How Tech Ticks
Math and melons
by Richard Lovegrove
Video by J. Scott Parker | Visual and Broadcast Communications
Imagine you're in the Middle Ages and preparing to lay siege to a castle that looks like, say, Burruss Hall. In that case, you'd want to employ a trebuchet, the more efficient and much more accurate cousin of the catapult. Until replaced by the cannon, the trebuchet was the most lethal weapon of its day.
Cadets Gabe Grewe and David Sinclair, along with 25 to 30 other members of the Virginia Tech chapter of the Society of American Military Engineers, aren't planning any sieges, but they have built a trebuchet for a competition Tech will host this fall. The team is hoping its machine can hurl a cantaloupe 500 feet while out-flinging a similar machine built by Virginia Military Institute cadets (and possibly one by Old Dominion University students).
• Lessons learned from the 2014 competition with VMI
• • One of the three most-important moments during a throw, according to cadets
• • • A note on efficiency
From the side of the trebuchet, a cadet pulls the firing pin, setting the entire system in motion.
The frame: The frame is 10 feet tall and 8 feet wide.
• Use 4x4s instead of 2x4s in high-stress areas to resist warping.
• Use a tongue-and-groove system on the horizontal plane so that the wheels glide smoothly.
The counterweights: The students cast 40- and 60-pound concrete disks. Although competition rules allow for a total of 300 pounds, the cadets' latest machine achieved 450 feet with just 200 pounds of counterweight.
The axle: The pivot axle slides back and forth horizontally, allowing the counterweight to fall straight down. As a result, the counterweight's vertical force remains true with gravity, yielding a theoretical maximum downward force.
• • The axle that holds the counterweights travels along a vertical path that must be narrow enough to guide the bar down, but not so tight that it causes undue friction and saps efficiency.
• • The wheels must hit the horizontal track at exactly the right spot to roll straight. In addition, both the wheels and the axle must be strong enough to withstand the forces without bending. Test-firing revealed the need to strengthen the axle even more.
The throwing arm: About twice the length of the short end, the long end moves at about twice the speed. As the beam rotates due to the falling counterweight, centripetal acceleration causes the payload to move outward. In the second half of the drop, the pivot axle passes over the counterweight, bringing the end of the arm and the attached sling over the top.
• • • Achieving the longest melon toss is somewhat counterintuitive. The acceleration of gravity can be amplified by using a 5:1 ratio of arm length—the long arm at 10 feet and the short arm at two feet—leading to a velocity five times greater at the long arm's tip, but then the counterweight drops a shorter distance. A long/short ratio of 2:1 greatly increases the drop distance and the power generated, even though the acceleration amplification of gravity is reduced.
The sling: The sling acts as a second fulcrum so that the projectile, moving both with the arm and rotating around it, ends up moving at up to twice the arm's speed.
• Use a resistant material for the sling pouch so that the melon will stay inside the pouch as force increases.
• • The pin or "finger" holding the ring onto one end of the sling must release at about 45 degrees—known as the sling stall point—right when the long end of the arm is at 90 to 100 degrees. The team has to adjust the sling length and the bend in the pin to get the right angle to take full advantage of centripetal acceleration.
The ammo: In April, cadets conducted test-firing with 4-pound cantaloupes and watermelons.
Richard Lovegrove is an editor with the marketing and publications unit.