When I first started pitching horseshoes, I wanted to put some sort of reference at the highpoint of my shoe flight. Unfortunately, the only information I was able to find was a recommendation to throw the shoe approximately 2 feet above your height. For me, about 8 feet. The location of the reference point was declared to be at about 2/3 of the distance to the stake. This proved to be incorrect. The actual highpoint downrange never reaches halfway. The table below shows the downrange location for any selected highpoint from 4 feet to 14 feet. The table is based on a calculation of releasing the shoe 1.5 feet from the 30 foot foul line and 3 feet from the ground. My personal highpoint is actually at 6.75 feet (6.8 for the plot values in 1/100th of a second increments).
The plot at the top of this page was calculated in 1/40th second increments. To provide more accurate results, I changed the plot by increasing the values to 1/100th of a second increments. I used the frame mentioned earlier to determine my release point of 3.0 feet, 1.5 feet in front of the foul line and highpoint downrange of 6.75 feet reached at 10.75 feet downrange.There was an added bonus by finding my release point. I was able to determine that my horseshoe rotates 580 degrees. I can now find two downrange points from this information. The location when my shoe is flat and open to the stake and the location when my shoe is flat and pointing away from the stake. So, in addition to the highpoint and downrange location, I can also place a marker before and after the highpoint location when the center of gravity offers a flat shoe in flight. This is important when throwing a flipping shoe. Since I am trying to pass the center of gravity through the appropriate points, a flipping shoe could occupy 7+ inches as it rotates in space. A turning shoe does not have this problem. I am hoping to create an animated GIF of the flight of my shoe as it rotates toward the stake.
There were many formulae found to produce results regarding distance when trajectory is known, but, nothing that talked about calculations that provided results when you knew the distance, height and release point. I have written a Perl program that calculates the XY plot of a horseshoe in flight when the release point and highest point of flight is known. In addition, it calculates the initial launch speed, time of flight, initial launch angle and location of the highpoint downrange. Each point on the plot is in 1/40th of a second increments. I decided to calculate the shoe flight from 30 and 40 feet. I later calculated the same plots at 1/100th of a second increments.
The PDF file below extracts the information from each plot and places the results in table form for a distance of 25.5 feet (Elders pitching from 30 feet with a foul line at 27 feet). My release point is actually 1.5 feet ahead of the 27 foot foul line.
Below is the plot of my shoe flight in 1/100th of a second increments. Double-click image for larger view. The number of plot points is equal to the time of flight X 100. My shoe flight plot contains 113 plot points.
The plot below shows the rotation of my shoe in flight. My shoe starts out 40 degrees below horizontal. It rotates 580 degrees total, i.e., 1-1/2 flips plus 40 degrees. I could now place markers downrange where the shoe is flat in flight. If you wanted to be adventurous you could place a post, rod or PVC pipe, etc. at the point where the shoe is perfectly open downward and vertical. That point is 5.57 feet downrange and 5.9 feet up. The flat shoe is just before the highpoint downrange and is located at 9.4 feet downrange and 6.7 feet up. Placing a string would best be placed where the shoe is horizontal open or closed. The shoe is flat in three places. The first at 1.7 feet downrange and 4.1 feet up. The second mentioned above and the third after the highpoint downrange. Placing more than one marker is more accurate than simply placing a string at the highpoint. The plot below is in 1/323rd second increments.
I couldn’t resist. I’ve animated the image below. Put the cursor in the image below and mouse click. The animated flight of my horseshoe is shown (it loops 4 times and stops).
I will be providing a table and plot for 40 foot pitchers at this point later.
If you would like a plot of your personal shoe flight, please provide three values. 1) Distance to the stake from your horizontal release point (how far to the stake); 2) Distance from the ground when shoe is released; 3) Your highpoint, if known, if not, provide a height range, i.e., 6.0 to 8.0 feet. I’ll run the plot software and generate the results as shown in the plot above with your highpoint/downrange locations. Email me with the three values to: bobrass at verizon dot net
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