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Old 06-09-2016, 02:46 PM   #1
lone speed
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Huey Mahl's Physics proof elaborated

The conservation of energy is a fundamental concept of physics along with the conservation of mass and the conservation of momentum. Within some problem domain, the amount of energy remains constant and energy is neither created nor destroyed. Energy can be converted from one form to another (potential energy can be converted to kinetic energy) but the total energy within the domain remains fixed.

In Physics:

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Huey Mahl used Physics to prove that for every fifth of a second of “energy expenditure” spent on the early pace will affect the finish by two-fifths. Huey Mahl accentuated and proved what Jim Bradshaw had been telling us for years. Mahl also stated that:

The early pace has a “telescopic effect” on the rest of the race.


It can be interpreted that the early pace has an “exponential effect” on the rest of the race. Therefore, according to Huey Mahl’s hypothesis; any linear math expression used to determine speed figures are incorrect or “not optimal.” In order to express an optimal speed figure equation, it must have account for the early pace “exponentially”. In other words, any linear “speed figure” formula that uses 1st fraction + 2nd Fraction + 3rd Fraction adjusted by a variant or [ (1st fraction) + (2nd fraction) ] or early pace + late pace equals Final Time adjusted by a variant is flawed.

The Paceline


1st Fraction + 2nd Fraction + 3rd Fraction = Final Time





We are aware of the above equation in measuring a paceline in the past performances of thoroughbreds. The final time is the sum of three fractions.

Knowing this equation; we can write:

We let F = Fractional time and being aware that the value of (1st F + 2nd F + 3rd F ) = Final Time or using the math principle of “substitution property of equality” we have:


1st F + 2nd F + 3rd F = [1st F + 2nd F + 3rd F ]



We move the 3rd F value across the other side of the equal sign; therefore we have:

1st F + 2nd F = [1st F + 2nd F + 3rd F ] -3rd F or

1st F + 2nd F = Final Time - 3rd F



Essentially, the sum of the early pace fractions is equal to the Final Time minus the 3rd Fraction. This is simple enough to comprehend.



Now we will focus on energy changes in the early pace and its effect on subsequent fractions and its effect on the final time as a consequence of changes of energy expenditure. We can express the changes of “fractional times” by using the above equation with changes of units of energy by this equation:

1st F(X) + 2nd F(Y) + 3rd F (-1)(X +Y) = Final Time



We let X equal the value of changes in the 1st Fractional time;


We let Y equal the value of changes in the 2nd Fractional time and/or 2nd call pace time



Now using this equation we now want X and Y to stand for the unit change in “fractional times” or unit change in energy; where energy will be express in changes in ticks of energy changes. In horse racing parlance, a tick of energy is a (fifth) of a second.


We inserted the factor (-1) to the 3rd Fraction to multiply the net changes of (X+Y) to adhere to the “law of conservation of energy” and to balance this energy equation to show that changes in energy will be accounted for in this equation and to show that energy is not created nor destroyed. So the number (-1) or negative 1 is very important for this equation and for us to adhere to the “law of conservation of energy.”

We acknowledge that horses are not machines but animals of flesh and muscles so we insert “limits of changes” like a “calculus equation” and acknowledge that any extreme exertion of energy can result in “energy dissipation” or “Entropy.”


In 2nd F(Y), we account for changes in fractional time as in the second turn time and/or second call pace time. In linear math, this will not make sense; but in Physics, it makes perfect sense as changes in time requires energy which is similar to going from 3G forces to 4G forces. It takes so much more energy to run the 4Furlong fractions under 44.0 in sprints or under 1:10 6Furlong fractions in route races.
Another example might be stepping on the car’s accelerator in the first mile to accelerate from 50mph to 60mph which will use up energy or work; then using the brakes to slow down the speedometer in the 2nd mile from 60mph to 50 mph. By using the brakes, we are slowing down the “momentum” of the moving car which expends energy and/or work. Momentum is extremely important in Physics because it is a quantity that is conserved in every closed system: that is, unless you put in or take out energy from a system, then the the sum of the momenta (plural of momentum) before an event will be the same as the sum of the momenta of all the parts after the event This energy expenditure in acceleration or deceleration must be accounted for in Physics.




Since we know that:

1st F + 2nd F = Final Time - 3rd F



In the following energy expression equation:

1st F(X) + 2nd F(Y) + 3rd F (-1)(X +Y) = Final Time



We move the 3rd Fraction property across the equal sign and to adhere to the “law of conservation of energy”, we have:


1st F(X) + 2nd F(Y) = Final Time – [ 3rd F (-1)(X +Y) ]



By focusing on energy changes exclusively; we have

(X)change in 1st F + (Y)changes in 2ndF = Final Time minus [ (-1)(X+Y) ]



We now let X = change in unit of energy>> faster or slower or ( +/- ) in the first fraction time and;

We now let Y = change in unit of energy>> faster or slower or ( +/- ) in the 2nd fractional time and/or 2nd call pace time.

Now it should be noted that if a horse changes a first fractional time and maintains his previous 2nd Fractional turn time, this changes the original 2nd call fractional time which will affect an energy change. More examples of this statement later….


Therefore we now have a formula to express the effects of changes in energy in the early pace of the race on the Final Time that follows the “laws of Physics” by using the “law of conservation of energy”.

We do not know how Huey Mahl proved Bradshaw’s statement exactly but we can follow the “law of Physics” by using the “law of conservation of energy” to retrace Huey Mahl’s thinking and to express Jim Bradshaw’s statement. It is given that we are dealing with horses who are animals; not mechanical machines- but energy expenditures and energy dissipation or “entropy” can be expressed mildly.

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Last edited by lone speed; 06-09-2016 at 02:53 PM. Reason: added negative sign
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Old 06-09-2016, 10:31 PM   #2
Ted Craven
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What a fascinating - and important - depiction of energy dissipation and leverage: the Matchup, in math. I feel certain that something could (and should) be done with this in software. Perhaps more than was done in EXDC/Thoromation.

Thank you lone speed, for your imagination and clarity!

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Old 06-10-2016, 11:55 AM   #3
lone speed
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Ted...

Thanks for your comments!!!

Looking forward with much anticipation to your future endeavors!!!!

Sometimes it is ironic that some complicated and intense subject can be condensed in a short and sweet mathematical equation.....

Albert Einstein's theory of special relativity>>> E = mc2

Issac Newton's Gravity formulas and his formula for measuring gravity>>>

g = GM/r2
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Old 06-10-2016, 12:54 PM   #4
lone speed
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Ten year old message post

I would like to answer Bill Lyster's questions (albeit) ten years after he had posted them to the Hat...(patience is a virtue... )

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Old 06-10-2016, 02:55 PM   #5
lone speed
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Using the energy change equation:

(X)change in 1st F + (Y)changes in 2ndF = Final Time minus [ (-1)(X+Y) ]


We now let X = change in unit of energy>> faster or slower or ( +/- ) in the first fraction time and;

We now let Y = change in unit of energy>> faster or slower or ( +/- ) in the 2nd fractional time and/or 2nd call pace time.

Bill Lyster's questions:

Base line "original paceline" fractions:

22.0 45.0 110.0 final time with 2nd fraction turn time of 23.0


A) If today's projected pace: 21.4 for 1st F and 45.0 for 2nd F

The new projected final time adjusted for today's match-up will be:

First Fraction>> Faster by one tick so we add (-1) for the 1st F of the equation.

2nd Fraction/2nd Pace call time>>a projected slower 2nd turn time (45.0 minus 21.4 equals 23.1(fifths) even though the projected 2nd call time is the same as the baseline's 2nd call time of 45.0 thus

Second Fraction>>Slower by one tick so we add (+1) for 2nd F of the equation

entering the above value into the equation we have:

X= (-1) and Y = (+1) >>>(-1) + (1) equals Final time -[(-1) + (1)] or

0 change in net energy spent equals Final time-(0) net energy change so

Final time stays the same or 110.0 Final time

so projected times will be 21.4 for 1st F and 45.0 for 2nd F and Final time of 110.0


2nd question:


B) If the projected pace is 21.4 for 1st F and 44.4 for 2nd F

The new projected final time adjusted by today's match-up will be:

First Fraction>> Faster by one tick so we add (-1) for the 1st F of the equation.

Second Fraction>>The 2nd fraction turn time stays the same at 23.0 but the 2nd call pace time is Faster by one tick so we add (-1) for 2nd F of the equation

entering the above value into the equation we have:

X= (-1) and Y = (-1) >>>(-1) + (-1) equals Final time -[(-1) + (-1)] or

Final time - (-2) since (-1 + -1) = (-2) but -(-2) equals (+2) since -(-2) is the same as (-1)(-2) thus

We have a new projected Final time of 110.2(fifths) so we have

21.4 for 1st F and 44.4 for 2nd F with a projected Final time of 110.2


Last question:

Energy is not lost forever>>> energy is not created nor destroyed according to the "laws of Physics."
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Old 06-14-2016, 11:15 PM   #6
lone speed
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Correction to Formula

After looking over the formula and gathering my thoughts on the formula that I put forth. I realized that I had prematurely posted my thoughts on Huey Mahl's Physics hypothesis. I did not account for energy used for acceleration when a horse adjusts to the projected matchup pace fractions from its previous "baseline" fractions.


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I did not factor in the energy used up for the acceleration from the starting gate to the first two furlongs from our baseline fractions to the match-up projected changes. We only consider the 1st fraction because it starts from a zero state of motion or at the starting gate whereas the 2nd fraction is the part of the race after running the 1st fraction. (we are trying our best to keep this simple as much as we can)




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Acceleration has nothing to do with going fast. A horse can be moving very fast and still not be accelerating. Acceleration has to do with changing how fast a horse is moving. If a horse is not changing its velocity, then the horse is not accelerating.
In Physics, acceleration (a) is the amount by which the velocity changes in a given amount of time. Given the initial and final velocities, vi and vf, and the initial and final times over which the speed changes, ti and tf, the acceleration equation is written like this:



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The Direction of the Acceleration Vector

Since acceleration is a vector quantity, it has a direction associated with it. The direction of the acceleration vector depends on two things:


A) whether the object is speeding up or slowing down (expending or conserving energy)
B) whether the object is moving in the + or - direction


The general principle for determining the acceleration is:
If an object is slowing down, then its acceleration is in the opposite direction of its motion


Instantaneous acceleration is simply the derivative of velocity.

Average acceleration in an interval is
a⃗avg=Δv⃗Δta→avg=Δv→Δt

Instantaneous acceleration is
a⃗=dv⃗dta→=dv→dt
a⃗(t)=limΔt→0v⃗(t+Δt)−v⃗(t)Δta→(t)=limΔt→0v→(t+Δt)−v→(t)Δt

Take the average acceleration in smaller and smaller intervals. As ΔtΔt goes to 00 , you get the instantaneous acceleration at tt .

Note that velocity is always continuous



Basically, we are comparing the difference in energy use to run one tick of energy slower or faster for each tick of a second of acceleration. In 99% of the races, horses are decelerating after the first and second fraction. The running of the 3rd fraction is an optical illusion when a closer runs by the race leaders. The closer is just decelerating the least when compared to the race leaders in the stretch. Thus no acceleration for the 2nd fraction and 3rd fraction. Elite turf runners are the rare exceptions.

But all this is too much math, so let’s just use one of Issac Newton’s Three Laws of Motion. Let’s use the third law of motion:

It states :

For every action, there is an equal and opposite reaction.

It means that for every interaction, there is a pair of forces acting on the two interacting objects. The intensity(energy) of the forces on the first object equals the intensity(energy) of the force on the second object. The direction of the force on the first object is opposite to the direction of the force on the second object. The forces always come in pairs - equal and opposite action-reaction force pairs.

So if we use one tick of energy moving in one direction; there is an equal one tick of energy for the opposite reaction. This has no math involved since the two are equal in energy.

The correct equation to keep this more simplistic is as follow:

Since Newton’s Third Law of Motion states that the two energy are equal.


1st fraction (energy used in acceleration in one tick of a second) + 1st fraction(X) or since (energy used in acceleration in one tick of a second) equals (X)
1st fraction (X) + (X) or 1st fraction(2X) therefore our revised and correct equation is:

1st Fraction (2X) + 2nd Fraction (Y) = Final Time minus [(2X) + (Y) ]


We let X = change in unit of energy>> faster or slower or ( -/+ ) in the first fraction time and;

We let Y = change in unit of energy>> faster or slower or ( -/+ ) in the 2nd call pace time exclusively


When projected fractional time is faster>>>use (negative value) (minus X or Y)

When projected fractional time is slower>>>use (positive value) (Positive X or Y)
I want to apologize to everyone who had read my earlier post and for the confusion. But I want to assure that it is easier than one thinks after working several examples using this corrected equation.

Last edited by lone speed; 06-14-2016 at 11:30 PM. Reason: changed -/+ variables
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Old 06-15-2016, 01:36 AM   #7
Bill Lyster
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Application in the field

While I have long been aware of this statement and the theoretical proof, my question relates to the 2:1 reduction in actual practice. My observation has always been that each horse has its own distinct exchange rate, so to speak - such that a two for one gain/loss is a bit of a simplification. In the screen shot from the E/L graph which, someone correctly if I am wrong, uses adjusted race lines, the horse in the 3rd back ran 92.0 early and 98.2 late. In its last race it ran 89/100. If it were truly 2:1, then running 3 ticks slower in race one would mean 106 late, for a total of 195, instead of 189. The horse won its last by 11 and finished 2nd in race 3. From the PPs you might expect that the best final fraction to be expected from this horse is 104.8 or thereabouts.

If you look at race 6 where the early/late was 95.8/97.2 and compare it to race 3's 92/98.2, again the 2.8 ticks slower early does not result in 5.6 ticks faster late and the LPR is not 102.8, but 98.2.

I picked this horse because it was an early or early presser, the most likely horse type to respond in a 2:1 factor. It is not an isolated example as you can find it every day in almost every race.

Too me, it looks like if the horse runs slower by 5 ticks next out, it can finish 5 ticks faster. IN this case the 189, 190.2 and the 193 appear to coincide with that observation when you compare the actual E/L data.

What am I missing?
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Old 06-15-2016, 10:44 AM   #8
Mitch44
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While all these formulas are impressive I seriously doubt 1 in 100 understand them completely, myself included. Algebra etc. was never my forte. Perhaps lone speed you can give some simplistic examples as it all relates to what we do know and use with RDSS basic numbers etc.

There are things in here that are assumptions such as horses accelerate in the 1st Fr and not on the turn. The Doc identified as many as 9 I believe different running patterns that horses run. Some run high 1st & 3rd Fr while decelerating on the turn. Perhaps they can't negotiate the turn or they need a breather but that's their style. Others run poor 1st Fr and great 2nd & 3rd Fr.
Additionally the Doc said it could be as high as 3 to 1 in routes.

Bill Lister brings up an interesting post so I'll enlighten it. While a basic formula is nice it really is dependent on the match up of the race and the actual running styles of the combatants in the race. This has much to do with class but different horses have different deceleration rates. For one horse the ratio can be 4 to 1 while most are probably 2 to 1 . The difference is how fast does that horse decelerates vs. the others and weather its pushed enough to its maximum. If not forced by the match up it'll conserve energy and its deceleration rate will change with it.

Bill your right that horses have different exchange rates and that rate varies by what it must do today by the match up of the horses in the race. Additionally because of cheap class, infirmaries and their inherent style some consistently stop on a dime regardless of the match up. Most are locked into a style that doesn't change much perhaps from poor early training. The race itself can change a horses style, E. g. a strictly E horses has a poor break and comes from off the pace to win.

Mitch44

Last edited by Mitch44; 06-15-2016 at 11:01 AM.
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Old 06-15-2016, 11:35 AM   #9
lone speed
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Thanks for the contributions Bill and Mitch

Bill...

I'm typing from a phone so bear with me here....

You are correct to suggest that the ability is dependent on the "potential" ability of the horses. The simplistic adjustments are for raw fractions and are rounded to be clean and simple.

Noble Bird.

The examples of the 3rd pace line and the 6th pace lens are very different on form cycles. The 6th pace line was a major effort race while the 3rd pace line was a prep race for the Pimilco Special.

Mitch.

Thanks for your input...

I believe we are not talking about acceleration within the same context in Physics.
In everyday life, we see car commercials about cars running fast and the use of acceleration from 0 mph to 60 in 6 seconds. This is not acceleration but "torque" power of the car. It is not the same nor your question about the horses accelerating on the turn or third fraction. Bear with me here.

Acceleration in physics is the change in velocity either when going faster or going faster in one instant of time.

In our examples, we are comparing the changes in energy to run 2 furlongs in 22.0 from the baseline race then changing it to 22.1 (slower) or to 21.4 (faster) in our virtual match up line. There are acceleration in both of these changes.

Acceleration is the change in velocity. Two distinct variables.


There will be more exchanges....

Thanks again for the participation
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Old 06-15-2016, 11:59 AM   #10
lone speed
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Please substitute the word bear to bare... Thanks..opps
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