Indoor glider

Introduction

A glider is a type of airplane with a large gliding distance feature. Gliders usually do not have engines or any means that can provide propulsion. It glides naturally in the air and loses height slowly. There are mainly 3 forces acting on a glider: weight, lift, and drag. Lift counters the weight. A glider is very light and can be made of carbon fiber, plastic, or nylon, so the lift produced by the wing is not necessarily large to support the plane. The thrust only occurs at the launching process. This force can be produced by another plane that drags the glider by a rope, by hand for a paper plane, or by spring-winch system. Gliders can include both indoor and outdoor gliders. They are same in the essence, but the outdoor glider has a special advantage.

Outdoor glider special feature:

It can retrieve its height and sustain to fly. When an outdoor glider loses height, it can glide to the region where air is heated by sun. This hot air ascends and lifts the glider again to its original height. Hot air can stay near the ground (ground is heated and conducts heat to air because it has low specific heat capacity), be trapped in the valley, or sometimes at the top of the mountain if it rises.

Indoor glider special feature:

For a paper plane (indoor glider), it also has a special feature: produce lift by flat wings. The lift is not produced by Bernoulli effect but simply by Newton’s third law (reaction force). Referring to the figure below, a paper plane should launch at an angle alpha above the horizontal line. When the air hits the wing, this angle makes the force to decompose into F1 and F2 components. F1 generates the lift while F2 is a drag force along the plane. The direction of F1 makes the plane tilt up, rise to a height, then drop. When it drops, the air hits the plane and this process repeats. Therefore, if the initial launching angle is large, the flight path looks like this in the figure below.

If the launching angle is small, F1 will not produce significant “tilting up” effect and the paper plane will just glide smoothly.

In this mini project, we focus on the indoor glider but use different materials and add more details to make it so that we can guarantee its stability and gliding distance.

Variables

Three main variables are defined: lift, drag, and weight

The lift corresponds to the aerodynamic force that is produced by the wings perpendicular to the oncoming airflow. The drag is the force exerted on the wings parallel with the oncoming airflow and tends to slow the glider down. Thus, it is ideal to have the greatest lift and the least amount of drag possible.

Lift: Air flows across the top surface at a higher velocity than the bottom surface. Consequently, the top surface will have a lower pressure than the bottom surface. Thus, the wing of a glider can generate lift due to this difference in pressure between the top and bottom surfaces of the glider. The wings of the glider would have to produce enough lift in order to balance the weight.

Drag: There are two types of drags that occur during flight: Induced drag and the profile drag. The induced drag refers to the direct result of a wing generating lift, while the profile drag refers to the side effect of moving the glider through air. As the glider moves forward, circular motion of air around the wing tips is generated and hence creates a drag force on the glider wings (induced drag). The form drag, categorized under profile drag, refers to the force that results from the difference in pressure between the front and back surfaces of the glider. To reduce form drag, we can reduce the glider’s cross-sectional area.

Weight: The weight of the glider depends on the usage of the glider. A lighter weight is advantageous for travelling further and staying aloft longer. On the other hand, a heavier weight allows the glider to travel at greater speed.

Bernoulli effect

A regular glider’s wing has curved shape (image below) (NASA, 2010), and it is called airfoil. After being thrown by hand, the airfoil (leading edge) hits the air, and it separates the air into its upper and lower surface. The air moving along the lower surface in a straight line, so its velocity and pressure remain same. The air flows along the upper side stretching out and rushing towards the trailing edge with higher velocity. According to Bernoulli’s equation:

P: pressure

𝜌: air density

V: velocity

h: height of the air molecule (in this case height from ground)

g: gravitational constant

The variable h is approximately same for the air in upper and lower sides (thickness of the airfoil is much lower than the flying height). The velocity of air is higher on the upper surface, so it has lower pressure. For the lower side, vise versa. Therefore, this pressure difference generates an upper force acting on the wing, which is lift.

Stability

A glider has 3 axes: roll axis, pitch axis, and yaw axis.

Roll axis: during gliding, we need to ensure our glider do not roll.

Solution: 1) make the wingspan large 2) lower the center of gravity 3) make the winglet tilt up so it can balance itself by the auto correction feature.

Pitch axis: it determines whether the plane tilt up or down. In our design, we want the pitch angle to be a little bit negative as it loses the height very quickly (glide ratio: 21/8).

Solution: make the lift center a little bit backward than the gravity center so that the glider has a small tilt down effect (has a counterclockwise moment in the pitch axis).

Yaw axis: it ensures the stability in z direction. Since our glider needs to hit a specific target, we want it to fly in a straight line so the yaw effect should be zero.

Solution: make the rudder straight. Make the vertical stabilizer large.

Design intents

Objectives

Stable glide (in x, y, z axis)
Controlled gliding distance (by adding or reducing weight, paperboard in this case)
Mainly use recycled materials
Hit the target on the ground (a 1-meter diameter circle)

Assumptions

Air is incompressible, almost inviscid, and density remains constant
The flow is mostly laminar
Initial launching speed does not vary too much (since it Is thrown by hand)
The initial launching speed is lower than 10 m/s (about 5m/s)

The resistance on the wing surface is low that will not produce significant drag

When the glider rolls (to the left), the winglet becomes horizontal and produces extra lift. This lift generates a clockwise moment to turn the glider to the right position. Whenever the glider rolls, the side in the lower position has a lift to rise and return to the original state.

Calculations

A typical glider has a drag coefficient between 0.1-0.5. Compared with our calculated value, it is reasonable. For the glide speed, we tested our glider several times and used slow motion camera to record its movement and estimated its speed. It may involve error but not significant.

To verify whether our glider has a good angle of attack, AOA graph is plotted to compare it with the theoretical AOA graph

Plotted lift coefficient vs. AOA

Lift coefficient vs. AOA (theoretical)

Find the optimum glide speed and AoA

The angle of attack, α, was calculated by using:

From plotted AOA graph, we vary the glide velocity to find the corresponding lift coefficient and angle of attack. The speed we changed is from 3-10. We ignore 1 or 2 values because the plane cannot glide at this speed.

Angle of attack when speed is 4.84 m/s:

This is within the range of the normal attack angle which is from 2 to 15 degrees.

One thing to notice is that we did not plot the critical point for stall angle. This is because stall angle is mostly found by testing an airfoil sever times, and because turbulent flow occurs at that point, it is hard to find a specific value mathematically. Therefore, our plot is still consistent with the real one as the lift coefficient generally has a linear relationship with the angle of attack before the stall angle point.

Glider flightpath at different masses

Predicted range and time for different masses

From the graph and table, we can observe that as the glider becomes heavier, it travels shorter horizontal distance. The vertical distance remains constant because the initial launching height is fixed.

The predicted range and time
From the table, we estimate several range and time when the mass is different. The way we estimate them is firstly to assume the glider is travelling in a straight line not a parabola or very curved path. Then we plug in the number in Vx and Vy equations and plot the graph. The predicted range is from 17.9 to 21 m (x intersections on the graph), and time vaies from 4.0 to 4.9 s.

Notes: Vx is travelling speed which is not gliding speed. Gliding speed is the speed when the glider remains in air, which is almost constant, not affected by the mass of the glider. Travelling speed, Vx, is affected by mass but not always linearly. Theoretically, travelling speed equals gliding speed.

However, in our case, since our glide ratio, 2.6:1, is much smaller than the regular one (10:1), we move the lift center a bit backward of the mass center to make it sink faster, because there is a forward moment, M (Figure 7). When the mass is added gradually, this moment becomes larger (M2 > M1) as more weight dragging down the glider nose. Therefore, more weight means shorter gliding distance (Figure 8) and smaller Vx. Also, there is a critical point where lift can no longer support the weight (M4) that the glider begins to swirl, rotate, and drop. Vx is nearly 0 in this case as the travelling distance is 0.

Drag calculation

We plotted the drag graph by varying the velocity. The reason for this is because speed is the easiest variable that we can change with a wide range. We change it from 4 to 10 m/s and plot the following graph:

Induced Drag:

AR: aspect ratio

K: drag due to lift parameter

We mainly change lift coefficient by varying speed and get the plot above.

From the graph, we can see that the induced drag is not very large. This is because our plane has a small projection area that will make the drag small.