Dynamics of Turns in Horse Racing by Larry Wellman


This work was conducted in the mid to late 1990ís.


Turn Dynamics:


A couple of weeks ago I posted an article relative to turns which had a mistake that I have now corrected.The post was in response to a question I received from Dr. Steve Roman relative to his observation that some horses out in the 3 and 4 path on the turn appear not to be handicapped by the extra distance traveled and actual look like they are handling the turns better then the horse on the rail.At that time I developed a spreadsheet to test his question.In the spreadsheet I allowed horses in the outer paths to increase speed to match the turn dynamics (forces) that the rail horse was experiencing.What the results showed was that the horses off the rail could run at a higher speed on the turn versus the rail horse.This extra speed increase would compensate for the extra ground covered.The net result was that the horse in the outer path actually only lost half what is the accepted standard.The standard is lose one length or 10-11 ft for each path removed from the rail.


Using my Energy Program I went in and tested some additional factors to show that a horse in the four path actually can run 6 furlongs faster then the rail horse when track and conformation parameters are match properly.The track I modeled is Laurel Park, which is a 9f track with 2.25f turns.I modeled a track with no track bias (resistance) around or across the paths.I did change two parameters that impact on turn dynamics.I modeled the proper conditions for a horse further from the rail so the extra distance does not handicap a horse.The two factors I adjusted are the bank angle of the turn and a factor called (beta) that represents the ankle pulley ratio as defined by Peter R. Greene (J. Biomech Vol 20, No7 pp667-680 1987).The ankle pulley ratio is a conformation parameter and represents the distance from the sole of the foot or hoof up to the ankle or fetlock on the horse.I used the number suggested by Greene since there is no publish info on horses.If the foot is allowed to roll into the turn the beta value will be reduced.So what I did was assume that the turn bank angle starts at zero in the one path and is 3.5 degrees in the 4th path.I

made the following assumption that the ankle pulley ratio is the maximum at the rail and reduced to zero in the four path.Below I will show the results of my program for both the path one and path four under the conditions I mention above.Path zero is if a horse ran on top of the rail while path one is the path a horse runs when on the rail.I modeled a 3.5 ft distance between paths.Each path away from the rail results in an extra 11 ft (3.5 X pi) traveled.I also show the time for a 6f race on a straight course having no turns.


††††††††† Bank††††††††††††††††††† |------turn------|

PathAngle Beta 1/4†††† 3/8††††† 1/2††††††† 5/8†††††† 3/4

0†††††† 3.5†† .27†††† 24.55†† 36.15†† 48.35†† 60.85†† 73.50

1†††††† 3.5†† .27†††† 24.55†† 36.25†† 48.50†† 61.0573.70

1†††††† 0.0†† .27†††† 24.55†† 36.25†† 48.60†† 61.20†† 73.90

4†††††† 3.5†† .27†††† 24.55†† 36.45†† 48.95†† 61.65†† 74.30

4†††††† 3.5†† .00†††† 24.55†† 36.35†† 48.75†† 61.25†† 73.85

Straight course†††† 24.55†† 36.05†† 48.00†† 60.25†† 72.85


Simulation run with a .05 sec delta


Now when you compare the 1 path with 0.0 degrees bank against the 4 path with 3.5 degrees banking and zero ankle pulley ratio (beta=0) we see that the horse in the 4 path runs about same race time for 6f race although this horse runs 33 ft longer distance (on turn) then the one horse.


What this means is that correcting a horse speed figures using a standard of one length lost per each path away could actually over estimate the horse speed figures.To do a proper adjustment we would need to know the bank angle distribution across the turn, conformation of each individual horse, (how this horse handles turns), a track bias if it exist across the track.The beta term is also dependent on the type of shoes the horse is wearing, etc.


I think this address Dr. Roman's question along with some possible errors that could exist in some of the speed figure services that make adjustments for ground lost on the turn.


I did not limited the turn forces on a horse like I did in the spreadsheet I mention earlier.Adding this factor in could lead to even better performance when running away from the rail.


For handicapping you need to assess each horses ability to run on the turns.


Follow up question.


Jetaway brought up a question relative to the bank angle I assumed for the horse in the one path.I made the assumption to show the maximum based on the two conditions discussed.If you go back and look at the table you will see that even if the bank angle is assumed to be 3.5 degrees for both horses the horse in the four path will only run slower by less then one length (.15 sec) if this horse can handle the turn better (beta=0).Beta as I mention is a function of conformation.The equation I used with this term also involves the following terms: the bank angle, the heel over angle, and Froude number.Froude number is a non-dimensional speed parameter using the turn radius.Heel over angle is the arctan of the Froude number.†† The difference between bank angle and heel over angle is called the mismatch angle.If we assume a horse can run with zero mismatch in the turn the bank angle matches the heel over angle then we have the condition I show as beta=0 for the horse in the four path.


From the table we see that if the conditions were the same for both horses then the horse in the four path runs an extra 33 ft and it takes him and .60 sec more time to cover 6f about one length per fifth of a second.Now under conditions when the horse in the four path has the ideal conditions then he cover the extra distance in only .15 seconds (bank=3.5 deg) compared to the one path.Resulting in a difference of two lengths.This correction would be equal to about 5 Beyer speed points if they corrected for trip.In the Sheets or Thorograph system this would equal a point or two.I'm not a Sheet

user so I'm not sure on the exact number.The point is that any service that corrects for trip on the turns is adding some additional noise in there product.How do they know what the conformation (beta terms factor), the banking or track bias across the turn and around the turn.The beta term is determined from observations and varies within a population.†† Based on this new research I would look closely at figures that are adjusted for very wide trips.Maybe some of the sheet users can offer some observations about figures that look out of line when the horses raced wide.I personally never adjusted my speed figures in the 80's for trip.Add factors like wind and bad weather and we are really shooting in the dark.


BTW, all races are for zero gate runup.


Turns and Breakdowns.


Because of all the discussion about the breakdowns in the Jim Beam I decided to present some information about turn dynamics and the relationship to potential breakdowns.I did not see the Jim Beam so I do not know where on the track the horses breakdown, however the turn or the transition from the turn to the straight would be critical areas.I will present a factor which is a combination of two other variable that I model in my Energy Program.The first variable is related to bank angle and the lean angle of the horse in the turn.Included in this term is the ankle pulley ratio which relates internal and external moment arms within the ankle.Research conducted by Peter Greene (J. Biomechanics, Vol 20 No.7, 1987) estimated values in the .27 range for humans and the same value to be used for dogs and horses.The ankle pulley ratio is a conformation variable of the distal end of the leg: i.e. length of the pastern and the distance between the sesamoids bones.Shoe designs variables also play a part.

Since there is no research data on horses I will use Peter Greene number.The second term is related to turn radius and speed on the turn.Together the two terms can be treated

as an equivalent increase in weight carried on the turn.The values shown in the following table is the combined term.Any number greater then one results in higher weight carried.I will show two different turn radius: 2f and 2.25f turns.I have not

modeled tighter turns (1.5f) or larger turns (3f).


The data shown is for the horse a half-furlong into the turn around 2.5f to 3f into the race.


Turn Size: 2f or 420 ft radius.

†††††††††† Bank Angle, degrees

Beta††††† 0†††††††††† 3.5††††††††† 7.0

0††††††† ††1.027†††† 1.027††††† 1.027

.27†††††† 1.0855†† 1.0711††† 1.055

.54†††††† 1.1428†† 1.1120††† 1.080


Turn Size:2.25f or 472 ft radius

†††††††††† Bank Angle, degrees

Beta††††† 0†††††††††† 3.5††††††††† 7.0

0†††††††† 1.025††††† 1.025††††† 1.025

.27††††† 1.0834††† 1.0670††† 1.051

.54††††† 1.1390††† 1.1090††† 1.076


The bank angle of 3.5 degrees represents a grade of 6 percent across the track.

This would be a rise of 6 ft over a 100 ft.I used this number based on some private communications about track designs.


**It would be very helpful to have this information

presented in the DRF.


If a track has no bank on the turn and we used Greens's number for beta (.27) the horse will be carry the equivalent of an additional 100 pounds on the turn.Bank the turn to 3.5 degress and we get only additional 80 pound based on a horse and rider of 1200 pounds.Based on gait analysis a individual fore legs will be subjected to almost three times the full body weight of the horse during a stride.Now add the impact of the turns dynamics and the horse would see an a additional 300 pounds of load on one leg.Increase speed or reduce turn radius will result in higher numbers.


This is only part of the answer about breakdowns.Other variables such as shoeing, bandages, conformation, track, and the riders all come into play.