# 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!

• There's so much more to this than you think, like if the ball starts rolling it really is more of a fluid simulation topic. If it's a real-time simulation for use in say a game (where accuracy isn't hugely important) usually you have a wind force, and some drag that will act proportionally to either velocity squared (REMEMBER to take into account the direction when you square!) or just the velocity Commented Jan 2, 2015 at 13:54
• If you take a look at the first half of this answer, you can see the formula being used in practice. Commented Jan 2, 2015 at 14:02
• Thanks for the input, I am still investigating this and reading other answers. Commented Jan 2, 2015 at 15:25

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!

• The final part is incorrect. F=m*a (Newton) with what a=F/m, so acceleration = forces / mass, considering acceleration constant (from one frame to another, small time delta) velocity = velocity0 + acceleration * timeDelta and position = position0 + velocity0 * timeDelta + 1/2 * acceleration * timeDelta * timeDelta. velocity0 and position0 are the previous ones. Commented Dec 8, 2018 at 21:23