# The Physics of Our Carriages

The physics for our carriages is actually pretty straightforward. Roller bearings have a very low coefficient of friction, in the neighborhood of .002, and thus it is usually ignored since it has almost no effect. If we forego the friction of the bearings, all we have left is the load and the rolling resistance of the wheels. Most carriages use hard rubber wheels, and if we look up a chart of those rolling friction values, we can find a max value of .303 (inches at 3mph).

Assuming flat ground, now we just use F= f x W/R where

F = the force required to overcome the friction, i.e. keep each wheel of the carriage moving

f = .303 (coefficient of friction in inches from readily available charts online for hard rubber on concrete)

W = load on each wheel, we will figure as max (1900lb horse x 3 = 5700lbs, 5700lbs/4 = 1425lbs per wheel)

R = radius of each wheel (in inches to match friction coefficient), we will use 35 inches as most carriages have 30" fronts and 40" rears

This gives us F= .303 x (1425/17.5), or F= 24.7 lbs per wheel

So 24.7lbs x 4 wheels = 98.8lbs for the carriage fully loaded

The starting load is always ~2-2.5 times the sustaining load, so that would be 98.8 x 2.25 = 222.3lbs figured at middle. You can see that a few hundred pounds wouldn't mean anything. Even a 1000lb difference in total weight would only decrease the forces required to 81.4lbs sustain and 183.2lbs start, which a draft horse would not even notice (.9% of his bodyweight, or 1.8lbs to a 200lb person)

Furthermore, if you look at the research that's been done on draft horses, you'll find that horses are at their most efficient when the sustained work they do is equivalent to 1 horsepower (no big surprise as that is where the term comes from). So how does that relate to the above?

For linear motion, Horsepower (HP) = (F x V)/33000, where F=force (lbs) and V=velocity (ft/min). We travel about 2 miles in an hour on a tour, which is 176ft/min

So the HP of the above = (99x176)/33000 or 0.53HP.

This is barely above half of what is considered ideal for a working horse to sustain all day without breaks, not to mention only an hour at a time.