Originally Posted by greenstork
The only physics in play here is the fact that the trailer itself is slightly heavier than racks and the trailer wheel does add some extra rolling resistance. But trailers don't add drag other than rolling resistance and as other have pointed out, and may actually decrease wind resistance compared to racks and panniers.
But you're still moving a given amount of mass up and down a slope using different gears. Take wind and rolling resistance out of the equation -- how that weight is positioned fore and aft, on the bike or off the back of the bike -- makes no difference on how much effort is needed.
I think the decision to tour with racks/panniers vs a trailer is more about ride characteristics, terrain, transportability, adaptability and personal preference than it is about physics. The bike will ride differently with a rack, cornering will be different for instance, and balance. The amount of force required to push the bike up a hill will be roughly the same however.
Actually, racks and bags aren't really lighter than a trailer. My bags (Ortliebs) and racks weigh in at about the same weight as a trailer.
The place where physics and a trailer really come into play is on corners. The bike, bags and rider are one unit with the forces of cornering applied only to the wheels of the bike. All forces are acting on this single unit and the two contact patches of the tires.
When a trailer used instead of bags, you now have a separate unit which the forces of cornering act on independently (or nearly
) of the towing vehicle. Because the trailer is typically attached low on the bike, it can effect the center of gravity and how the bike maintains contact with the road. As you enter the corner, the trailer has it's own momentum and a vector that it wants to follow off the road which the bike isn't following at the same time. This tends to push the back of the bike off line towards the outside of the corner. Additionally, the trailer can 'lift' the back of the bike and reduce the contact patch area a little, leading to more force towards maintaining the straight line and less force to continuing around the corner.
Other forces on the bike are frame flexure as the trailer wants to keep going straight. The frame flex can translate all the way to the front of the bike and change the steering characteristics of the bike. If you have a stiff frame, this flexure is less but still noticeable and, the higher the load, the worse this flexure would be.
I've ridden a flexible framed bike with a trailer and a stiff framed bike with a trailer and both have issues with corners. The flexible framed bike couldn't hold the line on a corner with as little as a 40 lb load. To be fair, this bike doesn't do well with much more than that in panniers. The other bike still had some problems but not as much but it also has a front shock which seems to help with the wandering on corners issue.
I do think that trailers have their place...like off-road touring or bikes that can't have racks mounted. I use one for off-road tours because the benefits of being able to loft the front wheel over obstacles outweigh the cornering issues. If I have to walk sections, I found that a trailer makes the bike a bit easier to handle than panniers, too.