Milković's inertial propulsion cart + some improvements.

[broli]

I'm still on the fence with this one. I would like to see these experiments like TK suggested. His "proof" in that video doesn't make much sense. If the plain was frictionless and air drag was gone the distance of the first experiment would be infinity.

Here's my explanation of this setup;

When the mass falls (ie goes forward), the cart goes backwards which is newtons third law. But when the mass almost reaches the bottom the cart stops going backwards, why? Well because the mass stops going forwards due to the centripetal force changing its direction. The reaction of this, the centrifugal force, thus stops the cart from going backwards. Theoretically the forward/backward speed of cart and mass is 0 when the mass is at the bottom. The cycle then repeats in reverse when the mass goes back up. According to this explanation though the whole setup just keeps oscillating back and forward while the horizontal center of mass remains at the same position. These videos do not show that, but if for some reason forward motion was allowed over backward motion due to some form of friction then that would explain the forward displacement of the center of mass.

That is why the appropriate experiments should be performed like suggested before. If my #1 suggestion was applied the setup will either not move at all as all force cancel out or move forward and we would have an inertial propulsion system.

Edit: I attached of what I believe to be a 1 dimensional equivalent design using a spring instead of the centripetal/centrifugal force.

[IotaYodi]

Basically this means that if the mass is dropped and moves forward the cart doesn't move backward slightly due to newton 3. This can be easily done by having two pendulums each 90° out of phase. When one mass is at the bottom ready to go up the other is at the top ready to go down. This interplay will leave the Center of Mass unchanged while the cart doesn't get jerked around.

Are you sure you dont mean 180 degrees? Or am I missing something?

[broli]

Are you sure you dont mean 180 degrees? Or am I missing something?

90° is correct. You first release one pendulum, then when it hits the bottom you release the second one. When you do this both will start out with 0 initial FORWARD velocity. And the forces they exert on the cart cancel out. As the pendulum at the top falls it will cause the cart to move backwards, while the pendulum at the bottom when rising will cause the cart to move forward.

[TinselKoala]

What the angled cart experiment is demonstrating is that, in fact, momentum is completely conserved and there is no excess energy from the pendulum drive at all.

The video demonstrates quite nicely the difference between perfectly elastic collisions and quite inelastic ones.

When the heavy ball is allowed to run down the ramp and strike the stop, not all its momentum is transferred to the cart. Much of it is lost in deformation of the parts, sound, friction, etc. Putting the mass on the pendulum and allowing it to swing is the mechanical analogue of an impedance matching transformer. Much less of the ball's momentum is lost uselessly; much more of it is retained and converted--over a longer time period-- to the linear momentum of the cart.

To repeat: rolling the ball down the inclined cart surface to strike the stop models an inelastic collision where momentum is transferred to the colliding objects and is eventually dissipated as heat. The pendulum models a perfectly elastic collision series, where the momentum is partitioned between the "colliding" objects and much less of it is lost uselessly. So the cart rolls further when the weight is swinging as a pendulum.

To test my hypothesis, it is only necessary to vary the elasticity (NOT the mass) of the ball. If a lead ball is used the ratio of cart travel in the two cases is Dr/Dp  (Distance with lead rolling down divided by distance with ball on pendulum).

The lead ball produces a certain ratio of travel lengths.

Now vary the elasticity of the collision. Use a ball of clay, or rubber, or some such. Do the experiments--rolling and pendulum-- and find the ratio. If I am right, the ratio will be very different from using the lead ball. If I am wrong and the device is working like the builder claims, the ratio should be the same regardless of the elasticity of the collision of the ball with the stop.

Broli's idea with a spring is doing the same impedance matching--less momentum will be wasted, more will be transferred to the cart. Varying the stiffness of the spring will vary the elasticity of the collision, and varying the mass of the ball (and/or the height of release) will vary the initial input momentum.
But since the ball is still rolling, it still won't be as good as the pendulum.

[Cloxxki]

Good points TK.

Also, the rolling balls will always "charge up" with spin energy. Hitting the stop or spring, does not transfer this energy into cart movement. For this reason, I'd suggest the most slippery of cart surfaces, to minimize spin in the ball. It may well accumulate more horizontal and vertical inertia, and make for a greater bump.

Another experiment would see a pendulum stand mounted on the cart. Starting and finishing points for the ball's trjectory would be identical for vertical and horizontal displacement, meaning the pendulum would swing in the same direction as the cart's path.
A lead ball of course, being smaller would need to overcome less air friction. The bumper setup as would be vital in stopping the ball with minimal heat/noise losses. My gut tells me that all available energy in the ball should be transferred in one go, but not in an infinitely short distance and time (hard bump stop). The cart seems to have significant rolling resistance (I consider it the ball's disadvantage that the front wheels are so much smaller, right where the ball's weight is transferred, the pendulum SEEMS to have better weight distribution over the wheels), so minimizing repeating small inputs should maximize cart distance travelled.

There is something interesting at work though, with such a pendulum.

The weight's push against the cart is determined by multiple factors: zero angular velocity at highest position, but also the steepest angle with surface.
Some factors at work I identify:
- vertical speed and acceleration of the weight need to be calculated, are not in geometrically easily indicated positions.
- at the bottom position, both are zero, but weight's inertia and forward push have reach maximum.
- the push seems to reduce, but still past the weight's botom position.
   
I've never been able to remember a formula (other than Pythagoras') in my life, but I'd love to see the above plotted in a graph, to see in what manner energy is transferred. Rate of acceleration, incresing vs decreasing, seems to play a great role here (hunch), making this switch between pulling and pushing the cart. And even then, the cart will respond to the switch with delayed direction switch, due to inertia built.

Until I see better proof than this nice little video I'll side with TK that little have been proved, other than that a greater noise und peak can be generated by a bumping ball than a swinging one, and that spin can be prevented to be turned into forward momentum with a simple bump stop.
The interesting non-lineair aspects of the pendulum IMO do call for further testing and especially calculation, to possibly find benificial parameters such as non-rigid swing rods and non-static pendulum mounts. Perhaps something better can be found than the typical 2-stage oscillator's vertical and slightly horizontal displacement of the first stage's pendulum mount.

I like the videos where a horizontally place pendulum oscillating high-frequency can propel a cart. Would be good if the inventors could back that up with calculations, as this would allow for determining the ideal parameters of such pendulums.