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Old Mar 12th 2018, 01:55 PM   #1
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How to find terminal velocity

DISCLAIMER: I am new to this forum so I am not entirely sure of how to layout and where to post, my post.

I am trying to get some physics in a program I am working on, and I want to know how to find the terminal velocity of a perfect sphere in air on Earth. The ball, perfect sphere, has a radius of 4cm (metric system). My code is this:

/*
Ball Physics

Ball has radius of 4cm
*/

PVector position;
float velocity = 0; // Velocity
float gravity = 9.80665; // Standard gravity
float airDensity = 0.001225; // In grams/cm^3


float mass = 75; // In grams
float radius = 4; // In cm's
float dragCoefficient = 0.47; // For perfect sphere in air

float volume = (4/3)*PI*(radius*radius*radius); // In cm^3
float density = mass/volume; // In grams/cm^3
float projectedArea = PI*radius*radius; // In cm^2

float terminalVelocity = sqrt((2*mass*gravity)/(density*projectedArea*dragCoefficient)); // Terminal velocity

NOTE: You don't really have to understand every bit of the code, but just by reading it you should hopefully understand what it's doing.

The terminalVelocity at the end is sqrt((2*75*9.8)/(0.001225*48*0.47)) which is 225.45198

I got 225.45198 as the terminal velocity is this correct? If not, what went wrong? Also what would it be measured in, in this case? m/s etc.:.

Thanks so much!
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Old Mar 12th 2018, 10:46 PM   #2
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Posts: 401
Here's the equation for drag on the falling sphere ..D = Cd * .5 * density * V^2 * A

Cd is the drag coeff ..... V is velocity ........ A is area of sphere = pie r squared (r=4)

Cd =0.47 (dimensionless )

density (air) =1.225 kg/m2

A= 0.005026 m2...

D= 0.47 * 0.5 * 1.225 * 0.005026 * (V squared)..... = 0.001447 * (V squared)

At terminal velocity D =mg = 0.075 * 9.80665 = 0.7355

0.7355 = .001447 * (V squared) V = 22.54m/sec

The density I calculate for the 4cm sphere is 0.28 .... not very dense , so 22.54 m/sec (50 MPH) sounds about right
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Old Mar 13th 2018, 04:26 AM   #3
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Join Date: Oct 2017
Location: Glasgow
Posts: 249
Originally Posted by MathGuy View Post
DISCLAIMER: I am new to this forum so I am not entirely sure of how to layout and where to post, my post.

I am trying to get some physics in a program I am working on, and I want to know how to find the terminal velocity of a perfect sphere in air on Earth. The ball, perfect sphere, has a radius of 4cm (metric system). My code is this:

/*
Ball Physics

Ball has radius of 4cm
*/

PVector position;
float velocity = 0; // Velocity
float gravity = 9.80665; // Standard gravity
float airDensity = 0.001225; // In grams/cm^3


float mass = 75; // In grams
float radius = 4; // In cm's
float dragCoefficient = 0.47; // For perfect sphere in air

float volume = (4/3)*PI*(radius*radius*radius); // In cm^3
float density = mass/volume; // In grams/cm^3
float projectedArea = PI*radius*radius; // In cm^2

float terminalVelocity = sqrt((2*mass*gravity)/(density*projectedArea*dragCoefficient)); // Terminal velocity

NOTE: You don't really have to understand every bit of the code, but just by reading it you should hopefully understand what it's doing.

The terminalVelocity at the end is sqrt((2*75*9.8)/(0.001225*48*0.47)) which is 225.45198

I got 225.45198 as the terminal velocity is this correct? If not, what went wrong? Also what would it be measured in, in this case? m/s etc.:.

Thanks so much!
You need to convert to SI units first. This makes sense, since you're using g = 9.81 m/s$\displaystyle ^2$, not g = 0.0981 cm/s$\displaystyle ^2$.

I get v = 1.4921 m/s by plugging values into that equation with SI units.
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