The Physics of FitFlix

Ooooh, you knew this post was inevitable. Any science blog has to have one of these posts.

In our age of technology and rising rates of obesity, the question is often pondered as to how can we get people moving when they can just sit on the couch and watch TV? It’s a rather trying question that I’m sure doctors, fitness specialists, and game developers have been working on for a while. Go on the app store and you can find many Couch to 5k applications. I actually use one myself called Zombies, Run! I like Zombies, Run! because it sorta makes the running worth it. There’s a podcast playing behind you and that makes the run a little more bearable than hearing the weezing of your scrawny pale body trying to move more than 2mph. So now there’s this post flying around on the internet about what if you had a bicycle that was hooked up to your computer and you could use the internet to maybe watch Netflix if you could pedal the bicycle to power your machine. Seems fairly plausible, right? Let’s find out.

So how are we going to evaluate whether or not this is possible? Well, if you go through my past of science posts, you’ll see that there’s a common principle between them all (all two of em): Conservation of Energy. It feels bad that I keep coming back to this well but it’s one of the guiding principles when it comes to problems like this. So what are we looking at?

The first thing we want to do is establish how much energy would be necessary to power your computer so that you may watch Netflix (or your service of choice). And this is hard to pin down. Well, let’s start with the basics. We want to know how much energy your computer and modem use. According to MichaelBlueJay a desktop computer uses “about 65 to 250 Watts” and then we need to add another “20-40 Watts” for the (LCD) monitor. Griffith University seems to agree with the range somewhat, shifting the lower bound by 20 Watts. These are rather large ranges, and rightly so. The factors that go into how much power your computer consumes are the components and peripherals. So let’s just use the worst-case numbers. If you can do it for the worst-case, you can probably do it for the best-case. So we’re dealing with 290 Watts (250 Watts for the desktop computer, and 40 Watts for the monitor). Now we need the modem because that’s how your computer will be connected to the internet. And this is where I run into trouble. Because I usually don’t go beyond page 2 of Google when looking for sources. MakeItCheaper sounds like some random blog and it says 2-20 Watts (but the average is around 6 Watts). So I’ll continue with my worst-case scenario calculation but we may want to come back later and run the numbers again. So, the final total: 310 Watts.

A Watt is a Joule per second. Which means that every second we must supply 310 Joules to the bicycle. We also have to assume that every Joule we supply to the bicycle is sent to the computer and modem without any loss due to resistance in the wire… but hey, we’re working with idealized systems here. So how do we determine how much energy we’re supplying to the bicycle. If your exercise bicycle is anything like mine, it only has one wheel, or at least one main wheel. And if we just look at that one wheel, we have our problem solved. There’s an equation we know for the energy of a rotating object: Hyperphysics to the rescue.

Untitled

Normally, if we were considering a rolling wheel we’d have to consider its rotational kinetic energy AND its translational kinetic energy. But exercise bicycles are notoriously stationary, so we only need to worry about rotational kinetic energy. Now we get to the I and the ω. What do these two symbols mean?

I denotes the object’s moment of inertia. You can think of it like resistance to rolling. It’s the rotational analogue to mass, resistance to external forces. The moment of inertia of an object depends on some factors like mass distribution and how the object is rotating. It is for this reason that the moment of inertia is better described as a tensor, but I won’t get into that. Just know that it’s easier to rotate some objects (like a wheel) about certain axes compared to others axes. The symbol ω represents the angular velocity, or how fast the object is rotating.

We’ll begin with the angular velocity, mostly because I want to make an assumption on it. I want to assume a constant angular velocity comparable to what a user may do. The question you want to ask yourself now is: why? Well I do this for two reasons. The first is that it simplifies the number of variables that we’re playing with from three to two (moment of inertia will have two components, plus the angular velocity). And the second reason is because I want to simulate real life as much as I can. And I find it highly unlikely that the rider will go race pace while they watch their show. So I plan to use a nice, leisurely pace for my calculations. On the exercise bicycle that we have here, I can do about 60-70 RPM comfortably. Let’s split the difference and say that when you’re biking you’ll do an average of 65 RPM for the duration of your show. Convert that that RPS (rotations per second) and we get 1.0833 RPS. Not quite done yet though, as we need to convert that rotations per second into radians per second. That’s not difficult though. 1 rotation per second is 2π radians per second. So at the end of it all, our angular velocity is going to be: 6.807 radians per second.

For the sake of this calculation, I’m going to imagine the wheel of the bicycle being a thin hoop (not terribly unrealistic I hope). The moment of inertia of a thin hoop (again from Hyperphysics) rotating about its center axis is:

Untitled

With M being the mass of the hoop and R being its radius. This is where we have room to play with numbers. I have an infinite number of moments of inertia to choose from, and I have to narrow it down to one realistic one we can use as a baseline. But since we’re going with the whole “bicycle” motif, let’s use a standard bike wheel size. Let’s use the racing wheel sizes here. According the wikipedia, a standard size for the rim of the wheel is 622 mm. But that’s a diameter, not a radius, so chop that number and half and we get a 311 mm radius for our wheel. That’s .311 meters. I convert everything to these base units because I want the kinetic energy equation to yield Joules without any conversion. Now we’re pretty much done. I’ll solve for the mass of the wheel, and we’ll just guess as to whether or not you believe you could push that wheel that fast.

So, what are we doing? We’re going to solve our kinetic energy equation for the mass of the wheel.

Untitled

We know that we must supply 310 Joules per second, and we’re going to use a leisurely pace of 1.0833 rotations per second as our angular velocity. We’re going to be using a wheel of radius 0.311 meters. So let’s plug in our numbers and see what we get.

Untitled

That 69.1719 is the mass in kilograms. To put that into perspective, that’s about the mass of a healthy adult human male. That’s far more massive than any wheel you’ve ever used in a bicycle, so the chances are that you being able to rotate that wheel fast enough are probably slim.

But that was a worst-case scenario. Let’s try a best-case scenario! 80 Watts for the desktop (using Griffith University source numbers) and 20 Watts for the monitor. Oh, and let’s use 6 Watts for the modem (the average power for modems cited above). This gives us 106 Watts of power that we must provide, or 106 Joules per second.

Untitled

23.6523 kilograms isn’t that bad. That’s close to 50 pounds. That’s still quite massive though. That weight is comparable to… maybe a large dog? My chalkboard weighs 60 pounds so slightly less than that. Anyway I still think that’s unreasonable. That’s bench press material… for me (I am not a strong person).

We see that we lose a lot of energy by treating the computer and the monitor separately. What if we instead used a laptop? Using the MichaelBlueJay numbers, a laptop uses 15 Watts in its best-case scenario. Tack on another 6 Watts for the modem and we get 21 Watts. Plugging in those numbers, we get:

Untitled

4.686-ish kilograms, about 10 pounds. Which isn’t bad at all. 10 pounds is about how much my cat weighs. So I think this one is reasonable. I’d say that the best-case scenario for the laptop works fine. But I don’t like judging things on their best-case scenario. How about we use the worst-case scenario for a laptop. How about we use that 60 Watts for the laptop plus the 6 Watts for the modem.

Untitled

That’s about thirty pounds or a little less than the weight of a 32-pack of water bottles. Not sure if that’s reasonable. But I think somewhere in the middle we can get a feasible case for FitFlix working on your laptop. Especially since when I was going 70 RPM the machine told me that I was producing some 80 Watts.

So where do we stand? FitFlix doesn’t work for desktop computers. It’s plausible that it could work for laptops. What about TVs? Simple answer to that: do TVs or more specifically: do Smart TVs (requiring that internet connection) consume comparable power to a laptop? Well according to RTINGS it’s 35 Watts for my 36″ LED TV. If it were instead an LCD TV, MichaelBlueJay would say around 100 Watts. So the answer really depends on your type of TV. But for my TV at least, Fitflix would work out.

Of course, we’re all missing the obvious solutions of using a phone or table, which use vastly less power. So you could definitely power your phone and Fitflix. Depending on your TV you could watch TV and Fitflix. And it’s plausible that you could use your laptop and Fitflix. However, I find it unlikely that you could desktop computer and Fitflix.

That’s just my take on it. If I’ve made any mistakes in the physics or the math or you have some problem with my method, or maybe you have a better method, please let me know. I’m more than welcome to criticism. That’s all for tonight though. Thanks for reading.

Artemis Hunt

 

Advertisements
The Physics of FitFlix

What do you think?

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s