How to calculate the RPMs needed to make a spincast lquid parabolic dish?

[CosmicVoyager]

Greetings,

Anyone know how to calculate the revolutions per minute needed to create a liquid parabola of given diameter and depth?

Thanks

 

[Andy Resnick]

A good accounting can be found here:
http://en.wikipedia.org/wiki/Liquid_mirror

AFAIK, the main problem is getting a motor that can run at low constant speed without any high-frequency jitter.

 

[CosmicVoyager]

A good accounting can be found here:
http://en.wikipedia.org/wiki/Liquid_mirror

AFAIK, the main problem is getting a motor that can run at low constant speed without any high-frequency jitter.

If I have done the math correctly, it seems the wider the radius is the fewer RPMs that are needed? Is that correct? That is the opposite for what I was thinking.

 

[Andy Resnick]

If I have done the math correctly, it seems the wider the radius is the fewer RPMs that are needed? Is that correct? That is the opposite for what I was thinking.

The larger the radius, the slower angular speed needed to generate the same profile... IIRC that's correct. Those large mirrors turn *very* slowly.

 

[pmacias]

for your question! I can provide some guidance on how to calculate the RPMs needed to create a liquid parabolic dish. The first step is to understand the physical principles involved in creating a parabolic shape. A parabola is a curve that is created by the intersection of a plane and a cone. In the case of a liquid parabolic dish, the plane is the surface of the liquid and the cone is the shape of the dish.

To calculate the RPMs, we need to consider the diameter and depth of the dish. The diameter will determine the width of the dish, while the depth will determine the curvature of the dish. The formula for calculating the RPMs is:

RPM = (v / (2πr)) * (360 / t)

Where:
v = velocity of the liquid (m/s)
r = radius of the dish (m)
t = time taken to complete one revolution (s)

To determine the velocity of the liquid, we can use the equation of motion for a falling object:

v = √(2gh)

Where:
g = acceleration due to gravity (9.8 m/s^2)
h = depth of the dish (m)

Once we have the velocity, we can plug it into the RPM formula along with the radius and time taken to complete one revolution. The time can be measured using a stopwatch while the dish is spinning.

It's important to note that this calculation assumes a perfect parabolic shape and uniform rotation of the dish. In reality, there may be some variations and imperfections that can affect the RPMs needed. It's also important to consider the properties of the liquid being used, such as its viscosity and surface tension, as these can also impact the shape and behavior of the dish.

I hope this helps guide you in calculating the RPMs needed for your spincast liquid parabolic dish. As always, it's important to double-check your calculations and take into account any potential variables in order to achieve the desired results. Happy experimenting!