What is the measured trajectory and amplitude when a horse jumps over a vertical fence?

Is there math involved in horse

jumping? Each time a horse jumps over different jumps with varying heights, the

trajectory of the jump from start to finish can be measured using several

different equations. When measuring trajectory in an object, there is a

specific formula to calculate the answer. This changes depending on the type of

object and situation being measured. With this question, height will be

measured, vertically. There are several equations that are part of the formula

to finding the trajectory. The formulas are as follows: and in order to calculate motion,

given

In order to find the answer, one

must separate horizontal and vertical measurements. One must also calculate

launch velocity, angle of launch, height, peak, and time in order to find

trajectory. Each component of calculating trajectory has its own equations.

Typically in the sport of jumping there is a pre-determined course of several

jumps at varying heights that the riders objective is to complete in a certain

manner and order. Sometimes the rider knows the course before hand, but more

often than not a rider will find out the course right before the show. There are several factors when riding a horse

in order to complete a jump. Finding the projected trajectory can be beneficial

to any rider attempting to jump a horse due to the fact that it can potentially

influence the riders decision making on timing, speed, and method used to

complete course. Because the jumps are typically at different heights, the

speed of the rider should be increased and or reduced accordingly. In the sport

riders use specific signals and commands to their horse to ask them to jump

over the jump. Knowing the proper timing component of trajectory is imperative

to successfully completing this process.

In this particular field of

research, previously recorded averages are vitally important to consider as

each component of the problem changes every time. A standard speed and time

should be considered for each different height.

The horses average size should also be considered, and the breed that’s

being measured and its average size as these numbers could change depending on

the breed. Thoroughbreds are often used as the quintessential jumping horse,

which stands at an average of 16 hands, and can travel at a approximately 44

miles per hour.

Materials

HorseTape

measure Computer

Arena

iphone

Background

An equestrian jumper must accomplish

two things to complete a jump in the air. They must be able to move their body

in a certain manner position and time, and to be able to sync their actions

with the horse they are riding. This takes a specific mathematical formula to

accomplish. When this happens simultaneously, when the formula is completed, the

jump is successful. Equestrian jumping includes hurdles in several different

fashions including: water, walls and

rails, gates, brush and rales, post and rail, triple bars, rail and plank,

oxer, and wall.

There are several different aspects

to consider when gathering data for jumps. One must consider including: the

height of the fence, speed of the horse, the angle of elevation between the

horse and the jump, the time of contact, the time of flight, and the total

distance from the takeoff point to the landing of the horse on the two front

hooves. Each part includes many different parts that are needed to accomplish

them.

Calculation

In order to calculate trajectory you

must find several things. You must have a “vertical position, (y), which can be

found with the equation . You must calculate

the horizontal position(x), the initial velocity (V0), the acceleration due to

gravity (g), and the initial velocity.

The units are measured in (M) meters.

As complex as it is to calculate

trajectory, one can easily display the data using a simple parabola format.

Other factors to consider when

conducting these experiments are their weight and food consumption. Horses can

only consume 2.5% of their weight every day. Weight estimation can be

calculated with the formula: (g2l)/12,000. You must also consider

the size of the arena, and area around and between jumps otherwise known as

“jump spacing”.

In an experiment conducted to

calculate horse trajectory, the conductor attempted to display all these

categories and use the proper according formulas to display the results of the

recorded trajectory for horses.

This graphs show and display data in regards to different

heights and different types of jumps, and their following results in trajectory

accordingly. (Bochis Flavia). The same experimenter recorded data for one

specific jump, (vertical fence) and included it in several tables.

Results

This experimenter used several

different types of jumps and materials under (as controlled variables) to get a

more valid result. The validity is increased significantly when the land under

the jump is changed because it increases your data for multiple cases.

Additionally the experiments validity was increased as they used several

different types of jumps which is an advantage for the same reasons. However,

the only downfall that would weaken the validity is the fact that they used one

horse, and a horse will get increasingly tired as they progress in jumping.

Works Cited

Panara, Sawyer.

“Parabola of a Horse’s Jump.” Prezi.com,

28 May 2013, prezi.com/oykccdzrzqwa/parabola-of-a-horses-jump/.

http://www.spasb.ro/index.php/spasb/article/viewFile/1413/1363

http://www.softschools.com/formulas/physics/trajectory_formula/162/