Calories Burnt by Running Harvard Stadium

Harvard Stadium. For decades, masochistic people with a desire to be extremely fit have run up the "seats" of Harvard Stadium. The November Project was pretty much born there. Some Harvard varsity athletes run it for extra endurance training. People bring their dogs, but it's so difficult the dogs say, "screw this noise" and go lie down. It's a beast of a run. You want ripped abs? Abs are made in the kitchen, eat less calories than you expend in a day. Want to earn a few extra calories? Run a stadium. Abs can also be made at the stadium.

Harvard Students running the Stadium. Source.

Harvard Students running the Stadium. Source.

Current articles suggest a normal 180 lbs. person will expend 9 calories per minute while doing stairs. We are not normal people. We are beasts. We are animals. Metrics for mere humans aren't for us. Let's do a serious math review so we know exactly how wrong this number is.

At the end I point out why stadiums are far better than running, even if they burn similar calories. As usual, skip to the end to read the important parts if you don't like details.

Maths!

1. Each stadium "step" is 15 inches, or about 0.38 meters.

2. There are 31 steps per section. If you don't cheat, that is. Most people cheat and skip the bottom-most and top-most one because they aren't wide. If you skip both of these, you are eliminating 74 whole steps, or 2.3 whole sections. This is nearly 7% of the workout. You are depriving the world of 7% of the exercise that's supposed to make you beautifully buff. Run all the steps.

3. There are 37 sections.

4. Each step traverses 30 inches horizontally.

5. We are using my weight. Last weigh-in I was 215 lbs, or slightly less than 100kg (it's 98, but much like 5' 10" people like to say they are 6' tall, I like to say I am 100kg). There is a chart at the bottom to adjust for other weights.

Part 1: Going Up!

 0.38 \frac{m}{step} \cdot 31 \frac{steps}{section} \cdot 37 \, sections = 437m

Hokay, so, 37 sections will net you 437m of vertical distance. Now it's time to figure out how much energy this is! We use the standard mass*gravity*height for this, using my mass. I'm aware that not everyone is a 100kg monster, so we'll have a scale farther on down.

 100kg \cdot 9.8 \frac{m}{s^2} \cdot 437m = 430KJ

Remember that 1 calorie equals 4.18 joules, but the calories we talk about with weight gain, etc., are actually kilocalories. So we have 430kj, and we need kilocalories.

430KJ / 4.18 = 102.9\, kilocalories

103 (kilo)calories?!? "Oh no!" you say, "I do all that work and only burn 103 calories? What a waste!" Now hold up there a second, we aren't done yet. We can assume a roughly 20% efficiency of turning our food into work output. So let's multiply this by 5.

103 \cdot 5 = 515 \, calories

So for a 100kg fatty like myself, the vertical distance alone from doing one stadium is about 515 calories.

The flats!

I measured the flat areas to be 30 inches, or about 0.762m. How far is an entire stadium? Well, first, we need to state that one of those 31 steps isn't traversed, cause it's the last step and we only do the vertical part before going back down. So we have 30 stairs per section that we move on the horizontal part of.

 30 \frac{steps}{section} \cdot 0.762 \frac{m}{step} \cdot 37 \, sections = 843m

Let's include the distance around the stadium, which we know to be about 250-300 meters (100 yard field + out of bounds areas traversed twice plus the 75 or so yards for the width plus out-of-bounds). So let's guess here and just call it 1100m, or 1.1km.

A 100kg man burns about 100 calories per km. See how well the metric system works? So I burn 110 calories doing the horizontal section of the steps (ie going forward as I go up)

We are now at 625 calories for 100kg person running a stadium, 515 from going up, and 110 from going forward.

Stepping Down

Okay. This is complicated. We are going to take a mulligan here and reference a pubmed medical journal article. That's right, when I mulligan, it's by referencing peer-reviewed science.

This particular article says going down steps takes roughly 1/3 the energy as going up them. Let's be a bit more conservative and assume we are in better shape than the average person, and say it takes 1/4 the energy. This might be false, but I'd rather come in slightly modest than slightly exaggerating when it comes to my calorie expenditure on a stadium.

515 calories for a 100kg man going up the stadium steps. One quarter of this is about 130 calories.

Summing It All Up, and Burn Rate

 515+110+130 = 755 \frac{calories}{stadium}

Okay, that's a lot. Now on a good day, I run the stadium in 35 minutes (yes, I'm slow, but I'm also 100kg. Also I'm recovering from whooping cough and a sprained knee, so right now I'm at more like 45 minutes). My average burn rate is 21 calories per minute. Compared to an estimated 9-11 for a normal person taking the stairs. So pretty much you're doubling the work rate of a normal person doing normal steps.

Comparison to Running:

To burn 750 calories from running, I need to run 7.5km. This is 4.66 miles. To have an equal calorie burn-rate, I need to run 7.5 minute miles. Which is easy for me.

In other words, I burn as many calories by running on the flat ground as I do on the stadium.

In fact, running is much easier for me than the stadium. Are we missing something? Probably. While doing stadiums, you are using far more muscle groups that while running, and you are likely engaging a lot more core. In other words, the numbers I've calculated here are a pure energetic viewpoint. It doesn't account for wasted energy/motion that is much more likely in the uphill push that is a stadium. Finally, stadiums actually work your muscles. Running, less so.

So What? The Difference Lay in the Details

Hokay. So. Stadium vs. running. Both burn calories. But where do these calories come from? Turns out when you do resistance training, IE take stadium steps, you are working your muscles a lot more than endurance training.

This is important. If you are trying to lean out, IE lose fat, running doesn't do a great job. When running, you are likely to lose muscle mass to produce some of those calories, or to burn them muscles afterwards when your body is starved for energy. When doing stadiums, you need those muscles, and your body preserves them.

This isn't random bullshit. There are solid scientific studies that show that a diet + resistance training (stadiums, lifting) results in loss of fat, but a diet + endurance (running) results in loss of fat and muscle. In other words, run all you want, but you're just gonna make yourself skinny fat. If you want to look good naked, you have to push iron, do body weight exercises, sprint, and/or do stadiums and hills.

Short story: you want abs for the summer? Run stadiums, lift weights, watch your calories.

More Times and Maths!

Here the math works out pretty well. If you run a 35 minute stadium, you have to run 5 miles in 35 minutes for equal calorie burn, or 7 minute miles. So a 30 minute stadium means 6 minute miles for 30 minutes, and a 25 minute stadium means 5 minute miles for 25 minutes for equal calories. Here is where the difference is. The fittest people I know can't run a 5 minute mile, much less five in a rown, but they can easily run 25 minute stadiums. Thanks for Adnan Khera for making me think about it that way!

Charts!

Okay, as promised, here is a chart for stadiums and calories burnt! Remember, these are probably an under-estimate!

For Normal Sized People

Now for some handy-dandy charts!

Don't you feel badass now?

Calories burnt from running a stadium (I made this!)

Now, why did I leave off people under 100 lbs.? Cause no one under 100 lbs should be counting calories. They are either children or need to eat several more sandwiches. And why would I go up to 280? Cause Harvard football runs this thing, and many of those guys make me look tiny.

That's all. Thanks for reading!

- Jason Munster

Tesla's Powerwall - Not Economical

Tesla Powerwall

I'm gonna open by saying that I really like Tesla's powerpack. Technology isn't pushed past the bleeding edge without loss-leaders pioneering. That being said, the numbers, as usual, don't lie. On a per-unit-energy cost basis, these things aren't economic in most of the US. Once you consider the externalities, however, the overall benefit does make them "profitable." Likely you will see subsidies to internalize these externalities, thus making the powerpack work.

Unless the inverter costs too much. More on that later.

One major implication I haven't seen anyone talk about? Utility companies currently have to pay people with solar panels who produce excess electricity at market rates. They've been trying to get rid of this for years. This technology gives utilities every reason to demand they no longer pay people for their excess produced solar power. This has enormous implications. It's now indefensible to force utilities to buy at market rates the extra power produced by homes with solar. Read more near the bottom.

It's in my weight class!

Tesla's Powerwall next to a car. Small-ish and sleek. 7 inches deep, weighing 220 lbs

What is this Powerwall?

Powerwall is a power pack that you hang on your wall. It costs $3,000 for a 7kwh pack designed for a daily cycle, meaning it's charged and used once per day. This is the cost without installation. Also, this is the cost if you already have solar cells and an inverter. If you want to work with the grid alone, you have to buy an inverter*. Even if you already have solar cells and don't need an inverter, this seems like it's a product designed for the wealthy. Let's look at the math (my favorite part!)

*Inverters. Batteries and solar panels produce DC current, or Direct Current. This means it doesn't change phase. What we use in our homes is Alternating Current or AC. The alternating current means that the positive and negative terminals switch sides of the power plug. In the US, they switch sides 60 times per second. DC means that the terminals do not switch sides. Hence batteries having a + and - terminal, and all your non-battery electronics not having these.

The Maths!

We are going to make some of the rosiest assumptions in the world. First, though, let's get some solid data lines up. Take a peak at NPR's cost of electricity infos.

1. On average, people pay 12 cents per kwh of electricity

2. In Hawaii, they pay 33 cents. We'll use this as a case study.

3. The Northeast and California, two other case studies, pay about 16 cents.

4. The average American uses 900kwh of electricity per month in their home (from eia.gov).

Really rosy assumptions

1. The sun shines for 300 days a year and provides enough electricity to power your house during shining and to fully charge the battery

2. The electricity grid doesn't buy back your excess solar*. If they do have to buy it back, then the economics discussed here don't play out

3. You've already paid for all of your solar installation and you aren't concerned about those costs of that electricity going into this powerpack

4. These things don't degrade over time (extremely rosy assumption)

Hokay!

300 days per year of 7kwh of electricity provided by this beast is:

 300\frac{days}{yr} \cdot 7\frac{kwh}{day} \cdot = 2100 \frac{kwh}{yr}

So 2100 kwh/year. What's that get you in most of the US?

 \$ 0.12 \cdot 2100 = \$ 252

So $252 per year. For a $3000 battery pack. In most of the US, if your solar panels worked perfectly for 300 days a year, it'd take you 12 years to pay back your investment. This is a 6% annualized ROI (Return On Investment). In other words, you'd make more money in the stock market, so it's a bad investment, not even accounting for installation costs and with impractically rosy assumptions, in most of the US.

What about in the Northeast and California, where electricity is $0.16?

 \$ 0.16 \cdot 2100 =\$ 336

Or payback in 9 years. This is an 8% ROI, making it a decent investment.

Let's be realistic, though. In the Northeast, we have storms and winter. Solar panels don't work so great here. We aren't getting 300 cycles per year out of this. We'd be lucky to get 150, making it an 18 year payback, or about a 3% ROI. What about California? They actually might get 300 days of viable sun a year. So in California, you could be break-even.

Now what's the problem here? Normal people don't look for 8% ROI on their home upgrades. They look for 15%. Pretty much they want 3-5 year payback periods. So pretty much, someone has to have a very green outlook on life to buy one of these. Or there have to be subsidies (more later)

Hawaii

Hawaii has sunshine and electricity costs 33 cents. Let's say you've paid off your solar panels in Hawaii.

 \$ 0.33.2 \cdot 2100 =\$ 700

In Hawaii, with our rosy assumptions and no installation cost, the powerpack will pay for itself in 4.25 years, for a whopping 18% return on investment, without any subsidies. There is a viable business model here.

Seriously, someone go start a powerpack/solar panel installation company in Hawaii.

Anywhere else, and these things will need hefty subsidies.

Subsidies

Why would you subsidize these things? Easy. There are only two reliable power sources that can compensate for variability in solar power: hydro and natural gas. Every other power plant takes far too long to spin up to be useful. In other words, nuclear power doesn't stop producing pretty much ever. Coal power takes about a day to get to capacity, so it can't cycle well.
Hydro power is a limited resource. We are pretty much tapped out in the US, and what we have is already being used, so it can't ramp. We'd have to replace what's currently being used with coal, natural gas, or nuclear to use hydro for solar-grid reliability, so that entirely defeats the point.
Natural gas ramps quickly, and we have excess capacity in the US. Natural gas still produces CO2 that spreads globally, and NO2 that spreads locally. NO2 becomes a strong acid when you breath it in, so we have healthcare reasons to reduce it. Thus it might make sense to subsidize these powerpacks to make people more likely to buy them.
Second, this is good tech. It's pretty much where it needs to be in order to make sense to buy in many parts of the country, if you already have solar. Subsidizing it will cause further advancement in battery tech, making it that much more viable in a wider array of applications. Battery tech is one of the things holding us back from so many viable technology applications, so if there is something to subsidize that will more than pay for itself, it is battery tech that is nearly cost-even now.
Some Extra Thoughts on my Rosy Assumptions
*If Solar Companies don't need to buy back Electricity
In most places, if you produce excess electricity that you don't use, the solar company has to buy it back at market rates. So buying this powerpack and storing energy for commercial purposes is useless. All of the economic discussion above is bunk if the grid needs to buy your excess power. In other words, only greenies would buy it.
One important thing to consider. This product makes storing electricity from solar into a break-even cost in any sunny part of the country. Utilities have always hated paying for this. They lose money on it. They've fought legal battles to get it repealed. And now they have the ammunition they need to repeal it, because it's now no longer a burden to consumers to store their excess electricity for later use themselves.
Maybe consider buying utility stocks if you find a company that is over-exposed to paying for home-solar-produced power? I'd tell you to look towards California here.
Inverter Costs
If you don't have solar already, you have to pay for the inverter to make this thing convert DC back to AC for your home. I can't see any reason to do this. The cost differential between peak power and non-peak is about 4-6 cents in most places. Far too little to justify the expense of both an inverter and a powerpack. A gas generator is a better bet if you need reliable power.
Large Scale Efficacy
I'm betting the large-scale systems are more cost-effective. They don't need to be as small and as sleek. And you can have one large inverter for all of the daisy-chained power packs. Who would buy these? Commercial electricity buyers, like stores.
Who wouldn't buy these? Industrial complexes. They make deals directly with electricity companies and pay $0.07 to $0.10 per kwh.
Thanks for reading!
 - Jason Munster