a pumpkin in flight eric lehnhardt & wade gyllenhaal honors project, physics 121
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A Pumpkin in Flight
Eric Lehnhardt & Wade Gyllenhaal
Honors Project, Physics 121
The Punkin’ Chunkin’The Punkin’ Chunkin’ Delaware countryside
First weekend in November Post Halloween
Kid’s Division, Adult’s Trebuchet
and Adult’s Cannon Divisions
www.punkinchunkin.com
Air CannonsAir Cannons Highest-achieving
Weight in excess of 14 tons
Barrels of varying length World-Record Holder
“Second Amendment” has barrel length of approx 100 feet, or 30 meters
AnalysisAnalysis
AnalysisAnalysis
Excel SheetExcel Sheet Frame by frame analysis
Use of t-Step
Use of variables Determine key variables like mass, density,
coefficient of drag, and velocity
A Pumpkin in Flight/Pumpkin Motion V3.xls
ProblemsProblems Error in sign
Use of sine and cosine functions became tricky once the pumpkin moved past its apex
Substitution of (v_x/v) and (v_y/v)
Proper range t-step size (0.2 to 0.01s added 200m of distance) Drag coefficient (0.44 for spheres, but pumpkin has ridges,
similar to golf balls and their dimples) Density of pumpkin (varieties, gourds)
Too many variables
Likely SolutionsLikely Solutions Aimed for Second Amendment record of 1,366
meters Known initial velocity of 500mph ≈ 203 m/s
Case One – small drag coefficient C_d = 0.2 M = 10 kg R= 0.15 m
This pumpkin has the dimensions and density of a typical store-bought pumpkin, such as used for jack-o-lanterns (verified at the local Safeway’s)
Likely SolutionsLikely Solutions Case Two – adjusted sphere drag coefficient
C_d = 0.3 M= 15 kg R = 0.15 m This pumpkin is denser than average (it
weighs close to 35 pounds) and may more likely be a gourd or “white pumpkin”
Likely SolutionsLikely Solutions Case Three – sphere drag coefficient
C_d = 0.44 M = 23 kg R = 0.15 m This pumpkin is very dense (weighing
approximately 50 pounds) and begins to approximate a cannonball
Forces on PumpkinForces on Pumpkin
Things to ConsiderThings to Consider Possible tail winds
Initial height of the cannon
Elevation change in the testing field
Density of air in Delaware (elevation, temperature)
Magnus Effect
