Fn is proportional to the mass of the trailer, so it is irrelevant for the deceleration (a) if it is empty or not (because Ff = m*a).
µ is a constant relying on the tire/ground connection. Comparable to the towing car (if you happen to have car tire quality ones on your trailer, which might be doubtful)
.

On top of that, typical car trailers use overrun brakes that per definition work by exerting an additional force on the towing vehicle in the direction of movement that is then used to activate the trailer brake.

[–] Norodix@lemmy.world 1 points 4 hours ago

That is an oversimplified friction model that does not apply well to emergency braking. I still don't think you get a better braking distance with a trailer in a typical situation but thats not the reason why.

[–] vorpuni@jlai.lu 2 points 6 hours ago (1 children)

Fair enough, car trailers do have garbage braking most of the time anyway. I may be biased because locomotives are so heavy and the traction you get with steel is shit so they actually benefit from some load behind…

[–] Multiplexer@discuss.tchncs.de 1 points 6 hours ago (1 children)

Locomotives? What is your profession?
In any case, I seriously hope that you are not tailgaiting ;-)

[–] vorpuni@jlai.lu 2 points 6 hours ago (1 children)

Freight train driver. I don't tailgate, I like to leave plenty of distance in front of my car.

[–] Multiplexer@discuss.tchncs.de 2 points 6 hours ago

I meant tailgaiting with your train ;-)
(but yes, I am aware of the systems that prevent that, heard some interesting talks about the topic and seen demonstrations in our local railway museum)