As far as I understand an inertial drive is more or less what I
explained in my "A Different Approach" mail, where we create an
imbalanced rotating body. The GIT drive, I am not sure wether the theory
behind it has something to do with gyro effects, or some people have
confused a supposedly gyro effect with that of an imbalanced rotating
body. At least in one of the animation files I saw in the web about a
working GIT drive, it can clearly be seen that, the devices moves
because of pure mechanical means interacting with the ground, and I
think we have better systems of purely mechanical movement, such as a
walking robot. The idea is not to use friction ( or interaction with any
external body ), and the GIT device will only be proved to be working
when it manages to move in the air, while it is suspended ( floating )
using a balloon, and well if possible to simply levitate ofcourse :)
Anyways, the purpose of this post is to give the mathematical theory
behind an inertial drive as I understand it, and if everything is
correct ( I plead everybody with the enough knowledge to confirm my
physics ) to proceed using physical designs in proving that "we can
actually move an object using inertia ( which I think is possible )
without contacting any other external object ( which I still have to see
to believe ! )"
Diagram:
======
F_a<-----(A)===r_a===X===r_b===(B)------>F_b
- (A) and (B) are the masses which will be rotating, each having
mass m_a and m_b respectively.
- X is the rotation axis which goes into the screen ( rotation being
clockwise).
- The ==== is the support which keeps the two masses together. r_a
and r_b being the length of each support from X to the mass.
- The lines <------ and ------> are the direction of the centrifugal
forces F_a and F_b for masses (A) and (B) respectively.
Mathematical theory:
==============
Variables and their units:
-------------------------
F = Force : ( since it comes from F=ma it's units are: ) Kg m /
s^2
(note: ^2 means to the power of 2, Kg = kilograms, m = meters
and s = seconds)
m = mass : Kg
a = acceleration : m / s^2
r = radius of rotation which in our case is the length of the
support : m
w = angular velocity : rad/s
(note: rad means radians. 1 rad = (Pi/180) x 1 degree.)
Equations:
----------
*We start of with what we know, I will not explain these cause it
would take time/space and it is hard to draw with text anyways :)
-From Newton's we know:
F = ma
-From rotating masses we know:
a = rw^2
*Now... we find out the equation relating Force to a rotational
body:
F = ma
a = rw^2
-substitute and we get :
F = mrw^2
*Now we try to relate the two centrifugal forces which affect our
masses in our example:
( F_net is net total force )
F_net = F_a - F_b
F_net = F_a - F_b = m_a r_a w^2 - m_b r_b w^2
-simplifying it :
F_net = F_a - F_b = ( m_a r_a - m_b r_b ) w^2
*We have the equation of the centrifugal forces which in our case
should not be equal and result in a net force F_net. Now let's see how
does the net force affect our system ( I assume that our system has a
mass of m=m_a+m_b, in another words, no other mass exists, but in
reality we need to add the support rods, the motor, etc...but these come
in when we actually get to make it):
F_net = ma
(note that m is the mass of our system ( m_a+m_b) and a is the
linear acceleration of our system towards the same direction as F_net)
a = F_net / m
-substituting what we have from F_net and from m:
a = ( m_a r_a - m_b r_b ) w^2 / (m_a + m_b)
----
Using the equation:
=============
Let's see some practical things now :
Our equation can be used for various models of inertial drives,
such as the following:
Something like the latest GIT models which are on the website
Jerry posted which had 2 rings which made a race I think it was called
the IndieGIT. Please note that IMHO that specific device does not move
solely because of inertia, but also because of friction, so it is not a
good enough proof for me. Also note that I am not sure yet as to how the
GIT is suppsoed to work, wether it's suppossed to be a gyro effect or
indeed an inertial imbalanced system. Whatever it is, I think it is a
good physical design for the latter and the idea I had in my last post.
As we can see the centrifugal Force depends on 3 factors, the
mass, the radius ( length of support ) and angular velocity. In my
original post I talked of mass being the variable. But ofcourse we can
keep the mass costant and vary the radius ( the race in the GIT device
). We can also think of another design where we have a rotating system
like in my original post or the one in the diagram above and we make
sure that the length of the support varies in such a way that facing the
direction we want to go, there there will be a longer length for
support.
Whatever the design... let's take the case of a length varying
design ( GIT race design or changing support length design or
any-other-one anyone ? ) where the mass is constant and the length
varies:
First of all let's see what angular velocity is, w = rad / s
.... in motors usually the term rpm is used, which is 1 revolution per
minute... so doing some simple maths we get that 1 rpm = Pi/30 rad/s. We
will use this to convert between rpm and rad/s.
We are going to calculate what it takes to float a device like
this:
What we have / we want:
Say we have a motor which with our masses should have a constant
rpm of 120 and that one radius is 0.1m and the other 0.12m ( outermost
part of the race or the longest support length ) and we want to
calculate how much mass we need for each weight.
Let's convert 120 rpm to rad/s: w = 120 rpm = 120Pi/30 = 4Pi rad
/s
a=9.8 m/s^2 ( this is the acceleration we have to achieve,
which is g, earths gravitational acceleration on us )
Since both masses are equal, we have: m = m_a = m_b. And the
mass of our system is m_a+m_b = m+m = 2m.
from the equation we calculated before we have:
a = ( m r_a - m r_b ) w^2 / 2m
a = ( r_a - r_b ) m w^2 / 2m
(m cancels out with 2m):
a = ( r_a - r_b ) w^2 / m
m = ( r_a - r_b ) w^2 / a
Now we just substitute our numbers into the variables :
m = ( 0.12 - 0.1 ) x (4Pi)^2 / 9.8
m = 0.02 x 16 x Pi^2 / 9.8
and m = 0.3 Kg !!!!!!!!
ridiculous isn't it ? either someone has to prove these
equations wrong, or someone has to build such a simple device, cause we
can't just ignore these simple facts.
I also calculated another case where we use a device like this
to move around ( assuming our only mass is the engine itself , i.e. the
two masses ) and that we want it to develop a speed of 18 Km / h in 10
seconds with the same specifications as the above example ( 120 rpm
constant motor and 0.02 meters of radius difference ) I calculated a
mass of 6.3 Kg !!! Not bad at all !!!
When I first thought of this idea of imbalanced rotational
bodies, I thought that either we would need a very strong rotation or a
very large mass to get this thing going, but I am _surprised_ to see
that not at all ... theoretically speaking we can make such a device
from spare parts which dont have to be anything special. Either this, or
I have forgotten some physics during my inactivity years !!!
All comments / corrections / correlations and confirmations
welcome specially physical confirmations !!!
Also please post me all the info you have about gyros specially
if they are physical info.
Regards,
Vano