I have wanted to design my own car ever since I was a child. That dream was to use my artistic expression and come up with a unique vehicle. As I gained insight I found that I could incorporate my design ideas into this wonderfully aerodynamic shape of the teardrop ,the result is a car that is more energy efficient on the one hand yet fulfills my creative needs on the other. All this is accomplished without having to grasp the principles of quantum physics.I just kept it simple using common sense.

Drag coefficient

In fluid dynamics, the drag coefficient (commonly denoted as: cd, cx or cw) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.

The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag.

The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross sectional area of the vehicle, depending on where the cross section is taken.

For airfoils, the reference area is the nominal wing area. Since this tends to be large compared to the frontal area, the resulting drag coefficients tend to be low: much lower than for a car with the same drag and frontal area, and at the same speed.

Two objects having the same reference area moving at the same speed through a fluid will experience a drag force proportional to their respective drag coefficients. Coefficients for unstreamlined objects can be 1 or more, for streamlined objects much less.


Main article: Drag equation

The drag equation:

[F_{d}\,=\,{\tfrac {1}{2}}\,\rho \,u^{2}\,c_{d}\,A]

is essentially a statement that the drag force on any object is proportional to the density of the fluid and proportional to the square of the relative flow speed between the object and the fluid.

Cd is not a constant but varies as a function of flow speed, flow direction, object position, object size, fluid density and fluid viscosity. Speed, kinematic viscosity and a characteristic length scale of the object are incorporated into a dimensionless quantity called the Reynolds number or [\scriptstyle Re\,] . [\scriptstyle C_{\mathrm {d} }\,] is thus a function of [\scriptstyle Re\,] . In compressible flow, the speed of sound is relevant and [\scriptstyle C_{\mathrm {d} }\,] is also a function of Mach number [\scriptstyle Ma\,] .

For a certain body shape, the drag coefficient [\scriptstyle C_{\mathrm {d} }\,] only depends on the Reynolds number [\scriptstyle Re\,] , Mach number [\scriptstyle Ma\,] and the direction of the flow. For low Mach number [\scriptstyle Ma\,] , the drag coefficient is independent of Mach number. Also, the variation with Reynolds number [\scriptstyle Re\,] within a practical range of interest is usually small, while for cars at highway speed and aircraft at cruising speed the incoming flow direction is also more-or-less the same. So the drag coefficient [\scriptstyle C_{\mathrm {d} }\,] can often be treated as a constant.


For a streamlined body to achieve a low drag coefficient, the boundary layer around the body must remain attached to the surface of the body for as long as possible, causing the wake to be narrow. A high form drag results in a broad wake. The boundary layer will transition from laminar to turbulent providing the Reynolds number of the flow around the body is high enough. Larger velocities, larger objects, and lower viscosities contribute to larger Reynolds numbers.[9]Drag coefficient Cd for a sphere as a function of Reynolds number Re.

For other objects, such as small particles, one can no longer consider that the drag coefficient [\scriptstyle C_{\mathrm {d} }\,] is constant, but certainly is a function of Reynolds number. At a low Reynolds number, the flow around the object does not transition to turbulent but remains laminar, even up to the point at which it separates from the surface of the object. At very low Reynolds numbers, without flow separation, the drag force [\scriptstyle F_{\mathrm {d} }\,] is proportional to [\scriptstyle v\,] instead of [\scriptstyle v^{2}\,] ; for a sphere this is known as Stokes law. Reynolds number will be low for small objects, low velocities, and high viscosity fluids.[9]

A [\scriptstyle C_{\mathrm {d} }\,] equal to 1 would be obtained in a case where all of the fluid approaching the object is brought to rest, building up stagnation pressure over the whole front surface. In a real flat plate, the fluid must turn around the sides, and full stagnation pressure is found only at the center, dropping off toward the edges . Only considering the front side, the [\scriptstyle C_{\mathrm {d} }\,] of a real flat plate would be less than 1; except that there will be suction on the back side: a negative pressure (relative to ambient). The overall [\scriptstyle C_{\mathrm {d} }\,] of a real square flat plate perpendicular to the flow is often given as 1.17.[citation needed] Flow patterns and therefore [\scriptstyle C_{\mathrm {d} }\,] for some shapes can change with the Reynolds number and the roughness of the surfaces.

Drag coefficient cd examples
General

In general, [c_{\mathrm {d} }\,] is not an absolute constant for a given body shape. It varies with the speed of airflow (or more generally with Reynolds number [Re] ). A smooth sphere, for example, has a [c_{\mathrm {d} }\,] that varies from high values for laminar flow to 0.47 for turbulent flow. Although the drag coefficient decreases with increasing [Re] , the drag force increases.

Shapes
cd Item
0.001 laminar flat plate parallel to the flow ( [\!\ Re<10^{6}] )
0.005 turbulent flat plate parallel to the flow ( [\!\ Re>10^{6}] )
0.075 Pac-car
0.076 Milan SL (one of the fastest practical velomobiles) [13]
0.1 smooth sphere ( [\!\ Re=10^{6}] )
0.47 smooth sphere ( [\!\ Re=10^{5}] )
0.15 Schlörwagen 1939 [14]
0.18 Mercedes-Benz T80 1939
0.186-0.189 Volkswagen XL1 2014
0.19 General Motors EV1 1996[15]
0.235 Renault Eolab
0.24 Tesla Model S[16]
0.24 Toyota Prius (4th Generation)[17]
0.25 Toyota Prius (3rd Generation)
0.26 BMW i8
0.26 Nissan GT-R (2011-2014)
0.27 Nissan GT-R (2007-2010)
0.28 1969 Dodge Charger Daytona and 1970 Plymouth Superbird
0.28 Mercedes-Benz CLA-Class Type C 117.[18]
0.29 Mazda3 (2007) [19]
0.295 bullet (not ogive, at subsonic velocity)
0.3 Saab 92 (1949), Audi 100 C3 (1982)
0.31 Maserati Ghibli Sedan (2014) [20]
0.324 Ford Focus Mk2/2.5 (2004-2011, Europe)
0.36 Citroen CX (1974-1991, France)
0.48 rough sphere ( [\!\ Re=\!\ 10^{6}] ),
Volkswagen Beetle[21][22]
0.58 Jeep Wrangler TJ (1997-2005)[23]
0.75 a typical model rocket[24]
1.0 coffee filter, face-up[unreliable source?][25]
1.0 road bicycle plus cyclist, touring position[26]
1.0–1.1 skier
1.0–1.3 wires and cables
1.0–1.3 man (upright position)
1.1-1.3 ski jumper[27]
1.28 flat plate perpendicular to flow (3D) [28]
1.3–1.5 Empire State Building
1.8–2.0 Eiffel Tower
1.98–2.05 flat plate perpendicular to flow (2D)
2.1 a smooth brick[citation needed]

Aircraft

 Aircraft use their wing area as the reference area when computing [c_{\mathrm {d} }\,] , while automobiles (and many other objects) use frontal cross sectional area; thus, coefficients are not directly comparable between these classes of vehicles. In the aerospace industry, the drag coefficient is sometimes expressed in drag counts where 1 drag count = 0.0001 of a [C_{d}] .[29]

Aircraft
cd Aircraft type
0.021 F-4 Phantom II (subsonic)
0.022 Learjet
0.024 Boeing 787
0.0265 Airbus A380
0.027 Cessna 172/182
0.027 Cessna 310
0.031 Boeing 747
0.044 F-4 Phantom II (supersonic)
0.048 F-104 Starfighter
0.095 X-15 (Not confirmed)

Bluff and streamlined body flows
Concept

Drag, in the context of fluid dynamics, refers to forces that act on a solid object in the direction of the relative flow velocity. The aerodynamic forces on a body come primarily from differences in pressure and viscous shearing stresses. Thereby, the drag force on a body could be divided into two components, namely frictional drag (viscous drag) and pressure drag (form drag). The net drag force could be decomposed as follows:

Flow across an airfoil showing the relative impact of drag force to the direction of motion of fluid over the body. This drag force gets divided into frictional drag and pressure drag. The same airfoil is considered as a streamlined body if friction drag (viscous drag) dominates pressure drag and is considered a bluff body when pressure drag (form drag) dominates friction drag.

[c_{\mathrm {d} }={\dfrac {2F_{\mathrm {d} }}{\rho v^{2}A}}\ =c_{\mathrm {p} }+c_{\mathrm {f} }=\underbrace {{\dfrac {1}{\rho v^{2}A}}\ \textstyle \int \limits _{S}(p-p_{o}).{\hat {n}}.{\hat {i}}dA} _{c_{\mathrm {p} }}+\underbrace {{\dfrac {1}{\rho v^{2}A}}\ \textstyle \int \limits _{S}T_{w}.{\hat {t}}.{\hat {i}}dA} _{c_{\mathrm {f} }}]

where:

[c_{\mathrm {p} }\,] is the pressure drag coefficient,
[c_{\mathrm {f} }\,] is the friction drag coefficient,
[{\hat {t}}] = Tangential direction to the surface with area dA,
[{\hat {n}}] = Normal direction to the surface with area dA,
[T_{\mathrm {w} }\,] is the shear Stress acting on the surface dA,
[p_{\mathrm {o} }\,] is the pressure far away from the surface dA,
[p\,] is pressure at surface dA,
[{\hat {i}}] is the unit vector in direction normal to the surface dA, forming a unit vector [d{\hat {A}}]

Therefore, when the drag is dominated by a frictional component, the body is called a streamlined body; whereas in the case of dominant pressure drag, the body is called a bluff body (some authors prefer blunt body [33]). Thus, the shape of the body and the angle of attack determine the type of drag. For example, an airfoil is considered as a body with a small angle of attack by the fluid flowing across it. This means that it has attached boundary layers, which produce much less pressure drag.

Trade-off relationship between pressure drag and friction drag

The wake produced is very small and drag is dominated by the friction component. Therefore, such a body (here an airfoil) is described as streamlined, whereas for bodies with fluid flow at high angles of attack, boundary layer separation takes place. This mainly occurs due to adverse pressure gradients at the top and rear parts of an airfoil.

Due to this, wake formation takes place, which consequently leads to eddy formation and pressure loss due to pressure drag. In such situations, the airfoil is stalled and has higher pressure drag than friction drag. In this case, the body is described as a bluff body.

A streamlined body looks like a fish (Tuna, Oropesa, etc.) or an airfoil with small angle of attack, whereas a bluff body looks like a brick, a cylinder or an airfoil with high angle of attack. For a given frontal area and velocity, a streamlined body will have lower resistance than a bluff body. Cylinders and spheres are taken as bluff bodies because the drag is dominated by the pressure component in the wake region at high Reynolds number.

To reduce this drag, either the flow separation could be reduced or the surface area in contact with the fluid could be reduced (to reduce friction drag). This reduction is necessary in devices like cars, bicycle, etc. to avoid vibration and noise production.

Practical example

Aerodynamic design of cars has evolved from 1920s to the end of 20th century. This change in design from a bluff body to a more streamlined body reduced the drag coefficient from about 0.95 to 0.30 in conventional cars.....or in the area of .175 for the purpose built Zoleco!  Thanks Wikipedia.







Low Drag Car Aerodynamics
Slipping easily through air
by Julian Edgar

Imagine for a moment that air was as visible as water.

As every car passed, you would be able to see the swirls and whirls of air disturbed by its passage. Some cars would drag behind them an enormous wake, larger even than the frontal area of the car. Others would have only a small area of disturbed air trailing them, these cars slipping easily through the air.

If air could be seen, you can be certain that car aerodynamics would have never gone out of fashion – after all, boats with flat fronts are pretty rare!

Cd and Frontal Area

There are two factors that decide how easily a car can pass through air.

The most commonly quoted factor is Cd, or coefficient of drag. A flat dinner plate moved face-first through air has a Cd of about 1.1. More slippery shapes have a lower Cd, such as the 0.45 Cd of a sphere.

The other important factor is size. The frontal cross-sectional area of a car is the height multiplied by the width, excluding open areas such as the space between the wheels and including additional areas such as those of the rear vision mirrors. (To gain an approximation of the frontal area, simply multiply height by width.)

Cross-sectional area depends on how big the car is, but the Cd is influenced by how the air flows over the car.

The total drag for a given speed is proportional to Cd multiplied by the frontal cross-section, a figure termed CdA. Note that the larger the car, the easier it is for its designers to achieve a low Cd – but the CdA figure is the one that is more important. Incidentally, many manufacturers’ Cd figures are quite rubbery - often, cars are retrospectively given a poorer Cd figure after the next model is released.

How Air Flows
If you imagine air being a series of thin layers, when the airflow remains in layers (laminar) as it passes over the car, the drag acting on the body is low. Anything that causes the laminar flow of air to separate from the body - and so become turbulent - causes drag. The ultimate low-drag shape is a teardrop with its hemispherical front end and long, tapering tail. Theoretically, a tear drop shape has a Cd of only 0.05! Note that it’s not the pointy end that faces forward, but the rounded end which goes first.

It’s worth thinking about why a tear-drop shape has such a low drag co-efficient.

When the smoothly-curved front end of the teardrop shape meets the air, the air is gently deflected around it, staying attached to the object in attached flow. The long tail of the drop allows the flows to rejoin with only very minor turbulence.

If the air had not remained attached to the shape (because of a sudden step in the shape, for example), the flow would have become turbulent at that point.

However, it is obviously impractical to have a car shaped like a teardrop. The closest that road vehicles currently come to this are the solar race cars – vehicles that have incredibly low Cd values (eg 0.1) matched with very low cross-sectional areas. These cars can travel at 100 km/h using only 1.5-2kW (2-2.7hp) of power. Even in normal road cars, the basic rules of having smooth surfaces with no abrupt transitions of shape, gentle front curves and long tapering tails continue to apply.

When a car moves, air is deflected above, below and around it. The point at which the air splits to pass above or below the car (termed the stagnation point) is important in deciding how slippery the car will be. The lower the stagnation point, the better, because then less air runs into the (usually) rough underside of the car. However, unless the car has a front spoiler extending almost to the ground, air will pass under the car. This has caused some manufacturers to start adopting low drag undersides for their cars. There is also another reason for entraining this air into a smooth flow – creating less lift, which we’ll get to in a moment.

So if the bulk of air doesn’t pass under the car, where does it go? Combustion air is drawn into the engine, usually from near the front of the car. This air movement normally doesn’t create much drag but the flows of cooling air through the radiator do create a lot of drag. On a car with a front radiator, a huge amount of air enters through the cooling duct opening, is forced to flow through the radiator, and then spills out untidily underneath the car. This turbulent movement of the radiator cooling air increases the Cd figure by as much as 10 per cent. For example, the radiator cooling airflow accounts for 8 per cent of the AU Ford Falcon’s drag. This means that without this drag penalty, the car’s Cd would drop from 0.295 to 0.271! (Back in the days of the AU Falcon, manufacturers actually released data on their cars’ aero-effectiveness.)

The use of a radiator intake duct that retains attached airflow for at least most of its length will give the best flow with the least drag. Controlling the flow of air after it leaves the radiator core is also important. Ducting air out through the wheel wells is efficient, but even better is the ducting of the air out through the top of the bonnet. Many sports homologation versions of road cars have taken the approach, fitting special vents to flow radiator air out through the bonnet. However, care needs to be taken that this flow does not disrupt the attached flow across the upper surface of the bonnet.

Air which is forced over the top of the car has to make its way from the relatively bluff nose area to the top of the bonnet, staying attached over the transition formed by the leading edge of the bonnet. This radius is critical. If this corner is too sharp, the air will separate from the car’s surface. A separation bubble will form on the bonnet, leading to the presence of turbulence at the front of the car. It is for this reason that most modern cars have very gentle transitions of shape in this area. One of the all-time great aero specials – the 1970 Plymouth Roadrunner Superbird with its enormous rear wing – had a curved nosecone substituted for its normally bluff front. This extension prevented bonnet separation and also reduced the amount of air passing underneath the car.

The radius formed by the transition from windscreen to roof is also vital. If this angle is too sharp, the airflow may not remain attached to the roof, causing turbulence and further problems towards the back of the car - it’s not much good having a rear wing placed in turbulent air!

What happens at the back of the car is extremely important in determining total drag, rear axle lift and, to a more limited extent, front axle lift. In many cases, the flow at the back of the car is more important than the flow behaviour at the front. The pattern of airflow at the rear of the car depends very much on the type of car being examined. If the airflow from the roof is to remain attached down onto the boot, a three-box sedan must have a very shallow-angled rear window. It is very important that this flow does remain attached – the area of the wake will be reduced, dramatically lowering the car’s overall Cd. When the profile of a three-box sedan is compared with an ultimate teardrop shape, it can be seen that separation at the roof/rear window transition can easily occur.

Cars with gently sloping rear windows – often hatchbacks or coupes – allow the airstream to remain attached right to the rear of the car, so producing only a small wake. The transitional curve between the roof and the hatch needs to be gentle if the airflow is to remain attached, and the angle of the hatch to the horizontal is also critical. It’s important to note that while it may look ‘obvious’ to the eye that the airflow remains attached across a coupe or hatchback’s rear, wool tuft testing needs to be carried out to prove this.

Even quite minor changes in rear hatch angle can cause major changes in drag. Tests carried out by Volkswagen have shown that the Cd of the car can vary from 0.34 to 0.44 as a result of slight alterations to the rear hatch angle. At one angle (30 degrees to the horizontal in this case) the airflow separation point jumped back and forth from the end of the roof to the bottom of the hatch, depending upon the curvature at the rear edge of the roof. It was this 30 degree rear hatch angle that produced the highest Cd value. This sort of substantial change in the car’s drag coefficient will have a large influence on the car’s top speed and fuel consumption. In some cars even a 10 per cent reduction in drag will decrease open road fuel consumption by 5 per cent.

Cars with a near-vertical rear hatch have airflow separation that occurs at the end of the roof. This means that the wake is as large as the frontal cross sectional area of the car. People who locate spoilers half way down the rear hatch should realise that they are achieving nothing with this placement!

A large wake is also present on most station wagon designs. For example, the Cd of the AU Ford Falcon wagon is sedan is 0.341, versus the sedan’s 0.295.

Side Flow

Airflow along the sides of the car is also important. The use of flush-mounted side glass is one approach that is taken to reduce the surface roughness; however, this is implemented more for noise reduction than for lowering drag. Rear vision mirrors have also changed in shape as their aerodynamic drag and the way in which they influence the behaviour of the airflow further down the side of the car is taken into account.

Also very important is the plan view shape of the A and C pillars. Very curved pillars are used to encourage the flow of air from the windscreen smoothly around onto the side glass. On three box sedans, the greater the flow of air that can be gained from the sides of the car onto the boot lid, the better. This air can be used with aerodynamic aids such as spoilers, and its presence also helps fill that ‘hole’ in the air created by the car’s forward movement, thus lowering drag.

A classic case of modification of the shape of a car to achieve laminar flow down its sides occurred way back with the design of the very first Volkswagen Kombi. Initially, the vehicle had an almost flat front and very sharp corners – a bit like a moving shoebox! In this form, severe turbulence occurred down each side of the vehicle and it had a Cd of 0.76. Slight rounding of the nose was then carried out, with special attention paid to smoothing the transition from the front to the sides of the vehicle. The Cd then dropped to just 0.42!

Wakes

As indicated previously, a car draws along a wake of disturbed air. The smaller this disturbance, the lower will be the drag. A very long tail which tapers in both height and width will cause the least drag – that teardrop shape again! While long, tapered tails aren’t practical in normal car design, a truncated version is often used. Cars using boat-tailing (a narrowing of the width of the rear when looked at in plan view) are common, with measured drag reductions of up to 13 percent achieved with this approach. The Opel Calibra – still one of the all-time aero greats - decreased its Cd by 0.01 with a total rear boat-tailing of 130mm.

Cars with tails that taper in profile are also common, but often the taper is abruptly cut off. This is a called a Kamm tail.

The flow of air over the car will create high and low pressure areas. Low pressure areas (creating lift and sometimes drag) occur most frequently where the airstream passes over an upper curved surface – the transition from grille to bonnet, windscreen to roof, and roof to rear window. The shape of the original Porsche 911 created very high lift coefficients - it’s a good example of where laminar airflow wraps around a long, upper-body curve. High pressure areas (creating downforce and sometimes drag) occur at the very front of the car, and in the transition from bonnet to the base of the windscreen.

The way in which these pressures act will result in an overall lift coefficient, or Cl. The lift coefficient is normally expressed for both the front axle (Clf) and rear axle (Clr). A negative lift value (shown by a minus sign in front of the coefficient) indicates that downforce occurs – something relatively rare in a road car.

The cabin ventilation inlets and outlets provide good clues as to the location of (respectively) high and low pressure areas. Intakes for the cabin ventilation system are almost always at the base of the windscreen, while outlet vents are placed in a range of areas. On most recent cars, the outlets are hidden behind the bumper bar in the low pressure wake, but in older cars, vents in the C-pillar or across the top of the rear window are used. While the location of these vents is not of direct use in modifying cars, looking at cars and thinking about the pressures present at these vent locations can be quite illuminating.

Conclusion

The current automotive fashion is for manufacturers to pay only lip service to aerodynamics. In fact, there has been little improvement in CdA figures in the last decade. However, at highway speeds, most of the power being developed by the engine is being used to push air out of the way. For cars of the future to improve their open road fuel consumption, CdA figures will have to once again fall: it is simply a physical requirement of efficient car design.







aerodynamic principles that led to the shape of the Zoleco