Reflection 11: Walk or Run in the Rain

In this article, the modelling of a common problem- whether or not we should walk or run in the rain- was created to get an idea of what factors constitute which form of movement. This was designed by integrating parameters into the original equation to dictate what may effect the ultimate outcome; things like surface area of your body, the density and angle of the rain, the distance to your front door, etc. The derivative of this equation was used to find what may be the optimum running velocity (an optimization of speed in this scenario, as related to the rain coming down). All of these concepts have been ideas covered in class, and can be applied to other scenarios of interest.

For example, I used to be an avid airsofter (essentially paintball for definition purposes), and a lot of situations can be modeled/optimized in the sport. Optimizing time spent on objectives, modelling the accuracy/shot placement of the BBs, and modelling the velocity/FPS speed of a BB leaving the barrel based on things like length, power of the spring in the gun, compression of the air, etc. are all possibilities. For this assignment, however, I will be modelling the optimal team size for succeeding at an objective (let's say capturing a base or rescuing a "hostage").

There are quite a few factors to take into account for. First off, our output from the equation should be a probability of success of sorts (above or below a certain value will indicate the probability of success or failure), which will be referred to as a Success/Fail Ratio (S/F). As for parameters, there should be three main portions to the equation; parameters relating to your team, parameters relating to the opposing team, Parameters relating to your team and the opposing team could be as follows; team size (x=number of individuals on team, or may be thought of as "number of weapons" since each player is only considered if they have a weapon), number of medics on team that can heal players back into game (typically game rules allow for one per ten players, so x/10), a constant assigned based on team skill (perhaps something on a scale of 1-10, ten being most skilled, 1 being least skilled, represented as a_skill), and a coefficient which would represent the gear being used by the players, which may include the probability of weapon/gear malfunction, which can be assigned a constant (a_malfunction, which is about 1 in every 15 rifles, so 0.067) and the availability of spare gear (how many spare batteries, gas, weapons, ammo, etc. is available), which can be represented by Gp- a coefficient of the supplies needed for the situation and the supplies currently held (S_h/S_n).

a_team skill(0.067(x_t+x_t/10)+Gp)-a_opponent skill(0.067(x_o+x_t/10)+Gp)

As for the environment, things such as area of cover as a proportion to area where combat is likely (Cover/Combat Area= Co/Ca) (integrated later) and desired amount of time to complete vs amount of time available in minutes (Tc/Ti).

a_team skill(0.067(x_t+x_t/10)+Gp)-a_opponent skill(0.067(x_o+x_t/10)+Gp)*(Tc/Ti)

Finally, none of this matters if your accuracy is poor, and you can't perform better than your accuracy except by chance, so it will act as the "carrying capacity" for the equation. The likelihood of hitting a target vs the likelihood of getting hit could be modeled as average accuracy at any distance in the combat area per 100 shots, represented as a percentage or a ratio related to the number of your team members versus the number of your opponents team members. Accuracy may be thrown off by cover, so cover available to your team vs cover available to the enemy team is now in consideration.

So, finally:
S/F=

((a_team skill(0.067(x_t+x_t/10)+Gp))/(Cot/Ca*Accuracy(x_o)*100))-((a_opponent skill(0.067(x_o+x_t/10)+Gp))/(Coo/Ca*Accuracy(x_t)*100))*(Tc/Ti)

Given my experience with modelling anything like this, this equation is probably not set up quite right and likely needs things to be shuffled around. However, it definitely delves into the ideas of what may control the outcome of certain things, which would lead to another portion of my model; what numbers constitute success, and which ones failures.

From this point one may optimize the equation to decide what the optimum time would be to complete an objective, what the optimum team size would be, the optimum amount of cover, the optimum amount of gear, the optimum area of combat, etc., depending on which variables are known and which ones are desired for manipulation.