Session 1: Foundations – Why Math Powers Design (Vectors & Basics)

Discuss

Review Captain's notes—math as core for creation (not available in Uganda, so build it now). Tie to Jonathan: "He used math to uncover a 'hidden effect' in baseball; you'll do it for flight."

Code

import numpy as np
import matplotlib.pyplot as plt

# Basic vectors for forces (thrust vs gravity)
thrust = np.array([100, 50])  # Tweak these!
gravity = np.array([0, -9.81])

# Plot
fig, ax = plt.subplots()
ax.quiver(0, 0, thrust[0], thrust[1], angles='xy', scale_units='xy', scale=1, color='b', label='Thrust')
ax.quiver(0, 0, gravity[0], gravity[1], angles='xy', scale_units='xy', scale=1, color='r', label='Gravity')
ax.set_xlim(-10, 110)
ax.set_ylim(-20, 60)
ax.set_xlabel('X Force')
ax.set_ylabel('Y Force')
ax.legend()
plt.title('Basic Aero Forces: Vectors')
plt.grid(True)
plt.show()

Onboard to dev env. Run this script plotting basic vectors (e.g., thrust vs. gravity). Tweak angles to see lift changes.

Excite

"See how changing one number makes the 'plane' climb? That's math designing reality."

Homework

Adjust script for different forces; commit to GitHub.

Math Focus

Vectors (direction/magnitude for aero forces).