Accuracy and understanding of the aerial mapping language.

When planning a photo mission to be utilized for any type of photogrammetric mapping purpose, certain principles must be taken into consideration when designing the initial flight plan. There are certain factors that must be addressed to ensure that accuracies are met and the mapping delivered will meet the client’s expectations. In certain situations, especially during RFP scenarios, a vendor can push flight heights in order to fly higher, cover more ground with fewer exposures and even reduce the required ground control. This in turn creates a design that provides the requested mapping at cheaper costs. This does not, however, produce an accurate photogrammetric product. Knowing the tricks of the trade will enable the client to look at quotes from different aerial companies and compare apples to apples. In the past, I have had a few clients call up to tell me they had received our proposal, it looked great, but they only understood the words aerial photography; the rest was written in another language. Understanding that “other language” will enable the client to fully understand the processes involved during the design and planning stages of a topographic mapping project. This article is a brief introduction to the primary factors involved; its focus is on a few of the main steps that can be taken to guarantee accuracy during that initial period.

One of the primary issues that must be addressed, especially if any surface modeling or contouring is required, is the overall contour factor, or C-factor. C-factor is an expression that is used to describe the relationship between the height of the aircraft (above mean ground level, or AGL) and the smallest accurate contour interval that can be generated from a given flight height.

When determining what flight height is required to achieve the desired accuracy of the contour interval for the end product, or vice versa, one starts with some simple equations, as follows:

Fh / Ci = Cf

Where Fh represents the flight height above mean ground level (in feet), Ci represents the contour interval and Cf represents the C-factor.

Cf x Ci = Fh

Where Cf represents the C-factor, Ci represents the contour interval and Fh represents the flight height above mean ground level (in feet).

However, before we utilize the above equations, we must ask ourselves who, or what, determines what C-factor calculation produces an accurate contour? In the United States, most photogrammetrists and map makers rely on two primary guides when it comes to map accuracy: The American Society for Photogrammetry and Remote Sensing (ASPRS) and the nationwide established National Map Accuracy Standards (NMAS). Both standards are very similar in purpose, and mapping at any scale performed within the states falls within the boundaries of either of these two specifications.

When determining C-factor, the two are incredibly similar, with ASPRS requirements being a little more stringent than NMAS. The maximum C-factor that each specifies to achieve accurate contouring and vertical accuracy is shown below:

1" = 40' planimetric overlay with 1' contours over a .25' pixel orthophoto. C-factor for this project was 1,800. Location: Avondale, Ariz.
Maximum C-factor*

ASPRS (Class 1) 2000

NMAS 2100

* As given when utilizing analytical stereoplotters or softcopy digital workstations.

1" = 40' planimetric overlay over a .10' pixel orthophoto. C-factor for this project was 1,500. Location: Santa Ana, Calif.
Now that we have some equations to execute and standards to adhere to, let’s try some examples:

C-Factor Example 1: You have a 1"=40' map with a 1' contour interval and you want to determine if the map meets ASPRS Class 1 accuracy for C-factor. The project was flown at a scale of 1"=300', or 1,800 AGL. Utilizing the first equation:

1800 / 1 = Cf

Cf = 1800

Hence, the C-factor for this project would be 1,800. It does not exceed the ASPRS maximum of 2,000, thus the map meets ASPRS Class 1 accuracy for C-factor.

1" = 40' topographic map with 1' contours. C-factor for this project was 1,500. Location: Costa Mesa, Calif.
C-Factor Example 2:Your goal is to produce an NMAS accurate map with a 2' contour interval, but don’t know exactly what altitude to fly. Utilizing the second equation:

2100 x 2 = Fh

Fh = 4200 AGL

Hence, the altitude of the aircraft cannot exceed 4,200 feet above ground level to preserve NMAS accuracy.

For the most part, the above equations will suffice for determining and maintaining C-factor, however there are other factors that can influence the precision of a project’s C-factor. The overall C-factor can vary reliant upon the type of compilation instrument being utilized. For the purpose of this article, I have assumed all mapping for the above examples would be performed on analytical and softcopy stereoplotters versus analog. Non-calibrated mapping cameras and meager photo control can also cause considerable errors that can negatively impact project C-factor and overall map accuracy.

Another extremely important issue when designing a photo mission is determining what the resulting enlargement factor will be. On large-scale mapping projects (i.e. 1"=40', 1"=50', 1"=100'), extreme amounts of planimetric, or cultural, features are collected. Examples of planimetric features include: curblines, power poles, signs, fences, sidewalks, lane striping, manholes, etc. As the final map scale gets smaller, or as the plane gets higher, more and more planimetric detail is omitted. This is due to the fact that planimetric features may not be visible on the photographs as altitude increases.

To preserve the visibility of planimetric detail, as well as horizontal accuracy, both the ASPRS and NMAS also maintain set factors for enlargement. The maximum that each specifies as maximum enlargement is shown below:

Maximum Enlargement Factor*

ASPRS (Class 1) 7.0

NMAS 7.5

* As given when utilizing analytical stereoplotters or softcopy digital workstations.

Calculation of photo scale is based on the preferred horizontal accuracy that is required for the end product. The following equation can be utilized to determine enlargement factor for a given photo scale or map scale:

Ms x Ef = Ps

Where Ms represents the map scale denominator (in feet), Ef represents the enlargement factor between the photo scale and the map scale, and Ps represents the photo scale denominator (in feet).

Enlargement Factor Example: You need to produce an NMAS accurate 1"=50' map and want to determine what photo scale will ensure horizontal accuracy. Utilizing the above equation for determining enlargement factor:

50 x 7.5 = Ps

Ps = 375, or 1" = 375'

Hence, to maintain NMAS horizontal accuracy for the above project, the project photo scale should not exceed 1"=375', or 1:4,500.

In most large scale mapping scenarios, you will find that C-factor and enlargement factor both have to be taken into consideration. During cases like this, the larger (due to lower altitude) of the two photo scales should be selected to ensure that both C-factor and enlargement factor accuracies are met. For example, if you are planning an ASPRS 1"=100' scale mapping project that requires a 2' contour interval, utilizing the aforementioned equations, you will arrive at a maximum C-factor photo scale of 1"=666' (4,000' AGL) and a maximum enlargement factor photo scale of 1"=700' (4,200' AGL). To ensure that both accuracies are met, the lower altitude, or smaller scale, flight needs to be selected and utilized for the project design. It is also commonplace to round down to an even denominator of, say, 1"=600' for the actual photo mission. After laying out the same project with the 1"=600' photo scale, it will ensure your project a C-factor of 1,800 and an enlargement factor of 6. Both are well within ASPRS accuracy requirements.

As you can see, C-factor and Enlargement Factor are essential aspects to pay special attention to when planning a topographic mapping project. Familiarizing yourself with the “language” used by aerial companies will assist you in ensuring that the product you receive is actually what you requested. There are a gross amount of horror stories floating around on the subject of flight heights being pushed and mapping not meeting accuracies. Always pay special attention at the design stage of any photogrammetric project and always check data provided to you. Don’t be afraid to pose questions to your aerial mapping provider. Any reputable company will take the time to explain their production methodologies and how their project design will meet the required project accuracies. Both ASPRS and NMAS standards have been designed and established through extensive research and testing. Used correctly, they can literally guarantee that any resulting photogrammetric mapping will maintain its published degree of accuracy.

References:

Manual of Photogrammetry, Fourth Edition, American Society of Photogrammetry, 1980

Edgar Falkner, Aerial Mapping: Methods and Applications, CRC Press, Inc., 1995

Richard Burns, PLS, Caltrans LS/LSIT Preparation Course