Physics final project

Anagha Sudhindra

Mission impossible: Rogue Nation

Field agent Ethan Hunt is attempting to single-handedly hijack a plane. With a running start, he leaps onto a taxiing Airbus A400M and hangs onto a protrusion on the side. As the plane starts its ascent, will Hunt be able to hang on?

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Airbus a400m

A400M Stats

For calculating net force

For calculating net force

For calculating thrust force

For calculating thrust force

Mass

Engine Power

Acceleration

Take off Velocity

*all obtained from online sources

115212 kg

1.47 m/s²

61.3 m/s

8200 kw

Forces

Calculating the forces

F_Net

m (mass) x a (acceleration) = F_Net

115212 x 0.15(9.8) = 169361.64 N

F_Thrust

P (power) / v (velocity) = F_Thrust

8200000 / 61.3 = 133768.3 N

F_Drag

F_Net - F_Thrust = F_Drag

169361.64 - 133768.3 = 35593.64 N

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Now that we know all the forces acting on the aircraft, we can analyze forces acting on Hunt.

Net force:

𝐹_Net=m a

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Ethan Hunt Stats

Hunt and aircraft are pretty much the same body, accelerating at the same rate.

Newton’s second law

Mass

Acceleration

*all obtained from online sources

68 kg

1.47 m/s²

𝐹_Net=m a

F_Net = 68 x 1.47

99.96 N Net Force

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F_Net = F_f - F_Drag

Drag force:

𝐹_D=1/2𝐶𝜌𝐴𝑣²

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Drag force Stats

For calculating F_D

For calculating net force

For calculating drag force

Density of air

Drag coefficient

Take off Velocity

1.225 kg/m³

0.9

61.3 m/s

Drag force Stats

Area of Hunt “in contact” with the air. Head, shoulders, arms, back. Surface area of average male on all those body parts.

Area

1.8 m²

𝐹_D=1/2𝐶𝜌𝐴𝑣²

F_D = .5 x .9 x 1.255 x 1.8 x 61.3²

3728.56 N Drag Force

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Hunt’s frictional force must ≥ drag force (air resistance) he faces on the exterior of the aircraft + net force.

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F_Drag = 3728.56 N

F_Net = 99.96

F_f ≥ 3828.52

Frictional force:

𝐹_f=𝐹_N x μ

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Ethan Hunt Stats

The exterior of aircrafts is a layer of aluminum alloy. Hunt’s is hanging on by his bare skin. This is the coefficient of static friction between skin and aluminum.

This force replaces the role of a typical normal force in this scenario. F_Normal is contact force, grip strength is the magnitude of contact. This value is the average max grip strength of an adult male.

Grip Strength

Frictional Coefficient

*all obtained from online sources

517 N

0.6

Calculating the forces

F_Normal x μ = F_f

517 x 0.6 = 310 N

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F_f = 310 N ＜ 3828.52 N

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Though Ethan Hunt has accomplished tons of crazy missions, it seems this one was truly impossible.

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• Air & wind pressure would compromise breathing
• Lack of oxygen as aircraft ascends
• Sound, heat of propeller

• This stunt was accomplished with the use of a harness

Thank you!

“A400M (Future Large Aircraft) Military Transport Aircraft.” Airforce Technology, 28 Apr. 2022, www.airforce-technology.com/projects/fla/.

Airbus A400M - Military Analizer, militaryanalizer.com/airbus-a400m/. Accessed 22 May 2023.

“Aircraft Performance Database.” Aircraft Performance Database, contentzone.eurocontrol.int/aircraftperformance/details.aspx?ICAO=A400. Accessed 21 May 2023.

Man, George, and Mao-Qiang Man. “Skin Friction Coefficient.” SpringerLink, 1 Jan. 1970, link.springer.com/referenceworkentry/10.1007/978-3-319-32383-1_20#:~:text=The%20skin%20friction%20coefficient%20on,(Seo%20and%20Armstrong%202009).

“Mission: Impossible - Rogue Nation (2015) - Ethan Catches a Plane Scene (1/10) | Movieclips.” YouTube, 23 July 2018, www.youtube.com/watch?v=elpUGB9Ap1Y.

“Tom Cruise Height, Weight, Age, Biography, Wife & More " Starsunfolded.” StarsUnfolded, starsunfolded.com/tom-cruise/. Accessed 22 May 2023.

Williams, Wayne. “World’s Strongest Bionic Hands.” Bionics For Everyone, 25 Mar. 2022, bionicsforeveryone.com/worlds-strongest-bionic-hands/#:~:text=The%20average%20maximum%20grip%20force%20for%20males%20is%20517%20Newtons,daily%20activities%20is%2070%20Newtons.