Why does the time per point get larger when I make my map larger??

Here is an example question and answer regarding this "quantum jumps" in map times/per point....

I discovered a behaviour I do not understand with large maps. What is
the explanation?


Consider the following LWS02 observation:

y		map
n		n rows
100		100"
n		n cols
100		100"
1		1 line
157.70		C+
4		standard 
n		not fast mode
30.143		very strong
0.1005E-13	very strong
24.		s/n
Running this case for various size (n x n) maps.
Note, the flux is so high the time is set
by the overhead.

n is stepped from 1 to 29 by 2. Below is recorded
n^2, and time/beam (i.e. time/n^2) in minutes below

Number of Beams    Time (min) per Beam
    1.00000        5.33333
    9.00000        1.74259
    25.0000        1.67800
    49.0000        1.55408
    81.0000        1.49239
    121.000        1.45579
    169.000        1.43166
    225.000        1.49548
    289.000        2.62543
    361.000        2.62368
    441.000        2.62241
    529.000        2.62146
    625.000        2.62072
    729.000        2.62014
    841.000        2.61968

Why does this make a jump after the 225 point map? One would
understand this if there were the need for illuminator flashes, but that 
overhead would then go down with increasing map sizes in the time per beam 


The logic in the LWS AOTs inserts illuminator flashes into the observation 
at intervals which are less than a fixed time TFLASH (currently set to 20 mins)
which is the time estimated to be the maximum time between illuminator flashes
which will allow a reasonable flux calibration to be made. It can only put 
these flashes in at certain times in the observation. These are:

1. At the start and end of the observation
2. At the start of each row of the map
3. At the start of each map point
4. Between scans on each map point

The flashes (1) are always included in an AOT the time taken for these (and
other fixed overheads, such as switching the grating on and off) is about 240s

The scans above on each point only take about 80 seconds to execute, so there 
is no need to insert flashes (4).

As the number of points in the map increases there comes a point when the
time taken to observe all the points in the map is greater than TFLASH. 
At this point it is necessary to insert a flash (2) at the start of each row 
of the map. This occurs when there are about 12 points in the map.

Similarly, when the number of points in a row of the map becomes so large that
the time taken for the row is greater than TFLASH, then flash (3) is inserted.
This occurs when the number of points in a row reaches 12.

This explains why the time per point decreases as the number of points 
increases until at a certain map size the time jumps up again. (There
is a bug in the software which puts flashes at odd times if the time per raster
line is exactly equal to the time between flashes - this explains why the 
15 by 15 map does not follow the rule).