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Really?

Badly Shaved Monkey said:
http://imgs.xkcd.com/comics/dimensional_analysis.png

I am sad enough to expect that the author of xkcd has done his sums correctly, but not quite sad enough to check his arithmetic for myself.

Is he right?
Click to expand...

An interesting aspect to that comic, which hadn't occurred to me before, is that MPG is dimensionally equivalent to 1/area; that is 1/m^2 in the metric system.

The inverse of that number is the cross-sectional area of a "thread" of gasoline that a car must "eat" as it travels down the road. A Prius's 49 MPG is about equal to 21 km^2, and the inverse of that is 0.05 mm^2. A tube of gasoline a twentieth of a square millimeter in cross-section is thus sufficient to power a Prius.

- Dr. Trintignant
 
Dr. Trintignant said:
An interesting aspect to that comic, which hadn't occurred to me before, is that MPG is dimensionally equivalent to 1/area; that is 1/m^2 in the metric system.

The inverse of that number is the cross-sectional area of a "thread" of gasoline that a car must "eat" as it travels down the road. A Prius's 49 MPG is about equal to 21 km^2, and the inverse of that is 0.05 mm^2. A tube of gasoline a twentieth of a square millimeter in cross-section is thus sufficient to power a Prius.

- Dr. Trintignant
Click to expand...

That's actually rather a cool way of looking at it.
 
Dr. Trintignant said:
An interesting aspect to that comic, which hadn't occurred to me before, is that MPG is dimensionally equivalent to 1/area; that is 1/m^2 in the metric system.

The inverse of that number is the cross-sectional area of a "thread" of gasoline that a car must "eat" as it travels down the road. A Prius's 49 MPG is about equal to 21 km^2, and the inverse of that is 0.05 mm^2. A tube of gasoline a twentieth of a square millimeter in cross-section is thus sufficient to power a Prius.

- Dr. Trintignant
Click to expand...

Does that number have a correlate in the physical implementation of the engine powering the car? Is it the average diameter of the stream of fuel entering combustion, i.e. averaging out the pulsatile flow into each cylinder into an aggregate equivalent continuous flow?
 
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And nobody here even questioned what would happen to Scotland and Wales in the event that a better Prius was built.

Shame on you.
 
Badly Shaved Monkey said:
Does that number have a correlate in the physical implementation of the engine powering the car? Is it the average diameter of the stream of fuel entering combustion, i.e. averaging out the pulsatile flow into each cylinder into an aggregate equivalent continuous flow?
Click to expand...

Yeah, that sounds about right. Most cars have one fuel injector per cylinder, so if you take the number of cylinders, multiply by the injector nozzle diameter, then by the stream velocity, then by the injector duty cycle, and finally divide by vehicle speed, should get the same number as the area of the gasoline thread.

Or, you could look at it like this: if the thread of gasoline came pre-mixed with air, the tube the Prius engine needs to eat would be about 23 mm in diameter. This volume is equal to that which engine cylinders pump (after accounting for the lowered pressure due to throttle position).

- Dr. Trintignant
 
bluesjnr said:
And nobody here even questioned what would happen to Scotland and Wales in the event that a better Prius was built.

Shame on you.
Click to expand...

Well a quick glance at Google Earth suggests in this game of global snooker the whole of the UK would cannon into the island of Ireland, which could find itself potted in the Baffin Sea, after hitting the knuckle formed by the southern tip of Greenland.
 
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