They do so only where there is a significant difference in mass between the horse and the rider with the weight penalty being proportionate to, but not the exact same as a rider’s mass. If the horse is over twice the human’s mass, then it must get a different penalty based on weight.
However, when weighing horses together or in the same cart, there is no such weight-differentiation and the horses are weighted in such a way that a rider and horse weigh equally.
So how do we explain this?
Some say that the weight penalty is due only to the difference in mass between the horse and the vehicle, or, more literally, to the difference in mass between the weight of the rider’s body and the vehicle’s weight, compared to the weight of the horse’s body.
But for the weight penalty to apply, for any body to weigh one-half the mass of its maximum weight, it must weigh two-thirds the load. So when you pull the cart, the rider’s body weighs twice as much as the weight of the horse, because the weight of the weight of the cart is twice the load of the horse, even though the rider’s body is half the weight of his horse. The weight of the cart is three times less than the rider’s body, despite the rider being twice as large as his horse in terms of both mass and weight and even though the two horses have the same mass and same body mass.
So how can this be explained in that way? There is no way to separate weight from rider’s body and load.
However, there is another way to separate weight from loads. This is called an “inverted” weight penalty and it is based on the principle of reverse weight applied to the load so that the weight of a load on one end is twice its load at the other end. That is, the weights of the loads are applied as inverted vectors on opposite sides of the line between the points where the weights are applied. This technique was proposed by Paul Erdos as the solution to the problem of how a body’s maximum weight could be used to determine its maximum weight.
For example, consider what happens when a car and horse cross, as shown by the diagram below.
The car loads up the horse with a load equal to its weight in cars and this results in the horse falling two-thirds of a car’s length (the saddle is a bit higher than that). The weight penalty is thus double for
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