The Physics of Riding Horses
Horses and Jumping
Horses are lovely creatures that possess a wild, marvelous beauty and can provide a thrilling ride. But you better wait to put on your riding gear. Do you have any idea of what to expect when you first get on a horse? The answer is one big mass of physics concepts.
And you want to jump, you say? Well, that is by far the most fun (though more dangerous) activities that are possible on horses. But, you must be asking yourself, how does it all work? What physics is she talking about? And, you mean, you're actually physically on the horse when it's jumping??
Yes. It's fun, and the concepts are rather simple. First we will look at balance, the key to a rider's success. Then, we will browse through the different speed options available on horses, and how Newton's laws play a part in that. Lastly, we will discuss other exciting things like potential and kinetic energies, velocity, acceleration, etc., and you will see horse jumping in the works.
Don't forget to check out the world record setter high jump link. Can you believe a horse managed to fly over 8 feet in the air? 8 feet!? How is that possible?! ...Physics, anyone?
How In the World Do You Stay On A Horse?
The answer is simple: balance. Equilibrium as defined by the Webster's Dictionary is: a state of adjustment between opposing or divergent influences or elements. Any and every horseback rider knows that one wrong command or one wrong move can throw her off balance and off the saddle. Balance is one of the most important things to master when riding a horse. It is easily understandable that balance is important if you look at the situation from the physics standpoint. According to the laws of physics, a rider is most stable if their center of gravity is above the horse's and their weight is equally distributed in the saddle. When a rider mounts a horse, it throws the horse's center of gravity off. Now, there is even more weight on the front of the horse than it was naturally.
Because a horse's weight is primarily located at its front, its center of gravity is not at the horse's center, but rather more near the front, approximately where its heart is (the red lint). The rider sits right behind the withers (the green line), which is slightly behind the center of mass, and reduces the riders surefootedness. As the horse moves forward, the rider will feel a force pushing her back. This is a perfect example of Newton's first law of motion: an object remains at rest or in motion unless acted upon by an outside force. To account for this movement, the rider has to adjust her position balancing herself on the horse by distributing her weight equally on both feet in her stirrups. If she just sits there, the motion of the horse will cause her to be thrown onto the horse's neck (thank you inertia).
Adjusting to the Four Gaits
The Walk
The walk has a distinct four beat rhythm. When the horse is walking, its movement is easily accounted for by the rider. All she needs to do is settle her weight into the heels of her feet in the stirrups.
The Trot
The trot has a two beat rhythm to it. It is much harder to adjust to the trot than to walking (and in my opinion cantering) because the rider is bounced up and down with each pace. This bouncing causes the rider to be thrown up and down, hitting the saddle pretty hard easily unseating her if she does not adjust properly to this movement. So, what's happening? Newton's third law: for every force, there is an equal and opposite force. The horse exerts a force on the rider as its hooves make contact with the ground. The rider in turn is bounced upward. To account for the bouncing, the rider can do something called posting, which is where for every other step, or beat, of the horse, the rider lifts herself (with the push of the horse) on her stirrups and misses the horses jerk. For the second beat she sits down lightly and then is pushed up again. Also, during this process, the rider must lean more toward the horse's front to keep her from falling backward with the force of the horse. Posting is a controlled way of trotting. The rider synchronizes her posts with the horses, and it makes the ride much less bumpy.
The Canter
During the canter, which is a three beat gait, there is a point where the horse has all four hooves off the ground. This is a much smoother gait than the trot. The speed however is much greater than the other two gaits, and the important thing is to keep the rider's weight distributed equally in both stirrups, and also to keep her center of balance above the horse's.
For Your Information
There is another gait in addition to the three previously mentioned, and that is the gallop. I find this gait the most thrilling of them all. The gallop is very similar to a canter, except it is a four beat movement and the horse's legs move one at a time. If the rider tries to sit in her seat in the gallop, she would surely be thrown off immediately. The speed that the horse is going at that time is caused by the great force it is exerting on the ground, which in turn causes a large movement. To prevent herself from falling, the rider must raise her seat above the saddle and stay in that position during the ride, sinking her weight into her heels.
Let's Talk About Jumping
Understanding that the more speed the horse has, the higher it can jump, is helpful when preparing to jump a fence. The faster the horse goes the more kinetic energy it has to turn into potential energy during a jump.
Potential energy = mgh
Kinetic energy = 1/2 mv2
There are three basic gaits that are very common to riders: the walk, trot and canter. A horse cannot easily jump from a walking pace. If the fence is not very high, it is probably not necessary to have a very high speed when jumping over it. So, a trot may suffice. However for very high jumps, one needs a lot of speed, and also a large horse. These seemingly logical concepts to a horse rider are also easily explained by physics.
The Mechanics of a Jump
When the horse leaps upwards, it exerts a jumping force on the ground. This force is applied only as long as its hooves are touching the ground. The greater that this force is, the higher the horse will be able to jump, because it increases the launch speed from which it's jumping. Once the horse's hooves touch off of the ground, its speed will immediately start decreasing, until it gets to the top of its arc where its vertical velocity equals zero. When airborne, only one force is acting on the horse (if we neglect air resistance), and that is gravity. Gravity is the force pulling the horse back to the ground at a rate of 9.8m/s2 (and that would be negative on the horse's way up). After the horse reaches the highest point of its jump it starts to descend. Its velocity then increases, at a rate of 9.8m/ s2 until the hooves reach the ground. The rate of gravity is only one of two components that make up the picture.
The velocity of jumping a horse is a vector that has two components, a vertical and horizontal. The one that has already been discussed above is the vertical velocity, which changes at a rate of 9.8m/s2. While in the air, the horizontal velocity stays constant; it does not change. These two vectors add up to what is called the resultant velocity. It is important to note that only the vertical component changes, and the horizontal stays the same.
Another important thing to note when jumping is the range of the jump. When it comes to directing a horse on when to jump there are a couple of factors to keep in mind. The angle at which the horse jumps will determine how far it will go. The most advantageous angle, where both the height and range are optimal, is a 45 degree angle. However, that may not be the best option for certain jumps. Attaining the right height is more important than going a long distance. Generally, the higher the jump, the steeper the launch angle needs to be. Also, there is no knob, or button to push on the horse that can set an angle at which to jump at, so the rider has to adjust the horse in other ways. First of all, the rider can make sure to estimate the right time to signal the horse to jump. This involves pacing the horse just right. If the horse leaves too early, it will not make it over the jump, and if it leaves too late, it will knock the jump over. The skill of timing the jump takes practice to get right.
Why Bigger Horses Are Better (for jumping that is)
First of all I would like to point out that larger horses are better only for jumping over very high jumps. I'm afraid that the little ponies (as cute and cuddly as they are) won't be able to make it over a six foot fence (unless they are on steroids). However, this is not their fault; blame it on physics.
The acceleration of a horse depends on its strength and mass. According to Newton's second law, objects accelerate according to how much net force acts on them and how massive they are. By the equation Force equals Mass times Acceleration
(F = m*a), acceleration is proportional to the force. Also, acceleration is inversely proportional to the mass, but the more mass a horse has, the more strength, or force, it has. Basically, the bigger the horse, the higher it can jump.
See It for Yourself: The Jump Revealed
This clip demonstrates a simple jump. A rider starts off from a canter jumping over a homemade jump: a bail of hay.
The physics of riding a horse. This graph illustrates the rider in the clip jumping over that bail of hay.
This is
a position time graph of the jump. It's a pretty fair representation of what
actually happened during the jump. The reference point of the "observer"
is the bail of hay. From its point of view the horse jumps over it, it is moving
away, and decelerating. After it reaches the top, it starts to go down, accelerating,
and moving towards the observer.
Since this is a position graph, we can calculate the acceleration from the distance equation: d=1/2at2+v0t+do
In this case we just substitute y for d, and since we don't have initial velocity, and initial distance, we plug in the numbers and the equation becomes:
-7.13=1/2a
acceleration= -14.26 m/s2
Even though the acceleration we are looking for is supposed to equal the rate of gravity (around -10m/s2), the resulting number, -14.26m/s2 is not that much off considering the estimations I had to make about the horse during the clips analysis. I think I over estimated the horse's height, and even so, it is hard to measure everything else very accurately.
Explanation
Well, when a horse jumps, it exerts an upward force. This in turn would cause the rider to bounce right off the horse if she wasn't prepared. Right before the jump, the rider prepares herself for the upcoming upward and forward motion of the horse by lifting her seat from the saddle slightly, and settling her weight into her heels (this is similar to what the rider does while galloping). During the jump, she allows the horse to move forward by moving her hands forward and giving the horse enough rein to stretch out its neck. At the beginning of the jump, it is important for the rider to lean forward so that the force of the horse that is pushing her back doesn't overtake the situation. However, if she forgets to lean backward when the horse lands, she is in danger of falling forward on top of the horse's neck (thanks again inertia). The impact of the ground coming in contact with the horse's hooves creates a large force pushing the rider forward. This is why it is so important to be prepared for that force and not lean forward too much.
This jump is not a very high one by far, and it is relatively easy to jump over. The extent to which the rider has to adjust her weight and position is not as extreme as it needs to be for higher jumps. For the very high jumps, the force of the horse is greater, along with the angle at which it jumps from, and also at which it lands. The following site takes you to a world record breaker horse jump. Notice that the rider has his stirrups very high on his horse, so as to be lifted very high above the horse's back. This allows the horse to move under the rider without the rider being knocked off by the intensity of the force.
Horse record jump site:
http://homepage.mac.com/john.brian/Living-with-Horses/HorseRecordHiJumpVideo.htm
Bibliography
Clark, Missy. "Horse Sports and Sportsmanship." Practical Horseman July 1999: 8. MAS Ultra - School Edition. EBSCOhost. May 23, 2005 <http://web8.epnet.com/citation.asp?tb=1&_ug=sid+ED2E756B%2D33B7%2D4793%2DBEC3%2D7C8E9E7A4AB5%40session>
*Provided great insight to horseback riders, and also had some great pictures.
Gittewitt, Paul. Conceptual Physics: Third Edition. California: Addison Wesley Longman, Inc., 1999.
*Textbook helped with general physics concepts/definitions.
Morris, Sue. The Gaits The Walk. Classical Dressage Notebook. May 23, 2005 <http://www.classicaldressage.co.uk/TheGaits/the_gaits.html>.
*Information on how to ride a horse, the basics, what to do and not to do. Also, had great information about the gaits of horses.
The Balanced Horse. Stablemarket: Free Equine Classifieds. May 23,
2005 <http://www.horsemanpro.com/articles/balance.htm>.
*Lots of great info on balance of horse. Also provided other concepts about
horses.
Wofford, Jim & Lliff, Elizabeth. "Where to Look Before Leaping." Practical
Horseman April 2005: 70-76. EBSCOhost.
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*Information on horseback riding in general, especially on jumping techniques.
World Record Horse High Jump. Outelaunee Horses. May 23, 2005 <http://homepage.mac.com/john.brian/Living-with-Horses/HorseRecordHiJumpVideo.htm>.
*Interesting video clip: the world's highest horse jump.
World's Record Highest Jump. The Ultimate Horse Site. May 23, 2005 <http://www.ultimatehorsesite.com/info/worldrecord_jump.html>.
* More info on highest record setting jump.