Lab - INTRODUCTION TO UNIT CONVERSION & SCALE PROBLEMS

Calculation of photo scale and the measurement of distances and areas are fundamental skills in remote sensing. However, the various combinations of available information (scale, height, distance, focal length, etc.) and the use of both metric and imperial units of measurement can be confusing. This lab is designed to familiarize you with the common scale and area computations performed in association with remote sensing.

Outline:

When looking at a paper map, probably the most important thing to bear in mind is the map scale. The scale represents the ratio of a distance on the map to the actual distance on the ground. Map scales are expressed in a variety of ways (RF, verbal, graphic). The representative fraction relates a unit of measure on a map to some number of the same units of measure on the earth’s surface. For instance, a map scale of 1:25,000, tells us that 1 unit of measure represents 25,000 of the same units on the earth’s surface. One inch on the map represents 25,000 inches on the earth’s surface. Often when using cartographic materials it is useful to convert from various units of measurement. If you have a good understanding of the concept of scale, the techniques are fairly simple.  Example of various ways to interpret RF  1:50,000 means that a length of 1 unit of measurement on the photograph represents 50,000 of the same units of distance on the ground  RF can be restated by applying conversion factors Ex 1: 1:24,000 can be stated as 1in on the map = 2,000ft on the ground 24,000in * 1ft / 12in = 2,000ft

Ex 2: 1:100,000 can be stated as 1cm = 1km 100,000cm * 1km / 100,000cm = 1km

Ex 3: 1:60,000 can be stated as 1in = .95 mi 60,000in * 1mi / 63,360in = .95mi

Photogrammetry refers to the technique of obtaining reliable measurements of objects from photographic images. The scale of aerial photographs is a function of the focal length of the camera and the altitude of the camera. There are several pieces of information that are required in order to determine the scale of a photo if you do not have a map as reference. Need to know: Flying height of camera (altitude) Focal length – distance between the center of the lens and the film plane Common focal lengths: 88mm (~3.5in) 152mm (~6in) 210mm (~8.5in) 305mm (~12in) 450mm (~18in)

FocalLengthDefined.png Use the following formula to determine scale using focal length and flying height

Where h = terrain elevation H = height above ground (AGL) H1 = height above mean sea level (MSL) ***H & f must be in the same units

Ex: focal length = 6in = .5ft Flying height = 20,000ft 1/(H/f) = 1/ (20000/.5) = 1/40,000 = 1:40,000

Focal Length Determination Ex: scale = 1:10,000 H = 5000 AGL 1/10000 = 1/(5000/f) 1/10000 * f = 1/5000 f * 10000 = 5000 f = 5000/10000 f = .5ft

Aerial Photo Scale Determination with Maps Incorporating reference maps of the photographed area allows you to determine photo scale by comparing distances on the map (with a known scale) with photo distance. Use the following two formulas (depending on given information) to determine scale.

Formula 1 1/((MD*MSD)/PD) Where MD = map distance MSD = map scale denominator PD = photo distance Ex: MD = 6in MSD = 240,000 PD = 9in 1/((6×240,000)/9)=1/(1,440,000/9)=1/160,000=1:160,000

To make sure the MD and PD have the same unit.

Formula 2: 1/(GD/PD) where GD = ground distance PD = photo distance

Ex: Distance from point A to B on map = 2.5mi Distance from point A to B on photo = 1.28in 2.5mi = 2.5mi * 63,360 = 158,400in 1/ (158,400)/1.28 = 1/123,750 = 1:123,750

Photo Format Format of photo designates size of image acquired by the camera Common formats: 23x23cm (9x9in) 5.7x5.7cm (2.2x2.2in)

So, if the scale is 1:10,000 and the film format is 9x9in then: 1:10,000 1 side (9in) = 90,000in = 1.42mi therefore the total image covers area of (1.42)2 = 2.02mi2

Useful Conversions

1. A scale of 1 inch = 1 mile is the same as what RF? (1 point)

   If a map has a scale of 1:120,000, approximately how many miles are represented by 1in?(1 point)

   A reference map has scale of 1:50,000. How many kilometers are represented by 1cm? (1 point)

2. On a 1:24,000 topographic sheet, a segment of a highway measures 4.5in. What is its ground length in miles? (1 point)

   An airfield measures 2.5cm on a 1:50,000 scale map. How long is it in kilometers? (1 point)

   How long is it in miles? (1 point)

3. If the RC-8A camera has a 6in focal length, what is its focal length in mm? (1 point)

   The KA-88A camera has 23 x 23cm format. What is the format in inches? (1 point)

4. Determine the RF of the following photographic prints by using the given aerial photographic information: (AGL = altitude above ground level) (2 points)

A) Altitude = 100,000ft AGL Focal Length = 6in RF = _________________

B) Altitude = 10mi AGL Focal Length = 254mm RF = _________________

5. An aircraft was taking black and white photographs, using a KC-4 Fairchild camera, while flying at an elevation of 15,000ft (H1) in the vicinity of Denver, CO. Suppose that the average ground elevation in the Denver area is 5,000ft (h) above mean sea level (MSL). (2 points)

A) If a camera on board had a focal length of 6in, what would be the scale of the photographs?

B) The KC-4 usually has a format size of 9x9in. How many square miles does a single frame of the photograph contain?

6. A photograph was taken at 10,000ft above mean sea level over a land surface having an elevation of 2,000ft above mean sea level. The scale of the photograph is 1:16,000. What is the focal length (in inches) of the camera? (1 point)

7. At 30,000ft AGL, what distance (in miles) would be covered by 3in on photography acquired with a 6in focal length camera? (1 point)

8. You have acquired four different photos, each one having been taken at a different altitude (AGL), but all the photos were taken with a SOM Plate Camera which has a 152mm focal length (6in length). Please note that the numbers in parentheses indicate altitude – ensure that you response corresponds with the appropriate altitude.

A) The first photo was taken by the SCS (Soil Conservation Service) at an altitude of 5,000 ft AGL. What is the scale? (1 point)

_______________ (5,000)

B) The other three photographs were taken by NASA from a U-2 aircraft at 10,000ft, 20,000ft, and 40,000ft. All these altitudes are AGL. What is the scale of each of these last three photos? (3 points)

_______________ (10,000) _______________ (20,000) ____________ (40,000)

C) If each photograph is in a 9x9in format size, what is the linear distance (in miles) for each photo on one side (ground distance)? (4 points)

__________ (5,000) _________ (10,000) _________ (20,000) _______ (40,000)

D) How many square miles does each photo cover? (4 points)

__________ (5,000) _________ (10,000) _________ (20,000) _______ (40,000)

E) How does doubling the AGL affect the following: (3 points)

Scale?

Linear distance?

Area?

9. Given the following information, calculate the photo scale: (2 points)

A) Map Distance = 12in Map Scale = 1:20,000 Photo Distance = 6in Photo Scale = ____________

B) Map Distance = 3in Map Scale = 1:20,000 Photo Distance = 50.8mm Photo Scale = ____________

10. You want to construct a grid cell overlay for your aerial photo, so that each cell is 8 acres in area. If the scale of your photo is 1:12,000, what is the length of a cell on the overlay to the nearest tenth of an inch? (2 points)

11. Two aircraft equipped with KA-20B Hycon cameras (usually for reconnaissance) are flying over terrain in Oregon which is approximately 4,000ft above sea level. Aircraft A is flying at an elevation of 16,000ft and the camera on board the plane has a focal length of 6.0in. Meanwhile, Aircraft B is taking photographs of the same area as Aircraft A; however, B is flying at an elevation of 13,000ft with a camera having a focal length of 9in. Which photographs, from Plane A or B, will show the greater detail? Remember that large scales will show small areas in large detail. (1 point)

    Aircraft (1 point) _____________

12. Itek nine-lens multispectral aerial camera was used to take aerial photographs (nine spectral bands for each scene) of the northeast Kansas region. The plane flew at an altitude of 9,050ft above sea level, and the camera had a focal length of 152mm. If the average ground elevation is 1,025ft, what is the scale of the photo? (1 point)

If the format size is 5.7x5.7cm, how many square miles does each photo cover? (1 point)

13. You have just acquired photography that was made from a Zeiss-A-15/23 single frame aerial camera with a 6in focal length at 20,000ft AGL. (5 points)

A) What is the scale of the photograph? ________________

B) What would it be at 40,000ft AGL? ________________

C) At 80,000ft AGL? ________________

D) Which of the above is the larger scale? ________________

E) If you measured 1in on the largest scale photo, what would be the ground length in miles?

14. You are doing a research project for NASA and they want you to make a general land use map of Kansas using Skylab photographs. A S-190A Skylab Multiband camera with a 150mm focal length was used by the astronauts in taking the pictures. The multiband camera was designed and built by the Itek corporation and the film used had a 70mm frame format. Skylab was orbiting around the earth at an average altitude (AGL) of 435km.

A) What is the scale of these photos? (1 point) _______________________

B) What is the linear ground distance across 1 side of the photo in km? (1 point)

C) How many square miles does each photo cover? (1 point) _________________

D) Use the information you calculated in Number 8 (for the 5,000 ft. AGL) and determine approximately how many SCS photographs would be needed to cover all the area in one Skylab photo? (1 point)

E) What can you conclude about the purpose of differing scales of photography? (1 point)

15. Two objects on a map are 2.25in apart. The same two objects are 3.25in apart on the photograph. The following bar scale goes with the map:

                       1  1             
                    0  4  2     1           2
                    |--|--|-----|-----------|
                              MILES
    

A) What is the RF scale of the map? (1 point)

B) What is the ground distance between the two objects on the map? (1 point)

C) What is the ground distance between the two objects on the photo? (1 point)

D) What is the RF scale of the photo? (1 point)

There is no need to save anything from this lab, so when done you can simply close without saving. Submit your answers to the questions on blackboard.