**Team:** 45

**School:** LAS CRUCES HIGH

**Area of Science:** Engineering

**Interim:** TEAM# 45

AKA "THE PENGUINS INTERNATIONAL CORPORATION"

INTERIM REPORT

The project began as Harold Brochmann published a web article, dubbed "The Mathematics of Falling Bombs". Therein Brochmann describes the mathematics of calculating bomb trajectories. Brochmann alludes in his article to the mathematical error of not using air resistance when computing a bomb's trajectory when compared to an equation with air resistance. Brochmann's graphed result depicted the trajectory of a particular bomb with air resistance falling slightly under par of the bomb in a vacuum environment. After a period of repeated returns to Brochmann's article, the error (in the two equations) being realized to have a quantified magnitude, the team has questioned:

What factor~ capable of being modeled influence said magnitude of said error?

The team progressed to elect this question as the purpose of their project. The team has also opted to model a ballistic projectile launched at the trajectory's initial nadir, i.e. a bullet, or a similar device possessing like characteristics, e.g. paintballs, or any other such projectile.

The following factors have been determined as reasonable, pertinent and capable of being modeled into the team's program: Mass [of the projectile], Velocity, Caliber (cross sectional area), Initial Angle of launch and initial altitude of launch (altitude affects air density). The team assumes the project's findings to entail applicable (and practical) purposes of such findings strictly within the earth's atmosphere, and therefore does not include an otherwise prominent factor, of gravity in the project.

Therefore, we conflate the hereinbefore-stated factors to be modeled, to form 72 different combinations of said factors, which translates into 72 separate results (See diagrams). The said factors are firstly organized under one main category, mass. Mass refers strictly to the mass of the projectile. Said section of mass is divided into three disjunct groups of 80, 60 and 40 pounds. Each element in this group of three is succeeded by its own subcategory, of velocity. Velocity refers to the velocity of the projectile, and for each of the three said categories (80, 60 and 40), has two velocity magnitudes:

2,000fps and 4,000fps. Furthermore, under this subcategory is a third category. This category is the factor Caliber, and is of two types: 120 mm and 200mm. Unto each of

These calibers entails Launch Angle, which is of three types: 10, 30 and 50. Lastly is the subcategory of initial altitude, at 0, and 10,000 feet above means sea level.

These 72 combinations dictate the initial inputs of the program. The program will execute its run once with added air resistance and once without. The magnitude of the error of the two shall then be evaluated and compared with the remainder of the group (71) to find which factors affected the error's magnitude.

**Team Members:**

Nathan Smith

Jeffrey Wang

Abraham Sanogo

Tom Burnham

**Sponsoring Teacher:** Gregory Marez