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Example 4.8. An EDM instrument has a carrier wave of 0.91m and is standardized at 20C and 1013.25hPa. A distance of 1885.864m was measured with the mean values P=1030hPa, dry bulb temperature t=30C, wet bulb temperature tw=25C. Calculate the velocity correction. Step 1. Compute the value for partial water vapour pressure e : logeses=tw+237.37.5tw+0.7857=25+237.37.525+0.7857=31.66hPa Using equation (4.27): e=ej0.000662P(ttw)=31.660.0006621030(3025)=28.25hPa Step 2. Compute refractivity (Ng) for standard atmosphere using equation (4.2.5): Ng=287.6155+24.88660+40.06800=287.6155+0.9124.88660+0.9140.06800=293.616 Step 3. Compute refractivity for the standard conditions of the instrument, i.c. 20C and 1013.25hPa, using equation (4.26) which for P and e in hPa becomes N8=273.15+tNg(0.2696P)273.15+t11.27e=273.15+179.159P273.15+111.27e 140 Engeering Sirineying. This in effect is the equation for computing what is called the reference or nominal refmetivity for the instrument Ns=273.15+2079.1591013.25273.15+2011.2728.25=272.52 Step 4. The reference refractivity now becomes the base from which the velocity correction is obtained. Now compute refractivity (Ne ) under the prevailing atmospheric conditions at the time of measurement: Ni=273.15+3079.1591030273.15+3011.2728.25=267.90 Velocily correction in ppm=272.51267.90=4.6ppm Correctioninmm=1885.8644.6106=8.7mmCorrecteddistance=1885.873m Using cquation (4.16) : (1) Velocity of light waves under standard conditions: ci=cot=2997924581.0002725=299710770m/s (2) Velocity under provailing conditions: Cp=299792458/1.0002679=299712150m/s As distance = (velocify x time), the increased velocity of the measuring waves at the time of measuring woald produce a positive velocity cocrection, as shown. Now considering equation (4.20) and differentiating with respect to 2.P and e, we have Nc=(273.15+t)20.2696NePbt+(273.15+1)0.2696NtsP(273.15+t)11.27d At f =15C,P=1013hPa,=10hPa and Nt=294, an error of 1ppm in NE and therefore in distance Wilt occur for an emor in temperature of 1C7 in presure of 3hPa and in e of 39hPa. Foom this itean be seen that the meavurementof humidity can ordinarily be igoored for instruments using light. Tempcratire and pecsare should be measured uting carefully calibrated, good quality equipment