1 Table of Contents Purpose...... 3 Procedure...... 4 Procedure- Field...... 5 Procedure- Office...... 6 Analysis...... 8 Conclusion...... 9 Observations...... 10
2 Purpose The purpose of this project is to calibrate an EDM, and to find the ppm corrections of an EDM. This is important, because without this correction, when we shoot a distance the measurement will be incorrect. We also performed this lab to help us learn the process for calibrating and EDM instrument. This is important because about every 6 months EDM instruments need to be calibrate.
3 Procedure The procedure for this project can be broken down into two sections: field and office. In the field section, the process for taking the measurements will be described, whereas, in the office section, the procedure for making the calculations and corrections will be described.
4 5 Procedure- Field
1. Obtain three tripods, the Topcon total station, two prisms (labeled #2 and #4), a PK nail, and a psychrometer (to record temperature and humidity.) 2. Setup the total station over point HAINES, and record the temperature and humidity. 3. Setup a tripod and prism over point ECKL and record the temperature and humidity. 4. Setup a temporary point with a tripod and prism on the line between HAINES and ECKL, and roughly one third of the distance between HAINES and ECKL. Place a PK nail in the ground where the prism is setup. Also, record the temperature and humidity in the field book. 5. Shoot the distance from HAINES to ECKL 10 times both direct and reverse. Record measurements in the field book. 6. Shoot the distance from HAINES to the temporary point 10 times both direct and reverse. Record the measurements in the field book. 7. Setup the total station on the temporary point. 8. Shoot the distance from the temporary point to ECKL 10 times both direct and reverse. Record the measurements in the field book.
6 Procedure- Office
1. Copy the measurements and atmospheric conditions into a table. 2. Calculate the First Velocity Correction (FVC). We must find the average of all the temperatures recorded. To get a more accurate temperature average we must weight the temperatures that were in the shade by the percent of the distance that was covered in shade.
Average temperature calculation:
Tavg. (Tshade %d shade ) (Tsun %d sun ) 13.9 ºC
Where Tshade is the average temperature in the shade, Tsun is the average temperature in the sun, and %d is the percent of the distance.
Then we calculate the refractive index of air under standard conditions using the equation given in the project manual:
4.8864 0.068 n 1 287.604 106 q 2 4 1 1
Where nq is the refractive index under standard conditions, and 1 is the wavelength of the infrared carrier beam in μm.
For the calculation above nq =1.000287
Now we must calculate the refractive index of air under conditions at the time of observation, which is represented by the equation:
0.359474n 1p q na 1 273.2 t
Where na is the refractive index under conditions at the time of observation, nq is the refractive index under standard conditions, and p is the pressure in mmHg.
For the calculation above na =1.000273
Next, we must calculate the reference index of refraction for the instrument by using the equation:
7 V0 n0 , 0 f 0
Where n0 equals the reference index of refraction for the instrument, V0 is the velocity of light in a vacuum, 0 is the modulation wavelength, and f 0 equals the wavelength modulation frequency.
For the calculation above n0 = 1.0002818.
Now we must calculate the manufacture’s EDM reference index using the equations:
6 N 0 (n0 1) 10 And, 6 N a (na 1) 10
In these calculations N 0 281.801 and N a =273.394.
Finally, we can compute the First Velocity Correction using the equation:
FVC( ppm) (N 0 N a ) ,
After computation we get the First Velocity Correction which is 8.407 ppm.
Now, we must apply the FVC to our 20 slope distances we recorded for each setup. To do this we use the equation:
6 Scorr S (FVC S) 10
After completing that step we must calculate the horizontal distance using those corrected slope distances and the recorded zenith angles. To do this we use the equation:
Horizontal Distance= Scorr sin(zenith)
Finally, we must calculate the constant error using the equation:
(d d ) D 1 2 ’ s n 1
Where s is the constant error, d1 is the horizontal distance from Haines to the temporary point, d 2 is the distance from the temporary point to ECKL, D is the distance from Haines to ECKL, and n is the number of setups. In this step the constant error equals 16.5 mm.
8 Analysis
In this project the constant error was calculated to be 16.5 mm. The constant error is more significant over shorter distances. The constant error means that the measurements taken in this project were accurate to plus or minus 16.5 mm.
The other part of the error calculated was the first velocity correction. The first velocity correction in this project was 8.407 ppm. This first velocity correction is the error that quantitatively explains that the measurements recorded were accurate to plus or minus 8.407 mm per kilometer.
The errors calculated above may not be correct though. This is because we are using the modulation wavelength, wavelength modulation frequency, and the wavelength of the infrared carrier beam values from a different instrument. This may help explain why the constant error is so high, and why the first velocity correction does not correspond with value the nomogram gives at the end of the project manual. Another reason why the calculated errors may not be accurate, is due to the temperatures recorded were to low when compared to the archives at www.phys.ufl.edu/~weather. This error could have been caused by a blunder such as, inaccurate reading, or may have been caused by the scale on the psychrometer being incorrect. One observation made is that each of the temperature measurements is off by 10°C. If this is truly the case, the temperature readings are more closely aligned with the temperature archives at www.phys.ufl.edu/~weather. This would also change the first velocity correction to 17.609 ppm.
9 Conclusion
It can be concluded that at 13.9ºC and at an atmospheric pressure of 759.206 mmHg, the Topcon GPT 1003’s calibration settings must be set at a constant error of 16.5mm and a first velocity correction of 8.407 ppm. This will make the measurements much more precise and accurate than if no corrections were made.
10 Observations
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