I apologize. It has been too long. I took a long break from blogging because I was busy and burnt out. Without getting into too much detail as to why I felt burnt out, I shall briefly state that working with a couple incompetent partners back to back is enough to burn anybody out. After witnessing all the drama, the greed, the deception, and even the swindling of company funds, I have had enough. I would rather jump back into a 9 to 5 and earn a steady, comfortable paycheck.

…which is exactly what I did. I even worked briefly at a large .NET shop staying under the radar and coding quietly in C#. That’s how bad it was; I worked at a Microsoft shop.

I tried everything to recover from this burnout, short of changing careers.

During these times, one major activity I picked up to assist in my recovery and escape from my stresses was sporting clays. For those that aren’t familiar with sporting clays, it is a challenging (but fun and addicting) shotgun shooting sport that began as simulated hunting. Unlike skeet and trap, sporting clays requires the shooter to migrate from station to station (usually 10 or more stations) either on foot or golf cart. At each station there are a pair of clay throwers that throw clay targets in a wide variety of presentations. No two stations are alike, and the shooter must shoot each pair as either a true pair (two targets at once) or a report pair (one target first, second target immediately after the first shot). The targets can fly overhead, come towards you, drop, cross, roll, etc. Scores are kept and represented as number of total targets broken. The easiest way to describe this sport is “golf with a shotgun”. It’s no wonder sporting clays is currently the fastest growing shooting sport.

You’re probably wondering why I’m talking about shooting. Well, as I became more involved in the sport, I began to analyze the targets in order to improve my score. It turns out to be a very fun problem to solve which involves a bit of trigonometry, physics, and software engineering.

Let’s begin with the knowns. A shooter is typically firing 1 oz or 1 1/8 oz of lead (7 1/2 or 8 shot) downrange at anywhere from 1100 to 1300 feet per second. The clay targets are typically thrown at 41 mph but can vary. Rarely, targets can be launched at blazing speeds up to 80 mph. The direction and position of the clay throwers are always different, but shots are usually expected to be taken in the 20-50 yard range. On occassion, you may be expected to take an 80 yard shot (or further) but that would be extremely rare. The “breakpoint” is where the shot meets the target and breaks the target.

Since we’re not shooting laser rifles, there’s a certain amount of “lead” seen by the shooter or else he/she would be missing from behind. So how do we calculate this lead?

I consider there to always be two different types of leads: the actual lead (how far ahead the pattern actually needs to be) and the visual lead (how the lead appears to the shooter from the shooter’s perspective)

For example, if a target was a straightaway target, all we would have to do is shoot right at it, making the “actual lead” unimportant and the “visual lead” non-existent. If a target was a 90 degree crosser, perfectly perpendicular to the gun’s shot path, that would simply require a conversion of miles per hour to feet per second (5280 feet = 1 mile) and determining how much quicker the shot pattern reaches the breakpoint before the clay target. But of course, nothing is this simple. The truth is, breakpoints vary, angles vary, distances vary, velocities vary, thus leads vary. Even the same target thrown from the same machine will have a different lead depending on where in its flight path you decide to shoot it.

This is how I began to tackle the problem:



1) I visualize the different points. S = shooter, T = thrower, B = breakpoint, P = target location.



2) I determine the distance between shooter and the breakpoint.



3) I determine the shooter’s angle between the breakpoint and the target location… in other words, the lead in degree angles



4) I determine the distance (actual lead).



5) I determine the visual lead which is actually just an adjacent side to the right angle of the triangle and opposite to the lead in degree angles.

6) I code this up using Python

Here is my implementation:

https://github.com/cranklin/clay-target-lead-finder

Of course since not all the triangles represented in this diagram are right triangles, I would have to utilize the law of cosines and law of sines to find certain distances as well as the angles.

Using my software, I conducted tests with the shooter shooting 1200 fps shot at a 0 degree angle at 41 mph crossing targets at varying distances. Here are the results of my tests:



{'shot_distance': 150.0, 'lead_ft': 7.52, 'pullpoint': (7.52, 150.0), 'lead_thumbs': 1.43, 'lead_angle': 2.87, 'breakpoint': (0, 150), 'target_distance': 150.19, 'trajectory': 270.0, 'visual_lead_ft': 7.52} {'shot_distance': 120.0, 'lead_ft': 6.01, 'pullpoint': (6.01, 120.0), 'lead_thumbs': 1.43, 'lead_angle': 2.87, 'breakpoint': (0, 120), 'target_distance': 120.15, 'trajectory': 270.0, 'visual_lead_ft': 6.01} {'shot_distance': 90.0, 'lead_ft': 4.51, 'pullpoint': (4.51, 90.0), 'lead_thumbs': 1.43, 'lead_angle': 2.87, 'breakpoint': (0, 90), 'target_distance': 90.11, 'trajectory': 270.0, 'visual_lead_ft': 4.51} {'shot_distance': 60.0, 'lead_ft': 3.01, 'pullpoint': (3.01, 60.0), 'lead_thumbs': 1.43, 'lead_angle': 2.87, 'breakpoint': (0, 60), 'target_distance': 60.08, 'trajectory': 270.0, 'visual_lead_ft': 3.01}



Based on the results of my test, at 20 yards, 30 yards, 40 yards, and 50 yards, the leads were 3 ft, 4.5 ft, 6 ft, and 7.5 ft respectively. Even more interesting is that the lead angles for each of these shots were virtually the same at 2.87 degrees! To get a better understanding of how to visualize 2.87 degrees, I added a “angle_to_thumbs” conversion method which returns 1.43 thumbs. What does that mean? If you hold your arm straight out in front of you and put your thumb up, the width of your thumb is approximately 2 degrees based on this link. So imagine, 1.43 thumbs; That is your visual lead. (your thumb width may vary. Mine happens to be smaller than 2 degrees)

So far, all the calculations are correct, but there is one gaping flaw: The physics aspect is incorrect (or non-existent rather). These numbers apply if clay targets and shot didn’t decelerate and were not affected by air resistance and gravity. Unfortunately, they do. So how do we adjust these calculations to take drag into consideration?





where F D is the drag force, C D is the drag coefficient, ρ is the density of air, A is the cross-sectional area of the projectile, and v is the velocity of the target. The drag coefficient is a function of things like surface roughness, speed, and spin. Even if we found an approximate drag coefficient, to further complicate things, one cannot simply plug the values into the equation and solve. Since the velocity changes at each moment (deceleration), the equation must be rewritten as a differential equation to be useful.

This is where I stop and let the reader take over the problem. Here are some good resources on drag force and drag coefficient:

http://large.stanford.edu/courses/2007/ph210/scodary1/

http://www.physicsforums.com/showthread.php?t=9066

http://www.physicsforums.com/showthread.php?t=157817

http://www.physicsforums.com/showthread.php?t=696022

To conclude, I would like to add that this program still leaves much to be desired. For starters, targets rarely fly straight but rather in an arc. Some targets slice through air (chandelles) and almost maintains its horizontal velocity. Others bend and drop rapidly (battues). Some pop straight up and/or straight down, allowing gravity to dictate its rate of change in velocity. Compound leads haven’t been considered, nor the unpredictability of rabbits’ sudden hops. But still, this gives you a good idea of how crazy some leads are and how counterintuitive it can be when you’re attempting to hit them.

Suffering from burnout or stress? Step away from that computer and enjoy some fresh air at a local sporting clays course near you.

If you’re looking for a course around the Los Angeles area, I suggest you check out Moore-n-Moore Sporting Clays in Sylmar, CA. The staff is inviting and will happily assist new shooters. You may also catch Ironman shooting there. 😉