Projectile Motion of a Cylinder using HYPERWORKS

AIM: To simulate the projectile motion of a cylinder (diameter = 2m) in a 2D plane (XY) as per the figure shown below.

- Initial translation velocity about the center of mass = 10 m/s, Initial angular velocity about the center of mass = 10 rad/s.

- All physical attributes for the model must be automatically taken from the geometry

- Plot the Y displacement vs X displacement plot of P1 w.r.t the ground

- Plot the velocity (X component) vs time graph for the cylinder at the center of mass of the cylinder

- Time of simulation = 5 sec

- Also, explain how you set up the simulation and explain the results

- Unit of length should be in meters

GOVERNING EQUATION: `v = u - g . t` `s = u . t - 1/2 . g . t^2` `v^2 = u^2 - 2 . g . s` where; `u` = Initial velocity (m/sec) `v` = Final velocity (m/sec) `s` = Displacement (m) `g` = Acceleration due to gravity (m/s2) `t` = Time (sec)

Point O is called the point of projection; θ is the angle of projection and OB is Horizontal Range or Simply Range. The total time taken by the particle from reaching O to B is called the time of flight.

Total time of flight; `T = (2 . u . sin theta) / g`

Horizontal range; `R = (u^2 . sin 2 theta) / g`

Maximum height; `H_(max) = (u^2 . sin^2 theta) / (2 . g)`

Equation of trajectory; `x . tan theta - (g.x^2)/(2.u^2.cos^2theta)`

THEORY: A projectile is any object thrown into space upon which the only acting force is gravity. The primary force acting on a projectile is gravity. This doesn’t necessarily mean that other forces do not act on it, just that their effect is minimal compared to gravity. The path followed by a projectile is known as a trajectory. A baseball batted or thrown is an example of the projectile. When a particle is thrown obliquely near the earth’s surface, it moves along a curved path under constant acceleration that is directed towards the center of the earth (we assume that the particle remains close to the surface of the earth). The path of such a particle is called a projectile and the motion is called projectile motion. The trajectory of the projectile motion always has the shape of a parabola.

In a Projectile Motion, there are two simultaneous independent rectilinear motions:

- Along X-axis: uniform velocity, responsible for the horizontal (forward) motion of the particle.

- Along Y-axis: uniform acceleration, responsible for the vertical (downwards) motion of the particle.

Projectile motion is a form of motion experienced by an object or particle (a projectile) that is projected near the Earth's surface and moves along a curved path under the action of gravity only (in particular, the effects of air resistance are passive and assumed to be negligible).

SOLUTION:

Software: HyperWorks Desktop

STEP 1: Select MotionView from the list of the dialogue box.

STEP 2: Check whether the gravity effect is enabled and set it to -9.81 m/s2 (negative Y-direction).

STEP 3: Set up the units for simulation from millimeter to meter as directed in the question.

STEP 4: Select the Add Point option as shown and create Point 0 (0,0,0) and Point 1 (10,10,0).

The points are created in the graphic window as shown below. (Click on the screen and press F to fit the screen)

STEP 5: Select the Add Body option as shown and create Body 0 and Body 1. Also, tick the Get Properties from associated Graphic(s) to obtain meaningful mass and inertia values.

The bodies are created in the graphic window as shown below.

STEP 6: Select the Add Graphics option and add Cylinder 0.

From Connectivity, Cylinder 0 was given Body 0 as parent body with origin as Point 0 and direction as Point 1.

From Properties, the radius of the cylinder was set to 1m (since diameter = 2m)

STEP 7: Select the Graphic Entity Attributes option and tick Opaque - Transparent for better visibility.

STEP 8: Select the Add Marker option and add marker Marker 0. To do so on CG, first create a Point 2 on CG (i.e. (5,5,0))

STEP 9: Select Initial Coordinates and enter given values for translation velocity and rotational velocity as shown below.

STEP 10: Select the Add Output option and add Output 0 and Output 1.

Output 0 was selected as Displacement and given Body 1 as Body 0 and Body 2 as Ground Body with point on Body 1 being Point 1 and point on Body 2 being Global Origin. (as the trace of point 2 was to be plotted)

Output 1 was selected as Velocity and given Body 1 as Body 0 and Body 2 as Ground Body with point on Body 1 being Point 2 and point on Body 2 being Global Origin.

STEP 11: Go to the Run Solver option, set the simulation time as 5 sec. Save the model and then click Run.

STEP 12: The processor MotionSolve runs in the background as follows.

STEP 13: Click the Plot and Animate button and select appropriate parameters to visualize the graphs and simulation.

Output: The results are simulated using postprocessors HyperView (top right) and HyperGraph 2D (bottom) as shown below.

Plot #1: The plot for Y displacement vs X displacement of Point 1 (i.e. trace of Point 1) with respect to the ground is shown below.

Plot #2: The plot for Velocity (X component) vs time for the cylinder at the center of mass of the cylinder is shown below.

CONCLUSION: Thus, the projectile motion of a cylinder was simulated in HyperWorks.