The Trajectory Event Teams will design, construct, and calibrate a device capable of launching a projectile into a target area and collect data to develop a series of graphs relating launch configuration to target distance and height.
Rules Read the rules Discuss the rules Read the rules Copy the rules Have the students copy the rules Read the rules again Highlight the rules Understand the rules
Rules Event Parameters Team size, Max of two (2) Must wear eye protection. (ANSI Z87+) Impound event (What does this mean?) The launch device, graphs, and all materials teams will use must be impounded (checked in at the event) prior to the competition. After all devices are impounded the target distance and heights will be announced.
Design Construction The Launching force MUST be supplied by non-metallic elastic solids. (rubber, wood, plastic, bungee cords, rubber tubing, etc.) Size: everything must fit inside a cube Division B – 70cm cube Division C – 60cm cube
Design Construction Triggering device is not part of the device: It may be Battery It may not be radio controlled It may not pose a danger
Construction Trigger This can be simple or complex Arrow Release Pelican Hook Panic Snap
Construction Trigger You can use eye hooks and a cotter pin You can use screen door hooks that have been altered.
Design Construction Teams will provide unmodified projectile.
Projectile Tennis Balls Racquetballs Ping-pong balls Practice Golf Balls
Video Catapult in action: http://www.sciencenc.com/Tournament_inf ormation/Event_rules_nc/Trajectory.cfm
Catapult Science Math behind the event: http://www.open2.net/diyscience/mangonel/ catapult_download.pdf http://www.open2.net/diyscience/mangonel/ catapult_download.pdf
Catapult Science We must calculate the Force (N) exerted by the throwing arm. To do this we need to know the velocity at take off calculated in meters per second (m/s) We also must work out how fast the arm accelerates. Acceleration describes changes in velocity (m/s 2 ). The force comes from the elastic bands attached to the arm.
If we know how long it takes to go from take off to landing we know it takes gravity X seconds to slow from take off speed to 0. Gravity will accelerate any object at 9.8 meters per second per second. Now we want to figure the Vertical Velocity. Catapult Science
Vertical Velocity V v = The final component of velocity in the vertical direction = 0 U v =The initial component of velocity in the vertical direction= (This is what we are looking for) A v =The component of acceleration in the verticle direction (-gravity) T = time taken Catapult Science
So our formula is: Vv = Uv + AvT We know Vv is 0, we are going to assume the time (T) is 1.6 seconds Therefore: 0 = Uv + (9.8 X 1.6) solve this equation and we have Uv = 15.7 meters/second This is our Vertical Velocity we will use it again later. Catapult Science
Ok, so the projectile does not just go up and down. We must look at Horizontal Velocity There is a component of velocity Vx in the horizontal direction. This is because they take off at angle theta (Θ) not vertically Since V y and V x can be treated as vector quantities the velocity of take off can be calculated from trigonometry. Catapult Science
Vt = Velocity (this is what we are looking for) It will be the hypotenuse of this triangle. Vy = Vertical Velocity (15.7 m/s) sin = sine – ratio of the height to the hypotenuse. Θ = theta – symbol to describe how big the angle is in degrees. Catapult Science
So our formula is: Vt = Vy /sin Θ We need to know what the angle is The distance the projectile travels depends upon the point it leaves the arm. If the angle of trajectory is Θ to horizontal then the projectile travels 90 – Θ when being thrown. Catapult Science
The circumference of a circle is 2pr In our case, r is the length of the throwing arm. We will estimate 50 cm. So if the arm traveled a full circle it would travel (2 X 22/7 X 50)cm or 314.3 cm So 90 – Θ means our arm moves 314.3(90- Θ)/360 cm. (assume 45 ) The arm must travel 39.3 cm. Catapult Science
The load needs to leave the arm before it reaches 90 or there is no vertical velocity. (the force of the arm drops off) You probably will max out at 70 . We used 45 . We will work from here. So Velocity V is 15.7 / sin45 = 22.2 m/s Catapult Science
We now know how much the arm accelerates with a final velocity Vf = 22.2 m/s. We will use this to calculate the forces. V 2 = U 2 + 2as V = final velocity (22.2) U = initial velocity (0) a = acceleration (what we are solving for) s = speed assuming constant acceleration over the distance moved we calculated the distance moved as 314.3 X 45 / 360 = (39.3 cm) Catapult Science
V 2 = U 2 + 2as 22.2 2 = 0 + 2 X a X 39.3 a = 22.2 2 / 78.6 a = 6.27 m/s 2 Catapult Science
To work out the forces we will use Newton’s First Law. F = ma F stands for the net force m is the mass of the projectile a is acceleration Catapult Science
If the mass of a racquet ball is 39.7 grams And our acceleration is 6.27 m/s 2 F = 39.7 X 6.27 F=.2489 Newtons (Km/s 2 ) If you use this much force and the ball stays in the air 1.6 seconds the ball should travel over 35 meters (115 feet). Catapult Science
Target Area Two target areas will be placed in front of the launch area centered on an imaginary line that bisects it.
Target Area The nearest target will be elevated above the floor, up to 1m for Div. B; up to 2m for Div. C in 1 cm intervals, measured from the floor to the top surface of the impact area. The furthest target shall be at floor level.
Target Area The targets will be either circle (1 meter in diameter) or square (1 meter on each side) with a rim no higher than 3cm.
Target Area The impact area will contain sand or cat litter ~1cm deep. Projectile impact location
Target Area The center of the areas will be marked so that the distance between them and the center of the initial projectile impact location ma be measured.
Scoring The winner will be the team with the lowest Final Score. To get the score you add: Lower Close Target Area score + Lower Far Target Area score – Graph Score + Penalties – Bucket Shot Deductions = Final Score
Scoring Teams will be ranked in tiers based upon; Devices meeting all specifications (Tier 1) Devices not meeting all specifications (Tier 2) Tiebreakers are: 1 st Lower total of the sum of the two scored shots (to reward consistency). 2 nd closest shot overall 3 rd non-scored shot at the far target 4 th non-scored shot at the far target
Scoring Scoring the toss (Students must indicate which target they are aiming to hit.) The close target area score shall be the distance in mm from the center of the initial projectile impact location to the center of the target area. (outside the target area or failure to launch scores 800 mm.) The far target area score shall be the measured similarly but measured to the impact location if outside the target area. (failure to launch measures from the front of the launch area to the center of the far target in mm.)
Scoring If you hit the target!!! (on the first attempt) A bucket shot may be requested. A 1-5 gallon bucket will be placed on the course. Hit the bucket but not staying in is a 50 pt. deduction. Hit and stay in the bucket is worth an additional 100 deduction points. Teams with bucket shot attempts will not have a third and/of fourth tie breaker and are scored behind those that do.
Penalties Ouch! A 100 point penalty will be added each time any of the following occurs: Not wearing eye protection Is in or in front of the launch area (when a launch occurs) Does not give a warning prior to launch (Fire in the Hole!!!!!) Any part of the device is outside the launch area.
Collect Data The purpose of data collection is to provide students with an understanding of test and result. Determine what data you can collect Distance thrown Length of action Number of bands Etc.
Graphs Each team starts out with 400 graph points These can be reduced by turning in four different graphs and data tables. Each of the 4 selected graphs may reduce the Graph Score by 100 points.
Graphs Any number of graphs can be impounded but the students must indicate which four will be used to determine the graph score. Graphs: Computer or hand drawn Graph/table together on a single (same) side of paper Labeled All variables Units identified Team name
Graphs One of the four graphs, Selected by the event supervisor, will be scored as follows: 20 point reduction for completed data table 20 point reduction for graph 20 point reduction if graph matches data table and is on the same side of the page 40 point reduction for proper labeling Title Team name X & Y axis variables Increments with units The score of the scored graph will be multiplied by the number of graphs turned in (up to 4).
Construction Measure carefully Use smooth action on the moving parts. Attach your elastic solids for force securely. Some rubber will wear with use. Be sure you calculate wear as you practice. Weight is not an issue. Metal angles will work in many cases.
Construction Make sure your boards and angles are square and tight. Be sure the projectile holder does not restrict the release of the projectile. Use plywood for stability Use solid construction with screws and or nails Hands on Review of Catapults.
Instructor Jim Roberts firstname.lastname@example.org Worked with Science Olympiad since 1998.