Going Up in the 18th Century

What goes up might come z Politics, Sex and Science down: Bernoulli z The renaissance brought to Europe the concept of personal advancement through achievement in science. Unit 2 study 3.4 z Those poised to make (or steal) grand discoveries were greeted with immense Lachlan Thompson prestige and reward. [email protected] z The race was to publish first.

The case of Bernoulli vs Newton The protagonists

z The "Bernoulli" position that lift is z Newton (1642-1727) published is generated by a pressure difference findings on motion and forces around across the wing 1687.

z The "Newton" position that lift is the z Bernoulli (1700-1782) Investigated blood reaction force (Newton’s 3rd Law) on a flow through the arteries and modelled body caused by deflecting the flow of air. these with pipes. Published 1738.

Bernoulli? Forces on an Aeroplane

z Bernoulli never attempted to explain the z Lift from the wing & tail aerodynamic lift of an object. z Weight a function of mass and gravity (Newton pops up his head here) z Thrust from the propulsion system z Neither did Newton z Drag due to the skin friction of the surface of the aeroplane with the air AND the profile drag or shape of the aeroplane

1 Drag Flight at Constant height & Velcoity

Skin friction is a function of z Profile drag is the z Equilibrium the surface area wetted resistance due to the by the air stream. shape of the aeroplane Any increase in surface disturbing the air. z For level flight area will increase skin z Lift = Weight friction drag. z For constant velocity Skin friction drag is affected by the fluid's z Thrust = Drag speed and viscosity z Newton’s 3rd Law (stickiness of air)

Equilibrium Torque and Moments But!

z What happens if the z For an airplane to be engine is not in line stable. with the Drag force?

z So……!

Level Flight Bernoulli’s Equation

a z What happens if the z The mathematical Lt z Bernoulli wanted to engine is not in line with statement of this energy understand blood conservation is stated in the Drag force? flow through the the BERNOULLI z As the pilot changes EQUATION: human body e Lt thrust (power) the b airplane wants to pitch z P1 + ½ρv12 = P2 + ½ρv22 z Newton’s 3rd Law Lt z The moment due to the tailplane must equal v2 > v1

z bLt = aT - eL P2 < P1

2 Can we prove this? Experiment 1

Does Bernoulli work? What did we see?

z The air travels a greater distance over the top of the wing. z Therefore must travel faster. z Therefore produces lower pressure. z Therefore pressure difference produces a lift force. z Score 1 for Bernoulli

Aerofoils Newtons Third Law

z The yellow car a z As we have just flat bottom seen an aerofoil z The red racing car has a aerofoil work at an angle to shaped under produce lift body z Observe the water spray angle z The red car generates 1 tonne of down force the yellow zero down force both at 210 kph.

z Newton is right!

3 Results Flight Tests

z What did we observe? z Glide Slope z Leaves blown by downwash of air z Research Question z The resulting upward reaction z Is the best glide angle of a glider change z Score 1 to Newton with change in payload (glider weight)? z Newton’s third law that for every action there is an equal z Is the velocity of the air realy faster over and opposite reaction works for aerofoils the top of a wing?

z It’s a Draw

Bernoulli verses Bernoulli Newton verses Hooke

z In 1734, Daniel Bernoulli submitted an entry z Robert Hooke (1635-1703) famous for Hooke’s law on for the Grand Prize of the Paris Academy elasticity and the definition of what we call a cell to giving an application of his ideas to astronomy. define microbe creatures. He published a partial work on gravitation ten years before Newton. His father also entered the competition being a z Intense rivalry ensured between Hooke and Newton. famous scientist in his own right. z Scandalous stories of Hooke’s formerly discrete taste z Daniel and his father were declared joint for young ladies (his “nieces'”) mysteriously became winners of the Grand Prize. public knowledge (believed to have cost him a z As a result, his father was furious to think that knighthood). his son was considered his equal, and banned z When Newton (1642-1727) became president of the Royal Society Hooke’s portrait disappeared from the Daniel forever from his house. Society never to be found. Ollie Leitl 2004

Postscript Unit Outline

Key knowledge z Daniel Bernoulli did produce other excellent scientific To achieve this outcome the student should be able to: work during these many years back in Basel. In total • apply the concepts of forces, torques and equilibrium to balancing an he won the Grand Prize of the Paris Academy 10 aircraft, including reference to Newton’s laws of motion; times, for topics in astronomy and nautical topics. He • explain lift in terms of Bernoulli’s principle and the rate of change of won in 1737 for work on the best shape for a ship momentum; • model lift and Bernoulli’s principle using a wind tunnel; anchor; 1740 for work on Newton's theory of the tides; • explain drag, skin friction drag, pressure drag and principles of thrust; in 1743 and 1746 for essays on magnetism; in 1747 • investigate experimentally the relationship between power and thrust; for a method to determine time at sea; in 1751 for an • analyse aircraft performance including takeoff, climb, descent and cruise, essay on ocean currents; in 1753 for the effects of with reference to Newton’s forces on ships; and in 1757 for proposals to reduce laws of motion and Bernoulli’s principle; the pitching and tossing of a ship in high seas. • investigate experimentally identified aspects of performance using a model; z Daniel Bernoulli and Sir Isaac Newton never met. • analyse risks in the use and testing of flying models using relevant data; • identify and apply safe and responsible practices when using and testing flying models.

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