2D Glider Simulator

Tested with: MATLAB Online (R2025a)

Goal: Simulate an unpowered glider released from given altitude and compare ground distance traveled and glide time across airfoils.

Model Used

State y = [vx, vy, x, h]^T

Forces:

• L = 0.5 * rho * v^2 * A * CL

• D = 0.5 * rho * v^2 * A * CD

Dynamics:

• v = sqrt(vx^2 + vy^2)

• dvx/dt = -(D/m) * (vx / v)

• dvy/dt = (L/m) - (D/m) * (vy / v) - g

• dx/dt = vx

• dh/dt = vy

Numerical solver: ode45 (RK4/5 adaptive step)

Integration is halted when h(t) crosses 0 (i.e., touchdown)

Assumptions

• Angle of attack is constant every run, so CL and CD are too

• ρ = 1.225kg/m^3 (sea-level)

• Lift + drag are calculated with planform area A

• No wind and no variation of density with altitude

• Lift is treated as purely vertical, drag is aligned with velocity vector

How to run

cd src 
main

Outputs

• plots/ contains figures

• results/summary.csv contains summary

• Console table has airfoil, CL, CD, range, flight time

Constants example

Cessna-172 geometry (m = 1040kg, A = 16.2m^2, g = 9.81m/s^2, ρ = 1.225)

Airfoil presets

Airfoil	CL	CD
FlatPlate	0.40	0.080
Eppler387	0.80	0.021
NACA2412	0.90	0.018

• Initial altitude: h0 = 100m

• Initial speed: Vbg = sqrt(2 * m * g/(rho * A * CL))

Sample Results

Airfoil	CL	CD	Range (m)	Time (s)
FlatPlate	0.40	0.080	456.0	10.8
Eppler387	0.80	0.021	610.8	18.1
NACA2412	0.90	0.018	625.3	19.5

We see that from a 100m release height, higher lift-to-drag ratios (ex. NACA2412) increase range by around 35% vs. a flat plate. Note that measured glide ratio range/h0 is lower than ideal CL/CD; this is since speed decays during the descent.

License: MIT