Hi everyone, Greetings from Aviation Dreamers..
By reducing the dimensions of a
full-sized aircraft proportionally, a scaled model will be obtained, however, it seldom becomes an easy flying one.The main aerodynamic differences between a model and a full-sized aircraft are originated from the boundary layer, the thin layer of air close to the wing
surface that is slowed down by skin friction.
According to Osborne Reynolds, there are two main types of flow: The laminar and the turbulent.
Which flow type occurs within the boundary layer at a given point of the wing's surface depends on the wing's form, the surface's roughness, the chord length, the airspeed and the ratio of density to viscosity of the air.Reynolds combined all those factors (except the surface condition) into a non-
dimensional number known as Reynolds Number Re.
Re = (air density/air viscosity) x air speed x wing chord
Air viscosity is measured in kilo grams per meter per second.
The standard value is: 0.0000179 kg/m/sec.
The Reynolds number is therefore dependent on the weather conditions, the wing chord and the airspeed.
Re increases as the airspeed, the air density and the wing chord increases.
Since the wing chords of model aircraft are often much less than 1 meter, one may get a Re value close enough for modelling purposes by using the following simplified formula:
Re = speed in kilometres per hour x chord in centimetres x 189 (Metric units).
Re = speed in miles per hour x chord in inches x 770 (Imperial units).
At low airspeed and small wing chord (as with a model aircraft) the air viscosity
is a dominant factor, whereas with the full-sized aircraft the viscosity effects of
the air are insignificant while the aircraft's mass inertia becomes more dominant.
That's why one should not expect a scaled model aircraft to have the same flight
characteristics as its larger counterpart.
The lift force is dependent on the density of the air r, the airspeed V, the wing's Lift Coefficient and the wing’s area according to the formula:
Lift Force = 0.5 x r x V2 x Wing's Lift Coefficient x Wing's Area
The Wing's Lift Coefficient is a dimensionless number that depends on the airfoil type, the wing's aspect ratio (AR), Reynolds Number (Re) and is proportional to the angle of attack (alpha) before reaching the stall angle.
However, the wing's generation of lift also produces Induced Drag, which along with Parasitic Drag are forces that oppose the aircraft's motion through the air.One may also say that Induced Drag is the price we pay for getting lift.
Induced Drag is also dependent on the density of the air r, the airspeed V, the wing's Drag Coefficient and the wing’s area according to the formula:
Drag Force = 0.5 x r x V2 x Wing's Drag Coefficient x Wing's Area
The Wing's Drag Coefficient is a dimensionless number that depends on the airfoil type, the wing's aspect ratio (AR), the shape of the wing tips, Reynolds Number (Re) and the angle of attack (alpha).
The relation between lift and drag is called the Lift to Drag ratio (L/D) and is obtained by dividing the Lift Coefficient by the Drag Coefficient.
The characteristics of any particular airfoil may be represented by graphs showing the amount of lift and drag obtained at various angles of attack as well as the Lift/Drag ratio. The same airfoil has different Lift and Drag Coefficients at different Reynolds Numbers
surface that is slowed down by skin friction.
According to Osborne Reynolds, there are two main types of flow: The laminar and the turbulent.
Which flow type occurs within the boundary layer at a given point of the wing's surface depends on the wing's form, the surface's roughness, the chord length, the airspeed and the ratio of density to viscosity of the air.Reynolds combined all those factors (except the surface condition) into a non-
dimensional number known as Reynolds Number Re.
Re = (air density/air viscosity) x air speed x wing chord
Air viscosity is measured in kilo grams per meter per second.
The standard value is: 0.0000179 kg/m/sec.
The Reynolds number is therefore dependent on the weather conditions, the wing chord and the airspeed.
Re increases as the airspeed, the air density and the wing chord increases.
Since the wing chords of model aircraft are often much less than 1 meter, one may get a Re value close enough for modelling purposes by using the following simplified formula:
Re = speed in kilometres per hour x chord in centimetres x 189 (Metric units).
Re = speed in miles per hour x chord in inches x 770 (Imperial units).
At low airspeed and small wing chord (as with a model aircraft) the air viscosity
is a dominant factor, whereas with the full-sized aircraft the viscosity effects of
the air are insignificant while the aircraft's mass inertia becomes more dominant.
That's why one should not expect a scaled model aircraft to have the same flight
characteristics as its larger counterpart.
The lift force is dependent on the density of the air r, the airspeed V, the wing's Lift Coefficient and the wing’s area according to the formula:
Lift Force = 0.5 x r x V2 x Wing's Lift Coefficient x Wing's Area
The Wing's Lift Coefficient is a dimensionless number that depends on the airfoil type, the wing's aspect ratio (AR), Reynolds Number (Re) and is proportional to the angle of attack (alpha) before reaching the stall angle.
However, the wing's generation of lift also produces Induced Drag, which along with Parasitic Drag are forces that oppose the aircraft's motion through the air.One may also say that Induced Drag is the price we pay for getting lift.
Induced Drag is also dependent on the density of the air r, the airspeed V, the wing's Drag Coefficient and the wing’s area according to the formula:
Drag Force = 0.5 x r x V2 x Wing's Drag Coefficient x Wing's Area
The Wing's Drag Coefficient is a dimensionless number that depends on the airfoil type, the wing's aspect ratio (AR), the shape of the wing tips, Reynolds Number (Re) and the angle of attack (alpha).
The relation between lift and drag is called the Lift to Drag ratio (L/D) and is obtained by dividing the Lift Coefficient by the Drag Coefficient.
The characteristics of any particular airfoil may be represented by graphs showing the amount of lift and drag obtained at various angles of attack as well as the Lift/Drag ratio. The same airfoil has different Lift and Drag Coefficients at different Reynolds Numbers
A large wing that is flying fast
has a higher Re and thinner boundary layer than a small wing that is flying
slow. The boundary layer is thinnest when its flow is laminar and thickens when
it is turbulent.
The turbulent flow may separate from the wing's surface, producing more drag and
decreasing the lift, which may lead to stall.
Thus, a low Re wing is more likely to suffer from laminar separation and to stall sooner than a wing with high Re.
The turbulent flow may separate from the wing's surface, producing more drag and
decreasing the lift, which may lead to stall.
Thus, a low Re wing is more likely to suffer from laminar separation and to stall sooner than a wing with high Re.
Typical Reynolds Numbers:
|
|
Full scale
airliner
|
above 10 000 000
|
Light
aircraft
|
above 1 000 000
|
Large
model aircraft
|
less than 400 000
|
Typical
model aircraft
|
less than 200 000
|
Indoors
and slow flyers
|
less than 30 000
|
The area of the flying surfaces (wings, fin and stabiliser) as well as the control surfaces (elevator, rudder and ailerons) should be proportionally larger in the model aircraft in order to obtain more controllable flights and landings.Wing loading is also more critical with smaller models. That means, a bigger model may have greater wing loading than a smaller one.
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