# Air Resistance, Drag Force

## Group 25
* Gauss Chang, Department of Civil Engineering, National Taiwan University
* Justin Yan, Department of Civil Engineering, National Taiwan University
* Fu-Tzer Jih, Department of Physics, National Taiwan University

## Abstract
The drag equation is $F_{D}=\frac{1}{2} \rho C_{D} v^{n} A^{m}$, we want to evaluate the value of $n,m$, by doing the dropping experiment with wooden balls. And lastly, we change the shape of the objects to determine the relation between shapes of the objects and $C_D$.

## Background and Objectives
In most cases, we often assume that the drag force is proportional to the square of velocity and the cross-sectional area of the object, and we throw all other factors like shape of the object into $C_{D}$, the drag coefficient, but in reality, that's not the case. So in this experiment, we will use wooden balls in different size, assuming that they have the same $C_{D}$, then calculate the power of $v$ and $A$.

## Methods, Steps and Progress

### Methods
Firstly, we drop a plumbum ball and use the trajectory to deduce the gravitational force, and because the plumbum ball has high density, the acceleration caused by drag force is neglectable. Then we drop a wooden ball from 2nd floor and use the ultrasound distance finder to get the position of the wooden ball. By regression analysis, we can find the $n$, which is to determine the relation between air drag force and the velocity.

Second, we change the size of the ball. With the $n$ we find, by the equation we assumed above, we can define $m$ in the equation.

### Timetable

| Week | Task |
|------|--------------------------------------|
|1 | Discuss the proposal direction |
|2 | Designing poster layout. |
|3 | Re-discuss our Topic. |
|4 | Work on the wooden balls. |
|5 | Preform 1st dropping test. |

### Responsibilities

| Name | responsibility |
|------------|--------------------------------------|
|Fu-Tzer Jih | TBD |
|Justin Yan | TBD |
|Gauss Chang | TBD |

## Expected Difficulties and Solutions
We use Arduino with ultrasound distance sensor. The sensor has a limitation of maximum measurable distance 2m, so we have to cut out those unreasonable data. And the ultrasound may not reflect well due to our object shape.

The solution will be the laser range finder, which has better accuracy of distance and measure range. We don't have it now, but we can buy or borrow one if necessary.

## Results and Evaluation
We expected the result will be very close to general assumption $n=1$(low speed), $m=1$. similar to Newton's inverse square law, the power is not exactly 2, but for simplicity , we will assume it's 2.
Through this experiment, we can learn

## References
[^ex]:See for example: G. H. Cross, Nature **374**, 307 (1995); M. Key *et al.*, Phys. Rev. Lett. **84**, 1371 (2000).
[^mcco02]: L. McComb, J. Dept. Phys. **75**, 234 (2002).