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Open Loop Dynamics of Zagi Flying Wing

Introduction

  • Zagi is a radio-controlled (RC) flying wing glider introduced in 1996 by Jerry Teisan in California.
  • Known in the RC community for:
    • Simplicity
    • Low cost
    • High durability --- often referred to as "nearly indestructible"
  • Construction: Lightweight expanded polypropylene (EPP) foam covered with vinyl
  • Flight Styles Supported:
    • Slope soaring (hill updraft)
    • Thermal soaring (rising warm air)
    • Electric-powered aerobatics
    • Combat flying
  • No tail surfaces: Stability and control achieved through wing geometry and elevons

Key Flying-Wing Advantages

  • High aerodynamic efficiency
  • Low drag due to no tail
  • Pitch stability from reflex airfoil
  • Compact and agile structure

Variants include Zagi 400X, Zagi Fixx, Zagi THL - all maintaining robust and efficient flying-wing principles.

Zagi Flying Wing

Airframe Breakdown

1. Wing Platform

  • Type: Swept flying wing (no fuselage or tail)
  • Span: Approximately 1.2 m (varies by model)
  • Planform: Tapered wing with moderate sweep
  • Material: EPP foam, laminated
  • Reinforcement: Carbon or fiberglass spar
  • Purpose:
    • Enhances natural yaw and pitch stability
    • Provides efficient lift distribution

2. Airfoil

  • Reflex or semi-reflex airfoil
  • Upward curvature near trailing edge creates positive pitching moment
  • Compensates for lack of tail
  • Examples: Zagi-specific foils, MH-series, Eppler reflex profiles
  • Allows trimmed hands-off stable flight

3. Control Surfaces (Elevons)

  • Two elevons on the trailing edge
  • Combined function of elevator and aileron
  • Symmetric movement provides pitch control
  • Differential movement provides roll control
  • No rudder - yaw stability through wing sweep and differential drag

4. Propulsion (Electric Versions)

  • Pusher motor mounted behind center section
  • Propeller behind trailing edge for improved aerodynamics
  • Battery placed in central fuselage pod

5. Stability and Aerodynamics

Features Purpose
Reflex airfoil Pitch stability (Positive Cm)
Wing Sweep Directional stability & yaw damping
Wing twist or wash out Improve yaw stability and reduce induced drag

Because it's tailless, the zagi requires careful CG placement. Too far back --> unstable pitch oscillations; too forward --> sluggish response

Simualtion of Zagi Flying Wing

The physical parameters, aerodynamic coefficients and propulsive (Thrust and Motor) coefficients are extracted from "Small Unmanned Aircraft: Theory and Practice" - Randal W Beard and Timothy W McLain

Parameter Value Category
mass (m) 1.56 kg Inertial
Ixx 0.1147 kg- $m^2$ Inertial
Iyy 0.0576 kg- $m^2$ Inertial
Izz 0.1712 kg- $m^2$ Inertial
Ixz 0.0015 kg- $m^2$ Inertial
Wing Area (S) 0.2589 $m^2$ Geometric
Wing span (b) 1.4224 m Geometric
Mean aerodynamic chord (c) 0.3302 m Geometric
$S_{prop}$ 0.0314 Geometric
$Density (\rho)$ 1.2682 kg-m³ Environmental
$k_{motor}$ 20 Propulsion
$k_{T_p}$ 0 Propulsion
$k_Ω$ 0 Propulsion
Oswald efficiency factor (e) 0.9 Aerodynamic
$C_{L_0}$ 0.09167 Longitudinal
$C_{D_0}$ 0.01631 Longitudinal
$C_{m_0}$ -0.02338 Longitudinal
$C_{L_\alpha}$ 3.5016 Longitudinal
$C_{D_\alpha}$ 0.2108 Longitudinal
$C_{m_\alpha}$ -0.5675 Longitudinal
$C_{L_q}$ 2.8932 Longitudinal
$C_{D_q}$ 0 Longitudinal
$C_{m_q}$ -1.3990 Longitudinal
$C_{L_{\delta_e}}$ 0.2724 Longitudinal
$C_{D_{\delta_e}}$ 0.3045 Longitudinal
$C_{m_{\delta_e}}$ -0.3245 Longitudinal
$C_{prop}$ 1.0 Longitudinal
M 50 Longitudinal
$α_0$ 0.4712 Longitudinal
$\epsilon$ 0.1592 Longitudinal
$C_{D_p}$ 0.0254 Longitudinal
$C_{Y_0}$ 0 Lateral
$C_{l_0}$ 0 Lateral
$C_{n_0}$ 0 Lateral
$C_{Y_\beta}$ -0.07359 Lateral
$C_{l_\beta}$ -0.02854 Lateral
$C_{n_\beta}$ -0.00040 Lateral
$C_{Y_p}$ 0 Lateral
$C_{l_p}$ -0.3209 Lateral
$C_{n_p}$ -0.01297 Lateral
$C_{Y_r}$ 0 Lateral
$C_{l_r}$ 0.03066 Lateral
$C_{n_r}$ -0.00434 Lateral
$C_{Y_{\delta_a}}$ 0 Lateral
$C_{l_{\delta_a}}$ -0.1682 Lateral
$C_{n_{\delta_a}}$ -0.00328 Lateral

Aerodynamic Coefficients

  • Lift Coefficient

    $C_L = [(1-\sigma(x))[C_{L_0}+C_{L_\alpha}\alpha] + \sigma(x)[2\alpha\sin^2 (\alpha )cos(\alpha)]] + C_{L_q}\frac{c}{2V_a}q + C_{L_{\delta_e}}\delta_e$

    $\sigma(x) = \frac{1 + e^{-M(\alpha - \alpha_0)} + e^{M(\alpha+\alpha_0)}}{(1 + e^{-M(\alpha - \alpha_0)}) (1 + e^{M(\alpha+\alpha_0)})}$

  • Drag Coefficient

    $C_D = C_{D_0} + C_{D_p} + C_{D_\alpha}\alpha + \frac{{C_L}^2}{\pi eAR} + C_{D_q}\frac{c}{2V_a}q + C_{D_{\delta_e}}\delta_e$

  • Pitching Moment Coefficient

    $C_m = C_{m_0} + C_{m_\alpha}\alpha + C_{m_{\delta_e}}\delta_e + C_{m_q}\frac{c}{2V_a}q$

  • Side Force Coefficient

    $C_Y = C_{Y_0} + C_{Y_\beta}\beta + C_{Y_p}\frac{b}{2V_a}p + C_{Y_r}\frac{b}{2V_a}r + C_{Y_{\delta_a}}\delta_a $

  • Rolling Moment Coefficient

    $C_l = C_{l_0} + C_{l_\beta}\beta + C_{l_p}\frac{b}{2V_a}p + C_{l_r}\frac{b}{2V_a}r + C_{l_{\delta_a}}\delta_a $

  • Yawing Moment Coefficient

    $C_n = C_{n_0} + C_{n_\beta}\beta + C_{n_p}\frac{b}{2V_a}p + C_{n_r}\frac{b}{2V_a}r + C_{n_{\delta_a}}\delta_a $

Propulsion Forces and Moments

  • Propeller Thrust

    $F_{x_p} = \frac{1}{2}S_{prop}C_{prop}((k_{motor}\delta_t)^2-V_a^2)$

$$ \mathbf{f}_p = \frac{1}{2}\rho S_{\text{prop}} C_{\text{prop}} \begin{bmatrix} (k_{\text{motor}}\delta_t)^2 - V_a^2 \\ 0 \\ 0 \end{bmatrix} $$

  • Propeller Torque

    $T_p = -k_{T_p}(k_\Omega \delta_t)^2$

$$ \mathbf{m}_p = \begin{bmatrix} (-k_{T_p}(k_\Omega \delta_t)^2 \\ 0 \\ 0 \end{bmatrix} $$

About

This repository focuses on simulating the open loop dynamics of Zagi Flying Wing in MATLAB and Simulink.

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