do, so apologies for the writing style (or lack thereof). Also, this is a thought exercise, not a thesis or paper on alternate fuel sources. This is why I am happy to accept rough figures for most of the math (and why it goes a bit pear shaped).

Someone invented a device that captures electromagnetic energy generated by walking to help charge your cell phone.

How much energy could that generate? If we have anything, we have a lot of potential biological energy generators on this planet. Maybe not as big on the walking as we once were, but whats the math here? On average, how far would 6 billion people have to walk have an impact? I found something from not too long ago suggesting that New York consumes 5 Gigawatt per annum. Another article that suggests it takes around 1 kilowat per hour to power an iPhone for a year. Add in a device on kickstarter that claims to be able to charge a phone from a 30 minute jog (can i get more info – the details are for backers only – if all the other variables pan out *should* I be investing in this?). Assume a daily recharge for the phone that never gets turned off. Yeah its rough and loose but this is just a feasibility study, not a thesis.

Puts on the math hat.

1 kw per hour = 24 kw per day – and a 30 minute jog charges the phone (assuming to full).

Multiply 24 kw per day by 365 to get 8,760 kilowatts per year, or 8.76 megawatts per year. A gigawatt is 1,000 megawatts (or a million kilowatts for those playing at home), so to generate enough energy to power a large city for a year we need to divide 5 gigawatts which is equal to 5,000 megawatts by the 8.76 megawatts generated by daily 30 minute jogs.

That is 570 and change rounded up to 571 people taking a 30 minute jog daily where if we found a way to capture that energy and transfer it in to our energy grids, we could power a city around the size of New York without ever requiring another power source.

So my maths must be flawed. Maybe the charging a phone with a 30 minute job claim is based on some non-smartphone model small print and not from fully empty, small print small print.

But even if the device where one tenth what they claim, that would just multiply the 571 people needed by 10 getting 5710 people. Still not a bid deal. If it were 1% as powerful as they claimed, it would still only be 57,100 people which is still less than 1% of the population of New York.

If we had the way to capture the energy this way, don’t tell me we wouldn’t get out there and get jogging. Sticking the capture devices on the kids, giving them sweets and soft drinks and then watching them light up the street?

It can’t be right.

Wait, how much electricty to power an electric car. OMG, if walking were an effective way to power an electric car I think my brain could explode.

Okay, a reference suggesting a Mini E uses 22 kw for 100 miles. That would apparently equate to around 3.2 gallons of fuel for the same distance.

Wait, didnt we establish earlier that the 30 minute jog charged 1 phone to full and that phone used 24 kw per day.

So for less effort than a 30 minute job, you could generate enough energy to power an electric car for 100 miles?

Apparently the average American driver logs 13,476 miles every year. 13,476 divided by 3.2 gallons of fuel per hundred miles = 431.23 gallons of fuel consumed per year per American driver – mulitply by what you last paid per gallon for fuel, and you could theoretically save that much money with the energy generated by a 30 minute jog.

It can’t be right.

Time to walk away and come back at this later with a fresh mind. Verify those variables. Do some conversions into proper measurements like Litres and Kilometres. Miles and Gallons indeed! Humbug!

Okay, I’m back and I had an idea. If we establish (a) how much electricity can be generated by walking, then check (b) how much energy a machine that simulates walking needs to be powered, then (a) cannot be greater than (b) or I just came up with the idea for a viable perpetual motion machine and broke physics.

Forgetting all previous values. Starting from scratch as that also forces me to revisit my variables.

First source: Kickstarter Campaign information for a device called SolePower.

The campaign claims that 2.5 to 5 miles (4-8 km ish) of walking will charge an iPhone to full. That is a lot less ambitious than the 30 minute jog claim and a much higher level of variability in the prediction. I’ll take it.

Second Source: lifehacker.com that does some research in to phone power consumption (for the purpose of cost of charging different phones comparisons).

In their methodology section they show their calculations and it calls out two things to me:

(1) They also used the assumption that a phone takes one full charge per day when estimating their annual costs.

(2) Galaxy SIII consumed 12.3 watt-hours to charge, taking 2hr 26 mins. iPhone 5 consumed 9.5 watt hours to charge taking 1hr 50 mins.

Awesome. That looks much more believable than whatever brought me to the earlier 1 kilowatt-hours assumption. I’ll take the higher value. Without a more universal profile of telephone usage and power consumption, it will do for such an inexact approach.

So, we are operating on the assumption that on average charging a phone takes 12.3 watt-hours (or 0.0123 Kilowatt-hours), and that it takes 2.5 to 5 miles (or 4 to 8 km) walking to charge the phone. That loosely translates in to a -range of 1.5 to 3 watt-hours of electricity generated per hour of walking. With that kind of charge rate, you are looking around 7 to 8 **million** people to generate enough electricity to charge an electric carover a distance of 100 miles.

Okay, now that looks much more realistic. If the earlier assumptions had proven true, then using humankind as a renewable energy source would be discussed at every climate change / carbon footprint forum. And I’m not even going to bother with the math to generate Gigawatts since it clearly stops being viable.

But can I still build a perpetual motion machine out of it?

Imagine my interest when the next source that catches my eye is entitled:

## BlueBiped: A human-like walking robot that requires no power source

The basis of this robot walking is that the robot requires a downward slope because it is ultimately powered by gravity. Since no infinite downward slop is available to us, Slinky powered perpetual motion is off the table.

Interesting diversion, though.

Figuring out how much electricity is needed to simulate walking is not as easy. There are a couple of cool robotics researchers who I could probably contact, but I’m not patient like that. So, I’ll try something else.

Plenty of kids toys today can walk around. And they run on AA batteries. This source indicates that a standard Energizer battery capacity is around 4.2 watt-hours. The article is not date stamped so I dont know how current that number is. We all know new and improved longer lasting batteries come out at fairly regular intervals. Date stamp your internet content people!

4.2 watt-hours capacity in a AA battery. So to charge a Galaxy SIII, it takes a little under three AA batteries worth of electricity.

Okay, this source has specs on a cool looking robosaur.

It states the robosaur is powered by 8x AA batteries (plus 3x AA batteries to power the remote controller). And this is enough to power the toy for 6 hours.

So 1x AA battery gives 4.2 watt-hours x 8 batteries required equals 33.6 watt-hours for 6 hours play. 33.6/6 = 5.6 watt-hours. Of course, walking only consumes a percentage of that watt-hour consumption, but lacking more accurate data, we can only make assumptions as to that percentage.

Applied to our objective of perpetual motion, we established earlier that a human walking generates somewhere around 1.5 to 3 watt-hours of electricity from 1 hour of walking.

Our Robosaur consumes 5.6 watt-hours per hour. So the energy required for our Robosaur walking would need to only consume around half of the battery charge to even begin to be viable. And based on my admittedly limited understanding of robotics, mechanical motion does tend to consume the bulk of the energy needs on robots like this. I would still be interested to see how economically in terms of electricity consumption robotic walking could potentially be sustained by. I wonder just how small the gap becomes between our technology’s level of sophistication to generate electricity vs our economy in our technology’s rate of electrical consumption. Science tells us that perpetual motion machines are impossible because they would have to violate the first or second laws of thermodynamics. But science also considers other ideas like *faster than light travel* or *shrinking* or *making a visible object truly invisible* are also theoretically impossible. That doesn’t mean there aren’t people out there trying to prove science wrong.

But how are my initial figures from the red section so insanely off target? First, let this be a lesson on using the internet as a source of truth. Verify, verify and verify your information.

**Variable 1 – how much electricity does it take to power New York? **

This source suggests 11,000 Megawatt-hours consumed daily (as at April 2012). x 365 gives a little over 4 Gigawatt-hours, so with a few assumptions around growth, the 5Gigawatt-hour figure looks reasonable.

**Variable 2 – how much electricity is needed to power an iPhone?**

Here is where things went astray. The 1kWh was sourced from this article in Forbes, which states;

Pop quiz: how much electricity (to the closest 10 kilowatt-hour) does it take to power your iPhone or **Android** for a year? 1 kWh? 10 kWh? Or 100 kwh? The answer: 1 kWh.

However, compared to the much more scientific approach with supporting methodology provided by lifehacker, we established that the iPhone 5 required 9.5 watt-hours to fully charge, or 0.0095 Kilowatt-hours. Over a year, that is closer to 3.5 Kilowatt-hour than 1kWh.

**But**, given that the question provides was looking for a closest answer from 1, 10 or 100 kWh, in that picklist, 1kWh is the closest option to 3.5 kWh. So strictly speaking, the statement made in Forbes is factually correct, and I misread the context. Again, thats why you verify, verify, verify.

Also, I misapplied that 1kWh by multiplying it by 24 to get a daily consumption rate. The methodology again provided by lifehacker.com shows that assuming one full charge per day, only 9.5 to 12.3 watt hours are required daily. Which multiplied by 365 gives a range of 3.46 kWh per year to 4.48 kWh per year, which is around half of 1% of the 8.76 megawatt-hours I reached last time. (Another lesson, don’t drink and math!)

**Variable 3 – how much electricity is generated by walking?**

Okay, revisiting this, it seems I misread another article. This article from mirror.co.uk suggests a 30 minute jog could charge your phone for 3 hours with a new device. Not for a full recharge, which is what I assumed earlier in the red text section. That gives credibility to the other device that suggested a 2.5-5 mile walk needed to give a full charge. Remember we are comparing walking jogging, and since the devices work on motion as opposed to speed or distance, and that with running you cover more distance per step. So we aren’t comparing apples and apples here.

**Updated result for how many people would it take to power New York?**

Given – walking generates 1.5 – 3 watt-hours per hour of walking (or 0.015 to 0.03 Kilowatt-hours)..

And – New York consumes at least 11,000 Megawatt-hours daily. Though perhaps we should assuming the growth rate behind the 5 Gigawatt-hour consumption figure, which would put that up to around 13,000 Megawatt-hours daily (or 13 million Kilowatt hours).

Then – we are talking about between 4.3 and 8.7 million people taking a 1 hour daily walk to generate enough electricity to power New York city.

Given that inefficient rate, it becomes easier to see why the idea of developing technology and the infrastructure needed to be able to transfer energy captured in that manner, why we aren’t trying to use this approach to power entire cities.

Using such devices to charge our phones can only reduce our overall energy consumption and reliance on fossil fuels, so it isn’t a bad thing. But it isn’t a solution. We still need to look in to other renewable energy sources if we want to eventually remove today’s society’s dependance on non-renewable fuel sources.

If 20% of the Earth’s population were generating 1.5-3 watt-hours per day (7.3 billion x 20% x 1.5 to 3 watt-hours) = between 2.19 and 4.38 billion watt-hours – or between 2.19 and 4.38 gigawatt-hours. That isn’t a lot in terms of global consumption. This wikipedia article calculates average power per capita (watts per person).

Compare the 1.5-3 hours generated by walking for an hour against some of these average power per capita (watts per person) rates:

Global Average: 313 (watts per person)

United States: 1683 (watts per person)

China: 458 (watts per person)

Australia: 1144

India: 90

Ireland: 648

New Zealand: 985

Russia: 808

Sierra Leone: 1

Though perhaps the clearest learning coming from this exercise was to always, always verify your data.