how would a trailing dog be used in SAR, and when is it better than air scent?

A mantrailer can establish a Direction of Travel in a situation where the there is a Last Known Place or Place Last Seen. This will help in the deployment of 'Ground Pounders' and Air-Scent Dogs.

Mantrackers can do the same thing. You can teach humans to track, but you cannot teach them to airscent. Dogs are probably faster than humans, but other than that, I don't see any point in training a tracking/trailing dog if you have mantrackers available as a resource. I'd love to hear differing opinions!

I agree, mantrackers(=signcutters) can establish a DoT. In my experience though, sometimes it's hard enough to find good SAR dogs in an area, let alone signcutters.
Like you said, dogs are probably faster. When it comes to tracking/trailing, dogs are almost certainly faster. Remember, a Search is an emergency first, time is of the essence.
BTW, trailing dogs are using their noses, and are not necessarily limited to ground scent; just like a good Air-Scent dog will use ground scent when necessary.

Don't get me wrong, I'm not totally disagreeing with you. These are all tools of a SAR mission, unfortunately, we rarely have all of these tools available at a given Search.

Depends on the situation and terrain. Typically, family and friends, etc. have stomped over the immediate area to the point that getting a track there is near impossible.("Well, we've tried everything else...let's call the dogs") Dropping outside the search perimeter and looking for sign may be your best bet.

Inexperienced searchers usually greatly underestimate how far someone can travel in a given time frame. The person you are attempting to find may, for whatever convoluted reason(s) not wish to be found. (Cchildren playing at not being found, EDP's who are afraid of people/dogs they do not know, suicide attempts, etc.) These "victims" may move ahead of or around the team, making a difficult job more frustrating.

A good trailing (TTD) dog will soon learn to use whatever he is given to make a "find". Teaching him to track will not prevent him from using air scent once it becomes strong enough to over-ride the track scent, but it does give you another option should you not have air scent to work with at any given time. Conditions such as heavy, damp air/fog, thick brush, swamps, etc. may be encountered where little to no air is moving, etc.

Trailing (TTD) is simply another tool in your team's toolbox, but it can be a very valuable one.

mantrailer, mantracker, signcutter........
what is the difference between mantracker and mantrailer? and what is a signcutter? never heard that before....

very cool. never heard of that before.
the more i learn, the less i know......

Are those mantrackers bullshivik? Have they actually found people? What kind of records are there?

What kind of conditions can they work. Certainly not urban or even rural that have people that frequently use the areas begin searched. I doubt one would be of any real help in a national forest in peak season either. Seems they would need virgin ground to track someone by clues?

Am I way out there?