Lab 6: Projectiles

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# Lab 6: Projectiles - PowerPoint PPT Presentation

Lab 6: Projectiles. CS 282. Overview. Review of projectile physics Examine gravity projectile model Examine drag forces Simulate drag on a projectile Examine wind forces Simulate wind affecting a projectile. General Concepts. Acceleration F = ma Translational velocity and state

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### Lab 6: Projectiles

CS 282

Overview
• Review of projectile physics
• Examine gravity projectile model
• Examine drag forces
• Simulate drag on a projectile
• Examine wind forces
• Simulate wind affecting a projectile
General Concepts
• Acceleration
• F = ma
• Translational velocity and state
• dv/dt = a , ds/dt = v
• Rotational acceleration
• torque = inertia * rotational_acceleration
• Equations of motion are separated into directional components
Reference Frame
• Let’s use Cartesian Coordinates for simplicity
Gravity-Only Projectile Model
• Fx = 0
• Fy = -mg
• Fz = 0
• vx = vx0
• vy = vy0 –gt
• vz=vz0
• ax = 0
• ay = –g
• az= 0
Exercise 1: Setting Up
• Available on the class website
• Examine the projectile class
• Look at the gravity_model function
• !!!! Fill in the missing update y-position !!!!
• Compile and run
• If necessary, WASD2X translates the camera (use at your own risk though  )
• ENTER toggles the simulation ON/OFF
Exercise 1: Setting Up
• Hopefully, you have come up with something like (without cheating) this…
• position.y + vy *dt+ 0.5*g*dt2
• For this lab, let’s just assume there’s a golf club (or something) is hitting that projectile 
• So, Gravity-Only models are…
• Really easy to implement
• Feasible to analytically solve
• Really unrealistic looking
Summary: Gravity-only model
• The only force on the projectile is gravity
• Only acts on the vertical (or the y) direction
• The motion in the three directions is independent.
• What happens in the y-direction , for example, does not effect the x- or z-directions
• The velocity in the x- and z-directions is constant throughout the trajectory
• The shape of the trajectory will always be a parabola
Aerodynamic Drag
• What is drag?
• The resistance that air or any other type of gas exerts on a body traveling through it.
• Drag directly resists velocity
• X, Y, and Z velocities
Drag: Overview
• Drag has two components
• Pressure drag: Caused by the differences in pressure between the front and back of the object
• Skin drag: As the projectile is moving through space, friction is created between it and the gas
Drag Coefficient
• The drag coefficient, Cd, is a scalar used to evaluate drag force.
• The shape of an object greatly affects how much drag affects it.
Exercise 2: Implementing Drag
• Examine the projectile class
• You will notice a function called “drag_model”
• This is where you will drag will be implemented
• You will also notice several data members in the class that are related to drag.
• Part of the drag_model function should look suspiciously familiar.
• Indeed, it is our favorite Runge-Kutta method!
• Or at least, a fragment of it…
Exercise 2: Implementing Drag
• The goal for this exercise is to finish the rest of the Runge-Kutta approximation of drag.
• The first step of runge-kutta is provided for you
• Here are some relevant equations:
• Fx = -Fd (vx/v) Fy = -mg -Fd (vy/v)
• Fz =- Fd (vz/v)
• The force due to drag is
• Fd = ½ p *v2 *A *Cd
• 0.5 * density * velocity2 * cross-area * drag coeff.
Exercise 2: Implementing Drag
• First , finish steps 2 through 4 of the Runge-Kuttaprocces
• Use step 1 and the equations as a reference
• Be careful! Because we have more than one velocity (as opposed to just x-velocity last time), you will have k’s for each component
• Don’t forget to average your k’s before you add it to the velocity, and update your position.
Summary: Aerodynamic Drag
• Drag force acts in the opposite direction to the velocity. The magnitude of the drag force is proportional to the square of the velocity
• Drag causes the three components of motion to become coupled (i.ex depends on y and z)
• The drag force is a function of the projectile geometry and is proportional to both the frontal area and drag coefficient of the projectile
Summary: Drag (end)
• The acceleration due to drag is inversely proportional to the mass of the projectile. Other things being equal, a heavier projectile will show fewer drag effects than a lighter projectile.
• The drag on an object is proportional to the density of the fluid in which it is traveling.
Getting Windy?
• Now that we have drag, it will be relatively easier to add wind into our simulation.
• The presence of wind changes the apparent velocity seen by a projectile
• Tail-wind adds to the velocity of the object.
• Head-wind subtracts from the velocity
Exercise 3: Wind
• Luckily for us, since we’ve implemented drag already, it will be easy to add wind.
• You may have already noticed a function, as well as parameters, hiding in the projectile class relating to wind.
• First of all, let’s keep all the work we did for drag. Go ahead and copy paste the contents of the function into the blank function “drag_wind_model”
Exercise 3: Wind
• Now, all we have to do is subtract the wind’s velocity components from each section of the Runge-Kutta steps
• Tail-winds will have negative velocity, thus increasing our end velocity
That’s all Folks!
• Save your finished product somewhere.
• Perchance commit it to a repository?
• You will be needing this for next week when we add on…
• Spin
• Different shaped objects
• Mystery?
(kind of) For next week…
• Plot the differences between the following combinations on a graph (position vs. time)
• Gravity only
• Gravity and drag
• Gravity and tail-wind