By construction

- The number of submaps is the area of the map divided by the area of a
submap

- The number of on per off is the number of independent resolution
elements in each submap

- The number of independent resolution elements in the map is the
product of number of submaps by the number of on per off

- The submap area is the product of the area velocity by the time to
cover it

- The time to scan a submap is the sum of the
independent
on integration time

- The relations between times per coverage and times integrated over
all the coverages are

(30) - Using the last two points, it is easy to derive

- Finally, the total time spent on and off is given by

(32)

(34) |

Using Eqs. , and , we obtain

(36) |