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Initial Design Guidelines
Aileron
35 - 40% of semi-wing span
Width typically 15-25% of the wing chord
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Elevator & Rudder
Generally begin at the side of the fuselage and extend to the tip or 90% of the tail span
Width is typically 25 - 50% of the tail chord
Control surfaces are usually tapered by same ratio as the wing or tail surface
For the elevator
hinge line perpendicular to fuselage centerline for manually-controlled aircraft
allows connecting left and right elevators
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portion of the control surface in-frontof the hinge line as shown below
lessens the force required to deflect the surface & reduces flutter tendencies
Notched balance not recommended for high-speed flight
Hinge axis SHOULD NOT be farther than ~20% of the avg chord of the control surface
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Aileron Design
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Recommended dimensions from Basics of RC Model book
35 - 40% of semi-wing span
Width typically 15-25% of the wing chord
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Mathematical analysis
Derived equations for evaluating aileron parameters exist and are summarized below. In summary, there are standards for roll rates in the aerospace industry. I.e. 30 degrees in 1.3s. This model predicts how long it takes for an aircraft to roll to the specified angle, and compares it with the requirement to determine whether the aileron dimensions are sufficient.
Source: Chapter 12. Desig of Control Surfaces (Aileron).pdf (us.es)
Key design parameters for an aileron are as follows:
Aileron planform area (S_aA)
Aileron chord/span ratio (C_aA/Cb_bA)
Maximum up and down deflection (delta_A)
Location of inner edge of aileron along the wing span (b_ai), location of the outer edge (b_ao)
Typical values:
Sa/S = 0.05 - 0.1, ba/b = 0.2-0.3, C_a/C = 0.15 - 0.25, b_ai/b = 0.6-0.8, delta_Amax = +/- 30 deg (some sources say 25 max is good enough to prevent stall)
Important aspects of aileron design:
Aerodynamic moments about the aileron hinge that must be overcome, same as hinge moments. When an aileron is deflected, air exerts pressure on the aileron surface, resulting in a moment about the hinge.
Aileron effectiveness depends on how well the aileron deflection can produce the desired rolling moment
Easier to use the rear wing spar as the hinge
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Layout design requirements:
Roll control requirements, critical flight phase for roll control, research standards i.e. time required for aircraft to roll from initial bank angle to a specific angle
Select inboard and outboard positions of the aileron. Determine b_ai/b, b_ao/b, and C_a/C.
Determine aileron effectiveness parameter tau_a.
Determine I_xx (moment of inertia about the roll axis, estimate since not everything is finalized)
Performing calculations:
Calculate aileron rolling moment coefficient derivative (C_l-delta-A). Use the following equation:
C_r = root chord. yo = outboard distance from fuselage, yi = inboard distance from fuselage, S = wing planform area, b = wing span
C_L_alpha_w = wing sectional lift curve slope - assumed to be in the constant region, therefore, the aileron sectional lift curve slope is also the same…
Calculate tau using the graph above. Tau(Ca/C)
Select maximum aileron deflection (delta_Amax). Typ +/- 25 degrees.
Calculate rolling moment coefficient (C_l) when aileron is deflected with max. deflection using
Calculate aircraft rolling moment (L_A) for maximum aileron deflection using
Determine steady-state roll rate (P_ss) using
Calculate the bank angle at which aircraft achieves steady state roll rate.
Calculate the rate of change of roll rate (before steady state is reached)
If phi_1 > phi_req (aka the total desired bank angle) determine time to reach phi_req using the formula
If phi_1 < phi_req (most likely not the case for general aviation and transport), use
the eqns below to solve t2
Compare t_2 with t_req. Minimum difference must not exceed 10%. If this isn’t the case, choose different aileron params and repeat the calculations.
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Workflow diagram
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Rudder sizing
The rudder controls the Yaw motion and is located on the vertical stabilizer. To determine the size of the Rudder we requires all the parameters below.
Rudder Area (SR) Vertical Tail Area(SV) SR/SV Rudder Chord(CR) Vertical Tail Chord (CV) CR/CV Rudder span (bR) Tail Span(bV) bR/bV
We have already determined that the area of the vertical tail is 0.0425 m^2 ( for more information please refer to the empennage design page). From this source:http://aero.us.es/adesign/Slides/Extra/Stability/Design_Control_Surface/Chapter 12. Desig of Control Surfaces (Rudder).pdf we can say that the SR/SV is equal to 0.38.
Using simple math we determine that SR=SV*0.38 = 0.01615m^2
Using the same method, we can compute the mean rudder chord length: CR=CV*0.42= 0.16832*0.42= 0.0707m
Now we need one more dimension, which is the rudder span. bR= SR/CR= 0.01615/0.0707= 0.22844m.
As you noticed the value used is for Light GA type which is the closest to the RC Type. Even though this might not the most optimal rudder, it gives us very good starting to see how flight characteristics behave which changes in these parameters, for more information, please refer to the source and the Fixed wing calculation Excel file.
We also have to determine the maximum deflection of the rudder was straightforward thanks to this source: https://www.fzt.haw-hamburg.de/pers/Scholz/HOOU/AircraftDesign_9_EmpennageGeneralDesign.pdf. So our maximum deflection will be 35 degrees because designing for the extreme case will ensure that all the elements will be intact during high manueavouring speed. In the case of control over sensitivity, we can reduce the max deflection angle of the rudder by manually limiting the angle rotation of the servo.
Elevator
The elevator controls the pitch motion of the aircraft and is located on the horizontal tail. Similar to the Rudder, the elevator requires the following parameter to determine the elevator size:-
Elevator Area (SE)
Horizontal Tail Area(SH)
SE/SH
Elevator Chord(CE)
Horizontal Tail Chord (CH)
Horizontal Tail Span (bH)
Elevator span (bE)
Based on the tail volume coefficient method, we determined the area of the horizontal tail is 0.0667 m^2. From this source:- http://aero.us.es/adesign/Slides/Extra/Stability/Design_Control_Surface/Chapter 12. Desig of Control Surfaces (Elevator).pdf we can say that the SE/SH equals 0.38.
Using simple calculation we can determine the SE; SE=SH*0.38=0.0667*0.38=0.0253 m^2
The span of the elevator(bE) will equal to span of the horizontal tail(bH). Using this information we can compute the chord length of the elevator. Area of the elevator (SE) = Elevator span (bE)* Elevator Chord(CE). We have one unknown and one equation which is enough to determine the chord length of the elevator. CE= SE/bE= SE/bH= 0.0253/ 0.4662= 0.0543m
This source also mentioned that having deflection above or below 25 degrees will reduce the effectiveness of the elevator and may result in a stall of the horizontal tail, even a small downward elevator deflection can produce flow separation and loss of pitch control effectiveness. If we require more pitch control authority, then we can increase the elevator area and recompute the chord length of the elevator.