Understanding Air Resistance Formula: Finding R, D, and p Variables

[FabioTTT]

the formula:

R = (.5)DpAv^2 is used to determine how much air resistance (resistive force) is being placed on the object.

R is the Resistive force.
D is some dimensionless empirical quantity called the drag coefficient
p is the density of air
A is the cross-sectional area of the object (surface area)
v is velocity

My question is, is the density of air some constant that should be already given to me? also, how would i go about finding the drag coefficient?

I'm asking this because in physics we're doing a lab in which we drop a cofee filter... and we record its time to reach a certain height (which I am guessing is to be able to calulate for the terminal velocity).

So in other words, I have all of these variables except for R, D, and p.

Can anyone help me out?

 

[GRQC]

Originally posted by FabioTTT
the formula:

R = (.5)DpAv^2 is used to determine how much air resistance (resistive force) is being placed on the object.

R is the Resistive force.
D is some dimensionless empirical quantity called the drag coefficient
p is the density of air
A is the cross-sectional area of the object (surface area)
v is velocity

My question is, is the density of air some constant that should be already given to me? also, how would i go about finding the drag coefficient?

I'm asking this because in physics we're doing a lab in which we drop a cofee filter... and we record its time to reach a certain height (which I am guessing is to be able to calulate for the terminal velocity).

So in other words, I have all of these variables except for R, D, and p.

Can anyone help me out?

Density of air is relatively easy to look up. It's about 1.2 kg/m³ at sea level (STP). It varies exponentially with altitude, though, so technically you have to take into consideration your elevation (for example, the air density in Denver is about 80% that of sea level).

For the drag coefficient, ultimately the way to determine it is through experiments like the one you're doing. There is really no good "theoretical" method of determining it, so you must ultimately rely on experimental determination.

 

[FabioTTT]

Originally posted by GRQC
Density of air is relatively easy to look up. It's about 1.2 kg/m³ at sea level (STP). It varies exponentially with altitude, though, so technically you have to take into consideration your elevation (for example, the air density in Denver is about 80% that of sea level).

For the drag coefficient, ultimately the way to determine it is through experiments like the one you're doing. There is really no good "theoretical" method of determining it, so you must ultimately rely on experimental determination.

thanks but based on that experiment I am at a loss for how to calculate the terminal velocity. we timed the coffe filters when they reached a height of about 50 percent from where they were dropped. with that time, the mass of the filter and its cross sectional area, i still don't know how to calculate the terminal velocity.

 

[GRQC]

Originally posted by FabioTTT
thanks but based on that experiment I am at a loss for how to calculate the terminal velocity. we timed the coffe filters when they reached a height of about 50 percent from where they were dropped. with that time, the mass of the filter and its cross sectional area, i still don't know how to calculate the terminal velocity.

Well, to calculate terminal velocity, you should be able to divide the fall into two portions: acceleration phase (which always last the same amount of time), and "terminal velocity phase". With enough measurements of drops from different heights, you should be able to cleanly find where/when the division occurs, and thus determine the terminal velocity from that.

What kind of equipment do you have at your disposal? Is this a stopwatch/pen-and-paper expt, or do you have computer-interfaced measuring devices (e.g. PASCO sensors)?

 

[FabioTTT]

Originally posted by GRQC
Well, to calculate terminal velocity, you should be able to divide the fall into two portions: acceleration phase (which always last the same amount of time), and "terminal velocity phase". With enough measurements of drops from different heights, you should be able to cleanly find where/when the division occurs, and thus determine the terminal velocity from that.

What kind of equipment do you have at your disposal? Is this a stopwatch/pen-and-paper expt, or do you have computer-interfaced measuring devices (e.g. PASCO sensors)?

stop watch/pen and paper.

 

[GRQC]

Originally posted by FabioTTT
stop watch/pen and paper.

Air resistance problems are notirously difficult (impossible) to solve exactly, so generally you have to do computer modeling for "accurate" solutions. However, with a coffee filter it probably won't make that big a difference.

My suggestion is: assume that it accelerates uniformly (but not at g) for some inteval of time before reaching terminal velocity. At that point, it's downward velocity is v_terminal, and it travels for an additional amount of time before hitting the ground.

The acceleration time is always the same, the latter time varies, but you should end up with enough equations to match your unkowns.

 

[Michael D. Sewell]

FABIOTTT,
TERMINAL VELOCITY = SQRT [(mg)/(AD1/2p)]
R = (mgv^2)/TERMINAL VELOCITY
ACCELERATION = g e^(-bt/m)
b = mg/TERMINAL VELOCITY

As GRQC said, these are approximations. The coefficient of drag changes with velocity. At low velocities, air resistance is proportional to velocity. At higher velocities, air resistance is proportional to the square of velocity(approximately sometimes). In ballistics we have to use numerical integration(based on empirical studies) to predict the flight path of the projectile.
Even though these are only approximations they work fairly well as evidenced by my very existence(I have 11 years experience as a skydiver and 10 years as a pilot).
If you are only interested in this subject to pass your course, this information should be enough. If you are interested in exploring this subject in depth, I have lots more information, and can give you web links and formulas. I hope this helps,
-Mike

 

[FabioTTT]

Yeah thanks you guys, you really helped me out.