Empennage Design

Task Description

This task will involve R&D and design of the empennage. I.e. choosing airfoil shapes, and dimensioning control surfaces (elevator and rudder) to ensure successful control.

Constraints

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Task Progression/Updates

Author: @Thushanth Parameswaran updating Date: 2024/07/03

Background Information

The empennage is the plane's Tail section composed of Horizontal and Vertical stabilizers, It also has a control surface to control the Yaw(Rudder) and Pitch(Elevator). There are various types of Epenage but to keep things simple, we have decided to go with the traditional empennage below. In the future, we will explore more empennage designs.

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Horizontal Stabilizer

We can imagine it as an upside-down wing. It aims to create a downforce similar to a wing on an F1 car. You might wonder why we need downforce. It is simple. As you see in the first image there 2 forces, lift force created by the wing which acts at the Center of lift and the weight of the aircraft which acts at center mass. Let's do some calculations. We first begin by giving an arbitrary value for the distance between CL and CG to be 1 m. We will also say that lift force is +1000N and weight is -1000N therefore net force is zero. Moment = F x Distance. Let’s calculate the moment at CL which is 1000N x 1m = 1000Nm Counter-clockwise. The Net Moment is not zero resulting in aircraft pitching down.

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Author: @Thushanth Parameswaran updating Date: 2024/07/17

Background continued…

Vertical Stabilizer

The vertical stabilizer is basically a wing but vertical ( normally symmetrical airfoil unlike a wing of a plane). Vertical stabilizer has a rudder which is responsible for creating Yaw which is movement around vertical axis as seen in the image below.

Lets see how Yaw is created. Before continue to read please refer to the airfoil section to understand how and why airfoil produce lift. The image below gives you a brief run-through of how yaw in created.

That is the background info on what empennage is and how it works.

Author: @Thushanth Parameswaran updating Date: 2024/07/21

Source: https://www.fzt.haw-hamburg.de/pers/Scholz/HOOU/AircraftDesign_9_EmpennageGeneralDesign.pdf

General Design Rules

1. The lever arm of the empennage should be as large as possible. (Lever arm is the distance between the aerodynamic center of the wing and the horizontal stabilizer). This will reduce the size of the empennage, saving weight.

2. The aspect ratio of the horizontal stabilizer should be about half the aspect ratio of the
   wing.

3. Horizontal Stabilizer is fixed, an incidence angle of around 2° to 3° downwards
   should be chosen to create a negative lift. (assuming we are using asymmetrical airfoil)

4. Symmetrical airfoils are exclusively selected for vertical Stabilizer. (NACA 0009 might be a good start)

5. Horizontal stabilizers can be either symmetrical or slightly cambered to produce negative lift.

Design by Calculation

https://www.fzt.haw-hamburg.de/pers/Scholz/Aero/AERO_PUB_INCAS_TailVolume_Vol13No3_2021.pdf

Using the tail volume coefficient, we can estimate the horizontal and vertical stabilizer sizes.

Tail Volume Coefficient

A Reddit gave what tail coefficient to use. It said .672 for CH and 0.0657 for CH. Based on this value

Airfoil is NACA 0009 for both Horizontal and Vertical.

Alexandria Moulding Hardwood Dowel 1/8 In. x 48 In. White | The Home Depot Canada

Author: @Smile Khatri Date: November 11, 2024

Servo selection

To size the servos for the elevator and the rudder an online calculator is used: RC Airplane Calculator

The chord length, and span of the control surfaces (identified as ‘length’ in the calculator) are input into the calculator, along with servo deflection and surface deflection. An assumption is made that a 30 degree deflection of the servo maps to a 30 degree deflection of the control surface, hence the input and output response is linear. For elevator and rudder, this is the best practice (RC Basics: The importance of good linkage geometry).

100 km/h is the maximum speed we expect this plane to fly at, so the servo selection is being made at the most extreme case. The cruising speed would actually be about 50 - 60 km/h.

From the results, the following servo is selected

2.5kg Goteck Metal Gear Micro Servo - RobotShop

Key specifications:

• Stall torque: 2.3 kg-cm(4.8v), 2.5 kg-cm(6.0v)

• Operating voltage: 4.8 - 6 V

• Weight: 14.7 g

• Size: 23 x 12.1 x 28.8 mm

Required torque for the rudder at maximum speed is 1.81 kg-cm, the stall torque at 6V is 2.5 kg-cm for the servo, giving us a safety margin of 0.69 kg-cm (1.38 safety factor)

For the elevator, 2 servos would be needed. The required torque is 3.34 kg-cm and the total stall torque from 2 servos is 5 kg-cm. This gives a safety margin of 1.66 kg-cm (1.5 safety factor).