Man on a Missile

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How much force can the body withstand upon impact?

Big Ideas: 
  • Average net force can be found from average acceleration using Newton's second law.
  • Peak acceleration is different from average acceleration.
  • Expressing acceleration in terms of g allows for a comparison of forces experienced to the force of gravity.

In the 1940s and 1950s, with the advance in speed of airplanes, the need arose to define the limits of human survivability and to develop the equipment needed to prevent death upon ejection or impact. A colonel in the US military, Colonel John Stapp was a pioneering researcher in this area, performing much of the research on his own body! One experiment he performed involved travelling approximately 1000 km/h on a rocket sled specially designed to come to an abrupt stop in 1.4 sec1. What was the net force on Col. Stapp upon impact?

His average acceleration, experienced in a time Δ t = 1.4 s with inital velocity vi = 1000 km/h (278 m/s) and final velocity vf = 0 m/s, was

$ a = \dfrac{v_f - v_i}{\Delta t} = -198 \textnormal{ m/s}^2  $

Note that because the acceleration calculated is in the direction opposite to the motion he decelerated at 198 m/s2. Using Newton's second law, the net average force experienced by Col. Stapp who had a mass of 75 kg was

$ F_{net} = ma = (75 \textnormal{ kg})(-198 \textnormal{ m/s}^2) = - 1.5 \times 10^4 \textnormal{ N} $

This is the force that the harness exerted on Col. Stapp, opposite to the direction of motion. 

The force you feel due to gravity, your weight,  is w = mg where m is your mass in kg and g = 9.8 m/s2 is the acceleration due gravity.   Acceleration is frequently expressed in terms of g's to give a comparison with the force felt due to gravity.  A typical deceleration you may experience while you are standing on a bus is around 0.5 g. The average deceleration experienced by Colonel Stapp then was 20.2 g !

We calculated the average deceleration experienced by Colonel Stapp. His deceleration was not constant while he was coming to a stop and it was measured that he experienced a peak deceleration of 46 g. At the time it was considered that 18 g was the maximum deceleration a human could withstand1. Colonel Stapp survived far beyond this, although he did experience physical injuries and temporary blindness due to the blood pooling in his eyes bursting the blood vessels in his eye1.

Safety note! :
Colonel Stapp survived because he was wearing a strong and specially designed harness to distribute the force of impact over his body and additionally had no windshield/dashboard to hit.  Colonel Stapp went on to play a prominent role in car safety conferences and the establishment of seatbelts being mandatory in cars which are meant for much smaller impacts. 2

Interpretation:

Newton's second law allows us to calculate the force on an object subject to a certain acceleration. The force sustained by Colonel Stapp due to the deceleration he withstood was tremendous, though special precautions and equipment are needed to survive such an impact.

Picture taken from2.

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