Real-Life Math
This weather business actually has a lot to do with business!
"The
information you give out in forecasts is often being used by farmers, airline
companies, the tourist industry, forestry companies and government agencies
to plan their short-term work schedules," says meteorologist Phil Jarrett.
For
example, forestry companies have to plan slash burning for times when local
forecasters predict the ventilation index will be high enough to allow smoke
to move quickly away from the fire.
"The calculations are usually made
using computer programs and tables. But forecasters should also be able to
do them quickly and accurately without those aids."
Let's say
you're working as a meteorologist in a city surrounded by forest. Your
computer has just crashed and the service technician says it will be 3 hours
before the system is up and running again. In the midst of all this, a logging
company calls your office to find out if its crew can slash burn today.
Your
computer can't help you, so you'll have to crunch the numbers yourself
and get back to them. Now, using the following information, calculate the
ventilation index. Then decide whether or not burning should be done. If you
get this wrong, city residents will be phoning to complain about the thick
smoke hanging over the city!
To find out if local ventilation will
be in the "good range" (22,000 foot knots or more) on any given day, meteorologists
must know the height above sea level of their observation station, the height
above sea level that the smoke will rise to (the mixing height) and the mean
winds in the area. Here are the values you'll be working with:
station
height = 346 meters
mixing height = 1,410 meters
mean
winds = 35 kilometers per hour
Part A
First, you
must calculate the effective mixing height by subtracting the station elevation
from the mixing height.
Part B
Next, convert the effective
mixing height to feet. To do this, you need to know that:
3.28 feet =
1 meter
Part C
Next, convert the mean winds to nautical
miles (knots). To do this, you need to know that:
1 kilometer = 0.621
miles
There are 1,760 yards in a mile.
There are 2,000
yards in a nautical mile.
Part D
Finally, calculate
the ventilation index by multiplying the effective mixing height by the mean
winds. If this number is over 22,000 foot knots, the company can slash burn.