Geometry of Dressage


Ebeling Rafalca

Dressage is a type of riding which many people consider an art. In the horse world it is referred to as “horse ballet”. The rider must direct the horse flawlessly to preform a series of predetermined movements. A standard dressage arena is 20 meters by 60 meters. The sides of the arena are split up by letters, the first letter, K or F, is 6 meters from the entrance. The following letters are all 12 meters apart until the last letter which, like the first letter, is 6 meters from the end of the arena. The lines of the arena (quarter lines and center line) are each 5 meters apart. It is super important that the rider remembers this because many of the actions preformed require a deep understanding of the dimensions of the ring. [1]

Screen Shot 2016-03-09 at 5.14.07 PM

Geometry plays a major role in mastering dressage. When entering a dressage ring the rider must direct the horse to the centerline. How the centerline is ridden is extremely important because it is the judge’s first impression of you. The first thing a rider must do is go past marker A while also remaining completely straight. If the rider and horse are not straight they lose points.

Next, the rider will complete circles. To complete a perfect 20-meter circle the horse must always be equidistant from the center of the circle. A horses average length is 2 meters which plays a major role in determining when to turn [2].

The steps to preforming a perfect circle:

  1. Leave the outside line at E aiming for the center line 2 meters before I
  2. As the horse approaches I the rider should already be focusing on B
  3. The rider should just hit B and begin to immediately look towards L, similarly to I, the Screen Shot 2016-03-09 at 5.23.07 PMrider aims for the center line 2 meters before L
  4. The rider then returns to E making sure to focus on the roundness of each quarter segment

The rider understanding the geometry of the arena and the spacing of the letters is paramount. If they don’t, the circle usually ends up being an oval and a lot of points are deducted.

The next step in a dressage competition is half-circles and turns. These are tricky because they require the horse to turn on the centerline. [3]

Steps to preform a perfect half circle and turn

  1. Turn left at E and go to X
  2. At X make a sharp left and ride straight towards GScreen Shot 2016-03-09 at 5.29.07 PM

The rider must remember that the arena is 20 meters wide so the turn from E to X should be done 4 meters before E staying straight for 2 meters followed by the turn at X.

Dressage is all about knowing how far you are from each letter. Most dressage riders walk the ring before the competition, learning where each turn should be preformed, remembering how many meters are in between each letter.



Works Cited:

[1]: Dressage Academy. “The Dressage Arena.” The Dressage Arena. N.p., n.d. Web. 09 Mar. 2016.

[2]: Heath, Marilyn. “The Art of Riding in a Dressage Arena.” The Judges Box(2013): n. pag. Print.


[3]: Ibid.

Weight of Jockeys affecting speed


Jockeys are small men and women whose weight averages around 116 pounds.[1] An average thoroughbred is 1,000 pounds meaning that with the jockey and tack, which is around 10 pounds, the horse only needs to carry 126 pounds.[1] According to Rubin Boxer’s “Analysis of Thoroughbred Racing”, for an 8 furlong (1 mile) race, every loss or gain in weight of 1.8 pounds will effect the horse’s race time by 0.2 seconds.[2]

116- (1.8 X 2)= 116- 3.6= 112.4

So if a jockey is 112.4 he/she will be .4 seconds faster.


Because weight affects race times, many jockeys use harmful tactics to lose weight. There are even “heaving bowls”, a bowl where jockeys can throw up before a race, at most racetracks. Jockeys will often use sweat suits, saunas, and starvation to keep their weight down [4]. Horse racing is a very dangerous sport, not only do the jockeys risk their lives riding at fast speeds but they also use unhealthy methods to lose weight which in the end negatively affects their health.


Works Cited:

[1]: Boxer, Rubin. “Engineering Analysis of Thoroughbred Racing.” Revelation Software (n.d.): n. pag. Print.

[2]: “Thoroughbred.” Thoroughbred. N.p., n.d. Web. 05 Mar. 2016.

[3] Boxer, Rubin. “Engineering Analysis of Thoroughbred Racing.”

[4] McKenzie, Sheena. “A Weighty Issue: Hidden World of Jockey Heaving Bowls.” CNN. Cable News Network, n.d. Web. 09 Mar. 2016.

Horse Racing


In horse racing it is all about the track and the weight of the jockey. The horses that race are thoroughbreds; they are slim with short leg bones, which allow long and easy strides. They are known for their agility, stamina and the ability to go into a quick burst of speed effortlessly. [1]

unnamed-2 copy
This is me on Paco an ex-race horse and thoroughbred

Most tracks are dirt, grass or synthetic. Race times vary from track to track depending on the surfaces. Horses wear horseshoes to protect their feet and increase the “grippiness” on the track. Similarly to running wearing spikes the shoes allow horses to turn with more power at high speeds without slipping. We will examine the coefficient of fiction on dirt, grass, and synthetic tracks. The coefficient of friction is the “measure of the amount of resistance that a surface exerts on or substances moving over it, equal to the ratio between the maximal frictional force that the surface exerts and the force pushing the object toward the surface.”[2] Because racehorses are in motion we use kinetic coefficient of friction. The average coefficient of friction for grass is .35, for synthetic tracks (rubberish) .68, and for dirt .35.[3] [4] The safest track is a synthetic track and then grass and dirt tracks. This is important to know because jockeys have to be careful during turns, slowing down, but on a synthetic track they do not need to slow down as much because it is grippier.


Works Cited:

[1] The Editors of Encyclopædia Britannica. “Thoroughbred.” Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 05 Mar. 2016.

[2] The Editors of “Coefficient of Friction.”, n.d. Web. 05 Mar. 2016.

[3] Elert, Glenn. “Friction.” The Physics Hypertextbook. N.p., n.d. Web. 05 Mar. 2016.


Anna:Lego Sagaponack


Jumping can look pretty scary but not to worry, the people jumping high fences have a lot of practice. Most horses approach a fence going around 12 ft./s (1 stride). To calculate when a rider should take off when jumping a 5.5 ft. fence will be shown below:

The average angle of takeoff=40°-45° (in our example we will use 40°) [1]

Screen Shot 2016-03-05 at 5.27.24 PM

To find x we must use SOHCATOA:

Sin θ= O/H Cos θ= A/H Tan θ=O/A

Because of the information we know we will use Tan θ=Opposite/Adjacent:

Tan 40°= 5.5 ft./X

1x 5.5/tan 40°=X

Tan 40°=.839 ft.

1x 5.5ft/.839 ft.= 6.55 ft.


Now we know that the horse should take off 6.55 feet before the jump to keep its consistent pace. For the rider this means when counting strides you should take off in the middle of your count. This means when going through a line (Jump A to Jump B) that is 70 feet (5 strides) in the middle of the 5th stride the rider should release the reigns and let the horse jump.

Screen Shot 2016-03-05 at 12.55.53 PM
This is an example of a good takeoff.


Works Cited:

[1]:Stinner, Art. “The Physics of Equestrian Show Jumping.” The Physics Teacher25 (2014): n. pag. Web. 5 Mar. 2016.

Counting Strides

When competing riders should maintain a good pace with an even rhythm neither speeding up nor slowing down. The horse must reach the “spot” or distance of takeoff in front of the jump correctly. A bad “spot” is when a horse jumps from too far or too closes causing a change in rhythm. When riding you count strides so preferably all your strides will be the same.

An average horse’s stride is 12 feet long [1]

In a class with a fence height of 2’6” or lower [2]:

  • 3 strides= 46’
  • 4 strides= 58’
  • 5 strides= 70’
  • 6 strides 82’

Strides are very important in horseback riding. When completing a course there are a prescribed number of strides one must complete between each jump to get the points. As stated above, the average stride of a horse is 12 feet. Below I am going to give a scenario:


A rider must calculate the correct number of strides in order to complete the course at a constant pace. Because we know the distance between the jumps we can figure out the number of strides.

  • Jumps 3 and 4 are 70 feet apart
    • 70/12 ≈ 5 strides
  • Jumps 7 and 8 are 82 feet apart
    • 82/12 ≈ 6 strides
  • Jumps 5 and 6 are 58 feet apart
    • 58/12 ≈ 4 strides

If the rider counts the strides correctly and maintains a consistent pace he or she will do very well.



[1]: USEF. “Hunter Course Design.” (n.d.): n. pag. United States Equestrian Federation. Web.

[2]: Ibid.

Measuring a horse

Before we can start analyzing the sport we must start at square one: The horse. Horses are beautiful and unpredictable animals. They are also incredibly cute. Horses are measured in hands, a unit of measurement most people have never heard of. Today, the unit is only used to measure the height of horses, but in the ancient times it was a common unit of measurement, used primarily by the ancient Egyptians, Hebrews, Greeks, and Romans [1]. A hand is equal to 4 inches. To measure a horse you measure the length of the ground to the highest point of the horse’s withers.

My horse Willy is 14.2 Hands

14.2 hands= X/4

X= 56.8 inches

measuring hands

Works Cited:

[1]: Britannica. “Hand.” Encyclopedia Britannica Online. N.p., n.d. Web. 05 Mar. 2016.