Understanding Flight: Newton Reigns in Aerodynamics! General Aviation. Scott Eberhardt March 26, What you will learn today. Descriptions of Lift

Transcription

1 Understanding Flight: Newton Reigns in Aerodynamics! General Aviation Scott Eberhardt March 26, 2007 Military Aviation Commercial Aviation What you will learn today Some of the things you learned might be wrong The physical description of lift, using Newton s Laws The connection between lift and power Some ideas about why wings look the way they do Descriptions of Lift 1

2 Explaining Lift Mathematical description Taught to Aeronautical Engineers Popular description Taught by flight schools, FAA, NASA, etc Physical description What you are learning today The Myth of the Bumblebee The Aerodynamicist s Bane The tabloids do it to science again? Aerodynamicist Proves Bumblebees Can t Fly! Seattle Muckraker $1..00 September 10 Elvis is Alive, Living in Argentina Guru remains in trance for 20 years..without food or drink A 380 News Flash. Giant fly Britney Spears devours to run for governor jumbo jet of New York. Hundreds missing Astrophysicists find dark matter its cosmic cow poop The Actual Origin of the Bumblebee Myth From A. Magnan, Le Vol Des Insects, Paris: Herman and Cle, 1934 (p. 8): Tout d abord, pouss e par ce qui fait en aviation, j ai applique aux insectes les lois de la resistance del air, et je suis arrive avec M. [Andre] SAINTE-LAGUE a cette conclusion que leur vol est impossible. Popular Description of Lift (what you might have learned) Bernoulli relates pressure to velocity Focuses on shape of wing to determine velocity Perpetuates Myths Physical Description of Lift Forget Bernoulli s Theorem Stick and Rudder, published 1944 Lift is a Reaction Force 2

3 Physical Description Based on Newton s laws Easy to understand without equations Leads to an understanding of power required for flight Newton s Third Law To every Action there is an equal and opposite Reaction Newton s First Law So. A body at rest will remain at rest, or a body in motion will continue in straight line motion unless subjected to an external applied force For a wing to go up it must force air down Lots of air! Cessna Citation flying over fog (Photo By Paul Bowen) A Rotating Wing Pushes Air Down 3

4 Does this picture show an airfoil generating lift? No, the air must experience a net change, as shown below Upwash Downwash Downwash Wing pulls air down -- Downwash Why does the air follow the top surface of the wing? Downwash is related to angle of attack and airspeed, which the pilot can control Nature Abhors a Vacuum Air could fill from below? This cannot happen 4

5 Air could fill from below? Air could fill from back Can t happen (except in superfluids ) Air could fill from back Stall on flat plate Air could fill from top Air could fill from top 5

6 Picture a curved hose Hose is like an airfoil Air Force Air Force Viscosity Newton s Second Law Force on glass The thrust of a rocket is equal to the velocity of the exhaust times the amount of mass ejected per second Force on water Newton s 2nd law applied to a wing The lift on a wing is proportional to the amount of air diverted per second times the vertical velocity of the air Lift = mass/sec * vertical velocity Lift So, wing diverts air down for lift Lift = mass/sec * vertical velocity or Lift = (m/t) * V downwash (m/t) is mass flow rate of air pumped down 6

7 Diverted Air The wing as a scoop The amount of air diverted is proportional to: The speed The air density The scoop can be calculated with the Biot-Savart Law. Vertical Velocity Vertical Velocity The vertical velocity is proportional to: The speed The angle of attack a: b: c: α Speed (x2) Downwash Speed α Downwash Speed α(x2) Downwash Vv Vv(x2) Vv(x2) Pilot controls airspeed and angle of attack Angle of Attack Lift is a Function of Angle of Attack Lift 1 Critical angle of attack Effective angle of attack (degrees) (at constant density and speed) 7

8 Vertical Velocity Vertical velocity is related to angle of attack and the airspeed of the wing Pilot controls airspeed and angle of attack How much air is pushed down? What s going on in this photo? A Cessna 172 diverts approximately 5 times its own weight per second! Summary of Lift Lift is proportional to: Amount of air diverted per second Downwash velocity of that air Amount of air diverted per second is proportional to: Speed of wing Density of air Downwash velocity of air is proportional to: Angle of attack Speed of wing T=0 Myth: 1 Particles reach trailing edge at same time. T f 8

9 With Equal Transit times, How Can... An airfoil fly upside down? A paper airplane fly? A wing fly in ground effect? Equal transit times says it can t happen Equal transit times is wrong! Reality Air goes much quicker over the top Lift is a Function of Angle of Attack Myth #2 Lift 1 Critical angle of attack These two pictures are not the same thing Effective angle of attack (degrees) Cessna Citation flying over fog (Photo By Paul Bowen) Summary of Lift Lift is proportional to: Amount of air diverted per second Downwash velocity of that air Amount of air diverted per second is proportional to: Speed of wing Density of air Downwash velocity of air is proportional to: Angle of attack Speed of wing 9

10 If Lift didn t require Power Power Planes would have same range empty or full Helicopters could hover at any altitude and load Propulsion would not require power either (same physics) Power required for lift Power is Force times Velocity Induced Power is the lift times the vertical velocity Induced Power = Lift * Vertical Velocity What is the Lift? Lift = Weight (for straight and level flight) Weight isn t changing Lift is constant So How does Vertical Velocity Change? As speed increases, more air passes past wing so the amount of air diverted per second increases. Therefore, as speed increases, downwash decreases Lift = (m/t) * vertical velocity or Vertical velocity = Lift/(m/t) 10

11 So, Induced Power= Lift * Vertical Velocity Induced Power decreases with speed! But, don t forget power to overcome skin and form drag Induced Power At half the speed: Half the air is diverted therefore, you need to double the vertical velocity by increasing the angle of attack Induced power goes as 1/speed Power Induced Power Cessna 172 Skyhawk Parasitic Power The energy loss to collision with the air is proportional to speed squared (1/2mv 2 ) Number of collisions is proportional to speed V - mph Parasitic power goes as speed cubed Parasitic Power Cessna 172 Skyhawk Power Required Power V - mph Power Ve V - mph 11

12 Langley s Law Summary of Power Lift requires power Power due to lift: Induced Power Wing Efficiency Wing Efficiency Induced power is proportional to lift times vertical velocity If you double the span of the wing you double the amount of air diverted and therefore halve the vertical velocity Induced Power and Induced Drag decrease as wingspan increases Gliders have efficient wings Classical Aerodynamics Lift does no work! But, classical aerodynamics assumes a wing of infinite span if span -> infinity power induced -> 0! 12

13 Summary Lift is a REACTION FORCE Lift is described using Newton s Laws Lift requires Power High span increases wing efficiency References English French Spanish Italian Japanese Many Thanks! 13