Patrol intersection and interval timing

[Outcast_Shadow]

A friend is going to be running a game soon for which she is looking to see if there is any easy way for her to calculate the intersection intervals of multiple patrol groups traversing routes of differing lengths.

I couldn’t help her directly, at least not off the top of my head, but I told her I’d be happy to ask around. This is the first of my attempts to do so.

So the variables as I first spot them would include number of patrols, number of routes, speed of patrols, and length of routes. Can anyone help rough out a formula?

I feel like this has something to do with harmonics and wave functions but I can’t pull anything up from that far back in my maths history.

Solution found staring in my face. Apologies.

[Pauly]

A friend is going to be running a game soon for which she is looking to see if there is any easy way for her to calculate the intersection intervals of multiple patrol groups traversing routes of differing lengths.

I couldn’t help her directly, at least not off the top of my head, but I told her I’d be happy to ask around. This is the first of my attempts to do so.

So the variables as I first spot them would include number of patrols, number of routes, speed of patrols, and length of routes. Can anyone help rough out a formula?

I feel like this has something to do with harmonics and wave functions but I can’t pull anything up from that far back in my maths history.

The information you need:
Number of guards per shift.
The split between guards on patrols (looking for bad guys) and in garrison. (Ready to Respond to the alarm)
Number of routes
Number of guards per patrol (it easiest if this is the same for all patrols)
Length of shift
Length of time for each route (it is easiest if each route takes the same amount of time).

Your frequency of patrols will flow from the available staffing.

[Outcast_Shadow]

I missed the dead simple solution on this one. I’m good now... and feel a bit foolish

[Malphegor]

I missed the dead simple solution on this one. I’m good now... and feel a bit foolish

Eh sometimes all that’s needed to solve a conundrum is to ask a question- tech guys call this the Rubber Ducky Method- you ask a yellow rubber duck how to solve the problem and in asking the question your mind resolves it.

[Beleriphon]

A friend is going to be running a game soon for which she is looking to see if there is any easy way for her to calculate the intersection intervals of multiple patrol groups traversing routes of differing lengths.

I couldn’t help her directly, at least not off the top of my head, but I told her I’d be happy to ask around. This is the first of my attempts to do so.

So the variables as I first spot them would include number of patrols, number of routes, speed of patrols, and length of routes. Can anyone help rough out a formula?

I feel like this has something to do with harmonics and wave functions but I can’t pull anything up from that far back in my maths history.

Solution found staring in my face. Apologies.

Line graph with time/distance and each patrol as a separate line?

[Outcast_Shadow]

Line graph with time/distance and each patrol as a separate line?

Prime factorization to find lowest common multiple.