Drag equation using wind to create 3d graph

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    3d Drag Graph Wind
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Discussion Overview

The discussion revolves around the application of physics principles to model the trajectory of a projectile, specifically a potato, using a spreadsheet. Participants explore the incorporation of wind effects into the drag equation to create a 3D graph of the projectile's flight path.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant describes their spreadsheet model for predicting projectile landing based on various parameters, including mass, launch angle, and environmental conditions.
  • Another participant emphasizes the importance of clearly stating assumptions regarding wind direction and its impact on the projectile's motion.
  • A participant expresses uncertainty about how to incorporate wind direction into their model, seeking guidance on starting points for implementation.
  • Discussion includes the complexity of estimating drag coefficients (Cd) for non-spherical projectiles and how wind affects drag calculations.
  • One participant suggests that the drag force can be calculated by considering both the projectile's normal motion and the wind's velocity components.
  • A hypothetical scenario is proposed where a perfect sphere with a known Cd is used to simplify drag calculations in the presence of wind.
  • Another participant provides insights on how to incorporate wind effects into both 2D and 3D models, suggesting methods for plotting the results.
  • A participant shares their progress in incorporating a headwind into their model, noting its significant impact on the results.

Areas of Agreement / Disagreement

Participants generally agree on the need to account for wind effects in the drag calculations, but there is no consensus on the best approach to model these effects, particularly regarding the complexities introduced by different projectile shapes and wind directions.

Contextual Notes

Limitations include the need for clear assumptions about wind direction and the challenges of estimating drag coefficients for non-standard projectile shapes. The discussion also highlights the lack of coverage of drag concepts in the participant's physics class.

geoff.miles
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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.
 
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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 won't 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?
 
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.
 
and the graph would only have a z-axis to show if the wind pushed the projectile to the left or right
 
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 traveling 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.
 
so for the sake of the problem, let's say I am 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
 
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.
 
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
 

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