(there is an edit at the bottom of this post)

Due to some commentary on my last post, I decided to calculate how much you pay for fuel when you fly.

While kilos lifted and moved might be a small fraction of the total cost, it is still a fraction of the total cost. But what fraction?

Wikipedia says that *new* aircraft consume about 3 L / 100 km for only the passenger, not the luggage. Thus, per passenger, we're looking at 30 cc per km. Let's assume an average weight of 72 kg per passenger. Now we've got .42 cc / (km * kg). Gas prices are tough, because they're over $6 in Europe but only $2.50 in the states (airplane fuel costs nearly the same amount as car fuel, I don't have a great source on this). We'll assume gas is $3.78 a gallon, or 1$ for 10^-3 cc. So fuel is .42 cc / (km * kg) * 1 $ / (10^3 cc), so the conversion between dollars and km * kg is:

4.2 * 10^-4 dollars / (km * kg).

NYC is about 6,000 km from Amsterdam. 20 kg * 6,000 km * 4.2 * 10^-4 $ / (km * kg) comes to (drum roll):

50$ (EDIT: This is overstated by a factor of 10 - see below)

I looked at ticket prices for a flight from NYC to Amsterdam in February. With tax, a round trip ticket is about $800. For 80 kg of load, that is $200 each way, or $400. Fuel is about *half* the price of your ticket. This meshes with what was presented in our 6.UAT lecture on estimation...wow, that class actually came in handy for something.

One further assumption is required for the above to be valid: burned fuel must scale linearly with weight. We'll leave that one to the reader.

If fuel is indeed half the cost of a plane ticket, why does a 60 kg person with 5 kg of luggage pay the same $800 as an 80 kg person with 20 kg of luggage? The 65 kg of weight should pay less than $700.

And why does going to a XXX2 matinee cost the same amount as going to see The Dark Knight?

EDIT: loyal reader asc has pointed out that the fuel efficiency should include the plane's weight. If we look at the weight of an A380, we see the plane is about 275,000 kg when empty. 555 passengers at 90 kg apiece (72 kg weight plus 18 kg luggage) weigh 50,000 kg. Including other weight (seats, fuel, etc.), it seems reasonable that the passengers account for at least 10% of the total weight. If we assume 50% of ticket price is fuel, we're looking at more than 5% of a ticket's price being fuel to move you and your stuff. Thus we're down to the Hamilton range:

Though this is hazy economics range, I maintain airlines could still turn a profit here. We know that $15 changes in ticket price have large effects on consumer behavior. Smaller customers would be more likely to fly an airline that charged by gross weight, meaning a charge-per-weight airline would be taking the smaller customers from its competitors, and leaving them with the larger (more expensive) ones. Furthermore, I haven't even mentioned non-financial incentives. Wouldn't you be happy flying an airline that charged people based on the amount of fuel they burn?

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## 5 comments:

I salute your estimation skills. But it looks to me like >3L/100km cost includes the cost of moving the weight of the plane -- that is, calculated cost per passenger = ((weight per passenger * number passengers) + weight of plane) * cost per pound / number of passengers. Still doesn't seem fairer to straight up divide by weight of passengers.

Example: using your 65kg vs 80kg -- I'm betting a plane is at least 10000kg (but I am totally making that number up), so the cost of moving light person by herself is 10065*n, cost of moving heavy person by herself is 10080*n, cost of moving both separately is 20145*n so if you're gonna split their shared flight proportional to weight, split it 10065/20145:10080/20145 which is 50.04:49.96, so one pays $800.60 and the other pays $799.40.

Except that there's now also the costs associated with weighing people as they check in and the fact that that's gonna make your checkin lines move slower because you'll still have to weigh luggage separately to make sure it's within the bounds of what your luggage handlers can/are willing to cope with. Or maybe you should be doing it at security instead, because it's trivial to sneak extra pounds past checkin (just have your buddy wait with your heavy backpack), but of course now your security procedure is different from other airlines; maybe you should be doing it at boarding, but now boarding takes longer because your personnel have to have a cash register at the gate...

Have to run to yoga now so I'm not gonna check my math.

re "wouldn't you be happy flying an airline..."

seriously? the last thing i want when packing + boarding an airplane is that additional dimension of complication. plus (to make a gross but probably fairly accurate generalization) show me a girl who says she's happy about standing on a scale in public and i will show you a girl who is lying to you.

p.s. i still think http://www.coinfacts.com/quarter_dollars/washington_quarter_dollars/1932-D_Quarter_Reverse.jpg

(and am vaguely annoyed that blogger won't let me embed that)

You wouldn't want to post an image of a 1932 D quarter, those contain silver and are worth a few dollars.

heh. point for you.

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