Additional Math Pages & Resources

Tuesday, November 10, 2009

What do you really want to know?

Asking a simple question and getting a complicated answer

Calculating fuel consumption is simple math. However, we often say gas mileage, or fuel economy, when we really mean fuel consumption. As when we ask, How much fuel does this thing burn?

In the US we calculate consumption in units called miles per gallon.

What was my consumption on my last fill-up? My tankful was 15.8 gallons. We traveled 330 miles. I estimate 16 gallons, 320 miles - that's 20 mpg.


Answering a simple question in a different way

In many countries using the metric system, the calculation is liters per 100 km.

What was my consumption on my last fill-up on vacation in Europe? A tankful of 49 liters took us 990 km. Or say 50 liters for 1000 km = 5 liters per 100 km.

Comparing results

How do these compare? 990 km x .62 = 614 miles. 49 liters = 13 gallons. That's around 47 mpg.

Asking a completely different question but getting the same old answer

Now suppose you ask, How hard is the wind blowing? And I answer, Weatherman says gusts of 8 knots (nautical miles per hour).  You reply, Does that mean my sailboat will go 8 knots?

NO. The speed of the wind varies all the time. You have to consider hull drag, your sails, your skill, the direction you want to travel, how large is your crew, tides and currents, etc. If you are Dennis Connor in an America's Cup sailboat, sure! Your sailboat can do 8 knots.

You ask,  Then can I sail 80 miles from San Diego to Santa Catalina Island in 10 hours?

NO. Because the wind is in your face, you're sailing into the waves, the course is never straight, it's often quite foggy, and it could take days to sail there as you tack back and forth. Or sit becalmed. So virtually everyone motors up to Catalina, even in a sailboat.

Well, how much fuel would I need? How many miles per gallon does a sailboat get?

Whoops, no odometer on the sailboat. Fuel consumption is measured in gallons (or liters) per hour.

What you meant to ask was, What do our engines burn per hour at cruising speed, and how many hours will it take to get there?

My local experts say you'll burn 1-2 gallons per hour, and you face 13-14 hours of cruising at 5-6 knots per hour. That means you better have at least 35 gallons of fuel.

Comparing results 

What is the fuel consumption of this sailboat in miles per gallon?  Assume 2 gallons per hour and 5 knots per hour. That's 2 gallons every 12 miles, or 6 miles per gallon.

Asking the same old thing again, and learning even more

Now suppose you ask me, What if we fly up there - how much fuel will we need? 

I answer, Do you think we measure in miles per gallon, liters per 100 km, gallons per hour, or what?

Having learned by now, you answer, What!

Right!  Some aircraft do measure fuel consumption in gallons per hour, but many use weight of fuel rather than volume (because volume varies as altitude increases).  So gauges are marked in pounds, and we think of burning pounds per hour.

Be prepared to learn more than you thought when you ask a simple question!

Math teaches you to state your questions clearly. What do you know already? What do you still need to learn?

Be prepared to learn more than you thought. And when lives are at risk, don't just do theoretical calculations, get some real-world advice.  When someone asks, Can we make it without refueling?

I would ask, Are you walking (swimming, sky-diving) if we don't?

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