Fueling Scoring Challenge

[BoilerMentor]

Last night during vigorous discussion of game play strategy at HBR we discovered what we believe to be a serious challenge with this year's game as related to typical FIRST strategy for repeatable goal alignment.

Because of the processing rate of the boiler (5 fuel per second) the maximum achievable pressure with teleop fuel scoring is 225 points of 675 fuel. In order to create a viable "cycle" this dictates that you have to exceed 5 fuel per second entering the boiler to maximize your scoring ability for fuel. At this point we believe something in the neighborhood of 15 fuel per second is needed to create an adequate processing time buffer to allow for transit, collection, and scoring of additional fuel.

The logical jump when considering this is to use the key immediately in front of the boiler as an alignment tool to create a repeatable scoring situation. The problem with this strategy is what I'll outline below.

As the distance traveled across the ground by the projectile decreases and apex height increases the ratio of vertical and horizontal velocity components becomes larger. Eventually this means that as projectiles reach apex and the vertical component of velocity is exhausted the total velocity of the projectile becomes quite small. As you consider a string of projectiles in this situation, convergence can be observed as projectiles move towards the apex. When projectiles actually converge in flight this creates very erratic behavior and has the potential to cause a significant number of missed shots.

The mathematical model required to describe and evaluate this situation is not clear to us at this point and we're looking for some help. Maybe someone here has an idea?