# Lab 6: Projectiles

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24-Feb-2016Category

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### Transcript of Lab 6: Projectiles

Lab 6: Projectiles

Lab 6: ProjectilesCS 282Review of projectile physicsExamine gravity projectile modelExamine drag forcesSimulate drag on a projectileExamine wind forcesSimulate wind affecting a projectileOverview

AccelerationF = ma

Translational velocity and statedv/dt = a , ds/dt = v

Rotational accelerationtorque = inertia * rotational_acceleration

Equations of motion are separated into directional componentsGeneral Concepts

Lets use Cartesian Coordinates for simplicityReference Frame

Fx = 0Fy = -mgFz = 0

Gravity-Only Projectile Model

vx = vx0vy = vy0 gtvz = vz0

ax = 0ay = gaz = 0

Please sit next to your partner (if possible)

Download the framework code for todayAvailable on the class website

Examine the projectile classLook at the gravity_model function!!!! Fill in the missing update y-position !!!!

Compile and runIf necessary, WASD2X translates the camera (use at your own risk though )ENTER toggles the simulation ON/OFF

Exercise 1: Setting UpHopefully, you have come up with something like (without cheating) thisposition.y + vy *dt+ 0.5*g*dt2

For this lab, lets just assume theres a golf club (or something) is hitting that projectile

So, Gravity-Only models areReally easy to implementFeasible to analytically solveReally unrealistic looking

Exercise 1: Setting UpThe only force on the projectile is gravityOnly acts on the vertical (or the y) directionThe motion in the three directions is independent. What happens in the y-direction , for example, does not effect the x- or z-directionsThe velocity in the x- and z-directions is constant throughout the trajectoryThe shape of the trajectory will always be a parabolaSummary: Gravity-only modelLets Spice Things Up!

What is drag?The resistance that air or any other type of gas exerts on a body traveling through it.Drag directly resists velocityX, Y, and Z velocitiesAerodynamic Drag

Drag has two componentsPressure drag: Caused by the differences in pressure between the front and back of the objectSkin drag: As the projectile is moving through space, friction is created between it and the gas

Drag: Overview

The drag coefficient, Cd, is a scalar used to evaluate drag force.The shape of an object greatly affects how much drag affects it.Drag Coefficient

Examine the projectile classYou will notice a function called drag_modelThis is where you will drag will be implementedYou 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 DragThe 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 isFd = p *v2 *A *Cd0.5 * density * velocity2 * cross-area * drag coeff.

Exercise 2: Implementing DragFirst , finish steps 2 through 4 of the Runge-Kutta proccesUse 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 ks for each component

Dont forget to average your ks before you add it to the velocity, and update your position.Exercise 2: Implementing DragDrag 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.e x 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: Aerodynamic DragThe 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.Summary: Drag (end)And like Renos Weather

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 projectileGetting Windy?

Tail-wind adds to the velocity of the object.Head-wind subtracts from the velocity Luckily for us, since weve 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, lets keep all the work we did for drag. Go ahead and copy paste the contents of the function into the blank function drag_wind_modelExercise 3: WindNow, all we have to do is subtract the winds velocity components from each section of the Runge-Kutta steps

Tail-winds will have negative velocity, thus increasing our end velocity

The reverse for head-windsExercise 3: WindSave your finished product somewhere.Perchance commit it to a repository?

You will be needing this for next week when we add onSpinDifferent shaped objectsMystery?Thats all Folks!

Plot the differences between the following combinations on a graph (position vs. time)Gravity onlyGravity and dragGravity and tail-windGravity, head-wind, and drag

Not due next week, but you will be adding more things to your simulation, so having this done will lesson your workload next week.

(kind of) For next week

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