I Rented A Helicopter To Settle A Physics Debate

A 2014 US Physics Team qualifying exam question asked which diagram best shows the shape of a flexible uniform cable suspended beneath a horizontally flying helicopter experiencing air friction.

• A: Hanging straight down • B: Hanging diagonally to the left • C: Hook shape • D: Inverted hook shape • E: S bend

There has been significant controversy about the correct answer to this question among physicists and students.

Veritasium rented a helicopter to conduct an actual experiment to settle the debate once and for all.

The pilot Craig has thousands of hours carrying sling loads, fire buckets, concrete buckets, and other objects that needed to be moved around mountains.

The main concern is that the rope could interact with the rotor wash, causing a whipping action that could potentially work its way back up towards the aircraft and get caught in the rotors or tail rotor.

Contact was made with Professor Paul Stanley, the question's author, who revealed that even faculty members and creative students who conducted their own experiments disagreed on the answer.

• Most YouTube viewers predicted C • Physics experts predicted B, C, D, and A • No one predicted E

A battle rope approximately 15 meters long and weighing 20 kilograms was deployed from the helicopter while flying horizontally.

The rope hung in a diagonal line to the left, clearly demonstrating answer B.

• Gravity pulling the rope downward • Air resistance acting to the left due to horizontal motion • These forces must be perfectly balanced by tension in the rope

The rotor wash does not extend far below the helicopter and dissipates quickly, so air resistance on the rope is entirely due to its motion through still air.

• Rope can be divided into many short sections of equal weight experiencing equal air resistance • Tension at any section must balance the sum of air resistance and weight of all sections beneath it • Tension is zero at the bottom and increases linearly to maximum at the top

Although tension magnitude changes throughout the rope, its direction remains constant because the ratio of air resistance to weight is the same at every point along the rope.

If the helicopter flies faster, the angle of the rope changes, but it still makes a diagonal straight line because the ratio of air resistance to weight remains constant along the entire length.

A uniform flexible cable hangs in a straight diagonal line when pulled at constant speed by a helicopter because both gravity and drag act uniformly along its length.

A 20-pound kettlebell (approximately 9 kilograms) was attached to the end of the rope for this experiment.

• Derek predicted option D • Others predicted B or C • One person predicted B after reconsidering

Flying at nearly 100 kilometers per hour, the rope made an inverted J shape, which is answer D.

With a large weight at the bottom, the tension must be nearly vertical to support the kettlebell. As you go up the rope, the ratio of total air resistance to weight increases, causing the rope to turn more horizontal to balance the increasing air resistance.

Professor Paul Stanley taught in Hong Kong and while hiking in the New Territories, he saw a helicopter flying with a cable carrying something to a remote area.

The cable Stanley observed had a weight hanging on the end, giving it a curved shape that looked counter-intuitive and interesting.

When Stanley shared the observation with fellow Physics Olympiad coach Andrew Linn, Linn suggested making the question even more challenging by removing the weight on the cable.

The question was designed to be thought-provoking for the US Physics Team selection exam because the answer without a weight is harder to imagine.

A Veritasium flag was attached to the end of the rope, adding significant air resistance but minimal weight.

The pilot noted this was a science experiment showing things you would never do in normal helicopter operations, with risks including getting caught in either the tail rotor or main rotor.

The rope remained relatively straight despite the flag attachment, suggesting the flag did not add enough drag to significantly change the shape.

Due to the unexpected result, the team decided to add a small parachute to the end of the rope to create more significant air resistance.

The parachute was bundled into a backpack to prevent it from flipping up into the rotors during deployment.

With the parachute at the end of the rope, it made a J shape, which is answer C.

With extra air resistance at the rope end but minimal weight, the tension must be nearly horizontal. As you go up the rope, the ratio of total air resistance to weight decreases, so the rope becomes more vertical to balance the increasing weight.

• Answer B occurs with an unweighted uniform rope • Answer C occurs with high air resistance and minimal weight • Answer D occurs with significant weight and moderate air resistance

Depending on what is attached to the end of the rope, the answer could be B, C, or D. The original physics exam question without any weight on the unweighted rope has answer B.

Hanging out the side of a helicopter was noted as not the safest moment, though Derek always feels safe at home.

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SimpliSafe sponsored the helicopter rental for this portion of the video. Visit simplisafe.com/veritasium to learn more and get at least 30% off the security system.