wheres thefire
TRANSCRIPT
Where’s The Fireby
Larry Rice
All
IntroductionAs a Cartographer you will be making maps from photos taken by satellite and airplane so that you can:
name specific locations on the map,
estimate how much of the ground area has been burnt by fire (or where there is fire), and
plan how you will fly your plane closer to the ground to take multiple smaller photos that will combine to show more detail.
Fly the plan, take the photos
Your work will be used by the community to estimate risk to residents, where to fight the fire, and to plan the recovery of natural resources. All
Topics CoveredMapping Basics
Estimating Map Areas
Digital Camera Basics
Aerial Photos
Unit conversions
Compass Directions
Flight Algorithm
Flight Plan
Mapping Basics
All
When combined, these are perpendicular
Lines for A GridA
vertical Line is
up-down
A horizontal line is left-
right
A map grid is made up of multiple
vertical lines, equally spaced (parallel)
And multiple equally-spaced horizontal lines
(parallel)
4th GradeHands-on: make vertical, horizontal, parallel, and perpendicular lines on paper
Labels on a MapNotice that our
map, as with most all maps, has
several labels and symbols...
The Compass Rose shows which way is north, always up on
maps, and it sometimes shows other directions:
south, west, east.
There are many other types of compass
rose, for example...
The scale shows us how far a distance on a map is, in this case, 2.5 Km (Kilometer) is
as far as the white line is long...
And a map may have titles explaining areas or points of interest
AllHands-on: Draw map labels and titles on photos or in GIS software
How Big is the PhotoBefore we draw our
grid, we need to pick an origin, the starting
point,
and determine the dimensions (width and height) of our photo-map, using the scale.
Km is Kilometer
The Origin is often the bottom left
corner
This is 20 Km high
8 x 2.5km
This is 30 Km wide
12 x 2.5km
AllHands-on: use scale on map to determine dimensions or distance between things
A quick Check on Terminology
AA
BB CC
__ Vertical Line__ Horizontal Line__ Compass Rose__ Scale__ Label__ Perpendicular__ Parallel
DD
EE
FFGG
AllHands-on: Identify on an actual map
Laying out a GridWe can now draw different grids.
(Remember, this photo map is 20Km high by 30Km wide)
A large grid has 3 horizontal, 4 vertical
lines (10Km apart)
A medium grid has 3 horizontal, 7 vertical
lines (5Km apart)
A small grid has 9 horizontal, 13 vertical
lines (2.5Km apart)
You should note that each area drawn is a square, all sides are of equal length and are perpendicular, since all grid lines are equally
spaced.All
Hands-on: Draw differing grids on actual maps
Coordinates for the Grid
We will now select our Origin to be the upper left corner
So we can now use letters going
down to label the vertical direction,
numbers going left to label the
horizontal direction, these
can be shown on two sides or all
four sidesLetters
BB
AA
Numbers
11 22 33
The Grid location name becomes the letter-number combination
A1A1 A2A2 A3A3
B1B1 B2B2 B3B3
All
Can you Label a Different Sized Grid ?
Using the same
method, type in the label and each grid location
____
____
____
____
__ __
__
__
AllHands-on: add labels on grids created previously
Estimating Map Areas
All
Estimating Fire Damage
4th Grade
To estimate how much forest is damaged by fire,
we will use different shapes that each have an area of 10 square miles
Use any number of shapes to cover all the areas in the
photo map that are dark red. You can rotate the shape to complete the
puzzle. Once all dark red is covered, count how many
shapes have been used, did you get 15 to 20 ?
The area burned is about 150 square miles
(15 shape x 10 square miles each)
Hands-on: Complete area estimate on actual maps / photos with cut-out shapes
Chart the Areas
4th Grade
You have made pie charts before, can you complete this chart,
showing how much area is burned (dark red), forest (green), rock
(dark brown), and other.
Fire Damage
______________
_______Hands-on: Draw Pie chart on paper
Estimating Fire DamageTo estimate how much
forest is damaged by fire, we will count the
number of squares that include mostly bright red areas (3 here),
then divide it by the total squares in the grid, in this case 6
If the photo map is 20Km by 30Km, then the area covered by
the map is the product of these, or 600 Square
Km
Mostly all dark
red
Three of the six squares2 / 6 = 1 / 3
33% of the area is burnedis our estimate, this is
about 200 Square Km (Km2)
7th Grade, High
School
Estimating Fire Damage
We can get a more detailed, or more
accurate, estimate by using a smaller
grid, in this case our grid with 8 vertical
labels and 12 horizontal labels,
this map has 8 x 12 squares, 96 total
27 of the 96 squares27 / 96 =
28% of the area is burnedis our estimate here, a little less
than 33% from before7th Grade,
High SchoolHands-on: On paper grids made previously
Can you complete an Estimate of the Fire
DamageGiven this grid,
what is your estimate of the fire-damaged
area?
Is it close to the previous
estimates?__ of the 24 squares
__ / 24 = __% of the area is burned,
this is __ Km2
7th Grade, High
SchoolHands-on: On paper grids made previously
Digital Camera Basics
7th Grade, High
School
Photo & Viewing Sizes
Media Horz Vert
DVDs 16 9
35mm Camera 3 2
Digital Cameras,
Monitors, TVs4 3
Photos, TVs, DVDs and other displays are generally not
square in size, they all have a specific ratio, horizontal to
vertical, sometimes called an aspect ratio. This is noted as a
ratio, Horizontal:Vertical
Digital Photos usually have a 4:3 ratio
7th Grade, High
School
Horizontal
Vertical
Hands-on: Measure distances on TV, computer monitor, DVD being played
Pixel ResolutionCamera Rating
HorzPixels
VertPixels
12 MP 4000 3000
6 MP 2828 2121
3 MP 2048 1536
7th Grade, High
School
The MegaPixel (MP) rating on a digital camera is a
specification of the number of pixels created / captured by
the camera, Mega referring to 106
With the aspect ratio at 4:3, the pixel dimension of the
longest side of a digital photo is
43
* MP
Hands-on: make calculations with calculator
Please note, a doubling of the MP rating only results in a 40% increase in pixels
(resolution)
Check your Understanding
What are the pixel dimensions of an 8 MegaPixel digital camera?
_____ X _____
7th Grade, High
SchoolHands-on: make calculations with calculator
Camera Lenses
7th Grade, High
School
Hands-on: for multiple zoom settings on the digital camera, measure multiple distances and photo width, calculate angles, make summary table.
The angle of photo captured from a camera is dependent
upon the length of the lense focal
length, measured in
mm
AngleLenseArea in Photo
Film or CCDs
The digital camera we will use changes lense length
through zoom, from 45mm to 55mm, we will use 50mm for this activity, a common sized
lense.
Some example angles by lense size include:
Lense Size (mm)
20 35 45 50 55 100
Horizontal Angle
83 53 45 39 36 20
Reference: Lense angle chart
Aerial Photo Resolution
7th Grade, High
School
Camera
Rating
HorzPixels
VertPixels
12 MP 4000 3000
6 MP 2828 2121
3 MP 2048 1536
In order to see fire areas in a photo, endangered species, or invasive species, we need to create aerial photos with a minimum resolution. There should be at least one pixel for every foot on the ground. It would be best if we have photos that have 10 or more pixels per foot. The MP resolution of the camera effects this, remember the table we had before.
Pixels per foot
Horz Distance
VertDistance
1 4000 ft 3000 ft
4 1000 750
12 333 250
In order to determine how high to fly our plane with the digital camera, we need to determine how much area should be covered by the camera on the ground.
If we use a 12 MP camera, there are 4000 x 3000 pixels captured, if we need 1 pixel per foot, then the area on the ground should be 4000 ft x 3000 ft, easy yes? How about four pixels per foot (divide distance by 4), twelve pixels per foot (divide distance by 12), what is the ground area for these?
Aerial Photo Resolution
7th Grade, High
School
Camera
Rating
HorzPixels
VertPixels
12 MP 4000 3000
6 MP 2828 2121
3 MP 2048 1536
Can you complete a table for a 3 MP camera ?
Pixels per foot
Horz Distance
VertDistance
1
4
12
Flying Height Calculations
High School
Hands-on: make calculations with calculator, Sine, Cosine, and Tangent
Given the table you completed for a 3 MP camera with a 50 mm lense. We will calculate the distance above the ground the Plane needs to fly in order to get 12 Pixels per foot resolution. This will take some Trigonometry...specifically Tangent
390
Height
512 Ft
Trig provides several functions to help in determining the length of sides on a right triangle, given an internal angle is known.So we create a right triangle between the camera and the ground. This bisects the lense angle (39/2) and the width of the photo area on the ground (512/2).
256 ft
Height
19.50
Please note, since two internal angles are known for this right triangle, the third angle can be found, all three angles in a triangle sum to 180. That angle is 70.50.
Height = 256 /Tan-1(19.50) =240 Feet
Tan (19.50) = 256 / Height
A Check on Understanding
High School
Hands-on: make calculations with calculator (TI83 or HP50, for example)
Pixels per foot
Horz Distanc
e
VertDistanc
e
Height above
Ground
1 2048 1536 2891
4 1024 768 722
12 512 384 240
Can you calculate the height above ground for this 3 MP camera with a 50 mm lense, given pixel resolutions of 4 per foot and 1 per foot.
Unit Conversions
7th Grade, High
School
Units and Conversions
7th Grade, High
School
So far we have used several types of unit measurements: KiloMeters, Milimeters, Feet, and Pixels. We will also be using Miles, so we need to review how to make distance unit conversions between Metric (meters, Km, mm) and English (Miles, feet).
References: Unit Conversion, Metric prefixes and Metric Conversions
Unit conversions can be made within the English or metric systems:
1000 meters = 1Km1000 mm = 1 MeterIn these cases, move the decimal three places.
Within the English system it is a bit more difficult, conversion factors must be used, for distance5280 ft = 1 mile, use the conversion factor of 5280 ft/Mi.
Show some example conversions and have student complete some conversions.
Aerial Photos
All
Photo RC Plane Flight PlanTo plan a flight path of an RC plane we will first assume a 3MP camera with a 50mm lense, this is a common digital camera you can buy in most any electronics store.
We require a resolution of 3 pixels per foot on the ground so that we have photos with sufficient detail for analysis (10X the detail of satellite photos).
This means we must fly the RC plane 250 feet above the ground while taking the photos. The photos will therefore cover a path of about 500ft wide by 375ft.
We will be flying over two new areas: Bone Creek Reservoir and Crawford Wildlife area. Both satellite photos are 1 mile in one dimension, about 5000 feet. On one we will calculate the area of water and on the other the forested area (no fires in either).
Above numbers are rounded for ease of calculation.
All
What is an ArrayThe map grid we
completed previously can also be thought of as an
array.
An array is pattern of shapes (squares in this
case), number of shapes high by wide: A 2 x 3
Array
Our RC plane photos are rectangles, not squares.
The ratio of width to height is 4:3. We will
create an array of photos using these rectangles.
2
3
All
What is the Flight Path?
Hands-on: Grade 4 - place photo-sized cutouts in two patterns over the photo map. Grade 7, High School - measure photo map and calculate array.
All
Can you create an RC Plane array of photos over this area? You can fly the plane in two directions, one up / down (North / South), the other left / right (West / East).
The full area needs to be covered, so the photo array from the plane would be 10 x 10 or 8 x 14Which is better (less photos, less flying, more accurate) ?
500’
375’
5000’
3750’
All
10 x 10(100 Photos)
(Best)
8 x 14(112
Photos)
How much area is covered by forest ?
66 photos x 500’ x 375’= 12.4 Million Sq. Ft.
What is the Best Flight Path?
All
5000’
6700’
500
375
Can you determine how many photos need to be taken for this area, to determine the area of water at the reservoir?
10 x 18 (180 photos ) (west <-> East Flight Path)
or 14 x 14 (196 Photos) (South <-> North Flight
Path)
Compass Direction
All
Angles on a Compass
N
S
W E
NNE
ENE
ESE
SSE
SE
NE
SW
SSW
WSW
WNW
NW
NNW
Example: ENE“East North East”at 150 increments
4th Grade?7th Grade,
High School
3600 / 00
450
900
1350
1800
2250
2700
3150
Zero is at the top, angles in degrees going clockwise, 360 degrees total
How about another Direction?
Hands-on: Grade 4 - place photo-sized cutouts in a pattern, at an angle. Measure the angle. Convert the angle to compass direction.
5000’
6700’
How about flying at a diagonal, could this require less photos, flying, and be more efficient ?
What angle (or compass direction) would be best?
Can you do better than 6 paths, 72 photos, at 75 degrees, ENE ?
4th Grade?7th Grade,
High School
Flight Algorithm
7th Grade, High
School
What is the Flight Algorithm?
An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, sometimes named a method, procedure, or technique (Wolfram).
7th Grade, High
School
As you can see from the last two examples, the method to create the smallest flight array could be on the longest or shortest dimension, dependent upon the product of the array dimensions. And the number of photos needs to cover an equal or greater area, not less (round up of the number).
So how would you explain the steps?
Hands-on: Can this be done electronically? Possibly only on paper?
Your Procedure ?
7th Grade, High
School
Ls
Ws
Lp
Wp
Step 1: divide Ls by Lp, round up answers to the nearest integer. Divide Ws by Wp, round up the answer to the nearest integer. Step 2: State the Array ratio. Step 3: Reverse the calculations (Ls / Wp and Wz / Lp), a flight path perpendicular to the first calculation.
Step 4: Select the lowest product of each, lowest total number of photos.
Hands-on: Can this be done electronically? Possibly only on paper?
Flight Plan
7th Grade, High
School
Flying the RC Plane
7th Grade, High
School
5000’
3750’
5000’
6700’
The final calculations to be made for the flight plan are time required to fly one path, all paths, with turns and time between photos. We will assume the RC plane flys at 15 MPH and a single-engine plane flys at 75 MPH (5X faster).
500
375
Unit conversions will be required to find travel times. 5280 ft/mi and 3600 s/hr (60 s/min X 60 min/hr) are to be used.
15 MPH x 5280 ft/mi = 22 ft/s, RC Plane 3600 s/hr
75 MPH x 5280 ft/mi = 110 ft/s, Plane 3600 s/hr
Flying the RC Plane
7th Grade, High
School
5000’
3750’
To fly 3750’
- The RC plane would take
3750 ft / 22 ft/s = 170 sec = 2.8 minutes to fly one pass. With 10 paths, this would take 28 minutes to fly (not counting the turns). Photos would need to be taken every 375 feet, or every 17 seconds (375 ft / 22 ft/s).
- The single-engine plane would take
3750 ft / 110 ft/s = 34 sec = 0.57 minutes to fly one path. With 10 paths, this would take 5.7 minutes to fly (not counting turns). Photos would need to be taken every 375 feet, or every 3.4 seconds (374 ft / 110 ft/s).
Flying the RC Plane
7th Grade, High
School
5000’
3750’
When we include the turns, 9 total, we need to determine the distance for the turn. Assuming it is circular, the diameter is 500 ft, Circumference = diameter x pie, 1/2 the circumference is used for the turn, so the turn is 250 ft x Pie = 785 ft, for 9 turns, 785 ft x 9 = 7070 ft total distance in turns.
For the RC plane (22 ft/s), the turns will add 320 seconds (7070/22) or 5 minutes. Total time is 28 + 5, 33 minutes total flying time (check the RC battery).
For the plane (110 ft/s), the turns will add 64 seconds, or 1.1 minute. Total flying time is 5.7 + 1.1, or 6.8 minutes total.
500’
Turn
Check your Calculations
7th Grade, High
School
5000’
6700’
500
375
Can you determine the total flying time for this photo, both the RC plane and single-engine plane. How many seconds between photos?
Topics CoveredMapping Basics
Estimating Map Areas
Digital Camera Basics
Aerial Photos
Unit conversions
Compass Directions
Flight Algorithm
Flying Plan
Final Project 12 Miles
8 Miles
For the satellite photo of Pittsburg, determine the following RC plane plan details, given a 12MP camera with a 55mm lense and 12 pixels per foot resolution:
Grade 4- Create labels for the photo- If the RC plane flys over the area and takes a photo 1 square mile, what is the minimum number of photos required for the full photo.-Show the path you would fly to cover just the city area with pictures- How big is Pittsburg in square miles- Draw a pie chart of the types of areas in the map (City (buildings/houses), farming, forest)
Hands-on: Assemble and fly the RC plane over an area, take photos by plan (camera MP and lense, flight direction, height, time between photos, distance between paths)
Grade 7 & High School- Determine minimum photos to be taken (array) for the full area, just the city, flying direction, % area is city (buildings and houses), farming, size of the city, total flight times.High School- How high should you fly the RC plane- How often, number of seconds, should you take photos over the area- Total flight time for RC and single-engine
SummaryAs a Cartographer you are now able to make maps from photos taken by satellite and airplane to:
name specific locations on the map,
estimate how much of the ground area has been burnt by fire (or where there is fire), and
plan how you will fly your plane closer to the ground to take multiple smaller photos that will combine to show more detail.
Fly the plan, take the photos
Your work will be used by the community to estimate risk to residents, where to fight the fire, and to plan the recovery of natural resources. All
Where’s The Fireby
Larry Rice
All