How much cheaper would an airplane ticket be if we weren’t overweight?

Posted on May 25, 2016

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In America,

  • More than 2 in 3 adults are considered to be overweight or obese.
  • More than 1 in 3 adults are considered to be obese. (So we’ll say 1/3 obese, 1/3 overweight.)

Body Mass Index is commonly used to assess overweight or obese.

  • 25 to 29 is overweight
  • 30 and up is obese

Extreme obesity is classified at a BMI of 40 and over.

BMI = (bodyweight in kilograms) / (height in meters^2)

We’ll say the median overweight person has a BMI in the middle, 27.5, and the median obese person has a BMI of 35. So we’ll say half of obese are lower than 35; half are higher.

Average U.S. adult height is 5’6″ or 1.68 meters.

Overweight people:

27.5 = bodyweight / (1.68^2)

(1.68^2) * 27.5 = 78 kilograms

The average overweight person in America has a bodyweight of 78 kilograms. 171 pounds.

Obese people:

35 = bodyweight / (1.68^2)

(1.68^2) * 35 = 99 kilograms.

The average obese person in America has a bodyweight of 99 kilograms. 217 pounds.

Let’s say we could wave a magic wand and get all these people with weight to lose down to a BMI of 22.5, right in the middle of what we consider the healthiest BMI range.

Adults:

22.5 = bodyweight / (1.68^2)

(1.68^2) * 22.5 = 64 kilograms or 141 pounds

Meaning:

Overweight people => 171 pounds – 141 pounds = 30 pounds

Obese people => 217 pounds – 141 pounds = 76 pounds

The average overweight person is unnecessarily carrying around 30 extra pounds, while the average obese person has 76. This is unnecessary weight a plane has to carry on a flight.

Alright, we’re going to use a Boeing 737 as our example flight, as this is the most produced aircraft for commercial purposes of all time, and still in heavy production.

The 737 has a subgroup of versions. The 600, 700, 800, 900. We’ll use the 700, as Southwest’s fleet is 67% this version. The passenger load is 143 people for a Southwest 700. Call it 147 with a four person crew.

147 * 1/3 = 49 overweight people on the flight

147 * 1/3 = 49 obese people on the flight

(and we’ll say the remaining third are normal weight)

Then,

49 * 30 pounds per overweight person = 1470 pounds

49 * 76 pounds per obese person = 3724 pounds

1470 + 3724 = 5194 extra pounds we can get rid of

In aerospace engineering there is something called fuel fraction. Whatever the mass we want to get somewhere, we must have a certain amount of fuel. If we want to transport 70 pounds, then we may need 30 pounds of fuel to get that 70 pounds somewhere. The fuel fraction would then be 100 total pounds / 30 pounds of which are fuel = 30%.

A ton of variables influence this fraction. Efficiency of the engines and aerodynamics being ones most of us non-aerospace people already have an intuition for. Meaning different planes have different fractions. For airliners, it can go between ~15% to ~50%. A big range.

To pin down the Boeing 737-700’s fraction, we can look at its flight planning and performance manual.

  • The maximum weight the aircraft can be without any fuel is 120,500 pounds.
  • The maximum weight the aircraft can be once it begins taxiing is 155,000 pounds
  • 155,000 – 120,500 = 34,500 pounds of fuel

Meaning,

34,500 (fuel weight) / 155,000 (total weight) = 22%

Our fuel fraction is 22%.

If we diminish the weight of the aircraft by 5194 pounds, we can,

5194 * 0.22 = 1143

Save 1143 pounds of fuel. (Assuming the flight is maximally filled every time. Not true, but makes things simpler for our purposes here.)

Jet fuel prices, like oil prices, jump around a ton. In 2008, when jet fuel was at its peakit was $3.89 per gallon.

1143 pounds of fuel equals ~156 gallons. 

156 gallons * $3.89 = $607

Now if we spread this out amongst our one flight,

$607 / 143 passengers = $4.24 per person

Or $8.48 on a roundtrip flight. It’s something. Oil has dropped a bunch recently, so our savings are currently less than this. As oil inevitably go back up, savings will approach and surpass this number.

However, if we spread this out amongst an airline,

  • Southwest owns 463 Boeing 737-700s
  • Each aircraft flies an average of 6 times per day

$607 saved per flight * 463 aircrafts * 6 flights per aircraft per day * 365 days = $615,479,790 per year

This does assume every flight is full, which it’s not, but we would get some more savings elsewhere. Less food would be needed on board, people wouldn’t use the bathroom as much (e.g. diabetics need to drink and pee more often), and the above doesn’t include Southwest’s 229 other planes!

We can see why airlines obsess over mass. Why Spirit airlines charges so much for checking a bag. Why when oil soared airlines were obsessing over literal specks of dirt! Why planes are de-iced not for temperature reasons, but because ice adds mass. According to an aerospace engineer I spoke to, “it can be hundreds of pounds.” We’re talking way more than hundreds of pounds with reducing people’s overweightness.

Credit: Design and Optimization of Lithium-Ion Batteries for Electric-Vehicle Applications ( https://deepblue.lib.umich.edu/bitstream/handle/2027.42/107299/courtrun_1.pdf?sequence=1 )

Credit: Design and Optimization of Lithium-Ion Batteries for Electric-Vehicle Applications
( https://deepblue.lib.umich.edu/bitstream/handle/2027.42/107299/courtrun_1.pdf?sequence=1 )

 

This is a different way to look at weight loss. All the indirect benefits. (You may also have less anger towards Spirit airlines now too.) While price wise we wouldn’t save a whole lot here on an individual scale, the airline industry would be grateful.

While you may not love them, in exchange for your generosity they’d have at least 5194 pounds per flight they could play around with. Or $607 they could play around with.

A row of seats is often four people. If a ticket was $150, the airline could take a row of seats out of the plane, and make the same amount of money, all while the customers enjoyed a little more movement. If you fly enough, you know how much a little difference matters. Yeah, yeah, airlines are greedy. Some would take the extra profit. But there are others like Virgin, who might in the long run make more money doing this, due to being more comfortable.

The other benefit is the climate change / energy usage one.

156 gallons per flight * 463 aircrafts * 6 flights per aircraft per day * 365 days = 158,179,320 gallons of fuel saved per year

For one type of plane…on one airline.

There were 8.5 million flights in 2015. The United States is a huge customer of commercial flight in the world, but it’s not the only. Assuming the rest of the world is on pace to be as overweight as us,

156 gallons * 8.5 million = 1.32 billions of gallons of fuel

Translates to 30.5 million barrels of oil per year. In the United States alone, we use close to 7 billion barrels of oil per year. So this could save us 0.004 of the United States’ yearly oil use. It’s a gigantic amount of barrels to save, but damn do we use a lot of barrels!

Fortunately, losing weight has reverberations elsewhere to help close this gap some.

“But the future” (electric aircrafts)

The above may provide a little extra kick in the ass for some to help lose weight. Having something be about more than yourself can provide extra incentive.

On the flip side, some may think “eh, we’ll figure this out through innovation. For example, in this case it won’t be long until electric planes.” Off to making your seat neighbor miserable with your wider-than-the seat-body you go.

-> My last flight. Two 260 pound+ guys sitting next to one another, as I’m getting in to sit next to them…

“They really make these seats too small.”

Or, you know, you’ve made your body too big. And think about it in the above context: asking an airline to make bigger seats (have less customers) as you increase its cost of business with your larger body is really not going to happen. Seats are going to get smaller and smaller, until the government perhaps intervenes over safety concerns, in which prices will then increase.

Electric planes, and cars, are more sensitive to weight.

This is a big reason Tesla’s Model S has flush door handles.

Credit: CarAndDriver.com

Credit: CarAndDriver.com

Because the battery is a hindrance, you try to make everything else as optimized as possible. By minimizing air resistance, you get more out of the same battery. It’s also why Tesla uses aluminum for their body, which is lighter than steel, and was very unusual when Tesla started making cars. It’s still not common.

Another benefit of gasoline is during a flight you dispose of the gas, so as you get say halfway through a flight, you’re lighter than you were at the beginning. Not true with battery powered flight. (Fuel cells are like gas in this regard, though are still heavy as hell and have all sorts of other issues.)

We’re currently doing everything we can to get as much energy out of each battery cell as we can. What’s commonly referred to as energy density (technically called specific energy). Current lithium-ion batteries get something like 200 watt hours per kilogram.

According to Elon Musk, Mr. Electric, once we get to 400 Wh / kg –Tesla is decently into the 200s by this point we’re in the realm of electric flight being feasible. According to the MIT guy researching them, MIT thinks it’s way higher than that. Musk thinks we need about another 1.5 to 2 fold improvement, MIT, and others, think it’s more like 10.

One reason for the potential discrepancy is Musk would basically get rid of the tail of the plane. Again, to save weight.

Perhaps the easiest way to think of this is fossil fuels are the result of millions of years of compressing the fuel. They have a very, very good energy density. Something like 60 times that of the best lithium-ion battery. Which is why this physicist doesn’t expect batteries to approximate the energy density of fossil fuels, ever.

This is not exponential growth. This is not Moore’s law.

lithium ion battery energy density by year

Green line is what we’re concerned with.

And we’ve been using batteries for a long time.

battery history energy density by years and types

Yellow bar is what we’re looking at. (Credit: http://www.hybridcars.com/wp-content/uploads/2013/07/battery_history.jpg )

-> There is another type called a lithium-air battery. It has the potential to rival the energy density of gasoline. It’s quoted many different times as being at least 10 to 20 years away -it seems very hard- and is apparently the theoretical limit of what batteries can provide energy density wise. However, it too would not dispose of its material during flight. It still wouldn’t be as good as gasoline. None of the curves match the dot:

Meaning we need more energy to get the same distance. More energy is proportional to more heat. CO2 not required.

And note the difference between theoretical capabilities and practical in the other chart above. (And who knows how much a more complex battery will cost. Complexity usually = more money.) Lead acid has been around over 150 years. We still haven’t come near the theoretical limit of it, or any other. Nor do we have any experience trying to cool a battery system operating with the power output of current aircrafts. (If it gets too hot, the lifespan of the battery goes down quickly.) More reason why some don’t think it’s possible to match gasoline tick for tack.

So, because when using batteries you end up needing more mass per unit of energy drawn than when using gasoline, that means the mass of everything else is even more important.

With a car being only at a 4 percent fuel fraction, compared to the 22% we found for our Boeing 737-800 (which we can see is low for a jet), it might not even be worth worrying whether someone losing 30 pounds matters. (Though spread out across the world of drivers, it only helps.)

However, for the Tesla Model S:

Total mass = ~4700 pounds

Battery mass = 1200 pounds

1200 / 4700 = 26%

We’ve taken a mode of transportation not very sensitive to mass, and made it as sensitive as a Boeing 737 i.e. the mass of the “fuel” doing the propelling becomes similar. Where did Tesla get the idea for using a lighter metal like aluminum? From the more mass sensitive industry of aerospace. All those overweight and obese people will matter more in the foreseeable future, not less.

And if you’re thinking “Ok, well it’ll all be solar powered by then though!” Sure, but solar powered machinery still has significant problems for future application. CO2 not required.

If you want a detailed look at electric flight, see here.

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