General > General Technical Chat
Mess with your minds: A wind powered craft going faster than a tail wind speed.
electrodacus:
--- Quote from: IanB on December 21, 2021, 07:59:25 pm ---
--- Quote from: bdunham7 on December 21, 2021, 05:07:35 pm ---As I pointed out much earlier, starting with reply #20 to this thread, you can pretty much explain it without much more than the principles of Archimedes.
--- End quote ---
Indeed, and for reference, here is an analysis of the cart/wheel/belt system.
Refer to the diagram attached below.
Assume that it is an ideal system, no friction losses, and both wheels are able to spin freely on their bearings.
There are five variables: \$v_W\$, \$v_R\$, \$v_M\$, \$v_G\$ and \$v\$
\$v_M\$ and \$v_G\$ are the rim speeds of the wheels, in m/s.
\$v_W\$ and \$v_R\$ are given, leaving three degrees of freedom.
Two equations can be written relating the belt velocities, the rim speeds of the wheels, and the cart speed:
$$v=v_M-v_W$$ $$v=v_G-v_R$$
These two equations take up two degrees of freedom, leaving one degree of freedom remaining.
With no additional constraints this system has an infinite number of solutions. The cart velocity, \$v\$ can have any value we choose.
This makes sense, intuitively, since the wheels are free running, and without friction losses any initial cart velocity will remain the same forever.
To remove the remaining degree of freedom in the system, the wheels can be linked with a connecting gear. If we let the gear ratio be \$\alpha\$, then we can write a linking equation:
$$v_G=\alpha\,v_M$$
For each revolution of wheel M, wheel G makes \$\alpha\$ revolutions.
(Note that the gearing could be mechanical, or it could be electrical. Mechanical is simpler.)
By making a suitable choice of \$\alpha\$, we can arrange for a desired cart speed, \$v\$.
For instance, suppose we wish the cart to move at 1 m/s to the right.
We set \$v\$ = 1 m/s, which gives \$v_M=v+v_W\$ = 5 m/s, and \$v_G=v+v_R\$ = 11 m/s.
From this, we have: \$\alpha = v_G / v_M\$ = 11 / 5 = 2.2
Therefore, with a gear ratio of 2.2, the cart will move to right at a speed of 1 m/s.
--- End quote ---
I appreciate the effort you put in to this but no vehicle without energy storage can move in this example from left to right.
You just looked at speed here no forces ? How will that even make sense for this particular problem ?
I wish I knew how to help you from here but you are just way off thus I'm sorry but I cant help.
fourfathom:
--- Quote from: IanB on December 21, 2021, 07:59:25 pm ---[...]
Therefore, with a gear ratio of 2.2, the cart will move to right at a speed of 1 m/s.
--- End quote ---
Thank you for this! It's also a good model for the "plank over rollers on floor" demonstration. Harnessing the speed difference of two media, zero energy storage required, moving "DWFTTW". Couldn't be much simpler.
Friction, drag, coupling efficiency, don't change the fundamentals either, they just set some requirements or limits for windspeed, transducer design, acceleration, and upper-bound on vehicle speed.
electrodacus:
--- Quote from: bdunham7 on December 21, 2021, 08:10:52 pm ---
--- Quote from: electrodacus on December 21, 2021, 08:08:34 pm ---If you remove the brakes those 600W will be available to vehicle instead of earth.
--- End quote ---
And if you release the brakes, but not all the way, so that the vehicle creeps, isn't most of your 600W still 'available to the earth'? The vehicle is still pushing on the earth...
--- End quote ---
As soon as you start moving those now less than 600W will be split between vehicle acceleration and brake friction (lost as heat).
Say you want to maintain a 1m/s then brakes will need to deal with 0.5 * 1.2 * 1 * (10-1)^3 = 437.4W
If your brakes where not designed to be able to get rid of those 437.4W then they will overheat and get damaged.
We can setup a scale down model of this if you do not believe that will be the case.
fourfathom:
--- Quote from: electrodacus on December 21, 2021, 08:19:32 pm ---I appreciate the effort you put in to this but no vehicle without energy storage can move in this example from left to right.
--- End quote ---
Look again. Actually think about it.
electrodacus:
--- Quote from: fourfathom on December 21, 2021, 08:27:52 pm ---
--- Quote from: electrodacus on December 21, 2021, 08:19:32 pm ---I appreciate the effort you put in to this but no vehicle without energy storage can move in this example from left to right.
--- End quote ---
Look again. Actually think about it.
--- End quote ---
I did look and I just hope IanB has no engineering degree.
He just looked at what gear ratio he will need if he wanted to push the vehicle with 1m/s (by push I mean apply external power to the system as that is the only way that vehicle can move from left to right).
Navigation
[0] Message Index
[#] Next page
[*] Previous page
Go to full version