Note: The telescope is stowed when the wind speed is 25 miles/hr = 11.1 m/s for a sustained period of 1 minute.

The user will define the worst pointing error, , that their science can accommodate while NRAO will define the best pointing error, , that we allow the specified frequency band to use. Currently since the pointing is dominated by wind these pointing errors correspond to wind speeds.

The user will define the worst pointing error, , that their science can accommodate. Currently since the pointing is dominated by wind these pointing errors correspond to wind speeds and the value of will correspond to a maximum wind speed (). As a default let us set as the wind speed that will produce a two-dimensional pointing error yielding a 10% rms flux error for a point source.

Let us define the minimum wind speed, , as the wind speed that will produce a two-dimensional pointing error yielding a 2.5% rms flux error for a point source. Also, let us set a user default value for the maximum wind speed, , as the wind speed that will produce a two-dimensional pointing error yielding a 10% rms flux error for a point source.

The normalized gain is given by Condon (2003, PTCSSN3)

But - 5% rms flux error is a maximum wind speed option we need to allow. So, this isn't going to work. Instead, let try a 2.5% rms error, as I show in the tables below (numbers in ()). I've also adjusted up the vmax numbers just to match the 10% rms numbers in the ptcs page. - KarenONeil

Yep, my mistake. I changed the text above and the table below. So we specify a range from 2.5% rms flux errors (better than the PTCS good performance) to 10% flux errors (the PTCS usable performance). - DanaBalser

where . A 5% error in flux corresponds to f = 0.14, while a 10% error in flux corresponds to f = 0.20.

The normalized gain is given by Condon (2003, PTCSSN3)

Pointing errors due to wind are approximated by (Condon 2003, PTCSPN26) where the two-dimensional pointing error caused by wind is

arcsec,

where . A 2.5% error in flux corresponds to f = 0.10, while a 10% error in flux corresponds to f = 0.20.

where V is the wind speed and is the one-dimensional pointing error.

For frequencies below 25GHz, the wind limit corresponds to a wind-induced pointing error which, when added in quadrature to the "benign conditions" tracking error of 2.8", would cause the total tracking error to exceed the respective limit. For frequencies above 25GHz, the wind speed at which the pointing variance contributed by wind is one quarter of the total allowed pointing variance at the specified observing frequency.

Pointing errors due to wind can be approximated by (Condon 2003, PTCSPN26)

Therefore,

• Frequency <= 25 GHZ

arcsec,

where V is the wind speed and and are the one and two-dimensional pointing errors, respectively. The wind speed is then given by

or

.

m/s

N.B., we need to adjust these numbers vis-a-vis Note 4 on the PTCS page.

The telescope is stowed when the wind speed is 25 miles/hr = 11.1 m/s for a sustained period of 1 minute. Therefore the lower frequency bands will never be observed. So we set for X-band and below to the value at X-band.

• Frequency > 25 GHz

Temperature Parameter

Weather affects the signal-to-noise ratio (S/N) in two ways: (1) it attenuates the signal; and (2) it increases the system temperature and therefore the noise. The signal, S, is proportional to , while the noise, N, is proportional to the system temperature . So we define a temperature parameter, T, that is inversely proportional to the S/N ratio as

or

,

m/s

where we have indicated that the system temperature and opacity are frequency dependent.

The user will specify the worst temperature, , for their observations while NRAO will specify the best temperature, .

Question: What is the best way to set the min and max temperature values? Maybe the value for could be the lowest values of T observed in the database, removing outliers. And the value for could be , the temperature at which one would have to integrate twice as much to achieve the same S/N ratio as the conditions of .

Atmosphere

Question: Since T is a non-linear function of frequency how do we compare values of T between frequency bands?

Weather affects the signal-to-noise ratio (S/N) in two ways: (1) it attenuates the signal; and (2) it increases the system temperature and therefore the noise. The signal, S, is proportional to , while the noise, N, is proportional to the system temperature . So we define a temperature parameter, T, that is inversely proportional to the S/N ratio as

,

where we have indicated that the system temperature and opacity are frequency dependent. As T increases our observing efficiency decreases. The integration time is inversely proportional to the noise squared. So we can parameterize the observing efficiency as .

Let us define the minimum wind speed, , as the wind speed that will produce a two-dimensional pointing error yielding a 5% rms flux error for a point source. Also, let us set a user default value for the maximum wind speed, , as the wind speed that will produce a two-dimensional pointing error yielding a 10% rms flux error for a point source.

Let us define the minimum wind speed, , as the wind speed that will produce a two-dimensional pointing error yielding a 2.5% rms flux error for a point source. Also, let us set a user default value for the maximum wind speed, , as the wind speed that will produce a two-dimensional pointing error yielding a 10% rms flux error for a point source.

Yep, my mistake. I changed the text above and the table below. So we specify a range from 2.5% rms flux errors (better than the PTCS good performance) to 10% flux errors (the PTCS usable performance). - DanaBalser

where . A 5% error in flux corresponds to f = 0.14, while a 10% error in flux corresponds to f = 0.20.

where . A 2.5% error in flux corresponds to f = 0.10, while a 10% error in flux corresponds to f = 0.20.

The temperature parameter is defined as

Weather affects the signal-to-noise ratio (S/N) in two ways: (1) it attenuates the signal; and (2) it increases the system temperature and therefore the noise. The signal, S, is proportional to , while the noise, N, is proportional to the system temperature . So we define a temperature parameter, T, that is inversely proportional to the S/N ratio as

where is the system temperature and is the opacity. The temperature parameter is frequency dependent.

where we have indicated that the system temperature and opacity are frequency dependent.

The user will specify the worst temperature, , for their observations while NRAO will specify the best temperature, .

Question: What is the best way to set the min and max temperature values? Maybe the value for could be the lowest values of T observed in the database, removing outliers. And the value for could be , the temperature at which one would have to integrate twice as much to achieve the same S/N ratio as the conditions of .

Question: Since T is a non-linear function of frequency how do we compare values of T between frequency bands?

N.B., we need to include the receiver temperature, the CMB temperature, and the spillover temperature in Ron's value of the system temperature.

But - 5% rms flux error is a maximum wind speed option we need to allow. So, this isn't going to work. Instead, let try a 2.5% rms error, as I show in the tables below (numbers in ()). I've also adjusted up the vmax numbers just to match the 10% rms numbers in the ptcs page. - KarenONeil

Define Wind (low) as the wind speed that will produce 5% rms flux errors and Wind (high) as the wind speed that will produce 10% rms flux errors for point sources. The normalized gain is given by Condon (2003, PTCSSN3)

The user will specify the pointing errors that they can tolerate in units of the half-power beam-width (HPBW). Let us define f as the two-dimensional pointing error in units of the HPBW given by

where is the two-dimensional pointing error and is the HPBW.

The user will define the worst pointing error, , that their science can accommodate while NRAO will define the best pointing error, , that we allow the specified frequency band to use. Currently since the pointing is dominated by wind these pointing errors correspond to wind speeds.

Let us define the minimum wind speed, , as the wind speed that will produce a two-dimensional pointing error yielding a 5% rms flux error for a point source. Also, let us set a user default value for the maximum wind speed, , as the wind speed that will produce a two-dimensional pointing error yielding a 10% rms flux error for a point source.

The normalized gain is given by Condon (2003, PTCSSN3)

where , , is the 2-dimensional pointing error, and is the beam FWHM. A 5% error in flux corresponds to f = 0.2, while a 10% error in flux corresponds to f = 0.14.

where . A 5% error in flux corresponds to f = 0.14, while a 10% error in flux corresponds to f = 0.20.

,

.

N.B., we need to adjust these numbers vis-a-vis Note 4 on the PTCS page.

The telescope is stowed when the wind speed is 25 miles/hr = 11.1 m/s for a sustained period of 1 minute. Therefore the lower frequency bands will never be observed. So we set for X-band and below to the value at X-band.

The temperature parameter is defined as

,

where is the system temperature and is the opacity. The temperature parameter is frequency dependent.

%META:TOPICINFO{author="DanaBalser" date="1165425300" format="1.0" version="1.1"}% %META:TOPICPARENT{name="WebHome"}%

Weather Requirements

Wind

Define Wind (low) as the wind speed that will produce 5% rms flux errors and Wind (high) as the wind speed that will produce 10% rms flux errors for point sources. The normalized gain is given by Condon (2003, PTCSSN3)

where , , is the 2-dimensional pointing error, and is the beam FWHM. A 5% error in flux corresponds to f = 0.2, while a 10% error in flux corresponds to f = 0.14.

Pointing errors due to wind can be approximated by (Condon 2003, PTCSPN26)

arcsec,

where V is the wind speed and and are the one and two-dimensional pointing errors, respectively. The wind speed is then given by

,

Temperature Parameter

-- DanaBalser - 06 Dec 2006