Chapter 4

Falling Bodies - a Calculator for the Viewer

There are four topics. The common thread is vertical motion in atmosphere.

In the first topic the differential equation for a falling body, taking into account gravity and atmospheric resistance, is presented. When resistance is proportional to velocity squared there is no analytical solution.

The second topic explores a method for the numerical solution of non-linear differential equations, on the Differential Analyzer. This method was published in 1931 by Vannevar Bush. A spreadsheet that the user may construct for modeling the fall of a body in atmosphere is introduced.

The third topic introduces and makes available a corresponding web-based calculator.

In the fourth topic the user is guided through the exploration of several applications of the calculator.

The topics of this chapter can be accessed by clicking their names.

Topic Name An Image from the Topic Brief Description
Falling Bodies in a Fluid or Gas Part A - Gravity - Fluid Mechanics - Aerodynamics - Differential Equations Aristotle




Lord Rayleigh
Falling Bodies in a Fluid or Gas Part B - Numerical Solution of Differential Equations for Falling Bodies Non-Linear Solution Method due to V. Bush - A Spreadsheet Version - Toy Balloons Falling in Air
An Interactive Spreadsheet Emulator for Solutions of a Differential Equation for Bodies Falling in Air Shape

Step Size

Reynolds Number


Input Errors
Using the Spreadsheet Emulator - Calculator for the Solution of a Differential Equation for Bodies Falling in Air  Falling of Rain and Hail

Clouds of Fog

The Tower of Pisa Revisited
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