Dimensionless numbers in engineering are mathematical ratios that represent the relationship between different physical quantities in a system. They are used to analyze and predict the behavior of systems without the need for specific units of measurement / Also Allows us to understand the effects of scale in a system without doing further work
How important is scale when working with dimensionless numbers?
The length and parameters have to be scaled proportionally to the size of the physical system (Ex: 1:10 Scale etc...)
What is the relationship between the number of parameters and the number of dimensionless numbers required for analysis?
N-3, where N=Number of Parameters
What are the limitations of dimensionless numbers?
Sometimes adding another parameter reduces accuracy of predictions by a larger amount than if another parameter was added instead.
What dimensionless number units are important in aerodynamics?
Force, density, speed, surface area, chord length (for moment coefficient), speed of sound and viscosity.
What does the Mach Number tell us about a system?
Tells us how close we are to the speed of sound, which influences compressible behaviour.
If the Mach Number is low, we can ignore compressibility.
What does the Reynold Number tell us about our system?
Tells us how thick the boundary layer is (the viscous regime we are in).
Accurate description of lift comes from expressing it as a lift to drag ratio.
What is the correlation between lift and angle of attack?
A linear corelation up until peak lift, where at angles of attack of around 15 degrees the lifting surface begins to stall and the aircraft cannot generate anymore lift. Any increase in angle of attack after that would result in a reduction in lift and an increase in drag in the aircraft.
What is the purpose of flaps?
It pushes the lifting coefficient peak up, thus, reducing approach and landing speed of an aircraft.
Each Mach and Reynold Number generates a unique lifting coefficient vs angle of attack curve.
What causes the parabolic curve between lift and drag coefficient?
Induced drag, thick boundary layer, skin friction, and pressure drag
What is a lift coefficient vs drag coefficient curve called?
Drag Polar Graph
When Lift coefficient (y-axis) is zero, the drag coefficient (x-axis) is not, what does that infer?
All components of the drag coefficient which are not life dependent occurs at that point, where the drag coefficient is renamed to (Cd knot).
What is the relationship between Mach number and Cd knot?
Increasing Mach Number Increases Cd knot due to increasing compressibility with increasing density (results in increasing shockwaves).
Force coefficients are only accurate if the other non-dimensional numbers (angle of attack, Mach, and Reynold) match the FULL-SCALE aircraft.
How can we achieve full scale accuracy of our model aircraft?
Increase density (pressurized wind tunnel), or reduce viscosity (cooling the wind tunnel), then play with the velocity until the Mach and Reynold numbers match the full-scale aircraft as a result.
What is the purpose of a transonic wind tunnel?
Can deliver a specific pressure to control the Mach Number.
Define Aeroelasticity?
Interaction between aerodynamics, aero, and elasticity. It can be static (constant in time) or dynamic (varying in time).
How is the speed index defined in aerodynamics?
The ratio of dynamic pressure to young's modulus.
What does the speed index tell us about the aircraft?
Tells us how much the wing will bend depending on different flight conditions. It needs to match the full-scale aircraft just like the Mach and Reynold numbers.
Define Dynamic Aeroelasticity?
Motion and Structure Vibration where energy is extracted from the air to analyse structural vibration.
How are pitch controls established on an airplane?
From the elevators. Pulling the control column towards you pulls the elevator up, forcing the tail down, thus, pushing the nose of the aircraft up.
What happens to the ailerons and the wings when the control column is moved to the left?
The ailerons on the left wing move up, while the ailerons on the right wing move down. This causes the right wing to move up due to more lift on the right side (allowing the aircraft to roll to the left).
Describe what happens to the tailplane and the airplane when the rudder moves?
The rudder controls the yaw. Due to this, if the rudder moves to the right, the tailplane moves to the left, thus, moving the plane to the right.
Elevators on the rear of the tailplane allow small changes in pitching moment to be made, to pitch the aircraft nose up or nose down.
What are the purpose of spoilers?
Used to control aircrafts as lower speeds. It is used symmetrically to increase drag and decrease lift in landing. It is also used after landing to decrease lift and decrease excessive speed and allow further braking upon landing.
When are inboard ailerons used?
High-speed aircraft or aircraft with swept wings often use inboard ailerons to improve roll control at high speeds.
What do spoilers provide on an aircraft?
Roll Control, lift dumping on landing, and drag control (to allow rapid descent without excessive speed).
As the spoiler angle increases, lift will decrease non-linearly.
Why did some airplanes deploy the spoilers to 7 or 9 degrees?
Use of Direct lift control where the spoilers retract, lift increases, and upwards acceleration increases (pitch is upwards).
Why is Direct Lift Control desirable?
It allows us to control the vertical force on the aircraft without rotating the aircraft in pitch when landing.
The vertical acceleration increases due to the spoilers, and NOT the elevator.
What is the purpose of full span flaps?
Helps in decreasing landing speeds.
What is the purpose of using a rudder with a flap on it (2-part rudder)?
Purpose is to improve the maximum lateral force on the tailfin following an engine failure, in the same way as flaps on the wing reduce the stall speed for landing.
Why do aircrafts have a tailfin that is too large for normal flight?
The extra area is there for safety when engines fail.
Why does the rudder with the flap not pivot in the same way as the tailplane?
The aircraft will yaw anyway under asymmetric conditions.
What is the purpose of slats on an aircraft?
Increases maximum lift coefficient, reducing stall speed and approachable landing speed.
Why does the drag polar graph portray a parabolic behaviour?
Due to induced drag as a result of changing lifting coefficient.