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Sailfast (Session 2) – 1/29/09 Recap of Session 1 True & Apparent Wind Upwind Believe in Lifts – Head Up, Even in Gusts! Be Wary of Headers – They May be Lulls Reaches Up in the Lulls, Down in The Puffs – Maybe Use Extra Speed to Your Advantage Speed & Time Extra Effort When the Going is Slow Pays Off

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Vectors & Scalars Scalars – Magnitude Mass Density - ρ Energy Power Speed Volume Time (usually) Pressure Vectors – Magnitude & Direction (underlined) Velocity Position - r Momentum - p Force Weight - - mg Area (Sometimes) Torque Vectors are often represented as a triplet of numbers r = x,y,z

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Homework Both problems have to do with gradients: one a temperature gradient and the other a wind velocity gradient. They both illustrate the plane wave approximation, a common trick of physicists used to make a difficult problem simple. Another similar idea is superposition, which we will see later. The velocity gradient problem explains why there are such big, confused waves between the Venice jetties with a west wind and an outgoing tide or, for that matter, in the Gulf Stream.

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Ground Temperature Decreases with Height Acoustic Source T1 T2 Acoustic Shadow T1 > T2 → V1 > V2 Wave Front Curves Up T2' T1' Speed of Sound Increases With Increasing Temperature

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Inversion (T Max) T Increase Upward T Increases Down T2 T1 T2 > T1 → V2 > V1 Wavefront Bends Down T2' T1T1'T1 Ground

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Surface Windspeed Increases with Height W1 W2 W4 Upwind the wave front is tipped up Downwind the wavefront is tipped down Gradient is Due to Viscosity (friction)

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Viscosity – Friction in Fluids Units are Force per unit area times time – pascal seconds (Pa s) = kg/m s (sometimes poise (P) are used – g/cm s)

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2 1 Strong Out-Going Tidal Current North Jetty South Jetty Wave Refraction - “Rage” West Wind & Waves

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Rage (2) The tidal “River” and “Rage” can extend far into the Gulf The process works just as well in reverse – an in-going tide will calm the seas between the jetties The process works on large scales – the Gulf Stream is notorious for being very rough when there is a counter- blowing breeze Lovec In the Yucatan Channel

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1. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. 2. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. 3. For every action there is an equal and opposite reaction. N.B., These are Laws, not Guidelines

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The 2nd law, F=ma, is not easy to interpret in a fluid such as air or water. First of all, let's generalize ma, mass time acceleration: acceleration is the rate of change of velocity and mass times velocity is momentum, so we can interpret ma as the rate of change of momentum. This concept is quite useful in many cases, especially “Impulse”, which is a force times the time that force is applied, t, and which results in a change of momentum. I = tF = mv(1) – mv(2) 1 where mv(1) 1 is the momentum before the impulse and mv(2) 2 is after. The symbol for momentum is “p” and its rate of change is dp/dt. F=dp/dt

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F u A fluid of density is flowing out of an area A with velocity u. What is the upward force F? The momentum flowing down in the column of fluid each second is mu, the mass m in the column is the area A times the length of the column which is u times the density, , or Au (this is the rate at which the mass in the column is increasing each second), so the rate of change of momentum is Aρu2.2. A Think Helicopter Au2Au2

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See you at the Skipper's Meeting – 10 Higel Park!

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