Physics Lends Plane Pull Challenge Participants a Hand

Think you can’t pull an 82-ton aircraft a dozen feet down a runway during Special Olympics Indiana’s annual Plane Pull Challenge?

Isaac Newton says you most certainly can.

Butler University professor Gonzalo Ordonez, the university’s department chair for physics and astronomy, said an average team of 15 people would need to exert about 184 pounds of force per person to get that big jetliner on the move.

“The jetliner is very heavy but is probably well-constructed to minimize forces such as friction and air resistance that hinder the plane’s motion,” Ordonez said. “The angle of the rope will play a role, but the estimation does say that the laws of physics can allow a team of people to pull a plane.”

Newton’s second law – force equals mass times acceleration – shows that a mass of 74,000 kg airplane must move at 0.165 meters per second to travel 12 feet in 6.66 seconds, which was the winning time in 2023.

Elite tug-of-war athletes have been shown to exert a pulling force of up to 183 percent of their body weight, so Ordonez said it is reasonable to think average adults can pull their own body weight.

For the kids’ pull, physics lends a hand because the required force is greatly reduced as acceleration rates drop. A group of 30 children taking 13.32 seconds to pull the plane the required length would need to exert an average of roughly 23 pounds of force.

“If the time is doubled, the required force actually drops by four times lower,” Ordonez said.

Registration is underway for the 2024 Plane Pull Challenge on Aug. 10 at the Indianapolis International Airport Postal Hub. Teams raise a minimum of $1,200 in pledges to take part.

Teams don’t need a lineup of beefy strongmen to compete for prizes and awards. A committed group that works in unison can accomplish great things together.

Then let Isaac Newton take care of the rest.

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Here are Ordonez’s calculations

• Mass (m) of the Boeing 757 jetliner: 82 tons or 74389.1 kg
• Distance (d) the plane is pulled: 12 feet or 3.66 m
• Time (t) to pull: The best time last year was 6.66 seconds

Average acceleration (a). When people are pulling the plane, the acceleration is not constant. However, one can estimate the average acceleration assuming the acceleration is constant. For constant acceleration, we can use the kinematic equation d = (1/2) a*t². Hence

• a = 2d/t² = 2*3.66 m/(6.66 sec)² = 0.165 m/s²

Average force (F). By Newton’s second law, F = ma, assuming the friction at the plane’s wheel bearings and air resistance are negligible. Hence:

• F = 74389.1 kg*0.165 m/s² = 12276 Newtons

Average force per person: Fp = F/N, where N=15 is the number of persons pulling. Hence:

• Fp =  15,000 Newtons/15 = 818 Newtons per person = 184 pounds per person.