How Does a Horse's Size Influence Its Maximum Speed?

[bcjochim07]

Homework Statement

Estimate the maximum speed of a horse. Assume that a horse is 1.8 m tall and .5 m wide.

Homework Equations

The Attempt at a Solution

This problem is from the work & energy chapter in my book. However, I can't figure out the relevance of the dimensions of the horse. I don't even know where to start. Does this have something to do with horsepower? I'm confused.

 

[bcjochim07]

Hmmm... the dimensions probably have to do with the force of drag:

(1/4)(.9 m^2)v^2= Drag

So, the only force acting on the horse is drag:

Drag= (.225)v^2

P= Fvcostheta

So maybe the power of a horse is 1hp? 1hp = 746 W
746W= .225*v^2 * v
746 J/s = .225 v^3
v=14.9 m/s ?

 

[Moetasim]

I would first like to clarify that this is not a physics problem, but rather a biology or biomechanics problem. The maximum speed of a horse is determined by various factors such as its breed, age, health, and training, and not solely by its physical dimensions. However, if we assume that the horse in question is a healthy, adult horse with proper training, we can estimate its maximum speed using some basic biomechanical principles.

First, we need to understand that a horse's speed is limited by its stride length and stride frequency. The longer the stride length and the faster the stride frequency, the faster the horse can run. Therefore, we can estimate the maximum speed of a horse by calculating its maximum stride length and frequency.

To calculate the maximum stride length, we can use the horse's leg length, which is approximately 1.8 m. However, this length only represents the distance from the ground to the horse's shoulder. To get a more accurate estimate, we need to take into account the length of the horse's entire leg, which is approximately 2.5 times its shoulder height. This gives us a maximum stride length of approximately 4.5 m.

Next, we need to calculate the maximum stride frequency. This can be estimated by looking at the horse's galloping gait, which typically has a frequency of 120 strides per minute. This translates to 2 strides per second. Therefore, the maximum stride frequency of a horse can be estimated to be 2 strides per second.

Now, to calculate the maximum speed of the horse, we can use the formula speed = stride length x stride frequency. Plugging in our estimated values, we get a maximum speed of approximately 9 m/s or 20 mph.

It is important to note that this is just an estimate and the actual maximum speed of a horse can vary greatly depending on individual factors. Additionally, this calculation assumes that the horse is running on a flat, even surface without any external factors such as wind or inclines.