of a chart or sketch. Trends in performance data are easier to identify with a graph than a data table.
Use cross section or graphing paper when drawing line graphs. Paper can be purchased or drawn. Draw by marking off 6 inches x 6 inches, and add vertical and horizontal lines every 1/4 inch.
• Values of units are chosen for each axis that will permit the graph to fit conveniently on the paper.
• The units are marked off on the vertical and horizontal axes.
• Points are plotted in relation to the two axes from the table of information.
• Finally, the points are connected with a straight line or curve.
Example 10—Draw a graph for pump performance showing the relationship between pressure (psi) and flow (gpm). Use the following table of pump performance data values.
Pump Performance Values
psi 50 75 100 125 150 175 200 225 250 275 295 gpm 79 77 75 69.5 63 56.5 51 46 40.5 29.5 0
Step 1. Pump performance charts are typically drawn with the flow on the horizontal axis and pressure on the vertical axis. Label the horizontal axis as flow in gallons per minute. Label the vertical axis as pressure in pounds per square inch.
Los Angeles, CA
Portland, OR Denver , CO
Tampa, FL Albuquerque, NM Fargo, ND Example 11—Using the graph in example 10, find the
indicated flow rate at a pressure of 263 pounds per square inch.
Step 1. Approximate the location of 263 pounds per square inch on the pressure axis. This will be halfway between 275 and 250 pounds per square inch.
Step 2. Move horizontally until the curved line is met.
Step 3. Move vertically from the curved line to the flow rate axis. Read or approximate the flow rate.
The flow rate is 35 gallons per minute at a pressure of 263 pounds per square inch.
Determining Slope of Curve from a Graph—The slope of the line can be determined from the plot by using the slope formula.
slope = rise/run
Example 12—Find the slope of the line drawn on the previous page from 50 to 150 pounds per square inch.
Since the line drawn is a curve, the slope will change with each section of line.
The pressure varies from 50 to 150 pounds per square inch as the flow rate varies from about 79 to 63 gallons per minute.
Pressure, pounds per square inch, is on the vertical axis, so it is the rise.
Flow rate, gallons per minute, is on the horizontal axis, so it is the run.
Slope = rise = (150 – 50) psi = 100 psi = –6 psi/gpm run (63 – 79) gpm –16 gpm
The negative slope indicates that the slope is decreasing.
The slope of the above line graph is –6 pounds per square inch per gallons per minute.
Reading Distance from a Map Table—Maps are generally broken into grids and labeled on the vertical and horizontal axes for ease of locating places or numbers. If the vertical and horizontal values are known, the value on the graph can be obtained by finding where the two lines intersect (cross).
Example 13—Use the mileage chart below to find the distance between Tampa, FL, and Albuquerque, NM.
Mileage Chart, miles
Los Angeles, CA 0 967 804 1,023 2,549 1,839 Portland, OR 967 0 1,366 1,236 3,064 1,494 Albuquerque, NM 804 1,366 0 439 1,760 1,272 Denver, CO 1,023 1,236 439 0 1,874 875
Step 1. Locate Tampa on the horizontal axis. Draw a vertical line through these grids.
Step 2. Locate Albuquerque on the horizontal axis. Draw a horizontal line across these grids.
Step 3. Read the mileage amount where the two lines cross.
Mileage Chart, miles
Los Angeles, CA 0 967 804 1,023 2,549 1,839 Portland, OR 967 0 1,366 1,236 3,064 1,494 Albuquerque, NM 804 1,366 0 439 1,760 1,272 Denver, CO 1,023 1,236 439 0 1,874 875
The distance between Tampa and Albuquerque is 1,760 miles. Albuquerque, NM Fargo, ND
EXERCISES Problem 1. Measure the angle.
K
Find the slope percent for problems 2 and 3.
Problem 2.
3 ft
Problem 3.
20 ch
Problem 4. A hill has a slope of 9 percent. The vertical distance is 5 chains. What is the horizontal distance?
Problem 5. A hill has a slope of 60 percent. The horizontal distance is 80 chains. What is the vertical distance?
Problem 6. Find the length of side b.
7 ft
12 ch
Problem 7. Raul spots a fire. He sees that the flames reach to the top of the shrubs. From this he determines that the flame height is 7 feet. The span of the fire is 9 feet. What is the flame length?
Problem 8. Find tan A = 0. 3.
Problem 9. Find tan 40°.
Problem 10. Sergio calculates the slope percent and finds it to be 35 percent. What is the measure of the angle?
Problem 11. Find the horizontal distance and the slope distance of the figure below.
Problem 12. Juanita is holding a 5-foot pole at the base of a hill. John is holding a 5-foot pole at the top of the hill.
Juanita reads the clinometer and gets a 40 percent slope.
The horizontal distance between John and Juanita is 30 feet. Find the slope distance and the vertical distance.
Problem 13. Mario is going to a fire. He has determined that his pace is 13 paces per chain. The distance to the fire is 20 chains on level ground. How many paces will Mario have to take to get to the fire?
Problem 14. Julie is determining her pace length. She has marked off 2 chains on level ground. It takes her 22 paces to walk the 2-chain distance. How many paces does she walk per chain?
b 8 ft
5 ft
65°
30 ft
Problem 15. Billy Joe’s pace is 12 paces per chain. He is measuring the distance to a fire from a stream. He takes 480 paces. How many chains is it to the fire from the stream?
Problem 16. The following table shows the relationship between depth and pressure upon bodies submerged in water. Draw a line graph using this information. On the horizontal axis, represent depth in feet. On the vertical axis, represent pressure in pounds per square foot. Find the slope of the line.
Pressure Depth
(psft) (ft)
123 2
250 4
375 6
500 8
625 10
750 12
1,250 20
1,875 30
Problem 17. From the line graph in problem 16, read the pressure at 25 feet.
Problem 18. The fireline intensity readings, in British thermal units per foot per second for the first 10 days of the fire were as follows:
Day Btu/ft/s
1 120
2 140
3 160
4 180
5 200
6 190
7 170
8 140
9 130
10 100
Draw a line graph using this information.
Problem 19. What is the slope of the line graph in problem 18 as it is increasing? On what day does the intensity of the fire peak? On what days is the intensity of the fire 130 British thermal units per foot per second?
Problem 20. Find the value that is in grid 3B.
D 9 4 0 3 25
C 1 8 42 8 16
B 5 6 22 2 33
A 6 5 15 7 14
1 2 3 4 5
Problem 21. Using the mileage chart in example 13, find the distance between Denver, CO, and Portland, OR.
The material in chapter 5 describes calculating area and perimeter of a burn, fire spread distance, and effective windspeed. How to read and use a map scale, convert map to ground distances, and use topographic maps are described in detail.
5.1 Burn Area and Perimeter Determining perimeter