Aileron Sizing
- Smile Khatri
Big Project | Project | Project Manager |
|---|---|---|
Post-comp fixed wing | Aileron | @Smile Khatri |
Task Description
Choose dimensions for aileron, and pick out servo motors.
Linkage stuff:
Constraints
Constraints | Written By | Append Date |
|---|---|---|
1 servo per aileron | @Smile Khatri | August 13, 2024 |
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Relevant Contacts
Subteam | Contact | Contact Description |
|---|---|---|
Subteam collaborating with | @ of contact | what is the contact responsible for? |
Assignees
Assignee | Asana Task | Date |
|---|---|---|
@ assignee | link to asana task assigned | Date assigned |
Task Progression/Updates
Author: @Smile Khatri Date: 2024/08/13
Sizing the Aileron
Before performing any calculations, some research was conducted into aileron sizing guidelines for RC planes. In “Basics of RC Model Aircraft Design”, the author Andy Lennon recommends the dimensions below:
In another research article focused on SAE micro-class RC planes, the following is suggested:
The same article informs that if the deflection of the aileron does not exceed 25 degrees (+/-), stall should not occur. However, this would have to be tested in sims. For now, aileron deflection of 20 and 25 degrees are used.
Mathematical equations and derivations for roll control are summarized in Sizing Control Surfaces - Mechanical - WARG (atlassian.net). A MATLAB script is created to simplify the calculations. In the script, only the aileron span and aileron chord ratios were changed, rest of the variables are held as constant. These constants are:
Air density = 1.225 kg/m^3
wing span (b) = 1.5 m
wing chord (C) = 0.23 m
Aircraft speed (depends on the flight level) = 25 m/s
Taper ratio = 1
Moment of inertia about the roll axis (Ixx) = 0.06 kg*m^2 (taken from initial frame design, could change in the future…)
Vertical stabilizer area (Sv) = 0.0423 m
Horizontal stabilizer area (Sh) = 0.0666 m
Lift coefficient slope (linear region) for NACA 4412 = 6.03 per rad
average roll drag from wings, fuselage, and tail = 0.9 (educated guess, no sims run yet)
The rest of the constants are minor and are present in the script. The roll requirement is chosen to be 90 degree bank angle in 1.7 seconds. The time required for the aircraft to bank at 90 degrees must be within 10% range of 1.7 seconds. This meets the class IV aircraft (highly maneuverable) requirement (refer to Sizing Control Surfaces for more details).
Several combinations of aileron span and chord ratios are tested in the script. The results are summarized in the table below.
Thus, a span ratio of 0.4 and a chord ratio of 0.25 meets the design requirement if the aircraft is cruising at 25 m/s and aileron has a max deflection of 25. The actual roll time may vary due to imperfections in manufacturing, or the cruising speed being different than what is calculated. But this aileron dimensions align with recommendations from RC Model Aircraft Design book and other sources, hence, they should be safe to implement.
Aileron design flow:
Force and Stall Analysis [WIP]
For analyzing stall, simulation is performed at maximum aileron deflection and at expected cruising speed. Initially, a steady state simulation was run but the plots of residuals, lift & drag struggled to converge and had a lot of oscillations. Hence, a transient simulation is conducted..
Mesh details:
Face sizing: 0.002 m applied only on the wing geometry
Surface mesh: enable curvature only, don’t need proximity feature
Boundary layers: last_ratio method with 5 layers. First layer height is 0.0001
Volume mesh: poly-hexcore method, everything else default. Poly-hexcore to reduce total cell count.
The minimum ortho quality of the mesh generated is 0.05 which isn’t the best, will mostly affect cd accuracy. But the average quality is pretty high so it’s acceptable.
Aileron deflection | Pressure plot | Velocity pathline | Normal force (surface integrated) | Drag coefficient | Lift Coefficient |
|---|---|---|---|---|---|
25 degrees DOWN | Top_face = -5.86 N Bot_face = 3.29 N Total: 9.15 N | 0.01519 | 0.4368 | ||
25 degrees UP |
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| Top = 2.175 N Bot = -5.04 Total: 7.22 N | 0.008457 | -0.01134 |
Using the force results obtained, torque about the hinge line is calculated. It is assumed that the force acts at the mid-point of the chord-line.
For down deflection, the torque is 0.0268 kg*cm. For up deflection, the torque is 0.0212 kg*cm. These values are pretty low compared to what online calculators give. So, an online calculator is used to double check…
Link: RC Airplane Calculator (radiocontrolinfo.com)
Some servo candidates:
Servo Model | Torque (kg*cm) | Weight (g) | Recommended RC Plane application | Cost $$$ |
|---|---|---|---|---|
HS-311 | 3.0 ~ 3.5 | 43.0 | 1.8 kg |
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HS 645 MG | 7.7 ~ 9.6 | 55.2 | 6.8 kg |
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DS 843MG | 4 - 4.8 | 11 g |
| $16.39 |
Roll rate and time calculation script:
%SI (m, kg, m/s, N)
%General
MASS_TOTAL = 5.137;
rho = 1.225;
V = 25;
Ixx = 0.06; %moment of inertia about the roll axis (kg*m^2)
Sv = 0.0423;
Sh = 0.0666;
%Wing geometry
b = 1.5;
fuselage_width = 0.132;
C = 0.23;
Sw = 0.345;
taper = 1;
MAC = 0.23;
NACA = 4412;
Cr = C;
%Control surface effectiveness param data points
CA_C_ratio = [0.004918032786885199,0.03442622950819667,0.06967213114754095, 0.09918032786885245, 0.12213114754098359, 0.19344262295081968, 0.28196721311475414, 0.4024590163934427, 0.5016393442622952, 0.5434426229508198, 0.6778688524590166
];
TAU = [-0.002272727272726982, 0.10000000000000009, 0.20000000000000007, 0.26363636363636367, 0.3045454545454547, 0.4, 0.5, 0.6068181818181819, 0.6886363636363637, 0.7181818181818183, 0.8136363636363637
];
%Aileron inputs
span_ratio = 0.4;
chord_ratio = 0.25;
bi = 1.5*0.5-span_ratio*1.5*0.5;
bo = 1.5*0.5;
Ca = chord_ratio*C;
tau = interpolate_tau(CA_C_ratio, TAU, chord_ratio); %Aileron efficiency paramter
delta_max = [25, 25]; % [UP, DOWN]
CLw_slope = 6.03;%cl per rad
C_DR = 0.9; %avg drag from wing, horizontal tail, vertical tail
yD = (b-fuselage_width)*0.25;
phi_req = 90;
t_req = 1.7;
%EQUATIONS
eq_Cl_deltaA = @(yi, yo) ((0.5*yo^2 + (2/3)*yo^3*(taper-1)/b)-(0.5*yi^2 + ...
(2/3)*yi^3*(taper-1)/b))*(2*CLw_slope*tau*Cr)/(Sw*b); %Cl derivative
eq_Cl = @(x) x*delta_max(1,1)*pi/180; %Cl - rolling moment coefficient
eq_LA = @(Cl) 0.5*rho*V^2*Sw*Cl*b; %Lift contribution from aileron
eq_Pss = @(LA) sqrt((2*LA)/(rho*(Sw+Sv+Sh)*C_DR*yD^3));
eq_phi1 = @(Pss) (Ixx)*(log(Pss^2))/(rho*yD^3 * (Sw+Sv+Sh)*C_DR);
eq_roll_rate_derivative = @(phi1, Pss) 0.5*Pss^2/phi1;
%Assume that phi1 is going to be larger than phi_req for GA
eq_t2 = @(phi, P_dot) sqrt(2*phi/P_dot);
%Testing the equation
Cl_deltaA = eq_Cl_deltaA(bi, bo);
Cl = eq_Cl(Cl_deltaA);
LA = eq_LA(Cl);
Pss = eq_Pss(LA);
phi1 = eq_phi1(Pss);
P_dot = eq_roll_rate_derivative(phi1, Pss);
tss = sqrt(2*phi1/P_dot);
if (phi1 > phi_req)
t2 = eq_t2(phi_req*pi/180, P_dot);
else
delta_t = (phi_req - phi1)/Pss;
t2 = tss + delta_t;
end
err = (t2-t_req)/t_req *100;
%Plotting some points
time_v_phi(0.01, 5, tss,P_dot,Pss,phi1);
function graph_t_v_phi = time_v_phi(time_step,max_time,tss,P_dot,Pss,phi1)
%Time vs phi
t_nonlinear = 0:time_step:tss;
phi = 0.5.*t_nonlinear.^2 .* P_dot;
plot(t_nonlinear, phi);
title("Time vs. Bank Position");
xlabel('Time (s)');
ylabel('Bank angle (deg)');
hold on
%Linear region
t_linear = tss:time_step:max_time;
b = phi1 - Pss*tss;
phi_lin = b + Pss.*t_linear;
plot(t_linear, phi_lin);
hold off
end
function tau = interpolate_tau(x_points, y_points, x)
data_x = x_points(:);
data_y = y_points(:);
if x < min(data_x) || x > max(data_x)
error('Outside the range!');
end
%Find indices of 2 points, 1st point less than x, 2nd point greater
indx1 = find(data_x <= x, 1, 'last');
indx2 = find(data_x >= x, 1, 'first');
%If x matches a data point, return corresponding y
if data_x(indx1) == x_points
tau = data_y(indx1);
end
%Linear interpolation
x1 = data_x(indx1);
x2 = data_x(indx2);
y1 = data_y(indx1);
y2 = data_y(indx2);
tau = y1 + (y2 - y1) * (x - x1) / (x2 - x1);
end