Calculating Centrifugal Force 8

[jamesxi]

I am designing a unique gyroscopic/centrifugal machine, but know little about the calculations involved, so am hoping that someone here will be able to help.

Assume I have a 10cm radius centrifuge, and a 1kg mass at the end of the centrifuge, with the weight's center exactly at the 10cm mark. The centrifuge is spinning at 1,000 RPM. How would I calculate the centrifugal force (in kg) that such a system generates. I don't really need to factor in friction yet.

So, my variables are:
r(radius) = 10cm
m(mass) = 1kg
RPM = 1000
Cf(centrifugal force) = ?

Jimmy
jamesxi@yahoo.com

 

[TD2K]

First, force is never measured in kg. That's a unit of mass.

Secondly, find the equation for centrifugal force and plug the numbers in.

Can you please post more a little more information on this problem?

 

On Earth under exactly 1g of gravity, force can be expressed in kg. This is proven with the following link:

http://www.ex.ac.uk/cimt/dictunit/ccforce.htm

 

[cowski]

Hopefully this will get you off on the right foot.

1. convert your rpm to radians/sec (cycles per sec, frequency)
1000 rev/min * 1 min/60 sec * 2pi radians/rev
1000/60 * 2pi = 104.72 rads/sec

2. compute velocity using standard units (in this case kilograms, meters, seconds)
v = 2pi * r * frequency
v = 2pi * 0.01m * 104.72rad/sec = 6.58 meters/sec

3. compute force F = m * a
for constant circular motion a = v^2/radius
a = (6.58 m/s)^2 / 0.01 m = 4329.64 m/s^2
F = m * a = 1 kg * 4329.64 m/s^2 = 4329.64 kg m / s^2

Since Weight = mass * gravity, this would be equivalent to 4329.64/9.81 = 441.3 kg.

note: this assumes horizontal circular motion (like a merry-go-round) and ignores the effects gravity would have; if it were vertical (ferris wheel) the force of gravity would play a bigger part in the calculations.

best of luck in all your inventing!

 

[jamesxi]

Thanks for the equation, it will definitely help me out. Check back in a few days to see my 100% great invention(or absolutely useless one).

 

[bgkms]

centrifugal force = m*w*w*r

m=Kg.

w= 2*3.14*speed in rpm / 60 rad/sec.

r=radius (dist.) m

centrifugal force= Newtons.

 

[svanels]

To

http://www.ex.ac.uk

(visitor),some people belief anything that is on the internet or in a calculator. kg is a unit of mass, in the past the term kgf or kilogramForce was used to express Force so 1 kgf = 1 kg * 9.8 * m/s[sup]2[/sup] = 9.8 Newton
Steven van Els
SAvanEls@cq-link.sr

 

[finiteelementanalyst]

Dear james,

You know radius, mass, and rpm.

You need to calculate the centrifugal force, right;

Its simple::
CF= mass * (rpm/2*PI)^2 * radius ....

from this relation u can calculate centrifugal force. R u satisfied.

with smile
kumaravel. S. Kumaravel,
Finite element Analyst,
Hyderabad - 500 033.

 

[GregLocock]

Sorry SK, you've made a mistake in that equation. There's a factor of 60 to convert rpm to rps that you've ignored. Cheers

Greg Locock

 

[jamesxi]

Here is the tough part: What happens when you have a negative radius? To imagine how this is possible, start with a large fan, with one fan blade having three times the length of the other blades. All the fan blades have a large mass at their tips. Fold the extra-long fan blade until it is the same length as the other blades. The mass will be past the center of the fan, but the force will be directed in the opposite direction. Should I just take the absolute value of the radius?

kumaravel, I would have to say that the 441kg cowski calculated sounds about right, but plugging in your numbers:

m: mass in kg
r: radius in meters
Cf: Centrifugal force in newtons?

Cf = m*(RPM/2*Pi)^2 * r
Cf = 1*(1000/2*Pi)^2 * .01 = 24,674 newtons(?)

That would be 2.77 tons of centrifugal force. That sounds a bit high, don't you think?

I did finally get my USPTO number though its looking more and more like my machine does not work, at least not as efficiently as I would like. I'll post a link tomorrow so people can see my lump of scrap.

 

[GregLocock]

I have a horrible suspicion I know what you are designing, but I'll leave that out, for the time being.

Instantaneously the centrifugal force will ALWAYS act away from the centre of rotation, so when you fold your long blade over then the force will still tend to fling the mass away. The shape of the folded blade affects the stresses in that blade, but do not affect the forec on the mass.

Build a model out of paper and tape, and coins, to check this.

Cf with your initial figures is 1096.6 N per 1 kg mass. Cowski has included an extra factor of 2*pi in working his velocity out.

This thread hasn't exactly been our finest hour, has it? Cheers

Greg Locock

 

[cowski]

Greg,

It is 2pi/60 to get from rpm to rads/sec and there is another 2pi in getting from a circular frequency to a linear velocity. I stand by my equations for now, but if you can provide corrections I will be glad to look at them.
Thanks

 

[FINN_imported]

I use this formula all the time. I design vibratory compactors using eccentric weights.
Given:
mass=1kg, radius=.01m, rpm=1000 and F=m*a
a=r*w*w
w=1000rev/min*2pi radians/rev*1min/60sec=104.72rad/s
a=.01m*104.72rad/s*104.72rad/s=109.66m/sec^2

Therefore:
F=m*a=1kg*109.66m/sec^2=109.66kg*m/sec^s=109.66 Newtons

I hope this clears up all this miscalculations. You must remember to carry your units along in order to keep from making a major error.

 

[RobWard]

What a fantastic thread from such a simple request!
I can't wait to get the link to see what's been designed.

 

[astroclone]

I may be just an Aeorspace Engineer, but isn't 10 centimeters .1 meter? All of the calculations I saw on the thread said .01 meter.
T

 

[ishvaaag]

metrication, yes

1 cm =0.01 m

hence

10 cm = 0.1 m

 

[GregLocock]

OK, let's take it from the top.

r=.1 m

w=2*pi*1000/60= 104.7 rad/s (roughly)

m=1 kg

centrifugal force = m*r*(w^2)

(which incidentally is the same as m*(v^2)/r, since v=r*w)

=1*.1*104.7*104.7 N

=1096.6 N, a number I have seen before.

You don't need a 2pi to convert from rad/s to velocity, it is in there already. Cheers

Greg Locock

 

[jamesxi]

Thanks for the calculation corrections guys. Here would be the complete all-in-one equation:

Cf: centrifugal force in newtons
m: mass in kg
r: radius in meters

Cf = (2*Pi*RPM/60)^2 * m* r
(2*Pi*1000/60)^2 * 1 * .1 = 1096.6N
This is equal to 247 pounds of force

Also, Greg, after thinking about its hard to see it any other way than what you were saying. ("Instantaneously the centrifugal force will ALWAYS act away from the centre of rotation&quot That would actually make my machine better than otherwise, so I'll raise my odds of it working to 25,000 to 1. I think I will have a link to it tomorrow evening.

One last question, why is w used as the symbol for radians/second?

 

[GregLocock]

w is the nearest roman equivalent to the greek letter omega, which in its lowercase form looks like a curly w. As to why we almost always use lowercase omega for angular velocity - beats me!



Cheers

Greg Locock

 

[FrenchCAD]

*Beats Greg*

Really interesting thread. A lot of formulas for a simple one at the end, I like this. When I read such stuffs, I know why I study engineering FrenchCAD
Université Joseph FOURIER
Département Génie Mécanique
Grenoble - France
cyril.guichard@wanadoo.fr