Help with Projectile Motion problem (including air friction)

In summary, Hoot thinks that he needs to recalculate the drag coefficient (based on the density of air) in order to get an accurate answer for the projectile's maximum distance.
  • #1
CopperHead4750
4
0
Hopefully you smart guys can understand this post

I recently have bought an airsoft pistol that shoots 302fps and I thought it would be fun to calculate the max distance & stuff for the bb including air resistance. The problem is including air resistance into the equation.

Here's the stats:
mass of bb= .12g
diameter of bb= 6mm (.006m)
muzzle velocity for .12g bb = 302fps (92.0496m/s)

After reading stuff on the net, I aparently need the equation D=(pCA)/2, where p is the density of air (about 1.2101 kg/m3), C is drag coefficient (around .47 probably?), and A is the area of the bb looking at front (pi*r2 = pi*(.003m)2 = 2.8274*10-5 m2)
When I plug the numbers in, D= 8.04046*10-6

I'm sort of lost after this step, aparently Acceleration=-DV2 --> Ax=-DV(Vx) and Ay=-DV(Vy)

I tried plugging the numbers in but the answer was only somewhere around .04 which I'm pretty sure isn't right at all.

My main goal is to put it into a parametric function so I can see it visually with distance and time:

SO, what I'm sure is right (without air resistance):
X1T=92.0496cos(35)
Y1T=92.0496sin(35)-(1/2)9.8T2


What is the air resistance acceleration and how do I plug it into that equation?
 
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  • #2
For small velocities (velocities less than 328 ft/s), air resistance is (approximately) proportional to velocity, rather than the square of velocity.

Change it to DV from DV² and see if that helps.
 
  • #3
Changing it to DV instead of DV2 makes the number even smaller (around .00074).

After reading some more... Acc(drag)=DV2/(mass) and after what you said, should I change that to DV/(mass)? This would make it around 6.168m/s2

So when I plug it into my equation, is this accurate:
X1T=92.0496cos(35)-(8.04046*10-6*92.0496cos(35)/.00012)T2
Y1T=92.0496sin(35)-(1/2)9.8T2-(8.04046*10-6*92.0496sin(35)/.00012)T2

I know I must be doing something wrong. Please help
 
  • #4
I'm sorry, I can't tell which equations of motion you are using. I would recommend using [itex]s = ut + \frac{1}{2}at^2[/itex]. You will need to know the inital height to solve for t, but this is easy to measure.

Regards,
-Hoot
 
  • #5
Sorry, that's the equation I was using, I just forgot to put the T in after the first velocities.

That equation still doesn't include air friction though.
 
  • #6
Okay, it seems that you have determined the [negative] acceleration due to air resistance. Now in the x - direction this is the only acceleration experience by the bb round, thus in the x-direction we have;

[tex]s_{x} = ut + \frac{1}{2}\cdot - a_{drag} t^2[/tex]

However, in the y - direction, there are two forces acting, gravity and drag but it is important to observe that in this case they are acting in opposite directions. The force of gravity it acting in the same direction as velocity (down) therefore the acceleration will be positive. The drag force is acting in the opposite direction to the velcoity (up). Therefore we can say that;

[tex]a_{total} = g - a_{drag}[/tex]

Thus the kinematic equation in the y-direction becomes;

[tex]s_{y} = ut + \frac{1}{2} (g - a_{drag})t^2[/tex]

Do you follow?

~Hoot
 
  • #7
I understand that part. The only problem is that I'm not sure if my adrag calculations are correct.

Lets work backwards. What's the equation for adrag?
 
  • #8
The relationship for drag is given by (as you correctly stated above);

[tex]F_{drag} = - \frac{1}{2}C\rho Av^2[/tex]

For a sphere c = 0.5, the density of air is approximately 1.25 kg/m^3.

Regards,
~Hoot
 

1. What is projectile motion?

Projectile motion refers to the motion of an object that is launched into the air and moves only under the influence of gravity and air resistance. It is a combination of horizontal motion at a constant speed and vertical motion due to the force of gravity.

2. How do you calculate the initial velocity in a projectile motion problem?

The initial velocity can be calculated using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (usually -9.8 m/s^2), and t is the time elapsed. In a projectile motion problem, the initial velocity is usually given or can be found using trigonometric functions.

3. How does air friction affect projectile motion?

Air friction, also known as air resistance, affects projectile motion by slowing down the object's velocity and causing it to follow a curved path. This is due to the fact that as the object moves through the air, it experiences an opposing force from the air molecules, which reduces its speed and alters its trajectory.

4. How do you factor in air friction when solving a projectile motion problem?

To factor in air friction, you can use a coefficient of air resistance, which is a number that represents the amount of air resistance acting on the object. This coefficient can be multiplied by the velocity squared to calculate the air resistance force. From there, you can use this force in your calculations for the object's motion.

5. What are some common strategies for solving projectile motion problems?

Some common strategies for solving projectile motion problems include breaking the motion into horizontal and vertical components, using the equations of motion to find the unknown variables, and using the kinematic equations for projectile motion. It is also helpful to draw a diagram and label all the known and unknown variables to better visualize the problem.

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