Latitude and Longitude, Plus Map Scale

Transcription

1 Name Lab 4 More Date: Latitude and Longitude, Plus Map Scale In the first few labs of the semester, you found that you needed to look at a variety of maps to answer all the questions. One reason you needed more than one map is because maps are drawn at different scales. On the relief map of California, features were visible that aren t drawn on a world map. Obviously, the information on any of these maps is reduced in size from reality, and the map scale tells you just how reduced the map is. The most common way for map scale to be represented is as a representative fraction (RF). This is either a fraction or a ratio of map distance (MD) to ground distance (GD). Map distance is what you measure on the map using a ruler. Ground distance is what you measure in the real world between two places. Let s say that the map scale as a representative fraction is /0,000, or :0,000. Notice that there are no units present in the scale (feet, cm, miles, etc.), regardless if it s written as a fraction or as a ratio. This is because ground distance and map distance must be measured in the same units. So the RF of /0,000 means that if you measure cm on the map, it represents 0,000cm on the ground. Or inch on the map represents 0,000 inches on the ground. Or of anything on the map represents 0,000 of anything on the ground. RF = MD GD You can use RF to find the distance between points on a map. To use the RF to your advantage, remember that RF equals map distance divided by ground distance. To find out how far apart two places are: () you need to know the map scale you re viewing, (2) you must measure the distance between the two places, and (3) you must do a little math. Let s say you re looking at a :0,000 scale map, and you measure two places on the map that are 3.5cm apart. You may be able to figure out in your head how far apart they are on the ground, but it s good to be able to set up the problem so you follow the same procedure each time. It will also help you work out other problems that have a twist to them. Start out like this: Then measure the map distance: 0,000 = MD GD. 0,000 = 3.5cm GD. Lab 4 4- K375_Farrell_L04.indd 8/2/3 2:00 PM

2 Any time you have two equal fractions, you can solve for a single unknown. In this case, ground distance is unknown so you can solve for it by cross-multiplying and dividing. You multiply the two known figures that are diagonal from each other. 0,000 = 3.5cm GD 3.5cm * 0,000 = 35,000cm Then you divide this answer by the remaining known value to find the unknown value. 35,000cm / = GD Ground Distance = 35,000cm This leads us to the topic of unit conversion. You need to convert 35,000cm into more usable units. It is not acceptable in this course to convert units by dividing or multiplying a number by another number, hoping it works, and slapping on the units you want to end up with. There is a simple way to take the guesswork out of unit conversion and ensure that you can convert units with confidence. Simple unit conversion:. Identify the units you re starting with, and the units you want to finish with. For example, let s say your task is to convert 48 inches into feet. You start with inches, and you want to end with feet. 2. Find a conversion that relates the starting and ending units. For example, this might be an equation like 2 inches = foot. 3. Convert this equation into a fraction that s equal to. This is simple, but it requires some algebra. When you have an equation like the one in step 2 above, remember that you can do anything you want to one side of the equation, as long as you do the same to the other side. You want to divide both sides of the equation by either side (you can pick). For example, if you divide both sides of the equation in step 2 by 2 inches, you get the following: 2inches 2inches = foot 2inches Remember: Anything that s divided by itself equals. On the left side, you have a fraction 2inches 2inches that equals, so you can rewrite the equation as = foot 2inches. This is useful because you can multiply anything you want by and you don t change the value foot of it. This means you can multiply any number or any value, or anything at all, by 2inches and you haven t changed the value of it. Here s why that s important. Let s return to our original task: Convert 48 inches into feet. To solve the problem, multiply 48 inches by a fraction (equal to ) that will change the 48 inches into an equivalent amount of feet. A way to make this less confusing is to write your original value of 48 inches as a fraction: 48inches. 4-2 Physical Geography Lab Manual K375_Farrell_L04.indd 2 8/2/3 2:00 PM

3 Now multiply 48inches foot *. Notice that you have inches in the numerator and inches 2inches 48feet in the denominator, so inches reduces to. You are left with, or 4 feet. 2 While you may have been able to figure out this one in your head, the same process allows you to be confident with your answers to more complicated problems. Finding the distance between two cities in the atlas: Imagine you re using a :00,000 scale map. You measure the distance on the map between two cities as 8cm. You re asked to find the ground distance in km. First, use the RF definition and cross-multiplication to find the ground distance in cm. Then convert cm to km. RF = MD GD = 00,000 = 8cm GD. Cross-multiply 00,000 by 8cm. This gives you,800,000cm. Divide that by to find your ground distance, which is,800,000cm. km = 00,000cm, so km,800,000cm km =, and * 00,000cm 00,000cm = 8km. Using the most detailed map in your atlas, find the distance in km between the following cities. Show all your work, including identifying the map scale, the map distance in cm, and your conversion of cm to km. Find the distance between Los Angeles and Sacramento. Find the distance between London and Paris. Find the distance between Paris and Barcelona. Find the shortest possible distance between Iraq and Afghanistan. Lab K375_Farrell_L04.indd 3 8/2/3 2:00 PM

4 You can also use the idea of the RF to calculate the map scale if you know the ground distance between two points and you can measure the map distance on the map. You use the same two fractions as before, but the denominator of the RF is what you ll solve for. Assume the two dots below represent cities that are 88km apart. What is the scale that they are shown at? Large scale and small scale: Here s a slightly confusing thing about map scales: The way geographers talk about large scale and small scale is opposite the way the terms are used in everyday life. A geographer can refer to a map scale as small or large relative to other maps, depending on the RF. A large value for the RF means the map is a large-scale map, and a small RF value means the map is a small-scale map. However, you must look at the entire fraction. A large RF means the denominator of the RF is small. One divided by a small number is a large value. It may be counterintuitive to say that a map of your neighborhood is a large-scale map, but a map of the world is a small-scale map. One way to remember which is which by looking at a map is that items appear small on a small-scale map, and the same item appears large on a large-scale map. So as a reminder: A large-scale map () has a small value in the denominator of the RF, (2) has a large value of the RF itself, (3) features are large on the map, and (4) the map shows a small area. Write the specific RF values for the following maps in the classroom, and rank them from smallest to largest, with being the smallest-scale map, and 3 being the largest-scale map. Map RF Rank from 3 World physical map on front wall Topographic map North America map on back wall 4-4 Physical Geography Lab Manual K375_Farrell_L04.indd 4 8/2/3 2:00 PM

5 Although the RF is the most common way to represent map scale, another kind of scale used on highway maps is called a written scale. A written scale might read: One inch is equal to 250 miles. You can convert an RF into a written scale with unit conversion. For the metric system (which is easier to work with), a written scale usually relates cm on the map to km on the ground. An American system usually relates inches on the map to miles on the ground. Let s convert an RF of :50,000 to written units using the metric system. 50,000 = cm unknown. When you cross-multiply and divide, your unknown is 50,000cm. To convert that to km, remember there are 00,000cm in a km. 50,000cm km 00,000cm = 0.5km. So in a written scale, cm is equal to 0.5km. Find the written scale in cm and km for a :7,500,000 scale map. In lab #2, you completed a number of exercises that required you to understand the latitude and longitude coordinate system used to define locations on the Earth s surface. You may have wondered what happens when you re looking for a location that doesn t fall exactly on a meridian and a parallel. For example, although 34 N, 8 W is a good estimate for the location of Los Angeles, those coordinates actually refer to a residential neighborhood in Hacienda Heights! And 34 N, 9 W would land you in the Pacific Ocean. Obviously, if you re going to use latitude and longitude to refer to locations at a local scale, you can t use whole degrees. Lab K375_Farrell_L04.indd 5 8/2/3 2:00 PM

6 Decimal Degrees One way to break full degrees into smaller increments is to use a decimal point to indicate location. For example, 34.5 N, 8.25 W would be halfway between the 34 parallel and the 35 parallel, and one quarter of the way between the 8 meridian and the 9 meridian. Coordinates written in this way are called Decimal Degrees (DD). As an introduction to using decimal degrees, estimate which letter (A through E) in the figure below matches the coordinates below and write the letter in the appropriate blank. For this part, you re only estimating the right answers. 35 N 9 W 8 W Decimal Degrees 34.5 N, 8. W Letter A B 34.8 N, 8.85 W C E 34.8 N, 8.3 W 34. N, 8.3 W 34.5 N, 7.9 W 34 N D Now that you understand the basics, refer to a large-scale map of California in your atlas. Find the city with the following DD coordinates. Hint: The cities all have a UC campus that shares its name. Decimal Degrees N, 9.72 W N, 7.7 W N, W N, 7.35 W N, W N, W N, 8.23 W N, 20.5 W City Decimal degrees are fairly easy to work with and make a lot of sense. Unfortunately, they re not widely used. A more common coordinate system involves breaking degrees into 60 minutes, and if more detail is needed, breaking each minute into 60 seconds. This is called the degrees, minutes, seconds (DMS) system. Although this sounds like the minutes and seconds we use when we talk about time, the only similarity is that there are 60 minutes and 60 seconds. Using DMS 34 degrees, 25 minutes, and 5 seconds, write Physical Geography Lab Manual K375_Farrell_L04.indd 6 8/2/3 2:00 PM

7 To convert from decimal degrees (DD) to degrees, minutes, seconds (DMS), take the decimal part of the DD and multiply it by 60. If this equals a whole number, keep the original degrees and write the new whole number as minutes. Complete the following conversions (the first one is done for you): N, 8.5 W If you convert DD to minutes but you don t end up with a whole number for your minutes, multiply the decimal portion of the minutes by 60, and write that answer as seconds. For example, if you start with 34.2 and you want to change it into DMS, first multiply 0.2 by 60, giving you 7.2. Instead of writing your answer as , multiply the 0.2 by 60, and make that seconds: Complete the conversions (the first one is done for you): To convert in the opposite direction (from DMS to DD), start with the seconds and divide them by 60. Then add the resulting decimal to the number of minutes. Divide this number by 60. Your answer is what goes after the decimal in the DD. Complete the conversions (the first one is done for you): = Divide 45 by 60 = Add this to 2 and divide by 60 = Lab K375_Farrell_L04.indd 7 8/2/3 2:00 PM

8 Here s a series of word problems to make sure you understand both DD and DMS. Find your new location coordinates in DD: If you re going in the same direction as your current latitude or longitude, you add the degrees to your current location. If you re going in the opposite direction, you subtract.. You re at 34 N 66 W. You go north 0.5 and west You re at 55 N 8 W. You go south 4.5 and east 9.5. (Remember what happens if the Equator, Prime Meridian, or IDL is crossed! You may want to refer to a globe or world map.) 3. You re at 34 N 8 W. You go south 5. and east You re at 34 N 8 W. You go north 0.9 and west Find your new location in DMS:. You re at N, W. You go north 5 34 and west You re at N, W. You go south 8 40 and east Physical Geography Lab Manual K375_Farrell_L04.indd 8 8/2/3 2:00 PM