Rail Blues

Greetings, Takers of the A-train,

Last night I went to a show in the big city. As you know, I don't own a car, so I took a subway car back, and noticed how very odd it was that about 100 rich patrons waited with me for over 20 minutes for a train. (My metropolitan area has notoriously infrequent trains, especially at night.) It got me wondering: how crazy is it (financially) to run trains infrequently at night?

Extra Costs

It's easy to say "Let's just run trains every minute," but the whole reason why public transit systems work is that many people going the same way can use just one vehicle and driver. Let's figure out the cost of splitting one infrequent but long subway trains into two shorter trains.

If the run lasts two hours and the driver costs $40/hour (including overhead, training, etc.) the personnel expense is $80. The necessary force (hence electricity cost) of pushing an additional train front through the air can be calculated using:

F = .5 A D p v^2,

where A is the area of the train front, D is a drag coefficient (usually about .25 for aerodynamic shapes), p is the density of the medium and v is the speed. Using A D = 4 m^2, p = 2kg/m^3, v = 20 m/s, electricity costs $.15/kWh and the distance traveled is 100 km, we see the extra energy costs is a measly $7. Let's round up and say an extra $100 would be needed to run an extra train.

Extra Benefits

So, how much shorter a commute would there be if an extra train came? The trains come every 24 minutes, and by the time a train came last night there were over 100 people waiting at my station and over 100 at the next station (the two busiest, mind you); let's lowball the estimate and say 250 people would be able to catch a train on average 6 minutes sooner if train frequency were doubled. Doubling train frequency means 25 commuter hours would have been saved at a cost of $100 to the system: $.40 per passenger or $4/hour of passenger time saved.

However, increasing service might increase ridership, so it's possible that the extra train would (at least partially) pay for itself. Increasing ridership eases burdens on parking and roads too; public transit is overall a good bargain.

Summary

It's time commuters got vocal about being willing to pay a fair amount for their time that gets wasted by sluggish schedules. I wish we'd get a consistent metric of how much our time is worth, and use it to make policy decisions. Check out my post on machine wages for equivalent cost-time comparisons; this concept may evolve into a wiki page soon.

Keep on track!

LeDopore

How Much do You Pay Your Machines?

Greetings, Robot Lords.

The Pitch

How much do you value your free time? In Stephen King's The Stand, the Walkin' Dude comes by Mother Abigail's place in the guise of a vacuum cleaner salesman, making the pitch that he's not actually selling her labor-saving vacuum cleaners. Instead, he's selling her cool lemonade sipped in the shade on a hot day, time to lazily read a novel, or time to do essentially whatever Mother Abigail likes best. The premise is simple and appealing: we buy (or make) machines which save us drudgery, and then allegedly have more free time.

The Catch

In reality, our time-savers often end up owning us instead. It takes a lot of time, energy and money to maintain every piece of equipment we buy. On the other hand, I have a lot more free time than any subsistence farmer I've heard about, so there must be a good side to this tech too. How do we know if a given piece of labor-saving tech is worthwhile?

The Players' Salaries

One interesting analysis is to figure out what effective wage you're paying your labor saving device for your extra free time. Everything doesn't always boil down to money: it's not as if chores are equally onerous (I enjoy gardening more than cleaning the bathroom), but quantifying the hourly rate of free-time-saving makes for an interesting analysis nonetheless. Here's a summary table, then I'm going to talk a little more about some entries. Here "machine wage" isn't how much you pay per hour of operation - it's how much you pay per every hour of labor it saves you. I've ordered this list in descending order of utility.

Item	Price	Cost/y	Lifetime (y)	Hours saved/week	Hours saved	Total Cost	Machine Wage
Dishwasher	500		5	3	780	500	0.64
Non-stick fry pan	100		20	0.05	52	100	1.92
Lawnmower (electric)	400	1	10	0.25	130	410	3.15
Newer computer	1500		2	1	104	1500	14.42
Kitchen Mixer	200	1	20	0.0096	10	220	22
Melon baller	10		10	0.00064	0.33	10	30
Car	5000	2000	5	1	260	15000	57.69

• I'm a dishwasher evangelist. I've been responsible for (or at least influential in) the decisions of no fewer than 5 households I know to acquire a dishwasher by hook or by crook. (If you're renting, look into portable dishwashers - that's what I own.) Until today I just always had a hunch that dishwashers were good time-savers, but the hard numbers really nail it for me. Operating a dishwasher (in hot water and dish soap) costs about the same as washing by hand, and by my analysis my $500 dishwasher will save me 780 hours of scrubbing. Since I value my free time more than 64¢/hour, owning a dishwasher is a no-brainer.
• I just bought a $100 super-high-quality frying pan, with (I kid you not) embedded diamonds as the non-stick coating. So far I have no complaints performance-wise: I get an even heat and the food has been scrumptious every time. As a side effect, I estimate that I spend about 3 minutes per week less cleaning, since now I can use this pan instead of my older stainless steel pan (which was a pain to scrub). Those 3 minutes per week over the 20 years the pan should last amount to 52 total hours saved, so I'm "paying" this machine $1.92/hour for the privilege of not washing dishes.
  
• If I were to buy a new computer (something I dream about way too often) I might spend about 1 hour less per week waiting for my numbers to crunch (I'm a "power user": I run intensive numerical operations on a regular basis; for word-processing I doubt a newer computer would save more than a minute or two per week). If the new computer I'd keep for about 2 years, then it would save me about 104 total hours, so upgrading now (for $1500) would be like paying the machine $14.42 for every hour I save not waiting for that progress bar to end.
• I broke down and bought one of those designer kitchen mix machines the other year. We barely use it, truth be told. If it were to save 15 minutes twice a year, this $200 machine would save us 10 hours of work over its 20-year lifetime. (Inside, I doubt it will save that much time, but the truth hurts sometimes.) It really sucks power too, so I guess its lifetime cost (price + power) will be $220; meaning we're paying it $22 per hour that it saves us. (Note: this mixer brings an invaluable quantity of ancillary joy to my better half merely by gracing our kitchen - which is precisely why this kind of analysis didn't have the last word.)
• We also own a melon baller! If it saves us 2 minutes a year (we hardly use it), we're paying it $30/hour for the privilege. Maybe single-purpose kitchen gadgets should be contraband.
  
• Last (but not least) we don't own a car. I can get to and from work without one (and, considering the parking around where I work, biking is faster), even though it makes doing errands a little more tricky. I estimate I spend about 1 hour more per week doing errands because I can't just hop into a rust bucket. (Aside: if I were to offset time I don't have to spend in the gym because I bike, this 1-hour figure could very well be negative!) In any case, were I to buy a car, over 5 years it could well cost $15,000 in insurance, depreciation, maintenance, parking and fuel. For each of the 260 hours it would save me, I'd be paying it $57.69: a pretty lousy deal. I guess I won't be buying a car until my lifestyle requires one.

The Last Inning

On that note, let me hand it over to you. The numbers I've presented are highly personalized and might not apply to you. I do a lot of serious computing, and even for me a new computer only barely makes sense. I live close to work, so biking is a great option. We do a lot of entertaining, and thus a dishwasher is pretty much essential. If you truly need a car, or if you don't entertain or run scientific computing experiments your personal table is likely to be quite different. Still, I encourage you to do the same sorts of analyses before listenening to the Walkin' Dude.

Rule your 'bots with an iron fist!

LeDopore