[Physics] Calculate a drag force on a sphere

dragforces

Objective

Work out a drag force for a unit sphere traveling through air at velocity. Values for formulae are below. The context of this question is that I am calculating this in an atmospheric environment. So the values provided are for air.

Information

Through my research I have come across the following information.

Data

NAME UNIT

Gravity = 9.80665 m/s/s
AirMassDensity = 1.204 kg/m^3
SphereRadius = 0.5 m
Velocity = 2 m/s

Formulae

Drag Coefficient: c = 2F \ p * (v * v) * A
Source: http://en.wikipedia.org/wiki/Drag_coefficient#Definition
Where:
c is the coefficient.
F is the drag force.
p is the density of the fluid/gas.
v is the relative velocity.
A is the reference area of the object.

Problem(s)

A) I don't know what F is in the Drag Coefficient formula. So I would be interested in finding this out, as I do not understand the description given.
B) I could calculate F if c is known, but c is also unknown.
C) As per this http://en.wikipedia.org/wiki/Drag_coefficient (at the bottom) it says that for some shapes, such as spheres, c is solely dependent on the Reynold's Number. It doesn't really go on to explain how and how I could calculate it for use in the Drag Coefficient equation.
D) Is this the correct way to do it, or am I way off? 🙂

Help/corrections appreciated as I'm stuck at this point unfortunately.

Misc Info

I'm basically wiring up my own physics simulation in a video game that I am programming for, and am doing this just to learn a little bit more about how forces interact, and advance my mathematics skills. One problem I have come across whilst learning complex things via online, is that often I am unsure what the question is I need to ask. I almost need to understand how physics works before I can ask a physics-related question. So forgive me if my terminology is incorrect, and I am very interested in any corrections to my understanding of the material thus far. Thanks!

Best Answer

OK so after some reading and research I have answered my question with the following - pseudo-code incoming:

// PHASE 1 - GRAVITY FOR THIS OBJECT
position = 0, 0, 0
mass = 1
gravity = 9.80665
fGrav = mass * gravity

// PHASE 2 - DRAG FOR THIS OBJECT
velocity = 0 // Object starts from rest
area = PI * (radius * radius)
airMassDensity = 1.204

dragForce = 0.5f * 0.47 * airMassDensity * Dot(velocity, velocity) * area
fDrag = -velocity.normalized * dragForce

// PHASE 3 - ACCUMULATE FORCES (TO BE USED IN CHANGE IN VELOCITY)
forces = fGrav + fDrag;

// PHASE 4 - UPDATE VELOCITY (TO BE USED IN CHANGE IN POSITION)
position += forces * timeDelta

In regards to my questions about calculating c which is the drag coefficient, that involved being a case of using some pre-calculated values, which for a sphere are readily available. I still wish to know how to calculate it for an object, but a lot of replies I got from people indicated its a pretty decent sized subject, and I would be well-advised to use those values available for things. Hope this helps someone in the future!

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