The Guy Who Jumped Without Parachute Calculations

When a person jumps from a great height without a parachute, the physics of free-fall and terminal velocity determine the outcome. This calculator helps you understand the key factors involved in such a scenario, including terminal velocity, distance fallen, and time to impact.

Introduction

Jumping without a parachute from a significant height is a dangerous scenario that involves complex physics. The human body experiences extreme forces during free-fall, and understanding these factors can help in emergency situations or safety planning.

Key factors in this calculation include:

Terminal velocity: The constant speed reached when air resistance equals gravitational force
Free-fall distance: How far the person falls before reaching terminal velocity
Time to impact: How long the fall lasts

This calculator provides estimates based on standard assumptions about human physiology and environmental conditions.

Terminal Velocity

Terminal velocity is the constant speed reached when the force of air resistance equals the force of gravity. For a typical person, this occurs when the body is in a spread-eagle position with arms and legs extended.

Terminal Velocity Formula:

v = √(2mg/ρAC_d)

Where:

v = terminal velocity (m/s)
m = mass of the person (kg)
g = acceleration due to gravity (9.81 m/s²)
ρ = air density (kg/m³)
A = projected area (m²)
C_d = drag coefficient (dimensionless)

The drag coefficient for a human in a spread-eagle position is typically around 1.2.

Free-Fall Distance

The distance fallen before reaching terminal velocity depends on the initial height and the time it takes to reach terminal velocity.

Free-Fall Distance Formula:

d = (v² - u²) / (2g)

Where:

d = distance fallen (m)
v = terminal velocity (m/s)
u = initial velocity (typically 0 m/s)
g = acceleration due to gravity (9.81 m/s²)

This distance is significant because it determines how much time the person has to deploy a parachute if available.

Time to Impact

The total time from jump to impact depends on both the free-fall phase and the terminal velocity phase.

Time to Impact Formula:

t = (v/g) + √(2h/g)

Where:

t = total time to impact (s)
v = terminal velocity (m/s)
g = acceleration due to gravity (9.81 m/s²)
h = initial height (m)

This calculation helps understand how quickly the fall occurs and the urgency of any rescue operation.

Real-World Example

Consider a person jumping from a height of 1000 meters (3281 feet) without a parachute. Using standard assumptions:

Mass: 70 kg
Projected area: 0.7 m²
Drag coefficient: 1.2
Air density: 1.225 kg/m³

Calculating these values would show:

Terminal velocity: approximately 53 m/s (190 km/h)
Free-fall distance: about 120 meters
Total time to impact: around 20 seconds

This example demonstrates the extreme nature of such a fall and the importance of understanding these physics principles.

FAQ

What factors affect terminal velocity?: Terminal velocity depends on body position, mass, air density, and the drag coefficient. A spread-eagle position typically results in the highest terminal velocity.
How accurate are these calculations?: These calculations provide estimates based on standard assumptions. Real-world conditions may vary due to factors like wind, body composition, and equipment.
Can a person survive a fall without a parachute?: Survival is extremely unlikely due to the extreme forces involved. Even with a parachute, survival depends on many factors including the impact force and medical condition.
What is the highest recorded terminal velocity for a human?: The highest recorded terminal velocity for a human is approximately 54 m/s (194 km/h), achieved by Felix Baumgartner during his record-setting jump from the edge of space.
How can I prepare for a high-altitude jump?: Proper training, equipment, and understanding of the physics involved are essential. Always follow safety protocols and never attempt such jumps without professional supervision.