5 Types of Drag
Flow separation - As fluids wraps a tight corner, it will separate from the body leaving a turbulent wake that results in high drag. Mitigated by an aerodynamic body
Skin Friction - Friction between the body and the fluid causes drag. Dominant in streamlines bodies. Mitigated by reducing surface area and surface roughness
Boundary Layer Pressure Loss - Also known as pressure drag. As fluid flows over a body, the fluid right on the surface sticks to the surface (called no-slip condition) and viscous effects in the fluid cause the fluid further from the body to be slowed. The boundary between the affected fluid and the free-stream fluid defines the “boundary layer”. The boundary layer grows as it proceeds down the body. This causes a pressure drop along the body which means that there is a pressure that needs to be overcome.
Induced Drag - All streamlined bodies can generate lift if at a given angle in the airstream. But lift always induces drag on the body (whether up or down). Minimum drag occurs when there is zero lift, so the aerobody should be oriented to minimize lift and therefore drag
Interference drag is caused by imperfections on the body such as joints and seams, or the mating of the canopy or fairings to the body. Reduced by disciplined manufacturing and quality control
Drag Equation
Cd is coefficient of drag and is an encompassing coefficient for all types of drag.
A is the characteristic area and is dependent on the dominant mode of drag. For streamlined bodies, skin friction is the dominant mode and so the area used should be the surface area of the body moving past the fluid. For a bluff body like a regular car, pressure drag is the dominant mode and so a projection of the front facing area is the most useful.
Geometry
Aerodynamic shapes are ones that minimize flow separation. In three dimensions the ideal shape is a cylindrically symmetrical teardrop, however factors require compromise on this design.
A solar car compromises to get power from a solar array, so the teardrop needs to be flattered or have a flat portion added. Bullet designs tend to add a streamlined large surface for the solar array to a general teardrop shape, where catamaran’s are example of where a teardrop is flattened to accommodate the solar array.
Near the ground there is a “ground effect” caused by an airfoil. When there is an aerodynamic shape moving near near the ground, there is a low pressure area created. This is because the flow under the must pass through a minimum ground clearance, as the area the flow can pass through opens up toward the rear, air cannot replace it, which causes low pressure and induced drag. This is fixed with camber, and I believe it can also be applied to the space between two fairings on a catamaran. Camber is a bending of the centerline for an airfoil.
Side Profile of an Airfoil
Camber: A measure of the curvature of the airfoil
The camber of the upper surface is more pronounced than the camber of the lower surface (usually somewhat flat).
Leading Edge: Forward-facing end that is rounded
Trailing-Edge: Rear-facing end that is narrow and tapered towards the rear
Chord Line: Reference line drawn from the centre of the leading edge straight through the wing till the trailing edge.
This reference line is used to find the magnitude of the upper or lower camber at any point along the wing (by measuring the distance between the chord line and the upper and lower surfaces of the wing).
Mean Camber Line: Another reference line drawn from the leading edge to the trailing edge.
However, unlike the chord line, this line is equidistant at all points along the wing from the upper and lower surfaces.
Airfoils are designed in such a way that the shape takes advantage of the air’s response to certain physical laws. Hence, two actions from the air are developed as the wing passes through. A positive or high pressure lifting action from the air mass below the wing, and a negative pressure lifting action from low pressure above the wing.
Teardrop wing profile results in the speed and pressure changes of the air passing over the top and under the bottom to be the same.
According to Bernoulli’s Principle, the faster a fluid moves, the lower its pressure. The slower a fluid moves, the higher its pressure. Airfoils are shaped to manipulate the flow of air to produce force. The design of the airfoil is dependent on aerodynamic characteristics and these characteristics depend on the speed, weight, and purpose of the car. There are essentially two types of airfoils - symmetrical and non-symmetrical. Symmetrical airfoil has identical upper and lower surfaces such that the chord line and mean camber line happen to be the same. Non-symmetrical airfoil, also known as a cambered airfoil, has different upper and lower surfaces such that the chord line happens to be placed above with large curvature. Furthermore, their chord line and chamber lines are different. The advantages of this type are a better lift to drag ratio and stall characteristics, thereby resulting in the production of a useful lift at zero angle of attack.
Camber in Design
The airfoil should be designed to maximize laminar flow to avoid pressure drag (as pressure drag is caused by a turbulent wake). For low traveling airfoils like a solar car, cambering the body is aerodynamically advantageous. NACA 66 airfoils are recommended for a basis for flat airfoils, but other optimized airfoils designs can be referenced for different car shapes. We may need to develop our own model to apply camber to a bullet design, as it’s shape varies about an axis.
The point of max thickness is the ideal position for a protrusion like a driver canopy. The positioning of the driver will influence airfoil design.
Top View Shape
The key design tradeoff in the shape from a top view of the car is the solar array area versus aerodynamic performance. The shape with the most favourable aerodynamic performance is a truncated airfoil. It features more pronounced curvature around the nose and a tapered end. The shape is not ideal for arranging rectangular panelling, and is harder to manufacture.
The other shape is a rounded nose design. This design features a rectanglular shape with a rounded nose to direct airflow around the edge. It is easier to arrange solar panels on and manufacture. This can be advnatageous as extra power can help overcome the poorly optimized aerodynamic performance.
Note on Fairings
Fairings that are completely rigid can be designed to mount onto a curve surface, but fairings that move are better mounted on flat surfaces and it can be worth it to flatten surfaces to get ease of manufacturability even at the cost of aerodynamics.
Body Drag
Reynold’s Number
Reynold’s number is a dimensionless quantity that gives information on turbulent flow.
The definition is above. D is the characteristic length. The Reynold’s number ranges that describe flow type are below.
This is an important constant as laminar vs turbulent flow comes with implications for drag. Recall that drag is a combination of skin drag and pressure drag primarily. An illustrative generalization would be that a bulk body has higher pressure drag where a streamlined body has higher skin drag. Despite this, a streamlined body will have superior drag characteristics to a bulk body as the skin drag will not be as large as pressure drag. This means for designing a body with the most important requirement being to have low drag, the first priority would be to prevent seperation by streamlining.
A streamlined body that maintains laminar flow for as long as possible is desirable because laminar flow results in less skin friction than turbulent flow. This is due to the proportionality of the normal velocity gradient to the drag force caused by viscous fluid effects. On the surface turbulent flow has a higher gradient than laminar flow which means more skin drag.
Car Shape
The following design principles are good to consider when designing solar cars.
A rounded nose that gradually widens will help maintain the laminar boundary layer. The laminar boundary layer will
Reducing the surface area will decrease drag, but may not be feasible due to neading surface area for a solar panel
A smooth surface is the most important factor in keeping a a laminar boundary layer.
A thinner body is desirable as well, because the reduced stagnation pressure at the rear of the car, and therefore the resultant pressure difference between front and back, will be acting on a larger area for a wider car.
Avoid abrupt angle changes along the body
Design to generate close to zero lift.
Note that these design ideas often contradict. If you want to maintain a solar array area but reduce thickness, the car must get longer which will increase the length that the skin friction acts on. It is about balancing these conflicting interests in the best way possible.
Section 2: Airfoil Design Parameters
Calculating Camber
The process for calculating camber comes from “The Winning Solar Car”.
Identify the specifications for a symmetric airfoil with superior drag characteristics and good optimization for laminar boundary layer length
Identify the point of max thickness, use this to record Xmax, the x coordinate of this point where x=0 is at the tip of the frontmost portion of the aerobody
Apply this formula to various points along the aerobody
This formula denotes the shift upward of the centerline at the X. C% is the desired camber and should be within 2%-5% for improved aerodynamic properties.