This paragraph describes the algorithm to do a time/sensitivity estimation for a position-switched On-The-Fly observation.

**Step #1: Computation of and**-

is just computed as the ratio . Using Eqs. and , we obtain

Using this equation, we start to compute for and . We want to enforce the integer character of in a way which decreases the product . To do this, we use

Eq. ensures that . The value of must be decreased so that Eq. is enforced. **Step #2: Computation of or**- We use the following
equations in descending order to compute the elapsed telescope time and
in ascending order to compute the rms noise level:

(39) (40) (41)

**Step #3: Computation of derived quantities**-

(42) (43) (44) (45)

**Step #4: Is an integer number?**- The interpretation of the
above equation to compute
has two cases.
- . This means that either the user tries to cover a too large sky area in the given telescope elasped time (sensitivity estimation) or the telescope need a minimum time to cover at the maximum velocity possible with the telescope and this minimum time implies a more sensitive observation than requested by the user (time estimation).
- . will generally not be an integer, we can think to decrease from to obtain an integer value. However, this must be done at constant . Decreasing thus implies increasing . It is not clear that this is possible because of the constraint . Another way to deal with this is to keep to its maximum value and to adjust (sensitivity estimation) or and thus (time estimation) to obtain an integer value of . However, this implies a change in the wishes of the user. The program can not make such a decision alone and we will only warn the user. Indeed, the worst case is when is changing from 1 to 2 because this can decrease the sensitivity by a factor 1.4 (sensitivity estimation) or double the elapsed telescope time (time estimation). The larger the value of the less harm it is to enforce the integer character of .