# Horse & Physics

PHYSICS
of
HORSE RIDING & TRAINING
(this chapter is designed as an university equine course)

Horse’s technique to move her/his centre of gravity (hcg):

Horse takes her/his leg(s) in the air and steps on the ground with 2 legs simultaneously or 1 leg in a specific sequence repeatedly to move her/his centre of gravity (hcg).

Step:

Horse uses 2 methods to make a step:

1- Swinging leg (back and forth & to the sides).
2- Stepping on the spot (by foreleg or by hind leg).

1-1- Swinging leg back and forth:
All legs just swing back and forth and lateral legs hoof prints follow the same track.

There are 3 kinds of pace by steps which are made by swinging legs back and forth.

1-1-1- Short pace:
Is when the hind legs step on the rear of the forelegs hoof prints.
1-1-2- Medium pace:
Is when the hind legs step on the forelegs hoof prints.
1-1-3- Long pace:
Is when the hind legs step on front of the forelegs hoof prints.

1-2- Swinging leg to the side:

When all legs swing to the sides in some degree (lateral movements) between more than 0′ up to close to the 90′ :

1-2-1-The foreleg and hind leg which are not in the direction of the travel cross the concerned leg which is in the direction of the travel.
1-2-2- Hind legs direct haunches and forelegs direct forehand/shoulders.

2-1- Foreleg Stepping on the spot:
Turning around the foreleg :
Horse’s hind legs and the foreleg which is in the direction of the travel also hcg turn on their own circle around the other foreleg as the centre of the circles.

2-2- Hind leg Stepping on the spot:
Turning around the hind leg (pirouette):
Horse’s forelegs and the hind leg which is not in the direction of the travel also hcg turn on their own circle around the other hind leg that moves on a small circle.

step length:

Is the distance that hcg moves on its horizon between two consecutive steps.

step time:

Is the amount of the time that horse takes between two consecutive steps.

Supporting phase (sup.):

Is when the leg is on the ground.

Sup. has 3 periods:

Starting, median, the end.

Supporting phase starting (sup. s):

At this period, Horse’s leg(s) support(s) a force on the vertical that is called F(v) ,

Fv = sum of vertical elements of the forces that are impacting the horse at this
period consist of :

– Horse’s weight .
– Rider’s weight.
– Rider’s signals.
– Horse momentum force: Is the force as the result of movement of the horse and it is measured by the horse’s weight mass times by her / his velocity.
– Rider momentum force: Is the force as the result of movement of the rider and it is measured by the rider’s weight mass times by her / his velocity.

1- Horse steps on the ground by 2 legs simultaneously or 1 leg.

2- Horse’s hind leg hip, stifle, hock and ankle joints are bent.

3- Horse’s foreleg elbow and ankle joint are bent and its knee is straight.

4- If there is 1 leg involved at sup. , The same leg should support all of the F(v).

5- If there are more than one leg engaged at sup. , F(v) should be divided to the all of them.

6- Handling Fv:
6-1- When horse steps on the ground without changing direction of the travel, horse has a balanced step .
6-2- When horse supports Fv, with changing direction of the horse’s centre of gravity (hcg), horse’s step is unbalanced but could be stable. In this case horse has to apply a force that is called “Equilibrium force ” or (fe) which is bigger than F(v) and in the appropriate direction to keep the horse in the stable margin that beyond that horse falls off.
Equilibrium force = fe = Fv + fu
Unbalanced force = fu
6-3- When horse is unbalanced but stable fu makes the horse’s centre of gravity (hcg) to change direction accordingly, then horse could apply a (- fu) at the next period to neutralize this force and bring back hcg with the consequences of
– Unnecessary swinging hcg or changing direction when no t asked.
– Wasting horse’s energy and force with the chance of not having her/him strong enough any more for the next period.
6-4- When horse is unbalanced but stable Some times horse is not able to neutralize (fu), so horse has to reach to the next supporting phase hastily to requite her/his lack of balance with the consequences of:
– Shortening the supporting phase time (sup.t) with the chance of not having enough time left for the horse to apply necessary force for the rest of operation at the next period of sup..
– Shortening the following suspension phase time (sus.t).
– Because of the above factors an unbalanced horse operates hastily and looks speeding up.
– As fu is not on the vertical so doesn’t increase impulsion.
6-5- When horse is unbalanced but stable Horse is not able to apply appropriate force at the next period of sup. because:
– Supporting phase time is not long enough.
– Horse’s leg(s) are/is not stable enough on the ground because of inevitable chang of direction that changes horse’s lag(s) angulations with the ground.
– Wasting some energy to apply fu.
6-6- Horse tries to apply such a (fu) to make a balanced step preventing deviation of hcg and spending more energy at the next step.

7- (Balanced forelegs) Is when forelegs are used equally to support a portion of the horse’s weight, at halt or at walk or at rein back when one hind leg is suspended.

8- (Balanced hind legs) Is when hind legs are used equally to support all or a portion of the horse’s weight, at halt or at walk or rein back or at take off for a big jump when one foreleg is suspended.

9- (Balanced legs) Is when the horse’s weight is distributed equally between forehand and hindquarters or in other word is when the horse’s weight is distributed equally between 1 hind leg and 2 forelegs (at walk) or vice versa or 1 hind leg and 1 foreleg (a diagonal) in a step by:
9-1- Shifting horse’s centre of gravity (hcg) back by moving neck to it’s vertical.
9-2- Swinging the hind leg(s) more underneath her/his body (collection).

10- The factors which are involved on a balanced step:
10-1- Type of the movement.
10-2- Type of the pace.
10-3- Path that horse is operating on a curved or on a straight line.
10-4- Horse’s posture.
10-5- Horse’s speed.
10-6- horse’s natural conformation.
10-7- Rider’s technique to ride the horse.
10-8- Amount of bfv).
10-9- Using 1 leg or 2 legs to step:
Having 2 legs or more (at the halt or the walk or the rein back) makes the balance easier.
10-10- Where horse step(s) on the ground with the proportion to the (hcg.
10-11- Horse’s leg(s) side swinging .
10-12- Horse’s leg(s) joints angulations
10-13- Shifting the rhcg by:
10-13-1- Horse’s head and neck: By bending the horse’s head and neck to the sides and/or flexing them and/or stretching them out and/or move them to their horizon and/or to their vertical up or down.
10-13-2- Shifting rider’s centre of gravity (rcg) location.
– Making momentum with the horse’s head and neck by moving them to deferent directions with deferent acceleration.
– Making momentum with horse’s suspended legs by moving them to deferent directions with deferent acceleration at their/its suspension phase.
10-13-4- Rider’s momentum changing.
10-14- Rider’s signals.
10-15- Horse’s physical fitness and athletic abilities.
10-16- Horse’s practice.
10-17- The material of the ground needs to:
– Disperse the pressure evenly through the horse’s hooves,
– Provide enough elasticity to diminish the shock of movement,
– provide enough grip/friction.
10-18- Sloped ground.
10-19- The horse’s hooves and shoeing needs to:
– Disperse the pressure evenly.
– Provide enough grip/friction.

11- Horse’s balanced step adjustment techniques:

– Stepping in the right spot.
– Centre of gravity location adjustment (13-3).
– leaning the leg(s) to the right direction.

Some definitions:

– Equilibrium band of diagonal hooves (eb): Is an imaginary straight band on the ground between the horse’s hooves on a diagonal step.

– Equilibrium line (el): Is a line from the rhcg and perpendicular to the ground

– Equilibrium spot (es): Is the spot that the el meets the ground.

– Equilibrium plate (ep): Is an imaginary plate perpendicular to the ground included the victor of velocity of the rider’s & horse’s centre of gravity (rhcg).

– Horse takes 2 leg steps at trot and the both 1 leg (foreleg or hind leg) and 2 leg steps at canter.

11-1- 2 leg balanced step:

– On a straight line or on a curved line :
– When the el is on eb, there is no changing direction of the travel at the rhcg (balanced step) and there is no deviation at rhcg in non of the directions.

There is a larger margin of taking a diagonal balanced step than 1 leg balanced step, because there is more room for el to meet the ground in the balanced area at a 2 leg step.

11-2- One leg balanced step:

11-2-1- With collection: When the horse steps on the (es), there is no changing direction of the travel at the rhcg (balanced step) and neither deviation at rhcg in non of the directions.
The hind leg needs to operate with fair collection.

How the horse’s legs could operate in this case

– On a straight line or on a curved line : If the diagonal step is balanced too, the outside hind leg follows the inside foreleg track and there are 3 tracks according to the travers:
1- outside foreleg, 2- outside hind leg and inside foreleg. 3- inside hind leg.

If even one step is not a balanced step there are four tracks, one track for each leg and the rhcg is not able to follow a straight line or a circle.

Just on a circle the inside hind leg could follow the inside foreleg in a small circle with bending horse’s body inside to have 2 tracks:
1- outside foreleg. 2- outside hind leg and inside hind leg and inside foreleg.

11-2-2- Without collection: When horse steps on the line that ep meets the ground, there is no changing direction of travel at the rhcg(balanced step) unless there is a small deviation of rhcg on the vertical.

How the horse’s legs could operate in this case

– On a straight line: If the diagonal step is balanced too, the outside hind leg follows the inside foreleg track and there are 3 tracks according to the travers:
1- outside foreleg. 2- outside hind leg and inside foreleg . 3- inside hind leg.

– On a curved line: If the diagonal step is balanced too, horse’s legs move in 4 tracks generally has:
1- outside foreleg. 2- outside hind leg. 3- inside foreleg. 4- inside hind leg.

– On a circle: Outside hind leg could follow outside foreleg track by horse’s body bending adjustment and inside hind leg could follow inside foreleg track if the horse’s neck is close to it’s vertical and a little bit bent inside or if the neck is close to it’s horizon needs to be bent more inside and there are 2 parallels tracks according to the circle: 1- outside foreleg and outside hind leg. 2- inside foreleg and inside hind leg.

11-2-3- Turning rhcg around the inside hind leg on a curve:
To make the rhcg to turn on a curve around the inside hind leg that steps on the spot or on a curve there are 4 tracks, one track for each leg.

11-2-4- (Pirouette) Turning rhcg around the inside hind leg on a circle:
Like the above item but tracks are 4 parallels circle if inside hind leg moves on a small circle and if inside hind leg moves on the spot there are 3 more track of parallels circles which share one centre.

How the horse’s legs could operate in this case to take balanced steps:

– The outside hind leg steps on the es taking a collected step to have a balanced step and prevent forward movement.
– The diagonal steps with a collected inside hind leg and under body outside foreleg, the both to prevent forward movement and making lateral movement and having the el on the eb to take a balanced step.
– horse’s neck is close to it’s vertical.to move hcg back also rcg is backed enough by the rider’s upper body to help outside hind leg.
– inside foreleg steps on the es to have a balanced step and prevent forward movement.
– all legs are lent inside to make the lateral movement.
– horse’s neck is inclined to the direction of the travel to facilitate it.
there is no changing direction of travel at the rhcg(balanced step) and there is no deviation of rhcg in non of the directions. there are 4 tracks, one track for each leg.

11-3- Horse’s hoof print track:If even one step is not a balanced step there are four tracks, one track for each leg and the rhcg is not able to follow a straight line or a circle.

11-4- Centre of gravity location adjustment by: Article (10-13).

12- The principles which conduct the horse to move her/his centre gravity (hcg).

12-1- Preventing harm to the horse.
12-2- Making the horse’s limbs to work according to their natural influences.
– Using legs swinging back and forth.
– Using hind leg at collection.
12-3- Making the horse’s operation to improve her/his athletic and mental abilities.
12-4- Saving horse’s energy by:
– Trying to have balanced steps.
– Minimize amount of time at this period and rest of supporting phase (sup.t) because at sup. horse has to spend energy.
– Increasing suspension time.
12-5- Minimizing rhcg deviation .
12-6- facilitating the communication between the rider and the horse.
12-7- operating with the best efficiency.

13- Assumptions: It is assumed that the horse makes an arrangement through all the factors considering articles 11 and 12 to move rhcg that requires following assumptions.

13-1- Legs swing just back and forth when horse moves on a straight line or on a curved line.
13-2- Legs swing to the sides just on lateral movements.
13-3- Legs angle to the sides just on a curved line enough to neutralize centrifugal force.
13-4- rhcg will be shifted just to minimize it’s deviation.
13-5- The hind leg follows the foreleg hoof print line at the same track on a straight line or on a curved line and outside track and inside track are parallel.
13-6- Outside foreleg/hind leg crosses inside foreleg/hind leg at lateral movements.

14- Balanced pace:
Horse makes a balance through all the factors considering articles 11, 12 and 13, to move rhcg by a kind of pace that is called here a balanced pace.

14-1- At walk:
Horse could take 4 balanced 1 leg steps at each stride with a large margin of balance and without deviation of rhcg in any direction at walk.
14-1-1- The margin of the balance is larger than trot because when horse steps at walk still 2 more legs are on the ground and in fact the horse has 3 legs at supporting phase (sup.) that widens the margin of the balance with comparison to the trot with 2 leg steps and canter with 1 leg and 2 leg steps.
14-1-2- Horse’s head and neck: As bellow at trot.
14-1-3- Horse’s hooves track: As bellow at trot.
14-1-4- Balanced legs: If horse uses her/his hind legs with enough collection, could make balanced legs that means when stepping with 1 foreleg, the hind leg supports the same force as the 2 foreleg together or when horse steps with 1 hind leg, the foreleg supports the same force as the 2 hind legs together.
14-1-5- Balanced forelegs: If the force that each foreleg supports is even with the force that other foreleg supports when horse steps with 1 foreleg.
14-1-6- Balanced hind leg: If the force that each hind leg supports is even with the force that other hind leg supports when horse steps with 1 hind leg.

14-2- At trot:
Horse could take 2 balanced diagonal steps at each stride with a large margin of balance and without deviation of rhcg in any direction at trot.
14-1-1- Horse’s had and neck: Horse’s head and neck could be straight or bending to the sides or flexing in up or down or stretching out or up or down through the large margin of the balance at this step for different kind of operation.
14-1-2- Horse’s hooves track: Hind legs could follow forelegs track on the both straight or curved line (2 parallel track movement).
14-1-3- Balanced legs: If horse uses her/his hind legs with enough collection, could make balanced legs (hind leg and foreleg support even force at the diagonal) diagonals.

14-3-At canter:
14-3-1- Outside hind leg step: Horse could take outside hind leg step with slight deviation of rhcg down and inside that could be reduced by shifting rhcg (article 10-13-) to the outside and/or back.
14-3-2- Outside diagonal step: Horse could take outside diagonal step balanced with a large margin of balance and without deviation of rhcg in any direction.
13-3-3- Balanced legs: If horse uses her/his outside hind leg with enough collection, could make a balanced legs (hind leg and foreleg support even force at diagonal) diagonal.
13-3-4- Inside foreleg step: Horse could take inside foreleg step with slight deviation of rhcg outside and down that could be reduced by shifting rhcg (article 10-13-) inside and/or forward.
14-3-5- Swinging rhcg at canter: According to this article (14-3) there is slight inevitable swinging of rhcg up and down and to the sides at each stride at canter for this period.
14-3-5- Swinging horse’s head and neck at canter: According to the article of (14-3) there is slight inevitable swinging of horse’s head and neck up and down and to the sides at each stride at canter for this period to minimize swinging of rhcg and horse’s head and neck.

Supporting phase median (Sup. m):

At this period, Horse’s leg(s) could generate force (fl) on top of the Fv or fe to conduct the horse’s motion accordingly.

1- Mechanism of generating force by horse’s leg(s) (foreleg or hind leg) to move her/his centre of gravity which are used for the both hind leg and foreleg.

1-1- Horse’s Leg(s) spring(s) off the ground to generate a force (fl) to move hcg.
1-2- This force is applied on the ground where hoof meets the ground.
1-3- This force impacts the horse in an angle that is called leg throw angle (ta) to move rhc. ta is variable from around zero up to 90′.
1-4- As the horse likes to save energy and use it in a way with the best sufficiency so the horse tries to adjust amount of the leg force (fl) and its angulations(ta) to have the resultant of all forces which impact the horse in desired angulations that is the angle which horse is thrown in the air and is called here horse throw angle (Ta). in fact “Ta” is the angulations of the resultant of the all forces which impact the horse with the horizon.
1-5- Leg force generates a velocity .
1-6- This force/velocity could be divided to three elements:
horizontal , vertical , lateral and a torsion.
1-7- Applying this force/velocity takes time that is called leg force/velocity time (ft).
1-8- QUICKNESS is the result of how much horse’s leg(s) impact(s) the hcg at this period in a smaller amount of the time.
1-9- Lateral movements: Horse swings the leg(s) to the sides to generate lateral force/velocity for lateral movements.
– The lateral elements of leg(s) force/velocity are smaller than other elements usually.
– As much as leg makes steps more far away from the horse’s side, leg could apply more lateral force/velocity.
1-10- The backwards horizontal element of leg force/velocity is not considerable.
1-11- Horse’s legs move “hcg” by just swinging legs without applying any force at this period at the walk and the rein back and the legs support the rider’s & horse’s weight as explained at sup.s .
1-11- Centrifugal force: This is a horizontal force that pushes the horse out on a curve, To neutralize this force the horse’s leg(s) angle(s) to the inside of the curve in proportionate to the sharpness of the curve to have her/his legs out of vertical to the inside of the curve to be able to apply enough horizontal force to neutralize centrifugal force.
1-12- Torsion: Is the result of two equal forces in opposite directions that horse could generate with her/his leg(s) (turning around the foreleg or hind leg).
– If hind leg(s) generate(s) torsion, make(s) the horse’s centre of gravity (hcg) to turn around the hind leg(s).
– If foreleg(s) generate(s) torsion, make(s) the horse’s centre of gravity (hcg) to turn around the foreleg(s).
1-13- Friction: To apply any force at supporting phase, there should be enough friction between the horse’s hoof and the ground.
– The material of the ground needs to provide enough grip/friction.
– The horse’s hooves and shoeing needs to provide enough grip/friction.
1-14- When a step is made by 1 leg of any side at this period, horse’s leg force (fl) -impacts the “rhcg” with the same criteria about balanced step and deviation of hcg as Fv at supporting phase starting period.

1-15- When a step is made by a diagonal:
1-15-1- Foreleg force makes the horse’s head and neck to turn up around the hcg.
1-15-2- Foreleg force makes the horse’s haunches to turn down around the hcg.
1-15-3- Foreleg force moves hcg up (impulsion) .

1-16- When a step is made by 2 hind legs, they could apply equal force without inevitable deviation of hcg (balanced leg force).
1-17- As a stride has more than one step, horse could have all her/his strides with the same equal velocity (amount and direction).
1-18- The force that moves the rhcg at each step (F’s) is as bellow according to sup.s and sup.m .
F’s= Fv + fl + fu
or
F’s= (rider’s & horse’s weight + rider’s signals + rider’s momentum + horse’s momentum) +leg(s) force + fu (extra force to requite an unbalanced step)
1-19- This force throws the horse in an angle (Ta) at each step.
1-20- Best sufficiency is when Ta= 45′ to have longer ground coverage and for jumping Ta goes bigger.
1-21- Each step has a force (F’s and a throw angle (Ta).

2- Mechanism of generating force by horse’s hind leg(s) (fh) to move her/his centre of gravity.

2-1- (fh) The extension of the hind leg force/velocity pass’ from hcg from side view.
2-2- (tah) The angle between this force and horizon is called hind leg throw angle and it is varied from tah = 45′ to 90′.
2-2-1- This angle is around 45′ degree when horse stands square .
2-2-2- (tah) could be increased up to 90′ degree during a motion or when the horse stands on her/his hind legs (Lavade ) where beyond that the horse moves back on her/his hind legs or falls off back .
2-3- The maximum vertical element of the hind leg force/velocity is when tah is 90′.
2-4- The maximum forward horizontal element of hind leg force/velocity is when hind leg cannon bone is on the vertical .

3- Mechanism of generating force by horse’s foreleg (ff) to move her/his centre of gravity.

3-1- Foreleg could apply maximum horizontal element force/velocity (ffh) at this period when foreleg is ahead of its vertical and as much as foreleg is more far forward , foreleg could apply more force/velocity .
3-2- Foreleg could apply maximum vertical element force/velocity (ffv) at this period when foreleg is on its vertical.
3-3- Foreleg force affects hcg with a “moment” that makes the horse to turn around hcg from side view.

Supporting phase the end:

1- Horse’s foreleg is swung back in opposite direction of the travel and her/his knee is straight and ankle is slightly bent.
2- Horse opens the hind leg joints (hip, stifle hock and ankle) at this period.
3- At a collected short pace:
– Foreleg is a little bit behind its vertical at this period.
– Hind leg’s cannon bone stays in front of its vertical.
4- At a collected medium pace:
– Foreleg is behind its vertical a little bit more than short pace at this period.
– Hind leg’s cannon bone swings a little bit up to behind it’s vertical.
5- At a long pace:
– Foreleg is far behind its vertical at this period.
– Hind leg’s cannon bone swings far back from its vertical.
6- Having rhcg to the direction of the travel pushes the balance of step to it ‘s edge to facilitate moving in the same direction.

Supporting phase time (sup.t):

Is the amount of the time that the leg is on the ground.

Leg suspension phase (l.sus.):

Is when the leg is in the air.

l.sus. has 3 periods:

Starting, median, the end.

Leg suspension phase starting (l.sus. starting):

Horse bends her/his leg joints and picks the leg in the air.

l.sus. median:

1- Horse swings her/his hind leg from the hip joint freely to the direction of the travel utilizing stifle, hock and ankle joints having them bent.
2- Horse swings her/his foreleg from the shoulder freely to the direction of the travel utilizing elbow, knee and ankle joints. having them bent.

l.sus. the end:

1- Horse bends her/his hip joint and stretches her/his hind leg to the direction of the travel pointing to where the leg is stepping.
2- Horse stretches her/ his foreleg to the direction of the travel from shoulder pointing to where the leg is stepping.

Leg suspension time (l.sus .t:

Is the amount of the time that the horse’s leg is in the air.

Horse suspension phase (h.sus.):

Is when all the horse’s legs are in the air.

Horse suspension time (h.sus.t):

Is the amount of the time that all the horse’s legs are in the air.

Stride:

When the horse uses all of her/his legs one time each to step on the ground or making supporting phase (sup.) plus a following suspension phase (sus.), a stride has been made.

Stride length:

Is the distance that the centre of gravity of the horse (hcg moves on its horizon when horse makes a stride.

Stride time:

Is the amount of the time that the horse takes to make a stride.

Beat or step:

When the horse steps on the ground makes a beat. Horse uses 1 leg or 2 legs to make a beat/step.

Pace:

Is a method that the horse utilizes her/his legs to step on the ground to move her/his hcg.

Horse uses 3 kinds of paces (walk, trot, canter) plus jumping to move her/his hcg

Walk:

Is a pace that horse steps on the ground in following sequence repeatedly.

1- left foreleg
2- Left hind leg.
3- Right foreleg.
4- Right hind leg.

Walk stride has 4 beats.

Trot:

Is a pace that horse steps on the ground in following sequence repeatedly.

1- Left hind leg and right foreleg simultaneously.
2- Right hind leg and left foreleg simultaneously.

Trot stride has 2 beats.

Right diagonal:

Is a beat or step with left hind leg and right foreleg simultaneously.

Left diagonal:

Is a beat or step with right hind leg and left foreleg simultaneously.

Canter:

Is a pace that horse steps on the ground in following sequence

1- Right hind leg.
2- Right diagonal.
3- Left foreleg.

1- Left hind leg.
2- Left diagonal.
3- Right foreleg.

Canter has 3 beats.

Jumping:

Is a pace that horse steps on the ground in following sequence

1- Take off: One hind leg or both of them simultaneously springing off the ground.

2- In the air: Horse is in the air taking the jump.

3- Landing: Horse steps with one of the forelegs followed by the other one and then all legs go in the air and then horse canters and usually on the lead direction of the same foreleg that horse landed with except other wise is required.

Jumping has 3 beats (for big jump) or 4 (for small jump) beats.

Aspects of horse’s motion;

PATH, POSTURE, MOVEMENT.

1- Horse’s Path:

is the track that a horse takes that could be a STRAIGHT line or a CURVE.

2- Horse’s Posture:

2-1- Horse’s legs.

2-1-1- Supporting phase.
2-1-2- Suspension phase.
2-1-3- Legs joints.
2-1-4- Coordination between legs.

2-3- Horse’s spine.
2-3-1- Horse’s neck.
2-3-2- Horse’s back and loin.

3- horse’s movement:

3-1- Horse’s GAIT.

3-2- Horse’s VElOCITY.
3-2-1- Forward speed (horizontal).
3-2-2- Lateral speed (horizontal).
3-2-3- Vertical speed ( impulsion ).

According to the above assumptions with the following variable factors a horse could adjust :

1- LEG FORCE .
2- MOMENTUM OF THE HORSE’S body.
3- Momentum of the HEAD and NECK of the horse .
4- Momentum of the horse’s legs.
5- RIDER’S momentum .
6 – RIDER’S SIGNALS , legs , hands , weight .
7- The spot of CENTRE OF GRAVITY OF HORSE AND RIDER together ( rhcg) .
8- The POSITION of the LEGS of the horse .
10- LEGS JOINTS of the horse .
11- SPINE of the horse .
12- LEGS SUPPORTING (sup.) PHASE .
13- LEGS SUSPENSION PHASE .

1- LEGS FORCE : according to the assumptions

2- MOMENTUM OF THE HORSE .

2-1- HORIZONTAL momentum ( speed ) helps to increases the speed of the horse that reduces TH .

2-2- VERTICAL momentum pushes the horse on the ground on the vertical at sup.ph so horse needs to support the mass of the horse plus this force so horse has to spend a portion of her / his force to cancel vertical momentum so this vertical momentum reduces TH .

2-3- LATERAL momentum affects like horizontal momentum increase’ lateral velocity .

3- Momentum of the HEAD and NECK of the horse :

Head and neck comprise around %20 of the mass of the horse also neck could be very flexible so these two factors could make determinative momentum with SUDDEN movements of the neck in different DIRECTIONS and QUICKNESS .

4- Momentum of the LEGS of the horse :

Legs don’t have considerable mass but they could make effective momentum with their QUICK and SUDDEN movements

5- RIDER’S momentum .

5-1- When rider’s velocity is equal with the velocity of the horse ( when rider follows the movement of the horse ) rider’s velocity will be added to the momentum of the horse and impacts alike.

5-2- When rider’s velocity is not equal with the velocity of the horse ( when rider doesn’t follow the movement of the horse ) this could happen in two ways:

5-2-1- Rider’s velocity is more or less than velocity of the horse .
5-2-1-1- when rider’s velocity becomes more than the velocity of the horse suddenly ( when rider falls ahead of the movement of the horse ) it enhances the momentum of the horse at that instance .
5-2-1-2- When rider’s velocity becomes less than the velocity of the horse suddenly ( when rider falls behind the movement ) it impacts in reverse of the momentum of the horse .
5-2-2- When rider swings around on the horse , that means some times rider’s velocity is less and some times is more than the velocity of the horse which is explained in the above .

5-3- HITTING on the horse :
When rider doesn’t follow the movement of the horse , rider might Hit on the horse because of : POOR PERFORMANCE or when horse makes a SUDDEN MOVEMENT .

5-3-1- Severity of the strike between rider and the horse is depend on :
5-3-1-1- The different between the VELOCITY of the horse and rider .
5-3-1-2- WEIGHT of the horse and rider .
5-3-1-2- Rider’s GRIP on the horse .

5-3-2- RIDER’S STABILITY to regain the position Is depend on :

5-3-2-1- Severity of the strike as explained in the above .
5-3-2-2- How LONG rider doesn’t follow the movement of the horse increasing the chance of having a RESONANCE when their velocities are in opposite direction that makes the strike stronger .
5-3-2-3- The rider’s GRIP : is a technique that rider could use on the horse :
5-3-2-3-1- To reduce the amount of difference between rider’s velocity and velocity of the horse .
5-3-2-3-2- To absorb the severity of the strike between rider and the horse .
5-3-2-3-3- To regain position when it is lost .

6- The spot of CENTRE OF GRAVITY OF HORSE AND RIDER together ( rhcg) .

6-1- When rhcg moves back:
6-1-1- th gets larger increasing tH.
6-1-2- Vertical element of Foreleg force increase’ TH .

6-2- When rhcg move sup:
Th gets larger increasing tH.

6-3- When rhcg moves down:
Th gets smaller reducing th.

6-4- When rhcg moves forward:
6-4-1- Th gets smaller reducing th.
6-4-2- Vertical element of Foreleg force still increase’ TH but less than when rhcg was back.

6-5- The factors that make the rhcg SPOT:

6-5-1- Posture of the horse :

6-5-1-1- Posture of the NECK of the horse :
Has very determinative role to determine the hcg spot from stretching out the neck down underneath of horizon and / or forward on the horizon to having it up and / or back on the vertical moving hcg from down and forward stoup and back and / or to the sides with bending the neck. In other word ( rhcg) SPOT MOVES PROPORTIONATE TO THE NECK of the horse.

6-5-1-2-Posture of Head of the horse :
Doesn’t have any considerable role to change hcg.

6-5-1-3- Posture of Legs of the horse :
Don’t have any considerable role to change hcg.
6-5-1-4- Posture of Back , loin and croup of the horse :
Doesn’t have any considerable role to change hcg but has avery determinative role for HIND LEGS POSITION ( is explained at 7-1 ) .

6-6- ( rcg) SPOT :
rhcg SPOT is proportionate to rcg spot

7- LEGS POSITION :
Is the result of how far the legs meet the ground out or underneath of the body of the horse both LATERALLY and LONGITUDINALLY.

7-1- HIND LEGS POSITION :

Hind legs position determines amount of the th so as much as hind legs meet the ground.more underneath the body of the horse longitudinally , Th/ TH gets bigger .

7-2- FORELEGS POSITION :

Forelegs force increase’ Th:

8- LEGS JOINTS :

8-1- Joints facilitate legs POSITION so they need to be FLEXIBLE enough.
8-2- Joints transfer FORCE through the legs so they need to be STRONG enough .
8-3- Joints regulate the QUICKNESS of applying the force so they need an OPTIMUM of FLEXIBILITY , over flexibility makes them slow .

9- SPINE of the horse :

9-1- NECK: Impacts hcg spot( 6-5-1-1 )and forelegs position :
9-1-1- When the neck is around the HORIZON or lower .
9-1-1-1- FORELEGS could get more FORWARD position increasing vfp / SPEED .
9-1-1-2- BACK and LOIN could concave to the ground more so HIND LEGS could get more FORWARD position increasing Th.
9-1-1-3- FORELEGS get more heavier / supporting time and less suspension time .
9-1-1-4- HIND LEGS get more lighter / suspension time and less supporting time .

9-1-2- When the neck is around the VERTICAL .

9-1-2-1- FORELEGS get less FORWARD position reducing vfp / SPEED .
9-1-2-2- FORELEGS get more lighter / suspension time and less supporting time ?.
9-1-2-3- HIND LEGS get more heavier / supporting time and less suspension time ?.

9-2- BACK and LOIN and CROUP position :
Impacts hind legs position :

9-2-1- As much as back and loin concave to the ground and hip joints of the horse get more closed , hind legs could meet the ground more forward underneath the body of the horse .

-Let’s assume at the end of first sup. the velocity of rhcg isV1 , we could divide V1 on the horizon that we called it SPEED ( s1 ) before and on the vertical and up that creates IMPLOSION and we call it ( Vi1 ) .
-With these velocities suspension phase ( sus.) starts and horse / rhcg moves in all directions( horizontally , vertically , laterally ) .
-At the peak of the sus.Vi1 comes 0 and horse moves horizontally almost according to s1and / or laterally .
-At the end of sus. horse moves horizontally almost according tos1 with a vertical and downwards velocity (VL1) that makes the leg to meet the ground .
– When horse lands on the ground , leg needs to absorb VL1and making it o while s1 still is affecting and moving the horse / rhcg on the horizon while horse/ rhcg could have lateral movement too .
– Now second sup .start s and horse needs to apply such a for top makeV2 . horse applies the force since the leg lands / making VL1 to 0 upon leaving the ground .
– When Foreleg is on the vertical and lands :
could apply maximum force to make maximum Vi

As much as rhcg is far back from foreleg vertical , ( vi ) could move rhcg more higher creating more impulsion.

10-1-
FORELEG sup.( at canter and landing spot of a jump )

Hind legs sup. time is in proportionate to the Th/ TH .
10-2- out of proportion with

BRIEF DESCRIPTION :

FORCE of the horse throws the horse according to the summary of above factors with the VELOCITY of V and THROW ANGLE of TH that could be varied between 0′ and 90′ ( 0′ < throw angle < 90′ ) At 0′ throw angle : the horse travels with MAXIMUM SPEED .

At 45′ throw angle : the horse travels with MAXIMUM GROUND COVERAGE .

At 90′ throw angle : horse has NO GROUND COVERAGE .

– How TRAINING OF THE HORSE impacts the rhcg SPOT.

– How do you ride a trained horse to impact the rhcg SPOT.

– How rider could impact the factors of Ground Coverage .
-1- With rcg
-2 With signals

For jumping wide , throw angle of the horse at take off spot needs to be 45′ degree . This angle is the result of applying hind leg(s) force and the momentum
of the horse ( momentum = velocity x weight ) .
As hind leg(s) of a collected horse with a hind leg(s) throw angle (ETA of more than 45′ degree that could be increased up to 90′ ( 45′ < TA< or = 90′ ) throw(s) the horse more up and less forward however when the TA is90′ degree horse will be just thrown up only without to be thrown any forward .
Horse could make this happen by collecting (her)himself and pushing her / his forehand up and back with her / his forelegs ( lavade ) .
This horse without having any forward momentum just will be thrown up vertically . So this horse to take a jump needs horizontal velocity to have a wide and high leap . to make this happen horse needs to be fast enough having horizontal velocity to regulate throw angle of the horse to modify it from 90′ to 45’letting the horse having widest jump / leap or longest stride or more ground coverage .

Definitions

1- These factors that are the results of the horse’s FLEXIBILITY:
1-1- SUPPLE
1-2- FLEXIBLE
1-3- LOOSE
1-4- FREEDOM
1-5- NO TENSENESS
1-6- EASE

2- These factors that are the results of the horse’s STAMINA:
2-1- BALANCE
2-2- SUSTAINED
2-3- LIGHTNESS
2-4- REGULARITY
2-5- HARMONIOUS
2-6- EASE
2-7- RHYTHM
2-8- UNITED canter

3- These factors that are the results of the horse’s STRENGTH :
3-1- IMPULSION:
3-2- LIGHTNESS of forehand.
3-3- ENGAGEMENT of hind legs.
3-4- ACTIVE
3-5- BALANCE
3-6- SUSTAINED
3-7- EASE
3-8- REGULARITY
3-9- UNITED canter

4- These factors that are the results of the horse’s MENTAL FITNESS:
4-1- ATTENTIVENESS
4-2- CALM
4-3- CONFIDENT
4-4- WILLING

5- These factors that are the results of the horse’s QUICKNESS:

6- These factors that are the results of the horse’s PHYSICAL FITNESS:

7- These factors that are the results of the horse’s ATHLETIC ABILITIES:

8- These factors that are the results of the horse’s ability to follow the rider’s SINALS.
8-1- NO RESISTANCE
8-2- SUBMISSIVE
8-3- NO HESITANTATION
8-4- KEEN
8-5- PRECISE
8-6- ACCORD