Understanding Cd^2 and Its Relationship to SR in Practice

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In summary, the conversation discusses the concept of special relativity in relation to a spinning CD, where the outer perimeter shrinks more than the inner perimeter due to its greater spatial velocity. The concept of length contraction is also mentioned, where measurements taken from a moving perspective may result in a shorter value for pi. The conversation also brings up the question of how a speeding fly would appear in a relative sense.
  • #1
ddr
this is about SR in practice...

imagine a Cd with inner radius r, outter radius R and middle radius d. the Cd starts to spin from 0 to some V spatial speed with respect to the radius d. as the speed increases all the perimeters shrink, but the outter one shrinks far beyound the inner because it has greater spatial velocity cause it corresponds to bigger radius. so when the speed of d-circle becomes some V (critical) the Cd will (in a SR kinda sense) turn into square ie. the outter and the inner parameters will equalize.
am I right?
 
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  • #2
No. The radius does not shrink as it lies on a direction perpendicular to the direction of motion. But relative to us at the centre of the CD which the cd is moving relative to, we will have length contraction, which leads us to a value for circumference that is shorter than that obtained if we were moving with the CD. Therefore, the moving measurement would give values of pi that are not 3.14159...
 
  • #3
I didn't meant that the radiuses are shrinking but the perimeters do cause the displacement is parallel with them.Ok?

I wonder what would a speeding fly look like in a relative sense?
 

1. What is Cd^2 and how does it relate to SR in practice?

Cd^2 is a measure of the drag coefficient, which is a dimensionless quantity that represents the resistance to motion of an object through a fluid. In practice, Cd^2 is used to understand the aerodynamic performance of various objects, such as airplanes and cars, and how they interact with their surrounding environment.

2. How is Cd^2 calculated?

Cd^2 is typically calculated using wind tunnel testing or computational fluid dynamics (CFD) simulations. In wind tunnel testing, the drag force acting on a model of the object is measured at different wind speeds and angles of attack. The Cd^2 value is then determined by comparing the drag force to the dynamic pressure of the air. In CFD simulations, complex mathematical equations are solved to simulate the flow of air around the object and calculate the Cd^2 value.

3. What factors can affect Cd^2?

Cd^2 can be affected by various factors such as the shape and size of the object, the surface roughness, the speed and direction of the flow, and the properties of the fluid (e.g. density and viscosity). Other factors, such as temperature and altitude, may also play a role in certain cases.

4. How does understanding Cd^2 help in designing more efficient vehicles?

Understanding Cd^2 allows engineers to optimize the aerodynamic design of vehicles to reduce drag and improve their overall efficiency. By reducing Cd^2, vehicles can achieve higher speeds with less energy, resulting in improved fuel efficiency and performance. This is especially important for modern vehicles, where reducing drag has become a key factor in meeting fuel efficiency and emissions standards.

5. Are there any limitations to using Cd^2 in practice?

While Cd^2 is a useful metric for understanding aerodynamic performance, it is important to note that it is based on idealized conditions and may not accurately represent real-world scenarios. Factors such as turbulence, wind gusts, and ground effects can impact the Cd^2 value in practice. Additionally, Cd^2 is only one aspect of overall vehicle performance and needs to be considered in conjunction with other factors such as weight, power, and handling.

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