## Friday, January 7, 2011

### Math Reasoning, Part III: Bugatti Veyron

Yesterday I posed a question - how much air does a conventional gasoline-engined vehicle consume at 200 mph? If you didn't read yesterday's blog, go back now and check it out so you can follow the rest of this solution.

I did some research, assembled some figures, and now (using only elementary school math) we have to make progress towards our solution by determining:

How much fuel will we burn in a minute, or more precisely, how many liters of fuel do we consume at 200 mph?

That's not so easy to learn! But fortunately when a Bugatti Veyron set the current record for fastest street car (257 mph), its fuel consumption was measured.

The Veyron achieves about 2.3 miles per gallon at 240 mph. If you divide 240 by 60 you find you are traveling 4 miles in a minute.

We only care about how much we burn in a minute, so:

4 miles ÷ 2.3 miles/gallon = 1.7 gallons

Thus in the Veyron we are burning roughly 1.7 gallons per minute, or (1.7 x 3.78) 6.4 liters.

Of course this is at 240-250 mph. Let's assume the fuel consumption is a bit less at 200 mph. Care to guess with me? I'm going to say 1.3 gallons per minute, or 5 liters per minute.

5 x 8500 = 42,500 liters of air per minute. That's more air than the Jaguar's gas turbines!

The breathe at the rate my math suggests, the Veyron must have large air intakes so it can gulp all that air. Yes, see? They are in the rear of the car over the occupants' heads.

NOTE: I just read an article quoting TOP GEAR presenter Jeremy Clarkson as saying at top speed the Veyron consumes 45,000 liters of air per minute. Confirmation our math is right!

Even elementary math can be useful. We might also predict that the Jaguar gets better fuel economy than the Bugatti at the same speed. It's lighter, smaller and more aerodynamic -  and because it consumes less air it must therefore be burning less fuel. Proving this prediction is another day's problem.

Let's go one step further today. Rather than being the fastest car in the world, the 2000-2006 Honda Insight was the most fuel-efficient gasoline vehicle.

At 60 mpg and 60 mph, it consumes 1/60 of a gallon per minute, or .063 liters a minute.
That means .063 x 8500 = only 141 liters of air per minute.