Thursday, July 9, 2015

Gets My Goat

Articles like this never fail to get my goat:
"Your city bus costs more per mile than a first class overseas flight" claims.

But the devil is in the details:

These public transit systems charge a flat cash fare to go one mile within the center of their cities. So if you're using one for a quick trip, you'll pay the following:
New York Subway, Boston T: $2 per mile
Chicago El: $2.25 per mile
Atlanta MARTA: $1.75 per mile
Los Angeles subway: $1.25 per mile
San Francisco MUNI: $1.50 per mile
London Tube: £4, or $5.63 per mile (plus more if you travel beyond the central city)
Paris M├ętro: €1.60, or $2.01 per mile
Cairo metro: 1 Egyptian pound, or 18¢ per mile
Hong Kong MTR: HKD$7.7 or 99¢ per mile

The author assumes that the default fair is for ONE mile of travel. Nevermind who uses that same transit fare to travel much further. UTA's default fare was $2.50 for a bit...but that provided 2.5 hours of travel time, enough to get from one end of the system to the other. Which takes 2.5 hours, and covers (fully) 83.1 miles of distance, or 0.03008423586 cents per mile. Given that the IRS allows you to deduct 57.5 cents per mile for driving.

Long story short, this points out two things:

FIRST: Short trips are more expensive than long ones.
Airplanes are different than buses.  Air resistance increases with the square of velocity. The faster a vehicle travels, the more air resistance opposes it, and the more power is needed to overcome it. An airplane traveling at 640 mph generates 16 times as much air resistance as an airplane traveling at 160 mph, despite the fact that it's only going four times as fast. To minimize this effect, airliners fly very high (39,000 feet) where the air pressure is much lower. (For reference, Mt. Everest is 29,000 feet at the peak). For a flight, all the cost is in getting up in the air, to cruising altitude (after which, the plane largely just maintains a semi-ballistic glide through the thin air of the upper atmosphere, all the way down. Most of the flight is spent at 'cruising altitude'. The cruising altitude is selected on the basis of algebraic equation containing the costs per unit of vertical travel at a given height, and the cost of getting to that height. The way the math works out, its always cheaper to go to where the air is thin, so the cost of a flight is largely invariant to the distance traveled.

It's not how good something is, it's how good it is compared to its alternative. Every trip takes time, and costs money. The default alternative for short trips is walking, which can be very time consuming, but costs (effectively) nothing. Whether it's worth spending money for higher speed depends on your own personal cost of time. If your time is worth $10 an hour, saving 1/2 hour is the same as saving $5. So every 6 minutes of your time is worth a dollar. If the bus fare is $2, take the bus anytime doing so will save you 12 minutes, or anytime you have to walk over 6/10 of a mile.