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 IMPORTANT CONVERSIONS

METEOROLOGIST JEFF HABY

An important conversion that arises for meteorologists is most often temperature conversions. How many times have you had to search for the Celsius to Fahrenheit temperature conversion? This section will show exact conversions between ░ F, ░ C and K and will also show you a trick to easily convert Celsius to Fahrenheit and vice versa in your head! Most upper air charts have temperatures in Celsius. If you are used to the Fahrenheit temperature scale, it is important to know how to readily convert Celsius to Fahrenheit in your mind or you won't be able to interpret the chart! The five exact temperature conversions are given below. Plug in the known temperature value on the right side of the equation to get the value of temperature on the left side of the equation.

 Celsius to Fahrenheit ░ F = 9/5 ū ( ░ C) + 32 Kelvin to Fahrenheit ░ F = 9/5(░ K - 273) + 32 Fahrenheit to Celsius ░ C = 5/9(░ F - 32) Celsius to Kelvin K = ░ C + 273 Fahrenheit to Kelvin K = 5/9 (░ F - 32) + 273

An approximate value for Celsius or Fahrenheit or vice versa can be found just by memorizing a few landmark values and by knowing there are about 2 ░ F in 1 ░ C. With each 10 degree Celsius temperature change there is an 18 degree Fahrenheit change. Let's start with the temperature conversion everyone knows, 0 ░ C = 32 ░ F, each time 10 ░ is added or subtracted to the Celsius temperature, add or subtract another 18 Fahrenheit. The result is the following table.

-10 ░ C = 14 ░ F
0 ░ C = 32 ░ F
10 ░ C = 50 ░ F
20 ░ C = 68 ░ F
30 ░ C = 86 ░ F
40 ░ C = 104 ░ F

After memorizing these key values, you can interpolate the values in between. For example, suppose an 850 mb observation has a temperature of 15 ░ C. You know that 10 ░ C is 50 ░ F and 20 ░ C is 68 ░ F, therefore 15 ░ C must be exactly in between 50 and 68, which is 59 ░ F. Now try, 18 ░ C. You know that 20 ░ C is 68 ░ F and you know that there are almost 2 ░ F in a degree Celsius (actually there are 1.8 ░ F in a 1 ░ C temperature change) therefore the temperature is approximately 68 - 4, or 64 ░ F.

The same process can be used to convert Fahrenheit to Celsius temperatures. Suppose you want to know what 100 ░ F is in Celsius. You have memorized that 104 ░ F is 40 ░ C, therefore the temperature is approximately 40 - 2, or 38 ░ C. The 2 came from the temperature difference between 104 and 100; that is a 4 degree difference in Fahrenheit but about a 2 degree difference in Celsius.

Another way to convert Celsius to Fahrenheit and vice versa in your head is to simplify the formulas to the two given below:

F = 2ūC + 30

C = (F-30)/2

Example, if it is 20░ C, then it is near 70░ F (2*20)+30 = 70. If it is 60░ F, it is near (60-30)/2 = 15░ C. This technique is most accurate when temperatures range from 0 to 20░ C (32 to 68░ F). The temperature this technique is exactly accurate is 10░ C (50░ F). Therefore, the further the temperature is from 10░ C, the least accurate this method will be.

One of the next most common conversions is wind velocity. On analysis charts and weather reporting observations, wind is most commonly given in one of three units: Miles per hour, knots, or meters per second. A mile per hour is a higher numerical wind speed than a knot. The way to remember this is that "m" in miles per hour stands for "more". To find miles per hour, multiple the knots value by 1.15. To find knots, divide the miles per hour value by 1.15.

1 knot = 1.15 miles per hour
1 mile per hour = 0.87 knots
100 knots = 115 mph

Metric unit wind speeds are often expressed as meters per second. The conversion below shows the change from miles per hour to meters per second.

(1 mi/hr)*(1 hour/3,600 sec)*(1.61 km/1 mile)*(1000 meters/1 km) = 0.45 m/s

Therefore, there are 0.45 m/s for every mile per hour. We can approximate that there are about 2 miles per hour for every 1 meter per second. Any value on an analysis chart with a value in meters per second can be multiplied by 2 to get an approximate wind speed in miles per hour. Here are some examples.

10 mph is about 5 m/s
20 mph is about 10 m/s
30 mph is about 15 m/s
40 mph is about 20 m/s

You may have wondered where the units of knots came from. A knot is exactly equal to 1/60th of a degree of latitude. A 1/60th of a degree of latitude is known as a minute of latitude. Therefore a knot is equal to one minute of distance. There are 90 degrees from the equator to the pole. Therefore a knot is 1/5,400th the distance from the equator to the pole. This number is found by multiplying 90 (degrees from equator to pole) ū 60 (number of minutes in a degree of latitude). At sea, one's position is always based on degrees, minutes and seconds, so therefore how fast you traverse the ocean is based on "minutes" traveled per unit time (hour); hence, the nautical mile per hour or knot. In centuries past, mariners determined the speed of their ships using a knotted "log line." The buoyant line was let out freely as the ship sailed along, and then the number of knots let out during a given time gave the shipmaster a measure of his vessel's speed.

A knot is related to meters per second much more closely than miles per hour is. A knot is very close to 0.5 meters per second!! Therefore, the table below is much closer to accurate than the table above. If a value on an analysis chart is given in knots, simply divide this by 2 to get the wind speed in meters per second. Most weather charts will report wind speed using the units of knots.

10 knots ū 1.15= 11.5 mph ū 0.45 = 5 m/s
20 knots ū 1.15 = 23.0 mph ū 0.45 = 10 m/s
30 knots ū 1.15 = 34.5 mph ū 0.45 = 15 m/s
40 knots ū 1.15 = 46.0 mph ū 0.45 = 20 m/s

A mile is a longer distance than a kilometer. To convert miles to kilometers, multiply the miles value by 1.61. To convert kilometers to miles, divide the kilometers value by 1.61.

Miles = kilometers / 1.61
Kilometers = miles ū 1.61

Now, here is a list of some most common formulas:

Pi = 3.141592654ģ.., this is the ratio of the circle's diameter to a circle's circumference (circumference / diameter)

Area of square = length ū width (x^2)
Volume of square = length ū width ū height (x^3)
Volume of sphere = 4/3 Pi ū r^3
Area of sphere = 4 Pi ū r^2
Volume of cylinder =Pi ū r^2 ū height
Area of circle = Pi ū r^2
Circumference of circle = Pi ū d or 2Pi ū r
Discharge = length ū width ū velocity = x^3/ sec.
Velocity = distance / time
Acceleration = distance / time^2

Example problems

 78 ░ F 41 ░ F 66 ░ F 80 ░ F

answers (26░ C, 5░ C, 19░ C, 27░ C)

 18 ░ C 25 ░ C 3 ░ C 33 ░ C

answers (64░ F, 77░ F, 37░ F, 91░ F)

3. Convert the following values to miles per hour.

 20 knots 45 knots 70 knots

answers( 23 mph, 52 mph, 81 mph)

4. Convert the following values to knots.

 16 miles per hour 167 miles per hour 57 miles per hour

answers (13.9 knots, 145 knots, 50 knots)

5. Convert the following values to meters per second.

 90 knots 78 knots 100 knots

answers (45 m/s, 39 m/s, 50 m/s)

6. Convert the following values to miles.

 67 kilometers 100 kilometers 34 kilometers

answers (42 miles, 62 miles, 21 miles)

7. Convert the following values to kilometers

 245 miles 45 miles 78 miles

answers (395 km, 73 km, 126 km)

8. What is the area of a square which has a side of 10 inches?

answer (10 inches ū 10 inches = 100 inches^2)

9. What is the volume of a square which has a side of 10 inches?

answer (10 inches ū 10 inches ū 10 inches = 1,000 inches^3)

10. What is the volume of a sphere with a radius of 2 millimeters?

answer (formula = 4/3Pir^3 = 4/3Pi(2mm)^3 = 33.5 mm^3)

11. What is the area of a sphere with a radius of 2 millimeters?

answer (formula = 4Pir^2 = 4Pi(2mm)^2 = 50.3 mm^2)

12. What is the volume of a cylinder with a radius of 10 inches and a height of 20 inches?

answer (formula = Pir^2h = Pi(10inches)^2(20 inches) = 6,283 in^3)

13. What is the area of a circle with a radius of 25 feet?

answer (formula = Pi ū r^2 = Piū(25 feet)^2 = 1,963 feet^2)

14. What is the circumference of a circle with a radius of 2 miles?

answer (formula = Pi ū d = Pi(2 + 2 miles) = 12.6 miles)

15. What is the discharge of a stream with an area of 5 feet squared when the velocity of water is 10 feet per second?

answer (formula = area ū velocity = (5 feet^2) ū (10 ft/sec) = 50 ft^3/sec)

16. What is the velocity of an object traveling 10 meters in 2 seconds?

answer (velocity is distance/time = 10meters/2 seconds = 5 m/s)

17. What is the acceleration of an object traveling 10 meters in 2 seconds per 2 seconds?

answer (acceleration is distance/time ū time = 10 meters / (2sec ū 2sec) = 2.5 m/s^2)