# Drag equation using wind to create 3d graph

1. Mar 5, 2013

### geoff.miles

Hey guys, I'm new to these forums so I am unsure if this is the right place to be posting this, but here it goes.

I have been working on a drag spread sheet using OpenOffice Calc to predict where a potato will land when fired from a potato gun.

I have gotten pretty far along, using:

projectile mass (kg)
launch angle (degrees)
initial velocity (m/s)
temperature (Fahrenheit) [this number is then converted to both Kelvin and Celsius]
humidity (%)
air pressure (InHg)
barrel radius (m)[which is used to determine cross-sectional area]
And projectile shape [which is used to determine Cd]

After typing in all of this information into the corresponding cells the spread sheet then does all the math and displays the projectiles flight path.

But what I am working on adding is wind, so I can add a 3rd, z axis, to my graph. I am not far along enough in my physics class to know how to do this, and I am not patient enough to wait to hear back from my physics professor on how to do this.

I know using a potato is a problem on its own because there are too many variables to account for, so I am planing on having a more stable projectile printed for me out of abs plastic.

Any help would be great.

Here is a link where you can find my spreadsheet and see it for yourself:
http://forum.openoffice.org/en/forum/viewtopic.php?f=9&t=60186

FYI: This is not a homework assignment, I started working on this my senior year of high school and now that I am in college I have the resources to finish it.

2. Mar 5, 2013

### Travis_King

First, you'll have to state your assumptions. For instance, are you assuming that your wind is acting 100% in the Z (which you've defined as horizontal, perpendicular to direction of motion) axis? That is, the wind isn't acting partially in the X and partially in the Z? Or maybe as an updraft? Having a wind that acts only in one axis simplifies the solution (you wont have to find the Cd for the potato while looking at it from some odd angle), but obviously restricts the model.

As far as the actual question is concerned, in what ways would the wind affect the body? That is, what do you know about the wind that would help you determine what force is acting on the body?

3. Mar 5, 2013

### geoff.miles

I guess what I am asking is where should I start? I want to be able to tell the spreadsheet that the wind is coming from north east and the projectile is being shot east, or north etc.

in my physics class we haven't even touched drag yet and its a college class which kind of disappoints me.

4. Mar 5, 2013

### geoff.miles

and the graph would only have a z-axis to show if the wind pushed the projectile to the left or right

5. Mar 5, 2013

### Travis_King

The problem you'll have is the drag will be dependent on the Cd of the projectile in that direction so you'll have the problem of estimating the Cd of an object with a strange cross sectional area (since it's not a sphere) at strange angles.

The drag, then, will be the drag due to the projectiles normal motion, plus the drag due to the wind (the velocity it is travelling with respect to the wind is then the wind's velocity plus the component of the projectiles velocity in the direction the wind is acting.)

If you know how to calculate drag in regular flight, you know how to do it (on a basic level) with wind.

6. Mar 5, 2013

### geoff.miles

so for the sake of the problem, lets say im firing a perfect sphere with a Cd of .47. I could reuse my initial equation to calculate the drag due to wind. but how would I implement it into my graph

7. Mar 5, 2013

### Travis_King

Well, as far as the 2d part goes, you would incorporate the component of the velocity acting opposite to the direction of motion of the projectile (i.e. head wind or tail wind) into the horizontal velocity of the projectile.

That is, the drag on a ball with velocity, V, and a direct headwind of velocity Vhw is equal to either (Drag due to V) + (Drag due to Vhw), or (Drag due to (V + Vhw)). You just have to find the component acting in the direction of the velocity.

For 3D, you would incorporate the orthogonal Z-component to determine movement in the Z.

To plot that, either learn to 3D plot (maybe incorporating a Matlab plot into excel) or simply add a version of the graph showing the X-Z plane.

8. Mar 5, 2013

### geoff.miles

Thank you so much, I just incorporated a headwind and it makes a world of difference, a cross wind is going to take me a bit more time