[mmaimcal]Antenna Acceleration

[Mark Holdaway]

Hi,

There is a bit of a stir with folks trying to change the antenna
specifications at this late date.  In this message, I look into the
possible effects of reducing the maximum acceleration in AZ from 24
deg/sec^2 to 18 deg/s^2.

First off, I don't think that this reduction will affect
fast switching capability, so I concentrate on OTF (On-The-Fly).

My model for the antenna motion and OTF capability is derived from top
secret VERTEX documents which I should not have seen -- but these are old
documents, based on VERTEX simulations and not on actual measured profile
motions, so nobody will have to kill me for looking at these docs. Anyway,
I created a mathematical model for antenna motion, loosely based on the
Vertex simulations, which does a simple parabolic acceleration turn-around
at the end of a constant velocity scan across the source.  The *jerk* (ie,
time derivative of the acceleration) is the dominant way that vibrational
modes will be excited in the antenna (if these vibrational modes are
excited, then we could get into situations where the antenna is
momentarilly bent up and isn't pointing where we think it should be), I
built in the constraint that the JERK always be less than 100 deg/s^3 --
this number coming from looking at the graphical Vertex simulation
results. 

OK, this possible antenna motion profile fits within
the constraints of what should be possible -- but will
not be optimal, but may be close to optimal.
Remember, for OTF total power work (where we need to
really zip fast to reduce atmospheric fluctuations), we don't
need to have the 0.7" repeatable pointing, we just
need to know where the antenna was pointed after the fact,
and not be so far off from the desired path so as to
result in unsampled parts of the source.

I, The Programmer, have the power to set the maximum AZ acceleration to
WHATEVER I WANT, be it 24 or 18 (or even 12) deg/s^2.  The max AZ velocity
is 6 deg/s.

The antenna specification for OTF motion states
0.5 deg/s is the top velocity on the sky.

With a decreased antenna acceleration, we won't be able to
turn around as quickly for a source at very high elevation
angles.  (At high elevations, we need to move faster and faster
in AZ to make the 0.5 deg/s on the sky; the time on source per
OTF scan will be the same, but as we are going faster, it will take
longer to turn around and the duty cycle will decrease.)
How much of an impact is this likely to be?

Consider a source 0.5 deg across, and we observe it
by zipping across it at 0.5 deg/s ON THE SKY in a constant
elevation path.  What is the duty cycle (t_on/t_total) for
the 12deg/s^2, 18deg/s^2 and 24 deg/s^2 maximum accelarations, as
a function of elevation?

# results for sourcesize =  0.5 deg  and velocity =  0.5 deg/s
# el   duty12   duty18    duty24
#[deg]
20    0.8135    0.8135    0.8135
25    0.8108    0.8108    0.8108
30    0.8072    0.8072    0.8072
35    0.8029    0.8029    0.8029
40    0.7975    0.7975    0.7975
45    0.7910    0.7910    0.7910
50    0.7830    0.7830    0.7830
55    0.7732    0.7732    0.7732
60    0.7609    0.7609    0.7609
65    0.7453    0.7453    0.7453
70    0.7232    0.7247    0.7247
75    0.6641    0.6960    0.6960
80    0.5701    0.6522    0.6522
85    0.3996    0.4996    0.5706


So, it is only above 80 deg elevation that there is
a difference between 18 deg/sec and 24 deg/sec.
In other words, the JERK constraint is usually limiting
the acceleration -- only at the highest elevations when we are zipping
like crazy does the decreased acceleration limit us.

Smaller (or larger) sources will have different values of the
duty cycles, but the duty cycle will not diverge between
the 18 and 24 deg/s^2 cases until we go above 80 deg.

If a slower velocity is used, we won't see an effect until
we go to even HIGHER elevations.

If a faster velocity is used (ie, above the 0.5 deg/s spec),
then we will see the divergence at lower elevation angles.


WARNING:  My antenna motion profiles are not magic.  There may be other
ones out there that might be good and would go a bit faster on the
turnaround, and would come up against the accleration limit at slower
antenna velocities (ie, lower elevations).

I don't see any problem with going to 18 deg/s^2 in AZ,
I don't see any problem with going to  9 deg/s^2 in EL,
and I have no official position on 12 deg/s^2 in AZ.


   -Mark