"One Giant Leap"
('The Jump' in terms of Conservation of Energy)

Equestrian Jumping, as a sport, can be broken down into a series of single jumps which are then combined together with both changes of direction and series' of multiple jumps.  These variations, with the addition of height, provide the different degrees of difficulty associated with 'jumping'.  The jump itself can be viewed in three parts:

• The 'Approach':Includes the three strides before a fence and the 'takeoff' in front of the fence.
• The Jump: The air time as the horse rises in the air, experiences 'hangtime', and begins to descend back down to the ground.
• The Landing: Includes actual 'impact' of the horse hitting the ground, and the follow through as horse and rider continue on to the next fence.

These three pieces combine to create that 'flying' sensation, but it is definitely not a simple process!  The most important thing in jumping a horse is regulating the speed of the horse on approach so that the horse has enough energy to clear the full height of the fence.  Now riders don't carry odometers on their wrists, but this page will examine the speed required to clear a fence based on the principle of conservation of energy.
 

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The Approach
 

 
• Upon approaching a fence, the horse and rider possess only Kinetic Energy, KE, if the ground is considered to be 'y-zero'.  This kinetic energy is expressed by:

                                                        KE = 1/2mv²

The Jump
 

• Over the top of the fence, the horse and rider reach maximum height and their velocity is reduced to zero; thus, they possess only Potential Energy, PE.  This Potential Energy is expressed by:

                                                       PE = mgy

The Landing
 

 
• When the horse returns to the ground, horse and rider are once again at 'y-zero' and thus possess only Kinetic Energy, KE, expressed by:

                                                    KE_f = 1/2mv_f²

Using conservation of Energy, the jump can be divided into two parts; the first part (which will include 'The Approach' and 'The Jump') will show that the initial Kinetic Energy, KE_i, can be set equal to the Potential Energy at the top of the jump and, using a known height, we can determine the necessary initial velocity.  The second part (which will include 'The Jump' and 'The Landing') will show that the Potential Energy, PE, can be set equal to the final Kinetic Energy, KE_f, to determine the landing speed, v_f.

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Now, for some numbers . . . If a rider wishes to jump a 5 foot fence, how fast will they need to be going on 'approach'? Also, If horse and rider do clear the fence, how fast will they be going on 'landing'?

        Part One:                                     KE_i = PE
                                                   1/2 mv² = mgy

• y= 5 ft. = 1.52 m because 1 meter is equal to 3.281 ft.
• In calculation, one should assume that the horse may jump up to six inches higher than the fence, depending on their perception, thus y = 1.52m + 0.15m or y=1.52m
• Due to non conservative forces, such as air resistance and heat, the potential energy reached at the top of the jump will only be about 80% of the kinetic energy present on approach.

                                                    1/2v² = 0.8(9.8m/s²*1.52m)
                                                         v_low = 6.1m/s
                                                     v_{high = 6.4m/s}

      Part Two:                                   PE = KE_f
                                                      mgy = 1/2 mv²

• Again, due to non-conservative forces, the kinetic energy present on landing will be only approximately 80% of the potential energy present at the top of the jump.

                                   9.8m/s²*1.52m = 0.8(1/2v²⁾
                                                    v_low = 4.88m/s
                                                     v_{high = 5.12m/s}
 

• One thing shown by these calculations is that, for a rider to guide a horse over a 'course' of fences ( a series of jumps with a set pattern), the horse is continually losing a large amount of speed in the effort of each jump.  Thus, the 'work' of the rider is often to urge the horse on throughout the course so that the horse does not approach a jump with too little energy to clear it.

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A few other 'Horsey Notes' :

•  The average Initial velocity, in miles per hour, would be: 0.23 mph, which is about 1/100 the speed of the average racehorse.
• Horse distances are usually measured in 'strides' which helps the rider determine the distance from which the horse should take off.  The average horse stride is 8 ft., or 2.44m.  If the horse is traveling at 6.4 m/s, then it takes the horse 0.38s to take one stride.

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*All photos from The Olympic Equestrian Site *
This page lovingly maintained by erinr@email.unc.edu
 
 

12-April-2003