Aerodynamic resistance

The aerodynamic shape, or simply drag, is the force that a body undergoes when moving through the air, and in particular the component of that force in the direction of the relative velocity of the body with respect to the medium. Resistance is always in the opposite direction to that of said speed, which is why it is usually said that, analogous to friction, it is the force that opposes the advance of a body through the air.

More generally, for a body in motion within any fluid, such a component is called fluid dynamic resistance. In the case of water, for example, it is called hydrodynamic shape.

Introduction

As with other aerodynamic forces, aerodynamic coefficients are used to represent the effectiveness of a body's shape in moving through the air. Its associated coefficient is popularly known as penetration coefficient, drag coefficient or aerodynamic coefficient, the latter name being especially incorrect since there are several forces aerodynamics, with their respective aerodynamic coefficients, and each of them has a different meaning.

The way in which aerodynamic resistance is studied presents some particularities depending on the field of application.

In aeronautics

The total drag of an aircraft in flight can be broken down into the following:

Parasitic resistance

This is the name given to any resistance that is not a function of lift. It is the resistance that is generated by all the small non-aerodynamic parts of an object. Is composed of:

• Profile resistance: The resistance of an elar profile can be decomposed in turn in two others:

1. Pressure resistance: Due to the shape of the trail.
2. Friction resistance: Due to the viscosity of the fluid.

• Form Resistance: It is the resistance caused by the components of a plane that does not produce any support, for example the fuselage or the gondolas of the engines.

• Interference resistance: Each outer element of a plane in flight has its limit layer, but due to its proximity they can interfere with each other, which leads to the appearance of this resistance.

Induced resistance

If a wing of finite span is considered, due to some eddies that appear at the ends of the wing due to the pressure difference between the extrados and the intrados, the so-called induced drag arises. This drag is a function of lift and hence it is directly proportional to the angle of attack, higher lift implies higher induced drag. It is the drag produced as a result of the production of lift. High angles of attack, which produce more lift, produce high induced drag.

Induced resistance formula:

Di=2L2π π ρ ρ v2eb2{displaystyle D_{i}={frac {2L^{2}}{pi rho v^{2}eb^{2}}}}}}}

Symbol	Name	Unit
Di{displaystyle D_{i}}	Induced resistance	N
L{displaystyle L}	Sustained	N
ρ ρ {displaystyle rho }	Fluid density	kg/m3
v{displaystyle v}	Speed	m/s
e{displaystyle e}	Efficiency factor depending on the shape of the wing (dimensional)
b{displaystyle b}	Larger	m

Induced resistance coefficient:

CDi=Di12ρ ρ v2S=CL2π π eA{displaystyle C_{D_{i}}}={frac {D_{i}}{{{{frac {1}{2}}{2}{2}}}{frac {{C_{L}{}{2}}{pi eA}}}}}}}

Symbol	Name	Unit
CDi{displaystyle C_{D_{i}}}	Coefficient of induced resistance
CL{displaystyle C_{L}}	Sustaining coefficient
e{displaystyle e}	Efficiency factor depending on the shape of the wing (dimensional)
A{displaystyle A}	Alargamiento del ala

Drag coefficient of profile for small Mach numbers

Simulation that shows the distribution of pressures in a profile subjected to laminar flow. You can see the resistance of the profile by increasing pressures on your attack edge.

Resistance to progress Qx{displaystyle Q_{x}} of the surface area of the infinite wing is usually called profile resistance. As resistance to the advancement of any body the resistance of the profile can be divided into the pure resistance of the profile and the induced resistance:

Qx=Qx,0+Qx,i{displaystyle displaystyle Q_{x}=Q_{x,0}+Q_{x,i}}}

Symbol	Name
Qx{displaystyle displaystyle Q_{x}}	Resistance to progress
Qx,0{displaystyle Q_{x,0}	Pure profile resistance
Qx,i{displaystyle Q_{x,i}	Induced resistance which depends on the support coefficient

The coefficient of induced drag is proportional to the coefficient of lift, to engender a great lift, the wing has to divert the airflow more intensely downwards. At the same time the wing does a great job and therefore suffers great resistance, its simplest form of calculation is:

Cx,i=BCand2π π λ λ {displaystyle displaystyle C_{x,i}=B{frac {C_{y}{2}}{pi lambda }}}}}

Symbol	Name
Cx,i{displaystyle displaystyle C_{x,i}}
λ λ {displaystyle lambda }	Alargamiento del ala
B{displaystyle B}	Ala geometric coefficient

For all of the above, the induced resistance coefficient would be expressed as follows:

Cx,i=0,18Cand2{displaystyle C_{x,i}=0,18C_{y}{2}}}

The pure resistance of the profile is composed of different types of resistances among which are the pressure (Qxp{displaystyle Q_{x}p}and friction (Qfr{displaystyle Q_{f}r}(c):

Cx,i=Cx,fr+Cx,p{displaystyle displaystyle C_{x,i}=C_{x,fr}+C_{x,p}}

There is also the wave resistance which in this case does not exist because since the phenomenon occurs to small numbers of Mach, the pressure resistance has only the turbulent nature.
However, it is necessary to calculate the value of the two resistance coefficients, the corresponding pressure and the corresponding friction with the profile surface. To determine the coefficient of resistance due to the distribution of pressures by the surface it is necessary to re-establish the constructive form of the model that is to be manufactured to have a determined derivative (ds) because it must be separated along the x axis of the body an elemental section dsmax=danddx{displaystyle ds_{m}ax=dydx} normal to axle x. The strength of resistance in this will be equal to:

Qx,p=(Pd− − Pt)dSmax{displaystyle displaystyle Q_{x,p}=(P_{d}-P_{t})dS_{max }}}

where:

Pd{displaystyle P_{d}}: Pressure at the front of the element.

Pt{displaystyle P_{t}}: Pressure at the rear of the element.

From the previous equation it can be deduced that the resistance force due to the distribution of pressures by the profile will be the integral taken by the area of the maximum section in the Y or Z surface.

Figure showing the coefficient of resistance to attack angle

Qx,p=∫ ∫ Smax(Pd− − Pt)dSmax{displaystyle displaystyle Q_{x,p}=int _{S_{max}(P_{d}-P_{t})dS_{max }}}}

Total resistance

The formula for the total aerodynamic drag created by an aircraft in flight is:

D=qSCD=CD12ρ ρ v2S{displaystyle D=qSC_{D}=C_{D}{frac {1}{2}}rho v^{2}S}

where:

D{displaystyle D,} - Resistance. "D" is used for the English term drag (drawling).

ρ ρ {displaystyle rho ,} - Fluid density.

v{displaystyle v,} - Speed.

S{displaystyle S,} - Alar surface on the floor.

CD{displaystyle C_{D},} - Aerodynamic resistance coefficient.

q=12ρ ρ v2{displaystyle q={frac {1}{2}}rho v^{2},} - This term is called dynamic pressure.

Therefore, the formula for the aerodynamic drag coefficient is:

CD=D12ρ ρ v2S{displaystyle C_{D}={frac {D}{{{frac {1}{2}{2}{2}{2}}rho v^{2}S}}}}}}}}}}

So, the total aerodynamic drag is the sum of the parasitic drag and the induced drag, so that:

CD=CDparasite+CDinducida{displaystyle C_{D}=C_{D_{text{Parasita}}}}

In the automotive industry

The formula for the total aerodynamic drag created by a moving car is identical to that used in aeronautics.

The use of the coefficient is much more comfortable than the use of forces.

Factors that affect the aerodynamics of a car

• The lacking bass are an unused but effective solution. In addition, they can be used to stick the car more to the firm, with very little penalty in the resistance (Renault Clío Sport 2006).
• The amount of surface facing the wind is along with the aerodynamic coefficient the two factors that determine the end aerodynamic resistance.
• Deceptive aerodynamic. Whether a car is more or less aerodynamic depends more on details such as the inclination of windshields than in spectacular ways (Citroën CX, Lamborghini Countach).

An example:

Lamborghini Countach launched in 1974. Its aggressive form has an aerodynamic coefficient of 0.42—this was thought for the wind to push the car down, achieving higher traction at high speeds. In this case, that of a super-sport car, the force of the wind is used to give stability and grip on manoeuvres.

As the aerodynamic resistance is reflected in a force that opposes the movement and that can be estimated from the previous coefficients, there will also be an additional energy expenditure necessary to overcome said resistance, which is usually quantified as a power, in case which is useful for us the following formula:

Power=LabourTime=Force⋅ ⋅ SpaceTime=Force⋅ ⋅ SpeedPower=δ δ Wdt=Fδ δ rdt=F⋅ ⋅ V=12ρ ρ SCxV3{cHFFFFFF}{cH00FF}{cHFFFFFF}{cHFFFFFF}{cHFFFF}{cHFFFF}{cHFFFF}{cHFFFF}{cHFFFF}{cHFF}{cHFF}{cHFF}{cHFF}{cHFF}{cHFF}{cHFF}{cHFF}{cHFF}{cH00}{cH00}{cHFF}{cHFFFF}{cHFFFFFF}{cHFF}{cHFF}{cHFFFF}{cHFF}{cHFFFF}{cHFF}{cH00}{cH00}{cHFFFF}{cHFF}{cHFF}{cHFF}{cHFF}{cHFF}{cHFF}{cHFF}{cH

Therefore, if we know the aerodynamic data of a body, we can also calculate the power required to move it through a fluid at a certain speed, as shown in the following example:

Data:

Vehicle considered: Audi A3 (Second generation, 2003-2012)

Front surface: S=2,13m2{displaystyle S=2,13 {text{m}}{2}}{2}} (Official data)

Coefficient of penetration: Cx=0,32{displaystyle C_{x}=0,32,} (Official data)

Air density: ρ ρ =1,225kg/m3{displaystyle rho =1,225 {text{kg}}/{text{m}}{3}{3}}} (density to 0 meters according to International Standard Atmosphere (ISA)

Speed: V=120km/h=33,33m/s{displaystyle V=120 {text{km}}/{text{h}}}=33,33 {text{m}/{text{s}}}}}

Calculation:

P=Fx⋅ ⋅ V=12ρ ρ SCxV3=12⋅ ⋅ 1,225⋅ ⋅ 2,13⋅ ⋅ 0,32⋅ ⋅ 33,333=15457,58W=21,03CV{displaystyle P=F_{x}cdot V={frac {1}{2}{2}{2}}{x}V^{3}={frac {1}{2}}}}{cdot 1,225cdot 2,13cdot 0,32cdot {33,33}{3}=15457,58text{cdot}{cdot}{cdot}}{c}{cdot}}{cdot}}{cdot}}}{cdot}{cdot}{cdot}}}{c, ==

However, it should not be forgotten that this is not the total power necessary, since in reality, in the propelled displacement of a car, in addition to the aerodynamic resistance, there are other resistances such as the friction with the ground, as well as mechanical losses.

Examples of aerodynamic coefficients of different vehicles and representative figures

• 1 Approximate values. Each model has a different Cx, but it will approach the value of the table.
  Apart from the shape other factors influence, such as surface roughness. For example, a golf ball, at the speeds that are usually moved, is more aerodynamic, by its holes, than an equivalent sphere.
• 2 The coefficients of Formula 1 cars can vary according to the configuration of their aerodynamic surfaces, which is adjusted for each circuit.