Calculating Coefficient of Air Resistance

[Bashyboy]

Hello,

For my Classical Mechanics Lab, my fellow students and I are to calculate the coefficient of air-resistance of several objects dropped from the roof of our science building. We are assuming that the air-resistance is linear in nature. The first method by which we calculate the drag coefficient is by measuring the diameters of the objects and their masses. The second method is to record the dropping of the objects and extrapolating data from the videos. Currently, I am working on the former method. We recorded the temperature on the day of the drop as 48 degrees Fahrenheit, with 85% humidity, and the pressure was 30.5 pounds/inch. I understand that the linear air-resistance coefficient is $b=\beta D$. I have searched the internet to find what beta is equal to, but all I can find is what is equal to at STP. Does anyone know of a formula for beta?

 

[SteamKing]

I don't know what a pressure of 30.5 pounds per inch means but it sounds pretty high, especially if it is supposed to be atmospheric. Are you sure your experiments aren't supposed to provide the data to calculate 'b'?

 

[PhanthomJay]

Barometic pressure 30.50 inches of mercury I guess, probably fine weather for an object drop. You probably can find an air density chart as a function of the given variables, which may not be much different from the standard air density usually given in slugs/ft^3 at 60 degrees F dry air at 29.95 inches barometric pressure. Not too much difference I would think. Also, I don't think it is a good assumption to use linear drag instead of quadratic drag.

 

[Bashyboy]

Yes, our experiment does provide us with the necessary data to calculate via the first method (that is, by using the video footage to extrapolate data). The second method of calculation is to use our diameter and mass measurements to get a "theoretical" value of b. Thus the reason for my wanting to know how to calculate beta.

 

[Nickie]

Hello,

It sounds like you are conducting an interesting experiment to calculate the coefficient of air resistance. The coefficient of air resistance, or drag coefficient, is a measure of the resistance an object experiences as it moves through a fluid, in this case, air. The value of beta, or the coefficient of air resistance, can vary depending on factors such as the shape and size of the object, the density and viscosity of the fluid, and the speed of the object.

To accurately calculate the coefficient of air resistance, you will need to collect data on the objects' diameter, mass, and the conditions of the air (temperature, humidity, and pressure), as you mentioned. However, there is no specific formula for beta as it can vary depending on the specific conditions and the object being tested. It is important to note that the value of beta is not a constant and can change with different conditions and objects.

To determine the coefficient of air resistance for your experiment, you can use the formula b=\frac{F_{d}}{\frac{1}{2}\rho v^{2}A}, where F_{d} is the drag force, \rho is the density of the fluid, v is the velocity of the object, and A is the cross-sectional area of the object. You can also use this formula to compare the results from both methods you are using to calculate the coefficient of air resistance.

Additionally, you can try using a software or app that can simulate or model the movement of objects in different conditions to get an estimate of the coefficient of air resistance. This can help you compare your experimental results and improve the accuracy of your calculations.

I hope this information helps and good luck with your experiment!