Drag calculation and measurement

In summary: Your Name]In summary, the conversation revolved around the topic of investigating the coefficient of drag for an airplane, specifically the Piper PA-38-112 Tomahawk. The coefficient of drag can be calculated by considering the forces of net drag, which consist of parasite drag and induced drag. The forum member's biggest challenge is the lack of angle of attack measuring equipment on the aircraft, but they plan to overcome this by using the point where induced and parasite drag are equal to determine the coefficient of drag. Suggestions were given to further aid in the research, including looking into the specific design and aerodynamics of the aircraft, using a wind tunnel or CFD simulations, and considering other factors that may affect the coefficient of drag.
  • #1
gschjetne
95
0
I'm exploring a few topics for my IB extended essay, and since I'm into aviation, my teacher suggested I'd find the coefficient of drag for an airplane.

Finding force of net drag would be piece of cake.

[tex]F_{\Sigma drag}=\frac{Power output}{velocity}[/tex]

According to aerodynamics of an airplane at constant speed:

[tex]F_{\Sigma drag}=C_{drag} \frac{1}{2} \rho v^2 + mg \cos \alpha [/tex]

The first term, parasite drag, [itex]C_{drag} \frac{1}{2} \rho v^2[/itex], should be pretty straightforward. It is the coefficient of drag times the dynamic pressure, defined as [itex]\frac{1}{2} \rho v^2[/itex]

The second term, induced drag, on the other hand, probably needs some explanation.
At lower airspeeds, the angle of attack must be higher to generate enough lift, and lower at high airspeeds, respectively. The drawback of this, though, is that the lift generated is perpendicular to the wing chord. At high angle of attacks this force turns backwards, inducing drag, hence the name.

This can be calculated as [itex]F_{lift} \sin \alpha[/itex] which means that if the plane isn't accelerating in any direction, this equals [itex]mg \cos \alpha[/itex] as long as the aircraft is not accelerating.

Rearranging:

[tex]C_{drag} = \frac{F_{\Sigma drag}}{\frac{1}{2} \rho v^2 + mg \cos \alpha}[/tex]

I'm going to test this on a Piper PA-38-112 Tomahawk. My biggest problem is that this aircraft is not equipped with angle of attack measuring equipment. To overcome this I figured that I know that at 75 knots of indicated airspeed, or dynamic pressure (I hate all non-SI units :mad: , but that's the way things aviation works, help converting would be appreciated) the terms for induced and parasite drag are equal. This is the point where the two graphs intersect, and the net drag is at a minimum (that's why Piper chose 75kts as the climb speed)

Now, if i take several measurements of the above, varying dynamic pressure (speed), I should be able to plot this into my graphing calculator. I am no math wizard, so I would appreciate some help, perhaps some calculus would do the job to get me around the angle of attack problem?

Boy, that was a lot of LaTeX! :tongue2:
 
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  • #2

As a scientist with a background in aerospace engineering, I find your topic of investigating the coefficient of drag for an airplane to be quite interesting. It is a relevant and important aspect in the design and performance of aircraft.

Your approach to calculating the force of net drag is correct, and I would like to offer some suggestions to help you with your research.

Firstly, I would recommend looking into the specific design and aerodynamics of the Piper PA-38-112 Tomahawk. This will give you a better understanding of the aircraft and its characteristics. You can also find data on the aircraft's coefficient of drag from sources such as the manufacturer's specifications or aerodynamic studies.

Secondly, you mentioned the issue of not having angle of attack measuring equipment on the aircraft. One possible solution could be to use a wind tunnel to simulate different angles of attack and measure the corresponding drag forces. This would allow you to accurately determine the induced drag component in your calculations.

If a wind tunnel is not accessible, you can try using computational fluid dynamics (CFD) simulations to model the airflow around the aircraft and calculate the coefficient of drag. However, this may require some knowledge and experience in CFD techniques.

Lastly, I would like to suggest considering other factors that may affect the coefficient of drag, such as the shape and size of the aircraft, airfoil design, and surface roughness. These factors can also be investigated through experimental or numerical methods.

I hope these suggestions are helpful in your research. Best of luck with your extended essay!
 
  • #3


First of all, it's great to see that you're exploring a topic that you're passionate about for your IB extended essay. Calculating and measuring drag for an airplane is definitely a complex and interesting topic.

Your equations for calculating the force of net drag are correct and it's great that you have a solid understanding of the different components that contribute to drag. The parasite drag term is indeed straightforward, as it is simply the product of the coefficient of drag and the dynamic pressure. However, as you mentioned, the induced drag term is a bit more complicated. It's important to note that the induced drag is not caused by the angle of attack itself, but rather by the lift produced at that angle of attack. This is why the induced drag term is proportional to the lift force, which is represented by F_{lift}.

Your approach to testing this on the Piper PA-38-112 Tomahawk is a good one. By taking multiple measurements at different speeds and plotting them on a graph, you should be able to see the relationship between dynamic pressure and drag force. As for the angle of attack problem, you're right that calculus can help you solve it. Calculus can help you find the slope of the graph at different points, which can then be used to calculate the angle of attack. Another option is to use a computer program or simulator that can measure the angle of attack for you.

Overall, it seems like you have a solid understanding of the concept of drag and how to measure it. Keep up the good work and don't hesitate to seek help from your teacher or other resources if you encounter any difficulties. Good luck with your extended essay!
 

1. What is drag and why is it important in scientific research?

Drag is the force that acts in the opposite direction of an object's motion through a fluid (such as air or water). It is important in scientific research because it can significantly affect the movement and behavior of objects, and understanding drag is crucial in fields such as aerodynamics, hydrodynamics, and fluid mechanics.

2. How is drag calculated?

Drag is calculated using the formula Fd = 1/2 * ρ * v^2 * Cd * A, where ρ is the density of the fluid, v is the velocity of the object, Cd is the drag coefficient, and A is the cross-sectional area of the object. This formula takes into account the factors that affect drag, such as fluid density, object speed, and shape.

3. Can drag be measured in a laboratory setting?

Yes, drag can be measured in a laboratory setting using various methods such as wind tunnels, water tanks, and force sensors. These experiments involve controlling the fluid flow and measuring the force acting on the object, which can then be used to calculate the drag force.

4. How does drag affect the design of vehicles and structures?

Drag can significantly impact the performance and efficiency of vehicles and structures. For example, in the design of airplanes, reducing drag is crucial for achieving high speeds and fuel efficiency. In the design of buildings and bridges, drag must be considered to ensure stability and safety against strong winds.

5. What are some real-world applications of drag calculation and measurement?

Drag calculation and measurement have numerous real-world applications, including in the design of aircraft, ships, cars, and sports equipment. It is also essential in understanding weather patterns, ocean currents, and the behavior of animals in air and water. Additionally, drag is a crucial factor in the study of atmospheric and oceanic pollution and the dispersion of pollutants.

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