paddle question

[vett]

I am scratch building a stern paddle wheeler based on the dumas Myrtle Corey, the orignal had 16 paddles mine will have 8 will that make a problem?

[ky paddlewheeler]

The only thing I would think it would do is slow it down and maybe not have as much pushing power.

[derekwarner_decoy]

Hi PD's  - from a purely mathmatical, scientific or academic point   I am not sure if it would make any real difference from point A to point B on the water

1) let's assume that the output shaft power & engine RPM is/are equal
2) 16 floats will hit the water each full 360 degrees & the resistance to the floats is relative to the unit of 16
3) 8 floats hit the water each full 360 degrees & the resistance to the floats is relative to the unit of 8 [or twice that of the former]

So from this with RPM & power output being constant, the result is

4) the individual floats on the 8 float wheel [being twice the distance of the 16 float wheel] will consume the paddleshaft output  power

5) the individual floats on the 16 float wheel [being 1/2 the distance of the 8 float wheel] will consume the paddleshaft output power

So all things being near equal   .... .... ...., apart from some duck waddleing   & smoothness or roughness.... there is no difference    [apart from the fact that the loading on the floats of the paddle wheel with 8 floats is twice that of the 16 float wheel]  .....Derek...

[vett]

Thanks for the replies. So I guess if I  were to speed up the drive a little it would be better.

[Bierjunge]

derekwarner_decoy wrote:

> Hi PD's -

Hi Ph.D.'s  ;-)

> from a purely mathematical, scientific or academic point  I am not sure
> if it would make any real difference from point A to point B on the water

Well, it makes some difference, depending on your premises:
Whether you keep engine torque, engine speed or engine power constant
while reducing the number of floats, and also depending on the slip
of the wheel (i.e. whether you hold the boat fixed, for example
when doing bathtub testing, or whether you let it run freely
during normal operation).

> 1) let's assume that the output shaft power & egine RPM is/are equal

And here you get a problem: You can't keep both output power AND
speed constant at the same time!
If you reduce the float, you reduce the torque at given rpm, and thus
you reduce the power (torque times rotational speed).

> So from this with RPM & power output being constant, the result is (...)

Therefore, I'm sorry not to agree fully with your following theorems.  

First, let's look at the simple case (bathtub testing):

- If you keep the TORQUE constant (as a steam engine would),
half the floats would result in engine speed and power both increased
to 141% (square root of 2!), but the pushing force (being directly
proportional to the torque) would be equal.

- If you keep the engine SPEED constant (as a geared electric motor
would approximately do), half the floats would result in
torque, pushing force and power consumption being all reduced to 50%.
Big difference, you see!

- If you finally keep the engine POWER constant (as by thermic
restrictions of the motor or restrictions of the power source such as
battery or boiler), half the floats would result in torque and pushing
force reduced to 79% while output rpm being increased to 126%.

Differences aren't this big however if you look at the moving boat.
Let's assume for the original configuration a ratio of float and
hull resistance producing a wheel slip (difference of circumferential
wheel speed and boat speed, divided by circumferential speed) of 20%
(typical value).
Half the floats would then result in an increased slip of 26% and
thus less efficiency of the drive.

- If you keep the TORQUE constant, half the floats would result in
engine speed and power both increased to 108%, but the pushing force
as well as the velocity of the boat would be equal.

- If you keep the engine SPEED constant, half the floats would result
in torque, pushing force and power consumption being all reduced
to 85%, while the velocity of the boat would drop to 92%.

- If you keep the POWER constant, half the floats would result in
torque and pushing force reduced to 95%, output rpm being increased
to 105% and boat velocity slightly dropping to 97%.

So finally, after all these calculations, for a free running boat I would
tend to agree to

> So all things being near equal  ....  

But for a towboat running at much higher slip, things would significantly
different.

Regards, Moritz

[derekwarner_decoy]

Hi PD's & thanks Moritz for your response....I do appreciate reading and understanding your  :post 'S to various mathmatical issues as raised in our PD's

However   to repeat myself....but if we had two  paddle wheel vessels - one with 16 floats, the other with 8 floats and "totally" identical in all other form/matter....and sent them off on a 50 metre straight run.... my guess is that there would need to be a FOTO finish as they would both cross the line together

Also if we were to be more deeply about this.... 12 volt DC versions of these paddlers would at the end of the FOTO finish confirm identical battery voltage & hence residual potential  which would further confirm the work output was =

We could compare current draw per revolution between both variants [8 to 16] & the resultant would be a greater/lessor sinusidal variance in wave form pitch, however the amplitude   would be NEAR identical...would it not :?:  :idea:  :?:  :arrow:  :wink:

But then again...the batteries in my solar powered ABBACAS may be low on VOLTZ..........

[ky paddlewheeler]

Are locale ferry under gone some work a few years back,that also inculed a new wheel,it was the same size in od. and the floats were also the same size as the old wheel but they added three floats to it,it droped the time the time it took to get across one side of the river to the other by 2sec. and thats useing the same engen and rpm,now thats my .2cents worth,but Im not saying derek is wrong ether.