6.1.1. Drag

In order to have long range or achieve maximum speeds, an aircraft must have as little drag as possible.

Most of a flight (the so-called “cruising” flight) is carried out at a load factor n = 1 and, therefore, at low incidence, without significant changes other than path corrections. In this case, the search for a minimum drag coefficient is a priority. This drag is divided into four parts:

• – pressure drag (or supersonic wave drag);
• – friction drag;
• – base drag;
• – accessory drag.

The first term indicates that the component, along the longitudinal axis of the integral of the pressures on the aircraft, “base excepted”, is not zero. A body drag can be assigned to each element of the aircraft (body, wings, control surfaces, etc.).

The second term is linked to the phenomenon of air viscosity; it varies according to the dimensions of the aircraft, its relative speed and the state of the external surface in contact with the air. This term relates to the viscous flow, which gives rise, over the entire surface of the aircraft, to shear stresses.

The aircraft can be broken down into its various parts, namely:

• – the body;
• – wings;
• – control surfaces.

For each element, the external surfaces in contact with the fluid, called bathed or wet surfaces, must be evaluated. They are related to the reference surface (the maximum diameter of an airplane, for example).

For the body, we have S_bc/S_ref (=1); for the wings, we have S_ba/S_ref; and for the rudders, S_bg/S_re (with S_re = π∗d²/4).

By definition, the tangential force T exerted by the fluid on a plate per unit area is given by the equation:

with:

μ = the fluid viscosity coefficient;

u = the component of the speed according to x in the vicinity of the wall;

y = the axis perpendicular to the wall;

V₀ = the speed of undisturbed flow;

C_f = the friction coefficient.

The third term is due to the appearance of lift-off flow behind the aircraft and the resulting depressions.

A reduction in drag can be obtained by improving, if possible, three components:

• – a reduction for the frontal surfaces of each element of the aircraft can be obtained by using a dihedral that is as low as possible for the leading and trailing edges and a very elongated nose cone, which makes it possible to reduce the wave drag of the aircraft;
• – the aircraft’s friction drag can be improved in very modest proportions by paying attention to the condition of the surfaces in contact with the air;
• – it is very difficult to significantly reduce the base drag of the aircraft;
• – for on-board accessories (antennas, fairings, etc.), no action is possible to reduce the drag.

Drag reduction is a compromise between the mission of the aircraft, on-board equipment and accessories.

6.1.2. Lift

An aircraft must be able to curve its trajectory, which gives it a load factor normal to its speed. This load factor can be produced by an incidence set by aerodynamic means (aerodynamic control surfaces).

Lift appears at the different parts of the aircraft (wings, body, control surfaces, accessories), which has the effect of creating a load factor.

6.1.3. Reynolds number

The coefficient of friction C_f is evaluated from the Reynolds number:

with:

V = the flow velocity;

D = the characteristic length (L_Ref);

υ = the kinematic viscosity of the fluid (υ = μ / ρ);

μ = the dynamic fluid viscosity (Pa⋅s or kg/(m⋅s));

ρ = the fluid density (kg/m³).

The Reynolds number represents the ratio of inertial forces to viscous forces.

The units are given for guidance only, as they are dimensionless numbers with the same value in any coherent system of units.

The Reynolds number also represents the (qualitative) ratio of the transfer by convection to the transfer by diffusion of the momentum.

It is important to note that the Reynolds number only gives an order of magnitude.

The fact that we can test cars (MatraEspace, for example) in a hydrodynamic basin, therefore in a fluid (water) different from their natural fluid (air), shows to what extent the Reynolds number reigns supreme over the flows of all fluids.

6.1.4. Flow velocity

The speed of sound in an ideal gas is a function of the Laplace coefficient γ (gamma), of the density ρ (rho) and of the pressure P of the gas and is theoretically calculated as:

with:

γ = C_P/C_V Laplace coefficient;

C_P and C_V are the isobaric and isochoric thermal capacities, respectively.

The speed of sound can also be calculated using the specific ideal gas constant:

R_S = R / M

with M being the molar mass, R the universal constant of ideal gases and T the thermodynamic temperature in Kelvin (K):

For air, mainly composed of dioxygen and nitrogen (diatomic gases):

• – R_S = 287 (J*kg^-1*K^-1);
• – γ = 1,405;
• – T = temperature at the considered altitude.

For each case, knowing the Mach number, the considered altitude and the corresponding temperature, the speed can be obtained:

6.1.5. Stability of an aircraft

An aircraft is aerodynamically stable when Cmα is negative, in other words, when the focus of aerodynamic forces is behind the center of gravity:

This represents the distance between the focus and the center of gravity.

More generally, since aircraft rarely have linear aerodynamic characteristics as a function of the incidence and the roll angle, it is necessary to consider, in order to characterize the stability of an aircraft:

• – the position of the application point of the aerodynamic resultant:
  
• – the focus of the aircraft in incidence:
  
• – the focus of the aircraft in roll:
  

The aircraft does not have to be stable throughout its flight envelope; it is the combination of aerodynamic and pilot characteristics that result in either:

• – the need to pilot the aircraft with natural and permanent stability;
• – the possibility of piloting with artificial stability.

It is through the relative positioning of the bearing surfaces on the body and their dimensioning that the stability of aircraft is regulated.

6.1.6. Resistance of structures

Mass gains have immediate repercussions on aircraft performance, such as:

• – greater acceleration in the propelled phase, resulting in a speed gain;
• – higher load factor for a given lift.

The mechanical elements must therefore be dimensioned as accurately as possible, taking into account the stresses they will have to withstand during all phases of the flight.

A particular point concerns the study of the hinge moments of the control surfaces and the search for solutions to reduce them.

During the flight of an aircraft piloted with the aid of aerodynamic control surfaces, a resulting force and a resulting moment appear on a control surface. These two terms are a function of the Mach number M, the sideslip β, the angle of attack α and the steering angle δ of the rudder.

Low hinge moments allow:

• – servomotors with smaller dimensions to be adopted;
• – the handling of the aircraft to be improved thanks to the higher turning speeds of the control surfaces (lower response time).

From a thermal point of view, under the effect of the compressibility and the friction of the air, the walls of the aircraft will heat up, hence the need to use materials resistant to temperature.

6.1.7. Sizing of an aircraft

Once the load factor requirements of an aircraft are known, it is necessary to size the surfaces, wings and control surfaces, which provide the necessary coefficient of lift C_z. The load factor requirements are very different depending on the aircraft considered (civil aircraft, military aircraft, surveillance drones, microlights, etc.).

6.2.1. Definition of the load factor

By definition, the load factor is the result of dividing the aircraft’s acceleration by g, which is 9.81 m/s².

6.2.2. Definition of the load factor requirements

For an aircraft that evolves aerodynamically, the process is as follows:

• – a deflection of the control surfaces, a deviation of the jet, etc., provide the aircraft with a moment;
• – under its action, there is a rotation around the center of gravity and the aircraft is in incidence;
• – the effect of the angle of incidence is to create a lift force, Rz = –(q * S * Czα * α), normal at aircraft speed, which therefore has a load factor:

Once the load factor requirements of an aircraft are known, it is necessary to dimension the surfaces of the wings and control surfaces, which provide the necessary lift coefficient C_z.